Parallel Thread Execution ISA Version 8.5

The programming guide to using PTX (Parallel Thread Execution) and ISA (Instruction Set Architecture).

1. Introduction

This document describes PTX, a low-level parallel thread execution virtual machine and instruction set architecture (ISA). PTX exposes the GPU as a data-parallel computing device.

1.1. Scalable Data-Parallel Computing using GPUs

Driven by the insatiable market demand for real-time, high-definition 3D graphics, the programmable GPU has evolved into a highly parallel, multithreaded, many-core processor with tremendous computational horsepower and very high memory bandwidth. The GPU is especially well-suited to address problems that can be expressed as data-parallel computations - the same program is executed on many data elements in parallel - with high arithmetic intensity - the ratio of arithmetic operations to memory operations. Because the same program is executed for each data element, there is a lower requirement for sophisticated flow control; and because it is executed on many data elements and has high arithmetic intensity, the memory access latency can be hidden with calculations instead of big data caches.

Data-parallel processing maps data elements to parallel processing threads. Many applications that process large data sets can use a data-parallel programming model to speed up the computations. In 3D rendering large sets of pixels and vertices are mapped to parallel threads. Similarly, image and media processing applications such as post-processing of rendered images, video encoding and decoding, image scaling, stereo vision, and pattern recognition can map image blocks and pixels to parallel processing threads. In fact, many algorithms outside the field of image rendering and processing are accelerated by data-parallel processing, from general signal processing or physics simulation to computational finance or computational biology.

PTX defines a virtual machine and ISA for general purpose parallel thread execution. PTX programs are translated at install time to the target hardware instruction set. The PTX-to-GPU translator and driver enable NVIDIA GPUs to be used as programmable parallel computers.

1.2. Goals of PTX

PTX provides a stable programming model and instruction set for general purpose parallel programming. It is designed to be efficient on NVIDIA GPUs supporting the computation features defined by the NVIDIA Tesla architecture. High level language compilers for languages such as CUDA and C/C++ generate PTX instructions, which are optimized for and translated to native target-architecture instructions.

The goals for PTX include the following:

• Provide a stable ISA that spans multiple GPU generations.

• Achieve performance in compiled applications comparable to native GPU performance.

• Provide a machine-independent ISA for C/C++ and other compilers to target.

• Provide a code distribution ISA for application and middleware developers.

• Provide a common source-level ISA for optimizing code generators and translators, which map PTX to specific target machines.

• Facilitate hand-coding of libraries, performance kernels, and architecture tests.

• Provide a scalable programming model that spans GPU sizes from a single unit to many parallel units.

1.3. PTX ISA Version 8.5

PTX ISA version 8.5 introduces the following new features:

• Adds support for mma.sp::ordered_metadata instruction.

1.4. Document Structure

The information in this document is organized into the following Chapters:

• Programming Model outlines the programming model.

• PTX Machine Model gives an overview of the PTX virtual machine model.

• Syntax describes the basic syntax of the PTX language.

• State Spaces, Types, and Variables describes state spaces, types, and variable declarations.

• Instruction Operands describes instruction operands.

• Abstracting the ABI describes the function and call syntax, calling convention, and PTX support for abstracting the Application Binary Interface (ABI).

• Instruction Set describes the instruction set.

• Special Registers lists special registers.

• Directives lists the assembly directives supported in PTX.

• Release Notes provides release notes for PTX ISA versions 2.x and beyond.

References

• 754-2008 IEEE Standard for Floating-Point Arithmetic. ISBN 978-0-7381-5752-8, 2008.

  http://ieeexplore.ieee.org/servlet/opac?punumber=4610933

• The OpenCL Specification, Version: 1.1, Document Revision: 44, June 1, 2011.

  http://www.khronos.org/registry/cl/specs/opencl-1.1.pdf

• CUDA Programming Guide.

  https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html

• CUDA Dynamic Parallelism Programming Guide.

  https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#cuda-dynamic-parallelism

• CUDA Atomicity Requirements.

  https://nvidia.github.io/cccl/libcudacxx/extended_api/memory_model.html#atomicity

• PTX Writers Guide to Interoperability.

  https://docs.nvidia.com/cuda/ptx-writers-guide-to-interoperability/index.html

2. Programming Model

2.1. A Highly Multithreaded Coprocessor

The GPU is a compute device capable of executing a very large number of threads in parallel. It operates as a coprocessor to the main CPU, or host: In other words, data-parallel, compute-intensive portions of applications running on the host are off-loaded onto the device.

More precisely, a portion of an application that is executed many times, but independently on different data, can be isolated into a kernel function that is executed on the GPU as many different threads. To that effect, such a function is compiled to the PTX instruction set and the resulting kernel is translated at install time to the target GPU instruction set.

2.2. Thread Hierarchy

The batch of threads that executes a kernel is organized as a grid. A grid consists of either cooperative thread arrays or clusters of cooperative thread arrays as described in this section and illustrated in Figure 1 and Figure 2. Cooperative thread arrays (CTAs) implement CUDA thread blocks and clusters implement CUDA thread block clusters.

2.2.1. Cooperative Thread Arrays

The Parallel Thread Execution (PTX) programming model is explicitly parallel: a PTX program specifies the execution of a given thread of a parallel thread array. A cooperative thread array, or CTA, is an array of threads that execute a kernel concurrently or in parallel.

Threads within a CTA can communicate with each other. To coordinate the communication of the threads within the CTA, one can specify synchronization points where threads wait until all threads in the CTA have arrived.

Each thread has a unique thread identifier within the CTA. Programs use a data parallel decomposition to partition inputs, work, and results across the threads of the CTA. Each CTA thread uses its thread identifier to determine its assigned role, assign specific input and output positions, compute addresses, and select work to perform. The thread identifier is a three-element vector tid, (with elements tid.x, tid.y, and tid.z) that specifies the thread’s position within a 1D, 2D, or 3D CTA. Each thread identifier component ranges from zero up to the number of thread ids in that CTA dimension.

Each CTA has a 1D, 2D, or 3D shape specified by a three-element vector ntid (with elements ntid.x, ntid.y, and ntid.z). The vector ntid specifies the number of threads in each CTA dimension.

Threads within a CTA execute in SIMT (single-instruction, multiple-thread) fashion in groups called warps. A warp is a maximal subset of threads from a single CTA, such that the threads execute the same instructions at the same time. Threads within a warp are sequentially numbered. The warp size is a machine-dependent constant. Typically, a warp has 32 threads. Some applications may be able to maximize performance with knowledge of the warp size, so PTX includes a run-time immediate constant, WARP_SZ, which may be used in any instruction where an immediate operand is allowed.

2.2.2. Cluster of Cooperative Thread Arrays

Cluster is a group of CTAs that run concurrently or in parallel and can synchronize and communicate with each other via shared memory. The executing CTA has to make sure that the shared memory of the peer CTA exists before communicating with it via shared memory and the peer CTA hasn’t exited before completing the shared memory operation.

Threads within the different CTAs in a cluster can synchronize and communicate with each other via shared memory. Cluster-wide barriers can be used to synchronize all the threads within the cluster. Each CTA in a cluster has a unique CTA identifier within its cluster (cluster_ctaid). Each cluster of CTAs has 1D, 2D or 3D shape specified by the parameter cluster_nctaid. Each CTA in the cluster also has a unique CTA identifier (cluster_ctarank) across all dimensions. The total number of CTAs across all the dimensions in the cluster is specified by cluster_nctarank. Threads may read and use these values through predefined, read-only special registers %cluster_ctaid, %cluster_nctaid, %cluster_ctarank, %cluster_nctarank.

Cluster level is applicable only on target architecture sm_90 or higher. Specifying cluster level during launch time is optional. If the user specifies the cluster dimensions at launch time then it will be treated as explicit cluster launch, otherwise it will be treated as implicit cluster launch with default dimension 1x1x1. PTX provides read-only special register %is_explicit_cluster to differentiate between explicit and implicit cluster launch.

2.2.3. Grid of Clusters

There is a maximum number of threads that a CTA can contain and a maximum number of CTAs that a cluster can contain. However, clusters with CTAs that execute the same kernel can be batched together into a grid of clusters, so that the total number of threads that can be launched in a single kernel invocation is very large. This comes at the expense of reduced thread communication and synchronization, because threads in different clusters cannot communicate and synchronize with each other.

Each cluster has a unique cluster identifier (clusterid) within a grid of clusters. Each grid of clusters has a 1D, 2D , or 3D shape specified by the parameter nclusterid. Each grid also has a unique temporal grid identifier (gridid). Threads may read and use these values through predefined, read-only special registers %tid, %ntid, %clusterid, %nclusterid, and %gridid.

Each CTA has a unique identifier (ctaid) within a grid. Each grid of CTAs has 1D, 2D, or 3D shape specified by the parameter nctaid. Thread may use and read these values through predefined, read-only special registers %ctaid and %nctaid.

Each kernel is executed as a batch of threads organized as a grid of clusters consisting of CTAs where cluster is optional level and is applicable only for target architectures sm_90 and higher. Figure 1 shows a grid consisting of CTAs and Figure 2 shows a grid consisting of clusters.

Grids may be launched with dependencies between one another - a grid may be a dependent grid and/or a prerequisite grid. To understand how grid dependencies may be defined, refer to the section on CUDA Graphs in the Cuda Programming Guide.

Figure 1 Grid with CTAs

Figure 2 Grid with clusters

A cluster is a set of cooperative thread arrays (CTAs) where a CTA is a set of concurrent threads that execute the same kernel program. A grid is a set of clusters consisting of CTAs that execute independently.

2.3. Memory Hierarchy

PTX threads may access data from multiple state spaces during their execution as illustrated by Figure 3 where cluster level is introduced from target architecture sm_90 onwards. Each thread has a private local memory. Each thread block (CTA) has a shared memory visible to all threads of the block and to all active blocks in the cluster and with the same lifetime as the block. Finally, all threads have access to the same global memory.

There are additional state spaces accessible by all threads: the constant, param, texture, and surface state spaces. Constant and texture memory are read-only; surface memory is readable and writable. The global, constant, param, texture, and surface state spaces are optimized for different memory usages. For example, texture memory offers different addressing modes as well as data filtering for specific data formats. Note that texture and surface memory is cached, and within the same kernel call, the cache is not kept coherent with respect to global memory writes and surface memory writes, so any texture fetch or surface read to an address that has been written to via a global or a surface write in the same kernel call returns undefined data. In other words, a thread can safely read some texture or surface memory location only if this memory location has been updated by a previous kernel call or memory copy, but not if it has been previously updated by the same thread or another thread from the same kernel call.

The global, constant, and texture state spaces are persistent across kernel launches by the same application.

Both the host and the device maintain their own local memory, referred to as host memory and device memory, respectively. The device memory may be mapped and read or written by the host, or, for more efficient transfer, copied from the host memory through optimized API calls that utilize the device’s high-performance Direct Memory Access (DMA) engine.

Figure 3 Memory Hierarchy

3. PTX Machine Model

3.1. A Set of SIMT Multiprocessors

The NVIDIA GPU architecture is built around a scalable array of multithreaded Streaming Multiprocessors (SMs). When a host program invokes a kernel grid, the blocks of the grid are enumerated and distributed to multiprocessors with available execution capacity. The threads of a thread block execute concurrently on one multiprocessor. As thread blocks terminate, new blocks are launched on the vacated multiprocessors.

A multiprocessor consists of multiple Scalar Processor (SP) cores, a multithreaded instruction unit, and on-chip shared memory. The multiprocessor creates, manages, and executes concurrent threads in hardware with zero scheduling overhead. It implements a single-instruction barrier synchronization. Fast barrier synchronization together with lightweight thread creation and zero-overhead thread scheduling efficiently support very fine-grained parallelism, allowing, for example, a low granularity decomposition of problems by assigning one thread to each data element (such as a pixel in an image, a voxel in a volume, a cell in a grid-based computation).

To manage hundreds of threads running several different programs, the multiprocessor employs an architecture we call SIMT (single-instruction, multiple-thread). The multiprocessor maps each thread to one scalar processor core, and each scalar thread executes independently with its own instruction address and register state. The multiprocessor SIMT unit creates, manages, schedules, and executes threads in groups of parallel threads called warps. (This term originates from weaving, the first parallel thread technology.) Individual threads composing a SIMT warp start together at the same program address but are otherwise free to branch and execute independently.

When a multiprocessor is given one or more thread blocks to execute, it splits them into warps that get scheduled by the SIMT unit. The way a block is split into warps is always the same; each warp contains threads of consecutive, increasing thread IDs with the first warp containing thread 0.

At every instruction issue time, the SIMT unit selects a warp that is ready to execute and issues the next instruction to the active threads of the warp. A warp executes one common instruction at a time, so full efficiency is realized when all threads of a warp agree on their execution path. If threads of a warp diverge via a data-dependent conditional branch, the warp serially executes each branch path taken, disabling threads that are not on that path, and when all paths complete, the threads converge back to the same execution path. Branch divergence occurs only within a warp; different warps execute independently regardless of whether they are executing common or disjointed code paths.

SIMT architecture is akin to SIMD (Single Instruction, Multiple Data) vector organizations in that a single instruction controls multiple processing elements. A key difference is that SIMD vector organizations expose the SIMD width to the software, whereas SIMT instructions specify the execution and branching behavior of a single thread. In contrast with SIMD vector machines, SIMT enables programmers to write thread-level parallel code for independent, scalar threads, as well as data-parallel code for coordinated threads. For the purposes of correctness, the programmer can essentially ignore the SIMT behavior; however, substantial performance improvements can be realized by taking care that the code seldom requires threads in a warp to diverge. In practice, this is analogous to the role of cache lines in traditional code: Cache line size can be safely ignored when designing for correctness but must be considered in the code structure when designing for peak performance. Vector architectures, on the other hand, require the software to coalesce loads into vectors and manage divergence manually.

How many blocks a multiprocessor can process at once depends on how many registers per thread and how much shared memory per block are required for a given kernel since the multiprocessor’s registers and shared memory are split among all the threads of the batch of blocks. If there are not enough registers or shared memory available per multiprocessor to process at least one block, the kernel will fail to launch.

Figure 4 Hardware Model

A set of SIMT multiprocessors with on-chip shared memory.

3.2. Independent Thread Scheduling

On architectures prior to Volta, warps used a single program counter shared amongst all 32 threads in the warp together with an active mask specifying the active threads of the warp. As a result, threads from the same warp in divergent regions or different states of execution cannot signal each other or exchange data, and algorithms requiring fine-grained sharing of data guarded by locks or mutexes can easily lead to deadlock, depending on which warp the contending threads come from.

Starting with the Volta architecture, Independent Thread Scheduling allows full concurrency between threads, regardless of warp. With Independent Thread Scheduling, the GPU maintains execution state per thread, including a program counter and call stack, and can yield execution at a per-thread granularity, either to make better use of execution resources or to allow one thread to wait for data to be produced by another. A schedule optimizer determines how to group active threads from the same warp together into SIMT units. This retains the high throughput of SIMT execution as in prior NVIDIA GPUs, but with much more flexibility: threads can now diverge and reconverge at sub-warp granularity.

Independent Thread Scheduling can lead to a rather different set of threads participating in the executed code than intended if the developer made assumptions about warp-synchronicity of previous hardware architectures. In particular, any warp-synchronous code (such as synchronization-free, intra-warp reductions) should be revisited to ensure compatibility with Volta and beyond. See the section on Compute Capability 7.x in the Cuda Programming Guide for further details.

3.3. On-chip Shared Memory

As illustrated by Figure 4, each multiprocessor has on-chip memory of the four following types:

• One set of local 32-bit registers per processor,

• A parallel data cache or shared memory that is shared by all scalar processor cores and is where the shared memory space resides,

• A read-only constant cache that is shared by all scalar processor cores and speeds up reads from the constant memory space, which is a read-only region of device memory,

• A read-only texture cache that is shared by all scalar processor cores and speeds up reads from the texture memory space, which is a read-only region of device memory; each multiprocessor accesses the texture cache via a texture unit that implements the various addressing modes and data filtering.

The local and global memory spaces are read-write regions of device memory.

4. Syntax

PTX programs are a collection of text source modules (files). PTX source modules have an assembly-language style syntax with instruction operation codes and operands. Pseudo-operations specify symbol and addressing management. The ptxas optimizing backend compiler optimizes and assembles PTX source modules to produce corresponding binary object files.

4.1. Source Format

Source modules are ASCII text. Lines are separated by the newline character (\n).

All whitespace characters are equivalent; whitespace is ignored except for its use in separating tokens in the language.

The C preprocessor cpp may be used to process PTX source modules. Lines beginning with # are preprocessor directives. The following are common preprocessor directives:

#include, #define, #if, #ifdef, #else, #endif, #line, #file

C: A Reference Manual by Harbison and Steele provides a good description of the C preprocessor.

PTX is case sensitive and uses lowercase for keywords.

Each PTX module must begin with a .version directive specifying the PTX language version, followed by a .target directive specifying the target architecture assumed. See PTX Module Directives for a more information on these directives.

4.2. Comments

Comments in PTX follow C/C++ syntax, using non-nested /* and */ for comments that may span multiple lines, and using // to begin a comment that extends up to the next newline character, which terminates the current line. Comments cannot occur within character constants, string literals, or within other comments.

Comments in PTX are treated as whitespace.

4.3. Statements

A PTX statement is either a directive or an instruction. Statements begin with an optional label and end with a semicolon.

Examples

        .reg     .b32 r1, r2;
        .global  .f32  array[N];

start:  mov.b32   r1, %tid.x;
        shl.b32   r1, r1, 2;          // shift thread id by 2 bits
        ld.global.b32 r2, array[r1];  // thread[tid] gets array[tid]
        add.f32   r2, r2, 0.5;        // add 1/2

4.3.1. Directive Statements

Directive keywords begin with a dot, so no conflict is possible with user-defined identifiers. The directives in PTX are listed in Table 1 and described in State Spaces, Types, and Variables and Directives.

Table 1 PTX Directives

.address_size	.explicitcluster	.maxnreg	.section
.alias	.extern	.maxntid	.shared
.align	.file	.minnctapersm	.sreg
.branchtargets	.func	.noreturn	.target
.callprototype	.global	.param	.tex
.calltargets	.loc	.pragma	.version
.common	.local	.reg	.visible
.const	.maxclusterrank	.reqnctapercluster	.weak
.entry	.maxnctapersm	.reqntid

4.3.2. Instruction Statements

Instructions are formed from an instruction opcode followed by a comma-separated list of zero or more operands, and terminated with a semicolon. Operands may be register variables, constant expressions, address expressions, or label names. Instructions have an optional guard predicate which controls conditional execution. The guard predicate follows the optional label and precedes the opcode, and is written as @p, where p is a predicate register. The guard predicate may be optionally negated, written as @!p.

The destination operand is first, followed by source operands.

Instruction keywords are listed in Table 2. All instruction keywords are reserved tokens in PTX.

Table 2 Reserved Instruction Keywords

abs	discard	min	shf	vadd
activemask	div	mma	shfl	vadd2
add	dp2a	mov	shl	vadd4
addc	dp4a	movmatrix	shr	vavrg2
alloca	elect	mul	sin	vavrg4
and	ex2	mul24	slct	vmad
applypriority	exit	multimem	sqrt	vmax
atom	fence	nanosleep	st	vmax2
bar	fma	neg	stackrestore	vmax4
barrier	fns	not	stacksave	vmin
bfe	getctarank	or	stmatrix	vmin2
bfi	griddepcontrol	pmevent	sub	vmin4
bfind	isspacep	popc	subc	vote
bmsk	istypep	prefetch	suld	vset
bra	ld	prefetchu	suq	vset2
brev	ldmatrix	prmt	sured	vset4
brkpt	ldu	rcp	sust	vshl
brx	lg2	red	szext	vshr
call	lop3	redux	tanh	vsub
clz	mad	rem	testp	vsub2
cnot	mad24	ret	tex	vsub4
copysign	madc	rsqrt	tld4	wgmma
cos	mapa	sad	trap	wmma
cp	match	selp	txq	xor
createpolicy	max	set	vabsdiff
cvt	mbarrier	setmaxnreg	vabsdiff2
cvta	membar	setp	vabsdiff4

4.4. Identifiers

User-defined identifiers follow extended C++ rules: they either start with a letter followed by zero or more letters, digits, underscore, or dollar characters; or they start with an underscore, dollar, or percentage character followed by one or more letters, digits, underscore, or dollar characters:

followsym:   [a-zA-Z0-9_$]
identifier:  [a-zA-Z]{followsym}* | {[_$%]{followsym}+

PTX does not specify a maximum length for identifiers and suggests that all implementations support a minimum length of at least 1024 characters.

Many high-level languages such as C and C++ follow similar rules for identifier names, except that the percentage sign is not allowed. PTX allows the percentage sign as the first character of an identifier. The percentage sign can be used to avoid name conflicts, e.g., between user-defined variable names and compiler-generated names.

PTX predefines one constant and a small number of special registers that begin with the percentage sign, listed in Table 3.

Table 3 Predefined Identifiers

%clock	%laneid	%lanemask_gt	%pm0, ..., %pm7
%clock64	%lanemask_eq	%nctaid	%smid
%ctaid	%lanemask_le	%ntid	%tid
%envreg<32>	%lanemask_lt	%nsmid	%warpid
%gridid	%lanemask_ge	%nwarpid	WARP_SZ

4.5. Constants

PTX supports integer and floating-point constants and constant expressions. These constants may be used in data initialization and as operands to instructions. Type checking rules remain the same for integer, floating-point, and bit-size types. For predicate-type data and instructions, integer constants are allowed and are interpreted as in C, i.e., zero values are False and non-zero values are True.

4.5.1. Integer Constants

Integer constants are 64-bits in size and are either signed or unsigned, i.e., every integer constant has type .s64 or .u64. The signed/unsigned nature of an integer constant is needed to correctly evaluate constant expressions containing operations such as division and ordered comparisons, where the behavior of the operation depends on the operand types. When used in an instruction or data initialization, each integer constant is converted to the appropriate size based on the data or instruction type at its use.

Integer literals may be written in decimal, hexadecimal, octal, or binary notation. The syntax follows that of C. Integer literals may be followed immediately by the letter U to indicate that the literal is unsigned.

hexadecimal literal:  0[xX]{hexdigit}+U?
octal literal:        0{octal digit}+U?
binary literal:       0[bB]{bit}+U?
decimal literal       {nonzero-digit}{digit}*U?

Integer literals are non-negative and have a type determined by their magnitude and optional type suffix as follows: literals are signed (.s64) unless the value cannot be fully represented in .s64 or the unsigned suffix is specified, in which case the literal is unsigned (.u64).

The predefined integer constant WARP_SZ specifies the number of threads per warp for the target platform; to date, all target architectures have a WARP_SZ value of 32.

4.5.2. Floating-Point Constants

Floating-point constants are represented as 64-bit double-precision values, and all floating-point constant expressions are evaluated using 64-bit double precision arithmetic. The only exception is the 32-bit hex notation for expressing an exact single-precision floating-point value; such values retain their exact 32-bit single-precision value and may not be used in constant expressions. Each 64-bit floating-point constant is converted to the appropriate floating-point size based on the data or instruction type at its use.

Floating-point literals may be written with an optional decimal point and an optional signed exponent. Unlike C and C++, there is no suffix letter to specify size; literals are always represented in 64-bit double-precision format.

PTX includes a second representation of floating-point constants for specifying the exact machine representation using a hexadecimal constant. To specify IEEE 754 double-precision floating point values, the constant begins with 0d or 0D followed by 16 hex digits. To specify IEEE 754 single-precision floating point values, the constant begins with 0f or 0F followed by 8 hex digits.

0[fF]{hexdigit}{8}      // single-precision floating point
0[dD]{hexdigit}{16}     // double-precision floating point

Example

mov.f32  $f3, 0F3f800000;       //  1.0

4.5.3. Predicate Constants

In PTX, integer constants may be used as predicates. For predicate-type data initializers and instruction operands, integer constants are interpreted as in C, i.e., zero values are False and non-zero values are True.

4.5.4. Constant Expressions

In PTX, constant expressions are formed using operators as in C and are evaluated using rules similar to those in C, but simplified by restricting types and sizes, removing most casts, and defining full semantics to eliminate cases where expression evaluation in C is implementation dependent.

Constant expressions are formed from constant literals, unary plus and minus, basic arithmetic operators (addition, subtraction, multiplication, division), comparison operators, the conditional ternary operator ( ?: ), and parentheses. Integer constant expressions also allow unary logical negation (!), bitwise complement (~), remainder (%), shift operators (<< and >>), bit-type operators (&, |, and ^), and logical operators (&&, ||).

Constant expressions in PTX do not support casts between integer and floating-point.

Constant expressions are evaluated using the same operator precedence as in C. Table 4 gives operator precedence and associativity. Operator precedence is highest for unary operators and decreases with each line in the chart. Operators on the same line have the same precedence and are evaluated right-to-left for unary operators and left-to-right for binary operators.

Table 4 Operator Precedence

Kind	Operator Symbols	Operator Names	Associates
Primary	()	parenthesis	n/a
Unary	+- ! ~	plus, minus, negation, complement	right
	(.s64)(.u64)	casts	right
Binary	*/ %	multiplication, division, remainder	left
	+-	addition, subtraction
	>> <<	shifts
	< > <= >=	ordered comparisons
	== !=	equal, not equal
	&	bitwise AND
	^	bitwise XOR
	|	bitwise OR
	&&	logical AND
	||	logical OR
Ternary	?:	conditional	right

4.5.5. Integer Constant Expression Evaluation

Integer constant expressions are evaluated at compile time according to a set of rules that determine the type (signed .s64 versus unsigned .u64) of each sub-expression. These rules are based on the rules in C, but they’ve been simplified to apply only to 64-bit integers, and behavior is fully defined in all cases (specifically, for remainder and shift operators).

• Literals are signed unless unsigned is needed to prevent overflow, or unless the literal uses a U suffix. For example:

  • 42, 0x1234, 0123 are signed.

  • 0xfabc123400000000, 42U, 0x1234U are unsigned.

• Unary plus and minus preserve the type of the input operand. For example:

  • +123, -1, -(-42) are signed.

  • -1U, -0xfabc123400000000 are unsigned.

• Unary logical negation (!) produces a signed result with value 0 or 1.

• Unary bitwise complement (~) interprets the source operand as unsigned and produces an unsigned result.

• Some binary operators require normalization of source operands. This normalization is known as the usual arithmetic conversions and simply converts both operands to unsigned type if either operand is unsigned.

• Addition, subtraction, multiplication, and division perform the usual arithmetic conversions and produce a result with the same type as the converted operands. That is, the operands and result are unsigned if either source operand is unsigned, and is otherwise signed.

• Remainder (%) interprets the operands as unsigned. Note that this differs from C, which allows a negative divisor but defines the behavior to be implementation dependent.

• Left and right shift interpret the second operand as unsigned and produce a result with the same type as the first operand. Note that the behavior of right-shift is determined by the type of the first operand: right shift of a signed value is arithmetic and preserves the sign, and right shift of an unsigned value is logical and shifts in a zero bit.

• AND (&), OR (|), and XOR (^) perform the usual arithmetic conversions and produce a result with the same type as the converted operands.

• AND_OP (&&), OR_OP (||), Equal (==), and Not_Equal (!=) produce a signed result. The result value is 0 or 1.

• Ordered comparisons (<, <=, >, >=) perform the usual arithmetic conversions on source operands and produce a signed result. The result value is 0 or 1.

• Casting of expressions to signed or unsigned is supported using (.s64) and (.u64) casts.

• For the conditional operator ( ? : ) , the first operand must be an integer, and the second and third operands are either both integers or both floating-point. The usual arithmetic conversions are performed on the second and third operands, and the result type is the same as the converted type.

4.5.6. Summary of Constant Expression Evaluation Rules

Table 5 contains a summary of the constant expression evaluation rules.

Table 5 Constant Expression Evaluation Rules

Kind	Operator	Operand Types	Operand Interpretation	Result Type
Primary	()	any type	same as source	same as source
	constant literal	n/a	n/a	.u64, .s64, or .f64
Unary	+-	any type	same as source	same as source
	!	integer	zero or non-zero	.s64
	~	integer	.u64	.u64
Cast	(.u64)	integer	.u64	.u64
	(.s64)	integer	.s64	.s64
Binary	+- * /	.f64	.f64	.f64
		integer	use usual conversions	converted type
	< > <= >=	.f64	.f64	.s64
		integer	use usual conversions	.s64
	== !=	.f64	.f64	.s64
		integer	use usual conversions	.s64
	%	integer	.u64	.s64
	>> <<	integer	1st unchanged, 2nd is .u64	same as 1st operand
	& | ^	integer	.u64	.u64
	&& ||	integer	zero or non-zero	.s64
Ternary	?:	int ? .f64 : .f64	same as sources	.f64
		int ? int : int	use usual conversions	converted type

5. State Spaces, Types, and Variables

While the specific resources available in a given target GPU will vary, the kinds of resources will be common across platforms, and these resources are abstracted in PTX through state spaces and data types.

5.1. State Spaces

A state space is a storage area with particular characteristics. All variables reside in some state space. The characteristics of a state space include its size, addressability, access speed, access rights, and level of sharing between threads.

The state spaces defined in PTX are a byproduct of parallel programming and graphics programming. The list of state spaces is shown in Table 6,and properties of state spaces are shown in Table 7.

Table 6 State Spaces

Name	Description
.reg	Registers, fast.
.sreg	Special registers. Read-only; pre-defined; platform-specific.
.const	Shared, read-only memory.
.global	Global memory, shared by all threads.
.local	Local memory, private to each thread.
.param	Kernel parameters, defined per-grid; or Function or local parameters, defined per-thread.
.shared	Addressable memory, defined per CTA, accessible to all threads in the cluster throughout the lifetime of the CTA that defines it.
.tex	Global texture memory (deprecated).

Table 7 Properties of State Spaces

Name	Addressable	Initializable	Access	Sharing
.reg	No	No	R/W	per-thread
.sreg	No	No	RO	per-CTA
.const	Yes	Yes1	RO	per-grid
.global	Yes	Yes1	R/W	Context
.local	Yes	No	R/W	per-thread
.param (as input to kernel)	Yes2	No	RO	per-grid
.param (used in functions)	Restricted3	No	R/W	per-thread
.shared	Yes	No	R/W	per-cluster5
.tex	No4	Yes, via driver	RO	Context
Notes: 1 Variables in .const and .global state spaces are initialized to zero by default. 2 Accessible only via the ld.param{::entry} instruction. Address may be taken via mov instruction. 3 Accessible via ld.param{::func} and st.param{::func} instructions. Device function input and return parameters may have their address taken via mov; the parameter is then located on the stack frame and its address is in the .local state space. 4 Accessible only via the tex instruction. 5 Visible to the owning CTA and other active CTAs in the cluster.

5.1.1. Register State Space

Registers (.reg state space) are fast storage locations. The number of registers is limited, and will vary from platform to platform. When the limit is exceeded, register variables will be spilled to memory, causing changes in performance. For each architecture, there is a recommended maximum number of registers to use (see the CUDA Programming Guide for details).

Registers may be typed (signed integer, unsigned integer, floating point, predicate) or untyped. Register size is restricted; aside from predicate registers which are 1-bit, scalar registers have a width of 8-, 16-, 32-, 64-, or 128-bits, and vector registers have a width of 16-, 32-, 64-, or 128-bits. The most common use of 8-bit registers is with ld, st, and cvt instructions, or as elements of vector tuples.

Registers differ from the other state spaces in that they are not fully addressable, i.e., it is not possible to refer to the address of a register. When compiling to use the Application Binary Interface (ABI), register variables are restricted to function scope and may not be declared at module scope. When compiling legacy PTX code (ISA versions prior to 3.0) containing module-scoped .reg variables, the compiler silently disables use of the ABI. Registers may have alignment boundaries required by multi-word loads and stores.

5.1.2. Special Register State Space

The special register (.sreg) state space holds predefined, platform-specific registers, such as grid, cluster, CTA, and thread parameters, clock counters, and performance monitoring registers. All special registers are predefined.

5.1.3. Constant State Space

The constant (.const) state space is a read-only memory initialized by the host. Constant memory is accessed with a ld.const instruction. Constant memory is restricted in size, currently limited to 64 KB which can be used to hold statically-sized constant variables. There is an additional 640 KB of constant memory, organized as ten independent 64 KB regions. The driver may allocate and initialize constant buffers in these regions and pass pointers to the buffers as kernel function parameters. Since the ten regions are not contiguous, the driver must ensure that constant buffers are allocated so that each buffer fits entirely within a 64 KB region and does not span a region boundary.

Statically-sized constant variables have an optional variable initializer; constant variables with no explicit initializer are initialized to zero by default. Constant buffers allocated by the driver are initialized by the host, and pointers to such buffers are passed to the kernel as parameters. See the description of kernel parameter attributes in Kernel Function Parameter Attributes for more details on passing pointers to constant buffers as kernel parameters.

5.1.3.1. Banked Constant State Space (deprecated)

Previous versions of PTX exposed constant memory as a set of eleven 64 KB banks, with explicit bank numbers required for variable declaration and during access.

Prior to PTX ISA version 2.2, the constant memory was organized into fixed size banks. There were eleven 64 KB banks, and banks were specified using the .const[bank] modifier, where bank ranged from 0 to 10. If no bank number was given, bank zero was assumed.

By convention, bank zero was used for all statically-sized constant variables. The remaining banks were used to declare incomplete constant arrays (as in C, for example), where the size is not known at compile time. For example, the declaration

.extern .const[2] .b32 const_buffer[];

resulted in const_buffer pointing to the start of constant bank two. This pointer could then be used to access the entire 64 KB constant bank. Multiple incomplete array variables declared in the same bank were aliased, with each pointing to the start address of the specified constant bank.

To access data in contant banks 1 through 10, the bank number was required in the state space of the load instruction. For example, an incomplete array in bank 2 was accessed as follows:

.extern .const[2] .b32 const_buffer[];
ld.const[2].b32  %r1, [const_buffer+4]; // load second word

In PTX ISA version 2.2, we eliminated explicit banks and replaced the incomplete array representation of driver-allocated constant buffers with kernel parameter attributes that allow pointers to constant buffers to be passed as kernel parameters.

5.1.4. Global State Space

The global (.global) state space is memory that is accessible by all threads in a context. It is the mechanism by which threads in different CTAs, clusters, and grids can communicate. Use ld.global, st.global, and atom.global to access global variables.

Global variables have an optional variable initializer; global variables with no explicit initializer are initialized to zero by default.

5.1.5. Local State Space

The local state space (.local) is private memory for each thread to keep its own data. It is typically standard memory with cache. The size is limited, as it must be allocated on a per-thread basis. Use ld.local and st.local to access local variables.

When compiling to use the Application Binary Interface (ABI), .local state-space variables must be declared within function scope and are allocated on the stack. In implementations that do not support a stack, all local memory variables are stored at fixed addresses, recursive function calls are not supported, and .local variables may be declared at module scope. When compiling legacy PTX code (ISA versions prior to 3.0) containing module-scoped .local variables, the compiler silently disables use of the ABI.

5.1.6. Parameter State Space

The parameter (.param) state space is used (1) to pass input arguments from the host to the kernel, (2a) to declare formal input and return parameters for device functions called from within kernel execution, and (2b) to declare locally-scoped byte array variables that serve as function call arguments, typically for passing large structures by value to a function. Kernel function parameters differ from device function parameters in terms of access and sharing (read-only versus read-write, per-kernel versus per-thread). Note that PTX ISA versions 1.x supports only kernel function parameters in .param space; device function parameters were previously restricted to the register state space. The use of parameter state space for device function parameters was introduced in PTX ISA version 2.0 and requires target architecture sm_20 or higher. Additional sub-qualifiers ::entry or ::func can be specified on instructions with .param state space to indicate whether the address refers to kernel function parameter or device function parameter. If no sub-qualifier is specified with the .param state space, then the default sub-qualifier is specific to and dependent on the exact instruction. For example, st.param is equivalent to st.param::func whereas isspacep.param is equivalent to isspacep.param::entry. Refer to the instruction description for more details on default sub-qualifier assumption.

Note

The location of parameter space is implementation specific. For example, in some implementations kernel parameters reside in global memory. No access protection is provided between parameter and global space in this case. Though the exact location of the kernel parameter space is implementation specific, the kernel parameter space window is always contained within the global space window. Similarly, function parameters are mapped to parameter passing registers and/or stack locations based on the function calling conventions of the Application Binary Interface (ABI). Therefore, PTX code should make no assumptions about the relative locations or ordering of .param space variables.

5.1.6.1. Kernel Function Parameters

Each kernel function definition includes an optional list of parameters. These parameters are addressable, read-only variables declared in the .param state space. Values passed from the host to the kernel are accessed through these parameter variables using ld.param instructions. The kernel parameter variables are shared across all CTAs from all clusters within a grid.

The address of a kernel parameter may be moved into a register using the mov instruction. The resulting address is in the .param state space and is accessed using ld.param instructions.

Example

.entry foo ( .param .b32 N, .param .align 8 .b8 buffer[64] )
{
    .reg .u32 %n;
    .reg .f64 %d;

    ld.param.u32 %n, [N];
    ld.param.f64 %d, [buffer];
    ...

Example

.entry bar ( .param .b32 len )
{
    .reg .u32 %ptr, %n;

    mov.u32      %ptr, len;
    ld.param.u32 %n, [%ptr];
    ...

Kernel function parameters may represent normal data values, or they may hold addresses to objects in constant, global, local, or shared state spaces. In the case of pointers, the compiler and runtime system need information about which parameters are pointers, and to which state space they point. Kernel parameter attribute directives are used to provide this information at the PTX level. See Kernel Function Parameter Attributes for a description of kernel parameter attribute directives.

Note

The current implementation does not allow creation of generic pointers to constant variables (cvta.const) in programs that have pointers to constant buffers passed as kernel parameters.

5.1.6.2. Kernel Function Parameter Attributes

Kernel function parameters may be declared with an optional .ptr attribute to indicate that a parameter is a pointer to memory, and also indicate the state space and alignment of the memory being pointed to. Kernel Parameter Attribute: .ptr describes the .ptr kernel parameter attribute.

5.1.6.3. Kernel Parameter Attribute: .ptr

.ptr

Kernel parameter alignment attribute.

Syntax

.param .type .ptr .space .align N  varname
.param .type .ptr        .align N  varname

.space = { .const, .global, .local, .shared };

Description

Used to specify the state space and, optionally, the alignment of memory pointed to by a pointer type kernel parameter. The alignment value N, if present, must be a power of two. If no state space is specified, the pointer is assumed to be a generic address pointing to one of const, global, local, or shared memory. If no alignment is specified, the memory pointed to is assumed to be aligned to a 4 byte boundary.

Spaces between .ptr, .space, and .align may be eliminated to improve readability.

PTX ISA Notes

• Introduced in PTX ISA version 2.2.

• Support for generic addressing of .const space added in PTX ISA version 3.1.

Target ISA Notes

• Supported on all target architectures.

Examples

.entry foo ( .param .u32 param1,
             .param .u32 .ptr.global.align 16 param2,
             .param .u32 .ptr.const.align 8 param3,
             .param .u32 .ptr.align 16 param4  // generic address
                                               // pointer
) { .. }

5.1.6.4. Device Function Parameters

PTX ISA version 2.0 extended the use of parameter space to device function parameters. The most common use is for passing objects by value that do not fit within a PTX register, such as C structures larger than 8 bytes. In this case, a byte array in parameter space is used. Typically, the caller will declare a locally-scoped .param byte array variable that represents a flattened C structure or union. This will be passed by value to a callee, which declares a .param formal parameter having the same size and alignment as the passed argument.

Example

// pass object of type struct { double d; int y; };
.func foo ( .reg .b32 N, .param .align 8 .b8 buffer[12] )
{
    .reg .f64 %d;
    .reg .s32 %y;

    ld.param.f64 %d, [buffer];
    ld.param.s32 %y, [buffer+8];
    ...
}

// code snippet from the caller
// struct { double d; int y; } mystruct; is flattened, passed to foo
    ...
    .reg .f64 dbl;
    .reg .s32 x;
    .param .align 8 .b8 mystruct;
    ...
    st.param.f64 [mystruct+0], dbl;
    st.param.s32 [mystruct+8], x;
    call foo, (4, mystruct);
    ...

See the section on function call syntax for more details.

Function input parameters may be read via ld.param and function return parameters may be written using st.param; it is illegal to write to an input parameter or read from a return parameter.

Aside from passing structures by value, .param space is also required whenever a formal parameter has its address taken within the called function. In PTX, the address of a function input parameter may be moved into a register using the mov instruction. Note that the parameter will be copied to the stack if necessary, and so the address will be in the .local state space and is accessed via ld.local and st.local instructions. It is not possible to use mov to get the address of or a locally-scoped .param space variable. Starting PTX ISA version 6.0, it is possible to use mov instruction to get address of return parameter of device function.

Example

// pass array of up to eight floating-point values in buffer
.func foo ( .param .b32 N, .param .b32 buffer[32] )
{
    .reg .u32  %n, %r;
    .reg .f32  %f;
    .reg .pred %p;

    ld.param.u32 %n, [N];
    mov.u32      %r, buffer;  // forces buffer to .local state space
Loop:
    setp.eq.u32  %p, %n, 0;
@%p: bra         Done;
    ld.local.f32 %f, [%r];
    ...
    add.u32      %r, %r, 4;
    sub.u32      %n, %n, 1;
    bra          Loop;
Done:
    ...
}

5.1.7. Shared State Space

The shared (.shared) state space is a memory that is owned by an executing CTA and is accessible to the threads of all the CTAs within a cluster. An address in shared memory can be read and written by any thread in a CTA cluster.

Additional sub-qualifiers ::cta or ::cluster can be specified on instructions with .shared state space to indicate whether the address belongs to the shared memory window of the executing CTA or of any CTA in the cluster respectively. The addresses in the .shared::cta window also fall within the .shared::cluster window. If no sub-qualifier is specified with the .shared state space, then it defaults to ::cta. For example, ld.shared is equivalent to ld.shared::cta.

Variables declared in .shared state space refer to the memory addresses in the current CTA. Instruction mapa gives the .shared::cluster address of the corresponding variable in another CTA in the cluster.

Shared memory typically has some optimizations to support the sharing. One example is broadcast; where all threads read from the same address. Another is sequential access from sequential threads.

5.1.8. Texture State Space (deprecated)

The texture (.tex) state space is global memory accessed via the texture instruction. It is shared by all threads in a context. Texture memory is read-only and cached, so accesses to texture memory are not coherent with global memory stores to the texture image.

The GPU hardware has a fixed number of texture bindings that can be accessed within a single kernel (typically 128). The .tex directive will bind the named texture memory variable to a hardware texture identifier, where texture identifiers are allocated sequentially beginning with zero. Multiple names may be bound to the same physical texture identifier. An error is generated if the maximum number of physical resources is exceeded. The texture name must be of type .u32 or .u64.

Physical texture resources are allocated on a per-kernel granularity, and .tex variables are required to be defined in the global scope.

Texture memory is read-only. A texture’s base address is assumed to be aligned to a 16 byte boundary.

Example

.tex .u32 tex_a;         // bound to physical texture 0
.tex .u32 tex_c, tex_d;  // both bound to physical texture 1
.tex .u32 tex_d;         // bound to physical texture 2
.tex .u32 tex_f;         // bound to physical texture 3

Note

Explicit declarations of variables in the texture state space is deprecated, and programs should instead reference texture memory through variables of type .texref. The .tex directive is retained for backward compatibility, and variables declared in the .tex state space are equivalent to module-scoped .texref variables in the .global state space.

For example, a legacy PTX definitions such as

.tex .u32 tex_a;

is equivalent to:

.global .texref tex_a;

See Texture Sampler and Surface Types for the description of the .texref type and Texture Instructions for its use in texture instructions.

5.2. Types

5.2.1. Fundamental Types

In PTX, the fundamental types reflect the native data types supported by the target architectures. A fundamental type specifies both a basic type and a size. Register variables are always of a fundamental type, and instructions operate on these types. The same type-size specifiers are used for both variable definitions and for typing instructions, so their names are intentionally short.

Table 8 lists the fundamental type specifiers for each basic type:

Table 8 Fundamental Type Specifiers

Basic Type	Fundamental Type Specifiers
Signed integer	.s8, .s16, .s32, .s64
Unsigned integer	.u8, .u16, .u32, .u64
Floating-point	.f16, .f16x2, .f32, .f64
Bits (untyped)	.b8, .b16, .b32, .b64, .b128
Predicate	.pred

Most instructions have one or more type specifiers, needed to fully specify instruction behavior. Operand types and sizes are checked against instruction types for compatibility.

Two fundamental types are compatible if they have the same basic type and are the same size. Signed and unsigned integer types are compatible if they have the same size. The bit-size type is compatible with any fundamental type having the same size.

In principle, all variables (aside from predicates) could be declared using only bit-size types, but typed variables enhance program readability and allow for better operand type checking.

5.2.2. Restricted Use of Sub-Word Sizes

The .u8, .s8, and .b8 instruction types are restricted to ld, st, and cvt instructions. The .f16 floating-point type is allowed only in conversions to and from .f32, .f64 types, in half precision floating point instructions and texture fetch instructions. The .f16x2 floating point type is allowed only in half precision floating point arithmetic instructions and texture fetch instructions.

For convenience, ld, st, and cvt instructions permit source and destination data operands to be wider than the instruction-type size, so that narrow values may be loaded, stored, and converted using regular-width registers. For example, 8-bit or 16-bit values may be held directly in 32-bit or 64-bit registers when being loaded, stored, or converted to other types and sizes.

5.2.3. Alternate Floating-Point Data Formats

The fundamental floating-point types supported in PTX have implicit bit representations that indicate the number of bits used to store exponent and mantissa. For example, the .f16 type indicates 5 bits reserved for exponent and 10 bits reserved for mantissa. In addition to the floating-point representations assumed by the fundamental types, PTX allows the following alternate floating-point data formats:

bf16 data format:

This data format is a 16-bit floating point format with 8 bits for exponent and 7 bits for mantissa. A register variable containing bf16 data must be declared with .b16 type.

e4m3 data format:

This data format is an 8-bit floating point format with 4 bits for exponent and 3 bits for mantissa. The e4m3 encoding does not support infinity and NaN values are limited to 0x7f and 0xff. A register variable containing e4m3 value must be declared using bit-size type.

e5m2 data format:

This data format is an 8-bit floating point format with 5 bits for exponent and 2 bits for mantissa. A register variable containing e5m2 value must be declared using bit-size type.

tf32 data format:

This data format is a special 32-bit floating point format supported by the matrix multiply-and-accumulate instructions, with the same range as .f32 and reduced precision (>=10 bits). The internal layout of tf32 format is implementation defined. PTX facilitates conversion from single precision .f32 type to tf32 format. A register variable containing tf32 data must be declared with .b32 type.

Alternate data formats cannot be used as fundamental types. They are supported as source or destination formats by certain instructions.

5.2.4. Packed Data Types

Certain PTX instructions operate on two sets of inputs in parallel, and produce two outputs. Such instructions can use the data stored in a packed format. PTX supports packing two values of the same scalar data type into a single, larger value. The packed value is considered as a value of a packed data type. In this section we describe the packed data types supported in PTX.

5.2.4.1. Packed Floating Point Data Types

PTX supports the following four variants of packed floating point data types:

1. .f16x2 packed type containing two .f16 floating point values.

2. .bf16x2 packed type containing two .bf16 alternate floating point values.

3. .e4m3x2 packed type containing two .e4m3 alternate floating point values.

4. .e5m2x2 packed type containing two .e5m2 alternate floating point values.

.f16x2 is supported as a fundamental type. .bf16x2, .e4m3x2 and .e5m2x2 cannot be used as fundamental types - they are supported as instruction types on certain instructions. A register variable containing .bf16x2 data must be declared with .b32 type. A register variable containing .e4m3x2 or .e5m2x2 data must be declared with .b16 type.

5.2.4.2. Packed Integer Data Types

PTX supports two variants of packed integer data types: .u16x2 and .s16x2. The packed data type consists of two .u16 or .s16 values. A register variable containing .u16x2 or .s16x2 data must be declared with .b32 type. Packed integer data types cannot be used as fundamental types. They are supported as instruction types on certain instructions.

5.3. Texture Sampler and Surface Types

PTX includes built-in opaque types for defining texture, sampler, and surface descriptor variables. These types have named fields similar to structures, but all information about layout, field ordering, base address, and overall size is hidden to a PTX program, hence the term opaque. The use of these opaque types is limited to:

• Variable definition within global (module) scope and in kernel entry parameter lists.

• Static initialization of module-scope variables using comma-delimited static assignment expressions for the named members of the type.

• Referencing textures, samplers, or surfaces via texture and surface load/store instructions (tex, suld, sust, sured).

• Retrieving the value of a named member via query instructions (txq, suq).

• Creating pointers to opaque variables using mov, e.g., mov.u64 reg, opaque_var;. The resulting pointer may be stored to and loaded from memory, passed as a parameter to functions, and de-referenced by texture and surface load, store, and query instructions, but the pointer cannot otherwise be treated as an address, i.e., accessing the pointer with ld and st instructions, or performing pointer arithmetic will result in undefined results.

• Opaque variables may not appear in initializers, e.g., to initialize a pointer to an opaque variable.

Note

Indirect access to textures and surfaces using pointers to opaque variables is supported beginning with PTX ISA version 3.1 and requires target sm_20 or later.

Indirect access to textures is supported only in unified texture mode (see below).

The three built-in types are .texref, .samplerref, and .surfref. For working with textures and samplers, PTX has two modes of operation. In the unified mode, texture and sampler information is accessed through a single .texref handle. In the independent mode, texture and sampler information each have their own handle, allowing them to be defined separately and combined at the site of usage in the program. In independent mode, the fields of the .texref type that describe sampler properties are ignored, since these properties are defined by .samplerref variables.

Table 9 and Table 10 list the named members of each type for unified and independent texture modes. These members and their values have precise mappings to methods and values defined in the texture HW class as well as exposed values via the API.

Table 9 Opaque Type Fields in Unified Texture Mode

Member	.texref values	.surfref values
width	in elements
height	in elements
depth	in elements
channel_data_type	enum type corresponding to source language API
channel_order	enum type corresponding to source language API
normalized_coords	0, 1	N/A
filter_mode	nearest, linear	N/A
addr_mode_0, addr_mode_1, addr_mode_2	wrap,mirror, clamp_ogl, clamp_to_edge, clamp_to_border	N/A
array_size	as number of textures in a texture array	as number of surfaces in a surface array
num_mipmap_levels	as number of levels in a mipmapped texture	N/A
num_samples	as number of samples in a multi-sample texture	N/A
memory_layout	N/A	1 for linear memory layout; 0 otherwise

5.3.1. Texture and Surface Properties

Fields width, height, and depth specify the size of the texture or surface in number of elements in each dimension.

The channel_data_type and channel_order fields specify these properties of the texture or surface using enumeration types corresponding to the source language API. For example, see Channel Data Type and Channel Order Fields for the OpenCL enumeration types currently supported in PTX.

5.3.2. Sampler Properties

The normalized_coords field indicates whether the texture or surface uses normalized coordinates in the range [0.0, 1.0) instead of unnormalized coordinates in the range [0, N). If no value is specified, the default is set by the runtime system based on the source language.

The filter_mode field specifies how the values returned by texture reads are computed based on the input texture coordinates.

The addr_mode_{0,1,2} fields define the addressing mode in each dimension, which determine how out-of-range coordinates are handled.

See the CUDA C++ Programming Guide for more details of these properties.

Table 10 Opaque Type Fields in Independent Texture Mode

Member	.samplerref values	.texref values	.surfref values
width	N/A	in elements
height	N/A	in elements
depth	N/A	in elements
channel_data_type	N/A	enum type corresponding to source language API
channel_order	N/A	enum type corresponding to source language AP
normalized_coords	N/A	0, 1	N/A
force_unnormalized_coords	0, 1	N/A	N/A
filter_mode	nearest, linear	ignored	N/A
addr_mode_0, addr_mode_1, addr_mode_2	wrap,mirror, clamp_ogl, clamp_to_edge, clamp_to_border	N/A	N/A
array_size	N/A	as number of textures in a texture array	as number of surfaces in a surface array
num_mipmap_levels	N/A	as number of levels in a mipmapped texture	N/A
num_samples	N/A	as number of samples in a multi-sample texture	N/A
memory_layout	N/A	N/A	1 for linear memory layout; 0 otherwise

In independent texture mode, the sampler properties are carried in an independent .samplerref variable, and these fields are disabled in the .texref variables. One additional sampler property, force_unnormalized_coords, is available in independent texture mode.

The force_unnormalized_coords field is a property of .samplerref variables that allows the sampler to override the texture header normalized_coords property. This field is defined only in independent texture mode. When True, the texture header setting is overridden and unnormalized coordinates are used; when False, the texture header setting is used.

The force_unnormalized_coords property is used in compiling OpenCL; in OpenCL, the property of normalized coordinates is carried in sampler headers. To compile OpenCL to PTX, texture headers are always initialized with normalized_coords set to True, and the OpenCL sampler-based normalized_coords flag maps (negated) to the PTX-level force_unnormalized_coords flag.

Variables using these types may be declared at module scope or within kernel entry parameter lists. At module scope, these variables must be in the .global state space. As kernel parameters, these variables are declared in the .param state space.

Example

.global .texref     my_texture_name;
.global .samplerref my_sampler_name;
.global .surfref    my_surface_name;

When declared at module scope, the types may be initialized using a list of static expressions assigning values to the named members.

Example

.global .texref tex1;
.global .samplerref tsamp1 = { addr_mode_0 = clamp_to_border,
                               filter_mode = nearest
                             };

5.3.3. Channel Data Type and Channel Order Fields

The channel_data_type and channel_order fields have enumeration types corresponding to the source language API. Currently, OpenCL is the only source language that defines these fields. Table 12 and Table 11 show the enumeration values defined in OpenCL version 1.0 for channel data type and channel order.

Table 11 OpenCL 1.0 Channel Data Type Definition

CL_SNORM_INT8	0x10D0
CL_SNORM_INT16	0x10D1
CL_UNORM_INT8	0x10D2
CL_UNORM_INT16	0x10D3
CL_UNORM_SHORT_565	0x10D4
CL_UNORM_SHORT_555	0x10D5
CL_UNORM_INT_101010	0x10D6
CL_SIGNED_INT8	0x10D7
CL_SIGNED_INT16	0x10D8
CL_SIGNED_INT32	0x10D9
CL_UNSIGNED_INT8	0x10DA
CL_UNSIGNED_INT16	0x10DB
CL_UNSIGNED_INT32	0x10DC
CL_HALF_FLOAT	0x10DD
CL_FLOAT	0x10DE

Table 12 OpenCL 1.0 Channel Order Definition

CL_R	0x10B0
CL_A	0x10B1
CL_RG	0x10B2
CL_RA	0x10B3
CL_RGB	0x10B4
CL_RGBA	0x10B5
CL_BGRA	0x10B6
CL_ARGB	0x10B7
CL_INTENSITY	0x10B8
CL_LUMINANCE	0x10B9

5.4. Variables

In PTX, a variable declaration describes both the variable’s type and its state space. In addition to fundamental types, PTX supports types for simple aggregate objects such as vectors and arrays.

5.4.1. Variable Declarations

All storage for data is specified with variable declarations. Every variable must reside in one of the state spaces enumerated in the previous section.

A variable declaration names the space in which the variable resides, its type and size, its name, an optional array size, an optional initializer, and an optional fixed address for the variable.

Predicate variables may only be declared in the register state space.

Examples

.global .u32 loc;
.reg    .s32 i;
.const  .f32 bias[] = {-1.0, 1.0};
.global .u8  bg[4] = {0, 0, 0, 0};
.reg    .v4 .f32 accel;
.reg    .pred p, q, r;

5.4.2. Vectors

Limited-length vector types are supported. Vectors of length 2 and 4 of any non-predicate fundamental type can be declared by prefixing the type with .v2 or .v4. Vectors must be based on a fundamental type, and they may reside in the register space. Vectors cannot exceed 128-bits in length; for example, .v4 .f64 is not allowed. Three-element vectors may be handled by using a .v4 vector, where the fourth element provides padding. This is a common case for three-dimensional grids, textures, etc.

Examples

.global .v4 .f32 V;   // a length-4 vector of floats
.shared .v2 .u16 uv;  // a length-2 vector of unsigned ints
.global .v4 .b8  v;   // a length-4 vector of bytes

By default, vector variables are aligned to a multiple of their overall size (vector length times base-type size), to enable vector load and store instructions which require addresses aligned to a multiple of the access size.

5.4.3. Array Declarations

Array declarations are provided to allow the programmer to reserve space. To declare an array, the variable name is followed with dimensional declarations similar to fixed-size array declarations in C. The size of each dimension is a constant expression.

Examples

.local  .u16 kernel[19][19];
.shared .u8  mailbox[128];

The size of the array specifies how many elements should be reserved. For the declaration of array kernel above, 19*19 = 361 halfwords are reserved, for a total of 722 bytes.

When declared with an initializer, the first dimension of the array may be omitted. The size of the first array dimension is determined by the number of elements in the array initializer.

Examples

.global .u32 index[] = { 0, 1, 2, 3, 4, 5, 6, 7 };
.global .s32 offset[][2] = { {-1, 0}, {0, -1}, {1, 0}, {0, 1} };

Array index has eight elements, and array offset is a 4x2 array.

5.4.4. Initializers

Declared variables may specify an initial value using a syntax similar to C/C++, where the variable name is followed by an equals sign and the initial value or values for the variable. A scalar takes a single value, while vectors and arrays take nested lists of values inside of curly braces (the nesting matches the dimensionality of the declaration).

As in C, array initializers may be incomplete, i.e., the number of initializer elements may be less than the extent of the corresponding array dimension, with remaining array locations initialized to the default value for the specified array type.

Examples

.const  .f32 vals[8] = { 0.33, 0.25, 0.125 };
.global .s32 x[3][2] = { {1,2}, {3} };

is equivalent to

.const  .f32 vals[8] = { 0.33, 0.25, 0.125, 0.0, 0.0, 0.0, 0.0, 0.0 };
.global .s32 x[3][2] = { {1,2}, {3,0}, {0,0} };

Currently, variable initialization is supported only for constant and global state spaces. Variables in constant and global state spaces with no explicit initializer are initialized to zero by default. Initializers are not allowed in external variable declarations.

Variable names appearing in initializers represent the address of the variable; this can be used to statically initialize a pointer to a variable. Initializers may also contain var+offset expressions, where offset is a byte offset added to the address of var. Only variables in .global or .const state spaces may be used in initializers. By default, the resulting address is the offset in the variable’s state space (as is the case when taking the address of a variable with a mov instruction). An operator, generic(), is provided to create a generic address for variables used in initializers.

Starting PTX ISA version 7.1, an operator mask() is provided, where mask is an integer immediate. The only allowed expressions in the mask() operator are integer constant expression and symbol expression representing address of variable. The mask() operator extracts n consecutive bits from the expression used in initializers and inserts these bits at the lowest position of the initialized variable. The number n and the starting position of the bits to be extracted is specified by the integer immediate mask. PTX ISA version 7.1 only supports extracting a single byte starting at byte boundary from the address of the variable. PTX ISA version 7.3 supports Integer constant expression as an operand in the mask() operator.

Supported values for mask are: 0xFF, 0xFF00, 0XFF0000, 0xFF000000, 0xFF00000000, 0xFF0000000000, 0xFF000000000000, 0xFF00000000000000.

Examples

.const  .u32 foo = 42;
.global .u32 bar[] = { 2, 3, 5 };
.global .u32 p1 = foo;          // offset of foo in .const space
.global .u32 p2 = generic(foo); // generic address of foo

// array of generic-address pointers to elements of bar
.global .u32 parr[] = { generic(bar), generic(bar)+4,
generic(bar)+8 };

// examples using mask() operator are pruned for brevity
.global .u8 addr[] = {0xff(foo), 0xff00(foo), 0xff0000(foo), ...};

.global .u8 addr2[] = {0xff(foo+4), 0xff00(foo+4), 0xff0000(foo+4),...}

.global .u8 addr3[] = {0xff(generic(foo)), 0xff00(generic(foo)),...}

.global .u8 addr4[] = {0xff(generic(foo)+4), 0xff00(generic(foo)+4),...}

// mask() operator with integer const expression
.global .u8 addr5[] = { 0xFF(1000 + 546), 0xFF00(131187), ...};

Note

PTX 3.1 redefines the default addressing for global variables in initializers, from generic addresses to offsets in the global state space. Legacy PTX code is treated as having an implicit generic() operator for each global variable used in an initializer. PTX 3.1 code should either include explicit generic() operators in initializers, use cvta.global to form generic addresses at runtime, or load from the non-generic address using ld.global.

Device function names appearing in initializers represent the address of the first instruction in the function; this can be used to initialize a table of function pointers to be used with indirect calls. Beginning in PTX ISA version 3.1, kernel function names can be used as initializers e.g. to initialize a table of kernel function pointers, to be used with CUDA Dynamic Parallelism to launch kernels from GPU. See the CUDA Dynamic Parallelism Programming Guide for details.

Labels cannot be used in initializers.

Variables that hold addresses of variables or functions should be of type .u8 or .u32 or .u64.

Type .u8 is allowed only if the mask() operator is used.

Initializers are allowed for all types except .f16, .f16x2 and .pred.

Examples

.global .s32 n = 10;
.global .f32 blur_kernel[][3]
               = {{.05,.1,.05},{.1,.4,.1},{.05,.1,.05}};

.global .u32 foo[] = { 2, 3, 5, 7, 9, 11 };
.global .u64 ptr = generic(foo);   // generic address of foo[0]
.global .u64 ptr = generic(foo)+8; // generic address of foo[2]

5.4.5. Alignment

Byte alignment of storage for all addressable variables can be specified in the variable declaration. Alignment is specified using an optional .alignbyte-count specifier immediately following the state-space specifier. The variable will be aligned to an address which is an integer multiple of byte-count. The alignment value byte-count must be a power of two. For arrays, alignment specifies the address alignment for the starting address of the entire array, not for individual elements.

The default alignment for scalar and array variables is to a multiple of the base-type size. The default alignment for vector variables is to a multiple of the overall vector size.

Examples

 // allocate array at 4-byte aligned address.  Elements are bytes.
.const .align 4 .b8 bar[8] = {0,0,0,0,2,0,0,0};

Note that all PTX instructions that access memory require that the address be aligned to a multiple of the access size. The access size of a memory instruction is the total number of bytes accessed in memory. For example, the access size of ld.v4.b32 is 16 bytes, while the access size of atom.f16x2 is 4 bytes.

5.4.6. Parameterized Variable Names

Since PTX supports virtual registers, it is quite common for a compiler frontend to generate a large number of register names. Rather than require explicit declaration of every name, PTX supports a syntax for creating a set of variables having a common prefix string appended with integer suffixes.

For example, suppose a program uses a large number, say one hundred, of .b32 variables, named %r0, %r1, …, %r99. These 100 register variables can be declared as follows:

.reg .b32 %r<100>;    // declare %r0, %r1, ..., %r99

This shorthand syntax may be used with any of the fundamental types and with any state space, and may be preceded by an alignment specifier. Array variables cannot be declared this way, nor are initializers permitted.

5.4.7. Variable Attributes

Variables may be declared with an optional .attribute directive which allows specifying special attributes of variables. Keyword .attribute is followed by attribute specification inside parenthesis. Multiple attributes are separated by comma.

Variable and Function Attribute Directive: .attribute describes the .attribute directive.

5.4.8. Variable and Function Attribute Directive: .attribute

.attribute

Variable and function attributes

Description

Used to specify special attributes of a variable or a function.

The following attributes are supported.

.managed

.managed attribute specifies that variable will be allocated at a location in unified virtual memory environment where host and other devices in the system can reference the variable directly. This attribute can only be used with variables in .global state space. See the CUDA UVM-Lite Programming Guide for details.

.unified

.unified attribute specifies that function has the same memory address on the host and on other devices in the system. Integer constants uuid1 and uuid2 respectively specify upper and lower 64 bits of the unique identifier associated with the function or the variable. This attribute can only be used on device functions or on variables in the .global state space. Variables with .unified attribute are read-only and must be loaded by specifying .unified qualifier on the address operand of ld instruction, otherwise the behavior is undefined.

PTX ISA Notes

• Introduced in PTX ISA version 4.0.

• Support for function attributes introduced in PTX ISA version 8.0.

Target ISA Notes

• .managed attribute requires sm_30 or higher.

• .unified attribute requires sm_90 or higher.

Examples

.global .attribute(.managed) .s32 g;
.global .attribute(.managed) .u64 x;

.global .attribute(.unified(19,95)) .f32 f;

.func .attribute(.unified(0xAB, 0xCD)) bar() { ... }

5.5. Tensors

A tensor is a multi-dimensional matrix structure in the memory. Tensor is defined by the following properties:

• Dimensionality

• Dimension sizes across each dimension

• Individual element types

• Tensor stride across each dimension

PTX supports instructions which can operate on the tensor data. PTX Tensor instructions include:

• Copying data between global and shared memories

• Reducing the destination tensor data with the source.

The Tensor data can be operated on by various wmma.mma, mma and wgmma.mma_async instructions.

PTX Tensor instructions treat the tensor data in the global memory as a multi-dimensional structure and treat the data in the shared memory as a linear data.

5.5.1. Tensor Dimension, size and format

Tensors can have dimensions: 1D, 2D, 3D, 4D or 5D.

Each dimension has a size which represents the number of elements along the dimension. The elements can have one the following types:

• Bit-sized type: .b32, .b64

• Integer: .u8, .u16, .u32, .s32, .u64, .s64

• Floating point and alternate floating point: .f16, .bf16, .tf32, .f32, .f64 (rounded to nearest even).

Tensor can have padding at the end in each of the dimensions to provide alignment for the data in the subsequent dimensions. Tensor stride can be used to specify the amount of padding in each dimension.

5.5.2. Tensor Access Modes

Tensor data can be accessed in two modes:

• Tiled mode:

  In tiled mode, the source multi-dimensional tensor layout is preserved at the destination.

• Im2col mode:

  In im2col mode, the elements in the Bounding Box of the source tensor are rearranged into columns at the destination. Refer here for more details.

5.5.3. Tiled Mode

This section talks about how Tensor and Tensor access work in tiled mode.

5.5.3.1. Bounding Box

A tensor can be accessed in chunks known as Bounding Box. The Bounding Box has the same dimensionality as the tensor they are accessing into. Size of each bounding Box must be a multiple of 16 bytes. The address of the bounding Box must also be aligned to 16 bytes.

Bounding Box has the following access properties:

• Bounding Box dimension sizes

• Out of boundary access mode

• Traversal strides

The tensor-coordinates, specified in the PTX tensor instructions, specify the starting offset of the bounding box. Starting offset of the bounding box along with the rest of the bounding box information together are used to determine the elements which are to be accessed.

5.5.3.2. Traversal-Stride

While the Bounding Box is iterating the tensor across a dimension, the traversal stride specifies the exact number of elements to be skipped. If no jump over is required, default value of 1 must be specified.

The traversal stride in dimension 0 can be used for the Interleave layout. For non-interleaved layout, the traversal stride in dimension 0 must always be 1.

Figure 5 illustrates tensor, tensor size, tensor stride, Bounding Box size and traversal stride.

Figure 5 Tiled mode bounding box, tensor size and traversal stride

5.5.3.3. Out of Boundary Access

PTX Tensor operation can detect and handle the case when the Bounding Box crosses the tensor boundary in any dimension. There are 2 modes:

• Zero fill mode:

  Elements in the Bounding Box which fall outside of the tensor boundary are set to 0.

• OOB-NaN fill mode:

  Elements in the Bounding Box which fall outside of the tensor boundary are set to a special NaN called OOB-NaN.

Figure 6 shows an example of the out of boundary access.

Figure 6 Out of boundary access

5.5.4. Im2col mode

Im2col mode supports the following tensor dimensions : 3D, 4D and 5D. In this mode, the tensor data is treated as a batch of images with the following properties:

• N : number of images in the batch

• D, H, W : size of a 3D image (depth, height and width)

• C: channels per image element

The above properties are associated with 3D, 4D and 5D tensors as follows:

Dimension	N/D/H/W/C applicability
3D	NWC
4D	NHWC
5D	NDHWC

5.5.4.1. Bounding Box

In im2col mode, the Bounding Box is defined in DHW space. Boundaries along other dimensions are specified by Pixels-per-Column and Channels-per-Pixel parameters as described below.

The dimensionality of the Bounding Box is two less than the tensor dimensionality.

The following properties describe how to access of the elements in im2col mode:

• Bounding-Box Lower-Corner

• Bounding-Box Upper-Corner

• Pixels-per-Column

• Channels-per-Pixel

Bounding-box Lower-Corner and Bounding-box Upper-Corner specify the two opposite corners of the Bounding Box in the DHW space. Bounding-box Lower-Corner specifies the corner with the smallest coordinate and Bounding-box Upper-Corner specifies the corner with the largest coordinate.

Bounding-box Upper- and Lower-Corners are 16-bit signed values whose limits varies across the dimensions and are as shown below:

	3D	4D	5D
Upper- / Lower- Corner sizes	[-215, 215-1]	[-27, 27-1]	[-24, 24-1]

Figure 7 and Figure 8 show the Upper-Corners and Lower-Corners.

Figure 7 im2col mode bounding box example 1

Figure 8 im2col mode bounding box example 2

The Bounding-box Upper- and Lower- Corners specify only the boundaries and not the number of elements to be accessed. Pixels-per-Column specifies the number of elements to be accessed in the NDHW space.

Channels-per-Pixel specifies the number of elements to access across the C dimension.

The tensor coordinates, specified in the PTX tensor instructions, behaves differently in different dimensions:

• Across N and C dimensions: specify the starting offsets along the dimension, similar to the tiled mode.

• Across DHW dimensions: specify the location of the convolution filter base in the tensor space. The filter corner location must be within the bounding box.

The im2col offsets, specified in the PTX tensor instructions in im2col mode, are added to the filter base coordinates to determine the starting location in the tensor space from where the elements are accessed.

The size of the im2col offsets varies across the dimensions and their valid ranges are as shown below:

	3D	4D	5D
im2col offsets range	[0, 216-1]	[0, 28-1]	[0, 25-1]

Following are some examples of the im2col mode accesses:

• Example 1 (Figure 9):

  Tensor Size[0] = 64
  Tensor Size[1] = 9
  Tensor Size[2] = 14
  Tensor Size[3] = 64
  Pixels-per-Column = 64
  channels-per-pixel = 8
  Bounding-Box Lower-Corner W = -1
  Bounding-Box Lower-Corner H = -1
  Bounding-Box Upper-Corner W = -1
  Bounding-Box Upper-Corner H = -1.
  
  tensor coordinates = (7, 7, 4, 0)
  im2col offsets : (0, 0)
  

  

  Figure 9 im2col mode example 1

• Example 2 (Figure 10):

  Tensor Size[0] = 64
  Tensor Size[1] = 9
  Tensor Size[2] = 14
  Tensor Size[3] = 64
  Pixels-per-Column = 64
  channels-per-pixel = 8
  Bounding-Box Lower-Corner W = 0
  Bounding-Box Lower-Corner H = 0
  Bounding-Box Upper-Corner W = -2
  Bounding-Box Upper-Corner H = -2
  
  tensor coordinates = (7, 7, 4, 0)
  im2col offsets: (2, 2)
  

  

  Figure 10 im2col mode example 2

5.5.4.2. Traversal Stride

The traversal stride, in im2col mode, does not impact the total number of elements (or pixels) being accessed unlike the tiled mode. Pixels-per-Column determines the total number of elements being accessed, in im2col mode.

The number of elements traversed along the D, H and W dimensions is strided by the traversal stride for that dimension.

The following example with Figure 11 illustrates accesse with traversal-strides:

Tensor Size[0] = 64
Tensor Size[1] = 8
Tensor Size[2] = 14
Tensor Size[3] = 64
Traversal Stride = 2
Pixels-per-Column = 32
channels-per-pixel = 16
Bounding-Box Lower-Corner W = -1
Bounding-Box Lower-Corner H = -1
Bounding-Box Upper-Corner W = -1
Bounding-Box Upper-Corner H = -1.
Tensor coordinates in the instruction = (7, 7, 5, 0)
Im2col offsets in the instruction : (1, 1)

Figure 11 im2col mode traversal stride example

5.5.4.3. Out of Boundary Access

In im2col mode, when the number of requested pixels in NDHW space specified by Pixels-per-Column exceeds the number of available pixels in the image batch then out-of-bounds access is performed.

Similar to tiled mode, zero fill or OOB-NaN fill can be performed based on the Fill-Mode specified.

5.5.5. Interleave layout

Tensor can be interleaved and the following interleave layouts are supported:

• No interleave (NDHWC)

• 8 byte interleave (NC/8DHWC8) : C8 utilizes 16 bytes in memory assuming 2B per channel.

• 16 byte interleave (NC/16HWC16) : C16 utilizes 32 bytes in memory assuming 4B per channel.

The C information is organized in slices where sequential C elements are grouped in 16 byte or 32 byte quantities.

If the total number of channels is not a multiple of the number of channels per slice, then the last slice must be padded with zeros to make it complete 16B or 32B slice.

Interleaved layouts are supported only for the dimensionalities : 3D, 4D and 5D.

5.5.6. Swizzling Modes

The layout of the data in the shared memory can be different to that of global memory, for access performance reasons. The following describes various swizzling modes:

• No swizzle mode:

  There is no swizzling in this mode and the destination data layout is exactly similar to the source data layout.

  0	1	2	3	4	5	6	7
  0	1	2	3	4	5	6	7
  … Pattern repeats …

• 32 byte swizzle mode:

  The following table, where each elements (numbered cell) is 16 byte and the starting address is 256 bytes aligned, shows the pattern of the destination data layout:

  0	1	2	3	4	5	6	7
  1	0	3	2	5	4	7	6
  … Pattern repeats …

  An example of the 32 byte swizzle mode for NC/(32B)HWC(32B) tensor of 1x2x10x10xC16 dimension, with the innermost dimension holding slice of 16 channels with 2 byte/channel, is shown in Figure 12.

  

  Figure 12 32-byte swizzle mode example

  Figure 13 shows the two fragments of the tensor : one for C/(32B) = 0 and another for C/(32B) = 1.

  

  Figure 13 32-byte swizzle mode fragments

  Figure 14 shows the destination data layout with 32 byte swizzling.

  

  Figure 14 32-byte swizzle mode destination data layout

• 64 byte swizzle mode:

  The following table, where each elements (numbered cell) is 16 byte and the starting address is 512 bytes aligned, shows the pattern of the destination data layout:

  0	1	2	3	4	5	6	7
  1	0	3	2	5	4	7	6
  2	3	0	1	6	7	4	5
  3	2	1	0	7	6	5	4
  … Pattern repeats …

  An example of the 64 byte swizzle mode for NHWC tensor of 1x10x10x64 dimension, with 2 bytes / channel and 32 channels, is shown in Figure 15.

  

  Figure 15 64-byte swizzle mode example

  Each colored cell represents 8 channels. Figure 16 shows the source data layout.

  

  Figure 16 64-byte swizzle mode source data layout

  Figure 17 shows the destination data layout with 64 byte swizzling.

  

  Figure 17 64-byte swizzle mode destination data layout

• 128 byte swizzle mode:

  The following table, where each elements (numbered cell) is 16 byte and the starting address is 1024 bytes aligned, shows the pattern of the destination data layout:

  0	1	2	3	4	5	6	7
  1	0	3	2	5	4	7	6
  2	3	0	1	6	7	4	5
  3	2	1	0	7	6	5	4
  4	5	6	7	0	1	2	3
  5	4	7	6	1	0	3	2
  6	7	4	5	2	3	0	1
  … Pattern repeats …

  An example of the 128 byte swizzle mode for NHWC tensor of 1x10x10x64 dimension, with 2 bytes / channel and 64 channels, is shown in Figure 18.

  

  Figure 18 128-byte swizzle mode example

  Each colored cell represents 8 channels. Figure 19 shows the source data layout.

  

  Figure 19 128-byte swizzle mode source data layout

  Figure 20 shows the destination data layout with 128 byte swizzling.

  

  Figure 20 128-byte swizzle mode destination data layout

5.5.7. Tensor-map

The tensor-map is a 128-byte opaque object either in .const space or .param (kernel function parameter) space or .global space which describes the tensor properties and the access properties of the tensor data described in previous sections.

Tensor-Map can be created using CUDA APIs. Refer to CUDA programming guide for more details.

6. Instruction Operands

6.1. Operand Type Information

All operands in instructions have a known type from their declarations. Each operand type must be compatible with the type determined by the instruction template and instruction type. There is no automatic conversion between types.

The bit-size type is compatible with every type having the same size. Integer types of a common size are compatible with each other. Operands having type different from but compatible with the instruction type are silently cast to the instruction type.

6.2. Source Operands

The source operands are denoted in the instruction descriptions by the names a, b, and c. PTX describes a load-store machine, so operands for ALU instructions must all be in variables declared in the .reg register state space. For most operations, the sizes of the operands must be consistent.

The cvt (convert) instruction takes a variety of operand types and sizes, as its job is to convert from nearly any data type to any other data type (and size).

The ld, st, mov, and cvt instructions copy data from one location to another. Instructions ld and st move data from/to addressable state spaces to/from registers. The mov instruction copies data between registers.

Most instructions have an optional predicate guard that controls conditional execution, and a few instructions have additional predicate source operands. Predicate operands are denoted by the names p, q, r, s.

6.3. Destination Operands

PTX instructions that produce a single result store the result in the field denoted by d (for destination) in the instruction descriptions. The result operand is a scalar or vector variable in the register state space.

6.4. Using Addresses, Arrays, and Vectors

Using scalar variables as operands is straightforward. The interesting capabilities begin with addresses, arrays, and vectors.

6.4.1. Addresses as Operands

All the memory instructions take an address operand that specifies the memory location being accessed. This addressable operand is one of:

[var]

the name of an addressable variable var.

[reg]

an integer or bit-size type register reg containing a byte address.

[reg+immOff]

a sum of register reg containing a byte address plus a constant integer byte offset (signed, 32-bit).

[var+immOff]

a sum of address of addressable variable var containing a byte address plus a constant integer byte offset (signed, 32-bit).

[immAddr]

an immediate absolute byte address (unsigned, 32-bit).

var[immOff]

an array element as described in Arrays as Operands.

The register containing an address may be declared as a bit-size type or integer type.

The access size of a memory instruction is the total number of bytes accessed in memory. For example, the access size of ld.v4.b32 is 16 bytes, while the access size of atom.f16x2 is 4 bytes.

The address must be naturally aligned to a multiple of the access size. If an address is not properly aligned, the resulting behavior is undefined. For example, among other things, the access may proceed by silently masking off low-order address bits to achieve proper rounding, or the instruction may fault.

The address size may be either 32-bit or 64-bit. 128-bit adresses are not supported. Addresses are zero-extended to the specified width as needed, and truncated if the register width exceeds the state space address width for the target architecture.

Address arithmetic is performed using integer arithmetic and logical instructions. Examples include pointer arithmetic and pointer comparisons. All addresses and address computations are byte-based; there is no support for C-style pointer arithmetic.

The mov instruction can be used to move the address of a variable into a pointer. The address is an offset in the state space in which the variable is declared. Load and store operations move data between registers and locations in addressable state spaces. The syntax is similar to that used in many assembly languages, where scalar variables are simply named and addresses are de-referenced by enclosing the address expression in square brackets. Address expressions include variable names, address registers, address register plus byte offset, and immediate address expressions which evaluate at compile-time to a constant address.

Here are a few examples:

.shared .u16 x;
.reg    .u16 r0;
.global .v4 .f32 V;
.reg    .v4 .f32 W;
.const  .s32 tbl[256];
.reg    .b32 p;
.reg    .s32 q;

ld.shared.u16   r0,[x];
ld.global.v4.f32 W, [V];
ld.const.s32    q, [tbl+12];
mov.u32         p, tbl;

6.4.1.1. Generic Addressing

If a memory instruction does not specify a state space, the operation is performed using generic addressing. The state spaces .const, Kernel Function Parameters (.param), .local and .shared are modeled as windows within the generic address space. Each window is defined by a window base and a window size that is equal to the size of the corresponding state space. A generic address maps to global memory unless it falls within the window for const, local, or shared memory. The Kernel Function Parameters (.param) window is contained within the .global window. Within each window, a generic address maps to an address in the underlying state space by subtracting the window base from the generic address.

6.4.2. Arrays as Operands

Arrays of all types can be declared, and the identifier becomes an address constant in the space where the array is declared. The size of the array is a constant in the program.

Array elements can be accessed using an explicitly calculated byte address, or by indexing into the array using square-bracket notation. The expression within square brackets is either a constant integer, a register variable, or a simple register with constant offset expression, where the offset is a constant expression that is either added or subtracted from a register variable. If more complicated indexing is desired, it must be written as an address calculation prior to use. Examples are:

ld.global.u32  s, a[0];
ld.global.u32  s, a[N-1];
mov.u32        s, a[1];  // move address of a[1] into s

6.4.3. Vectors as Operands

Vector operands are supported by a limited subset of instructions, which include mov, ld, st, atom, red and tex. Vectors may also be passed as arguments to called functions.

Vector elements can be extracted from the vector with the suffixes .x, .y, .z and .w, as well as the typical color fields .r, .g, .b and .a.

A brace-enclosed list is used for pattern matching to pull apart vectors.

.reg .v4 .f32 V;
.reg .f32     a, b, c, d;

mov.v4.f32 {a,b,c,d}, V;

Vector loads and stores can be used to implement wide loads and stores, which may improve memory performance. The registers in the load/store operations can be a vector, or a brace-enclosed list of similarly typed scalars. Here are examples:

ld.global.v4.f32  {a,b,c,d}, [addr+16];
ld.global.v2.u32  V2, [addr+8];

Elements in a brace-enclosed vector, say {Ra, Rb, Rc, Rd}, correspond to extracted elements as follows:

Ra = V.x = V.r
Rb = V.y = V.g
Rc = V.z = V.b
Rd = V.w = V.a

6.4.4. Labels and Function Names as Operands

Labels and function names can be used only in bra/brx.idx and call instructions respectively. Function names can be used in mov instruction to get the address of the function into a register, for use in an indirect call.

Beginning in PTX ISA version 3.1, the mov instruction may be used to take the address of kernel functions, to be passed to a system call that initiates a kernel launch from the GPU. This feature is part of the support for CUDA Dynamic Parallelism. See the CUDA Dynamic Parallelism Programming Guide for details.

6.5. Type Conversion

All operands to all arithmetic, logic, and data movement instruction must be of the same type and size, except for operations where changing the size and/or type is part of the definition of the instruction. Operands of different sizes or types must be converted prior to the operation.

6.5.1. Scalar Conversions

Table 13 shows what precision and format the cvt instruction uses given operands of differing types. For example, if a cvt.s32.u16 instruction is given a u16 source operand and s32 as a destination operand, the u16 is zero-extended to s32.

Conversions to floating-point that are beyond the range of floating-point numbers are represented with the maximum floating-point value (IEEE 754 Inf for f32 and f64, and ~131,000 for f16).

Table 13 Convert Instruction Precision and Format

		Destination Format
		s8	s16	s32	s64	u8	u16	u32	u64	f16	f32	f64
Source Format	s8	–	sext	sext	sext	–	sext	sext	sext	s2f	s2f	s2f
	s16	chop1	–	sext	sext	chop1	–	sext	sext	s2f	s2f	s2f
	s32	chop1	chop1	–	sext	chop1	chop1	–	sext	s2f	s2f	s2f
	s64	chop1	chop1	chop	–	chop1	chop1	chop	–	s2f	s2f	s2f
	u8	–	zext	zext	zext	–	zext	zext	zext	u2f	u2f	u2f
	u16	chop1	–	zext	zext	chop1	–	zext	zext	u2f	u2f	u2f
	u32	chop1	chop1	–	zext	chop1	chop1	–	zext	u2f	u2f	u2f
	u64	chop1	chop1	chop	–	chop1	chop1	chop	–	u2f	u2f	u2f
	f16	f2s	f2s	f2s	f2s	f2u	f2u	f2u	f2u	–	f2f	f2f
	f32	f2s	f2s	f2s	f2s	f2u	f2u	f2u	f2u	f2f	–	f2f
	f64	f2s	f2s	f2s	f2s	f2u	f2u	f2u	f2u	f2f	f2f	–
Notes		sext = sign-extend; zext = zero-extend; chop = keep only low bits that fit; s2f = signed-to-float; f2s = float-to-signed; u2f = unsigned-to-float; f2u = float-to-unsigned; f2f = float-to-float. 1 If the destination register is wider than the destination format, the result is extended to the destination register width after chopping. The type of extension (sign or zero) is based on the destination format. For example, cvt.s16.u32 targeting a 32-bit register first chops to 16-bit, then sign-extends to 32-bit.

6.5.2. Rounding Modifiers

Conversion instructions may specify a rounding modifier. In PTX, there are four integer rounding modifiers and four floating-point rounding modifiers. Table 14 and Table 15 summarize the rounding modifiers.

Table 14 Floating-Point Rounding Modifiers

Modifier	Description
.rn	mantissa LSB rounds to nearest even
.rna	mantissa LSB rounds to nearest, ties away from zero
.rz	mantissa LSB rounds towards zero
.rm	mantissa LSB rounds towards negative infinity
.rp	mantissa LSB rounds towards positive infinity

Table 15 Integer Rounding Modifiers

Modifier	Description
.rni	round to nearest integer, choosing even integer if source is equidistant between two integers.
.rzi	round to nearest integer in the direction of zero
.rmi	round to nearest integer in direction of negative infinity
.rpi	round to nearest integer in direction of positive infinity

6.6. Operand Costs

Operands from different state spaces affect the speed of an operation. Registers are fastest, while global memory is slowest. Much of the delay to memory can be hidden in a number of ways. The first is to have multiple threads of execution so that the hardware can issue a memory operation and then switch to other execution. Another way to hide latency is to issue the load instructions as early as possible, as execution is not blocked until the desired result is used in a subsequent (in time) instruction. The register in a store operation is available much more quickly. Table 16 gives estimates of the costs of using different kinds of memory.

Table 16 Cost Estimates for Accessing State-Spaces

Space	Time	Notes
Register	0
Shared	0
Constant	0	Amortized cost is low, first access is high
Local	> 100 clocks
Parameter	0
Immediate	0
Global	> 100 clocks
Texture	> 100 clocks
Surface	> 100 clocks

7. Abstracting the ABI

Rather than expose details of a particular calling convention, stack layout, and Application Binary Interface (ABI), PTX provides a slightly higher-level abstraction and supports multiple ABI implementations. In this section, we describe the features of PTX needed to achieve this hiding of the ABI. These include syntax for function definitions, function calls, parameter passing, support for variadic functions (varargs), and memory allocated on the stack (alloca).

Refer to PTX Writers Guide to Interoperability for details on generating PTX compliant with Application Binary Interface (ABI) for the CUDA^® architecture.

7.1. Function Declarations and Definitions

In PTX, functions are declared and defined using the .func directive. A function declaration specifies an optional list of return parameters, the function name, and an optional list of input parameters; together these specify the function’s interface, or prototype. A function definition specifies both the interface and the body of the function. A function must be declared or defined prior to being called.

The simplest function has no parameters or return values, and is represented in PTX as follows:

.func foo
{
    ...
    ret;
}

    ...
    call foo;
    ...

Here, execution of the call instruction transfers control to foo, implicitly saving the return address. Execution of the ret instruction within foo transfers control to the instruction following the call.

Scalar and vector base-type input and return parameters may be represented simply as register variables. At the call, arguments may be register variables or constants, and return values may be placed directly into register variables. The arguments and return variables at the call must have type and size that match the callee’s corresponding formal parameters.

Example

.func (.reg .u32 %res) inc_ptr ( .reg .u32 %ptr, .reg .u32 %inc )
{
    add.u32 %res, %ptr, %inc;
    ret;
}

    ...
    call (%r1), inc_ptr, (%r1,4);
    ...

When using the ABI, .reg state space parameters must be at least 32-bits in size. Subword scalar objects in the source language should be promoted to 32-bit registers in PTX, or use .param state space byte arrays described next.

Objects such as C structures and unions are flattened into registers or byte arrays in PTX and are represented using .param space memory. For example, consider the following C structure, passed by value to a function:

struct {
    double dbl;
    char   c[4];
};

In PTX, this structure will be flattened into a byte array. Since memory accesses are required to be aligned to a multiple of the access size, the structure in this example will be a 12 byte array with 8 byte alignment so that accesses to the .f64 field are aligned. The .param state space is used to pass the structure by value:

Example

.func (.reg .s32 out) bar (.reg .s32 x, .param .align 8 .b8 y[12])
{
    .reg .f64 f1;
    .reg .b32 c1, c2, c3, c4;
    ...
    ld.param.f64 f1, [y+0];
    ld.param.b8  c1, [y+8];
    ld.param.b8  c2, [y+9];
    ld.param.b8  c3, [y+10];
    ld.param.b8  c4, [y+11];
    ...
    ... // computation using x,f1,c1,c2,c3,c4;
}

{
     .param .b8 .align 8 py[12];
     ...
     st.param.b64 [py+ 0], %rd;
     st.param.b8  [py+ 8], %rc1;
     st.param.b8  [py+ 9], %rc2;
     st.param.b8  [py+10], %rc1;
     st.param.b8  [py+11], %rc2;
     // scalar args in .reg space, byte array in .param space
     call (%out), bar, (%x, py);
     ...

In this example, note that .param space variables are used in two ways. First, a .param variable y is used in function definition bar to represent a formal parameter. Second, a .param variable py is declared in the body of the calling function and used to set up the structure being passed to bar.

The following is a conceptual way to think about the .param state space use in device functions.

For a caller,

• The .param state space is used to set values that will be passed to a called function and/or to receive return values from a called function. Typically, a .param byte array is used to collect together fields of a structure being passed by value.

For a callee,

• The .param state space is used to receive parameter values and/or pass return values back to the caller.

The following restrictions apply to parameter passing.

For a caller,

• Arguments may be .param variables, .reg variables, or constants.

• In the case of .param space formal parameters that are byte arrays, the argument must also be a .param space byte array with matching type, size, and alignment. A .param argument must be declared within the local scope of the caller.

• In the case of .param space formal parameters that are base-type scalar or vector variables, the corresponding argument may be either a .param or .reg space variable with matching type and size, or a constant that can be represented in the type of the formal parameter.

• In the case of .reg space formal parameters, the corresponding argument may be either a .param or .reg space variable of matching type and size, or a constant that can be represented in the type of the formal parameter.

• In the case of .reg space formal parameters, the register must be at least 32-bits in size.

• All st.param instructions used for passing arguments to function call must immediately precede the corresponding call instruction and ld.param instruction used for collecting return value must immediately follow the call instruction without any control flow alteration. st.param and ld.param instructions used for argument passing cannot be predicated. This enables compiler optimization and ensures that the .param variable does not consume extra space in the caller’s frame beyond that needed by the ABI. The .param variable simply allows a mapping to be made at the call site between data that may be in multiple locations (e.g., structure being manipulated by caller is located in registers and memory) to something that can be passed as a parameter or return value to the callee.

For a callee,

• Input and return parameters may be .param variables or .reg variables.

• Parameters in .param memory must be aligned to a multiple of 1, 2, 4, 8, or 16 bytes.

• Parameters in the .reg state space must be at least 32-bits in size.

• The .reg state space can be used to receive and return base-type scalar and vector values, including sub-word size objects when compiling in non-ABI mode. Supporting the .reg state space provides legacy support.

Note that the choice of .reg or .param state space for parameter passing has no impact on whether the parameter is ultimately passed in physical registers or on the stack. The mapping of parameters to physical registers and stack locations depends on the ABI definition and the order, size, and alignment of parameters.

7.1.1. Changes from PTX ISA Version 1.x

In PTX ISA version 1.x, formal parameters were restricted to .reg state space, and there was no support for array parameters. Objects such as C structures were flattened and passed or returned using multiple registers. PTX ISA version 1.x supports multiple return values for this purpose.

Beginning with PTX ISA version 2.0, formal parameters may be in either .reg or .param state space, and .param space parameters support arrays. For targets sm_20 or higher, PTX restricts functions to a single return value, and a .param byte array should be used to return objects that do not fit into a register. PTX continues to support multiple return registers for sm_1x targets.

Note

PTX implements a stack-based ABI only for targets sm_20 or higher.

PTX ISA versions prior to 3.0 permitted variables in .reg and .local state spaces to be defined at module scope. When compiling to use the ABI, PTX ISA version 3.0 and later disallows module-scoped .reg and .local variables and restricts their use to within function scope. When compiling without use of the ABI, module-scoped .reg and .local variables are supported as before. When compiling legacy PTX code (ISA versions prior to 3.0) containing module-scoped .reg or .local variables, the compiler silently disables use of the ABI.

7.2. Variadic Functions

Note

Support for variadic functions which was unimplemented has been removed from the spec.

PTX version 6.0 supports passing unsized array parameter to a function which can be used to implement variadic functions.

Refer to Kernel and Function Directives: .func for details

7.3. Alloca

PTX provides alloca instruction for allocating storage at runtime on the per-thread local memory stack. The allocated stack memory can be accessed with ld.local and st.local instructions using the pointer returned by alloca.

In order to facilitate deallocation of memory allocated with alloca, PTX provides two additional instructions: stacksave which allows reading the value of stack pointer in a local variable, and stackrestore which can restore the stack pointer with the saved value.

alloca, stacksave, and stackrestore instructions are described in Stack Manipulation Instructions.

Preview Feature:

Stack manipulation instructions alloca, stacksave and stackrestore are preview features in PTX ISA version 7.3. All details are subject to change with no guarantees of backward compatibility on future PTX ISA versions or SM architectures.

8. Memory Consistency Model

In multi-threaded executions, the side-effects of memory operations performed by each thread become visible to other threads in a partial and non-identical order. This means that any two operations may appear to happen in no order, or in different orders, to different threads. The axioms introduced by the memory consistency model specify exactly which contradictions are forbidden between the orders observed by different threads.

In the absence of any constraint, each read operation returns the value committed by some write operation to the same memory location, including the initial write to that memory location. The memory consistency model effectively constrains the set of such candidate writes from which a read operation can return a value.

8.1. Scope and applicability of the model

The constraints specified under this model apply to PTX programs with any PTX ISA version number, running on sm_70 or later architectures.

The memory consistency model does not apply to texture (including ld.global.nc) and surface accesses.

8.1.1. Limitations on atomicity at system scope

When communicating with the host CPU, certain strong operations with system scope may not be performed atomically on some systems. For more details on atomicity guarantees to host memory, see the CUDA Atomicity Requirements.

8.2. Memory operations

The fundamental storage unit in the PTX memory model is a byte, consisting of 8 bits. Each state space available to a PTX program is a sequence of contiguous bytes in memory. Every byte in a PTX state space has a unique address relative to all threads that have access to the same state space.

Each PTX memory instruction specifies an address operand and a data type. The address operand contains a virtual address that gets converted to a physical address during memory access. The physical address and the size of the data type together define a physical memory location, which is the range of bytes starting from the physical address and extending up to the size of the data type in bytes.

The memory consistency model specification uses the terms “address” or “memory address” to indicate a virtual address, and the term “memory location” to indicate a physical memory location.

Each PTX memory instruction also specifies the operation — either a read, a write or an atomic read-modify-write — to be performed on all the bytes in the corresponding memory location.

8.2.1. Overlap

Two memory locations are said to overlap when the starting address of one location is within the range of bytes constituting the other location. Two memory operations are said to overlap when they specify the same virtual address and the corresponding memory locations overlap. The overlap is said to be complete when both memory locations are identical, and it is said to be partial otherwise.

8.2.2. Aliases

Two distinct virtual addresses are said to be aliases if they map to the same memory location.

8.2.3. Multimem Addresses

A multimem address is a virtual address which points to multiple distinct memory locations across devices.

Only multimem.* operations are valid on multimem addresses. That is, the behavior of accessing a multimem address in any other memory operation is undefined.

8.2.4. Memory Operations on Vector Data Types

The memory consistency model relates operations executed on memory locations with scalar data types, which have a maximum size and alignment of 64 bits. Memory operations with a vector data type are modelled as a set of equivalent memory operations with a scalar data type, executed in an unspecified order on the elements in the vector.

8.2.5. Memory Operations on Packed Data Types

A packed data type consists of two values of the same scalar data type, as described in Packed Data Types. These values are accessed in adjacent memory locations. A memory operation on a packed data type is modelled as a pair of equivalent memory operations on the scalar data type, executed in an unspecified order on each element of the packed data.

8.2.6. Initialization

Each byte in memory is initialized by a hypothetical write W0 executed before starting any thread in the program. If the byte is included in a program variable, and that variable has an initial value, then W0 writes the corresponding initial value for that byte; else W0 is assumed to have written an unknown but constant value to the byte.

8.3. State spaces

The relations defined in the memory consistency model are independent of state spaces. In particular, causality order closes over all memory operations across all the state spaces. But the side-effect of a memory operation in one state space can be observed directly only by operations that also have access to the same state space. This further constrains the synchronizing effect of a memory operation in addition to scope. For example, the synchronizing effect of the PTX instruction ld.relaxed.shared.sys is identical to that of ld.relaxed.shared.cluster, since no thread outside the same cluster can execute an operation that accesses the same memory location.

8.4. Operation types

For simplicity, the rest of the document refers to the following operation types, instead of mentioning specific instructions that give rise to them.

Table 17 Operation Types

Operation Type	Instruction/Operation
atomic operation	atom or red instruction.
read operation	All variants of ld instruction and atom instruction (but not red instruction).
write operation	All variants of st instruction, and atomic operations if they result in a write.
memory operation	A read or write operation.
volatile operation	An instruction with .volatile qualifier.
acquire operation	A memory operation with .acquire or .acq_rel qualifier.
release operation	A memory operation with .release or .acq_rel qualifier.
mmio operation	An ld or st instruction with .mmio qualifier.
memory fence operation	A membar, fence.sc or fence.acq_rel instruction.
proxy fence operation	A fence.proxy or a membar.proxy instruction.
strong operation	A memory fence operation, or a memory operation with a .relaxed, .acquire, .release, .acq_rel, .volatile, or .mmio qualifier.
weak operation	An ld or st instruction with a .weak qualifier.
synchronizing operation	A barrier instruction, fence operation, release operation or acquire operation.

8.4.1. mmio Operation

An mmio operation is a memory operation with .mmio qualifier specified. It is usually performed on a memory location which is mapped to the control registers of peer I/O devices. It can also be used for communication between threads but has poor performance relative to non-mmio operations.

The semantic meaning of mmio operations cannot be defined precisely as it is defined by the underlying I/O device. For formal specification of semantics of mmio operation from Memory Consistency Model perspective, it is equivalent to the semantics of a strong operation. But it follows a few implementation-specific properties, if it meets the CUDA atomicity requirements at the specified scope:

• Writes are always performed and are never combined within the scope specified.

• Reads are always performed, and are not forwarded, prefetched, combined, or allowed to hit any cache within the scope specified.

  • As an exception, in some implementations, the surrounding locations may also be loaded. In such cases the amount of data loaded is implementation specific and varies between 32 and 128 bytes in size.

8.5. Scope

Each strong operation must specify a scope, which is the set of threads that may interact directly with that operation and establish any of the relations described in the memory consistency model. There are four scopes:

Table 18 Scopes

Scope	Description
.cta	The set of all threads executing in the same CTA as the current thread.
.cluster	The set of all threads executing in the same cluster as the current thread.
.gpu	The set of all threads in the current program executing on the same compute device as the current thread. This also includes other kernel grids invoked by the host program on the same compute device.
.sys	The set of all threads in the current program, including all kernel grids invoked by the host program on all compute devices, and all threads constituting the host program itself.

Note that the warp is not a scope; the CTA is the smallest collection of threads that qualifies as a scope in the memory consistency model.

8.6. Proxies

A memory proxy, or a proxy is an abstract label applied to a method of memory access. When two memory operations use distinct methods of memory access, they are said to be different proxies.

Memory operations as defined in Operation types use generic method of memory access, i.e. a generic proxy. Other operations such as textures and surfaces all use distinct methods of memory access, also distinct from the generic method.

A proxy fence is required to synchronize memory operations across different proxies. Although virtual aliases use the generic method of memory access, since using distinct virtual addresses behaves as if using different proxies, they require a proxy fence to establish memory ordering.

8.7. Morally strong operations

Two operations are said to be morally strong relative to each other if they satisfy all of the following conditions:

1. The operations are related in program order (i.e, they are both executed by the same thread), or each operation is strong and specifies a scope that includes the thread executing the other operation.

2. Both operations are performed via the same proxy.

3. If both are memory operations, then they overlap completely.

Most (but not all) of the axioms in the memory consistency model depend on relations between morally strong operations.

8.7.1. Conflict and Data-races

Two overlapping memory operations are said to conflict when at least one of them is a write.

Two conflicting memory operations are said to be in a data-race if they are not related in causality order and they are not morally strong.

8.7.2. Limitations on Mixed-size Data-races

A data-race between operations that overlap completely is called a uniform-size data-race, while a data-race between operations that overlap partially is called a mixed-size data-race.

The axioms in the memory consistency model do not apply if a PTX program contains one or more mixed-size data-races. But these axioms are sufficient to describe the behavior of a PTX program with only uniform-size data-races.

Atomicity of mixed-size RMW operations

In any program with or without mixed-size data-races, the following property holds for every pair of overlapping atomic operations A1 and A2 such that each specifies a scope that includes the other: Either the read-modify-write operation specified by A1 is performed completely before A2 is initiated, or vice versa. This property holds irrespective of whether the two operations A1 and A2 overlap partially or completely.

8.8. Release and Acquire Patterns

Some sequences of instructions give rise to patterns that participate in memory synchronization as described later. The release pattern makes prior operations from the current thread¹ visible to some operations from other threads. The acquire pattern makes some operations from other threads visible to later operations from the current thread.

A release pattern on a location M consists of one of the following:

1. A release operation on M

   E.g.: st.release [M]; or atom.acq_rel [M]; or mbarrier.arrive.release [M];

2. Or a release operation on M followed by a strong write on M in program order

   E.g.: st.release [M]; st.relaxed [M];

3. Or a memory fence followed by a strong write on M in program order

   E.g.: fence; st.relaxed [M];

Any memory synchronization established by a release pattern only affects operations occurring in program order before the first instruction in that pattern.

An acquire pattern on a location M consists of one of the following:

1. An acquire operation on M

   E.g.: ld.acquire [M]; or atom.acq_rel [M]; or mbarrier.test_wait.acquire [M];

2. Or a strong read on M followed by an acquire operation on M in program order

   E.g.: ld.relaxed [M]; ld.acquire [M];

3. Or a strong read on M followed by a memory fence in program order

   E.g.: ld.relaxed [M]; fence;

Any memory synchronization established by an acquire pattern only affects operations occurring in program order after the last instruction in that pattern.

¹ For both release and acquire patterns, this effect is further extended to operations in other threads through the transitive nature of causality order.

8.9. Ordering of memory operations

The sequence of operations performed by each thread is captured as program order while memory synchronization across threads is captured as causality order. The visibility of the side-effects of memory operations to other memory operations is captured as communication order. The memory consistency model defines contradictions that are disallowed between communication order on the one hand, and causality order and program order on the other.

8.9.1. Program Order

The program order relates all operations performed by a thread to the order in which a sequential processor will execute instructions in the corresponding PTX source. It is a transitive relation that forms a total order over the operations performed by the thread, but does not relate operations from different threads.

8.9.1.1. Asynchronous Operations

Some PTX instructions (all variants of cp.async, cp.async.bulk, cp.reduce.async.bulk, wgmma.mma_async) perform operations that are asynchronous to the thread that executed the instruction. These asynchronous operations are ordered after prior instructions in the same thread (except in the case of wgmma.mma_async), but they are not part of the program order for that thread. Instead, they provide weaker ordering guarantees as documented in the instruction description.

For example, the loads and stores performed as part of a cp.async are ordered with respect to each other, but not to those of any other cp.async instructions initiated by the same thread, nor any other instruction subsequently issued by the thread with the exception of cp.async.commit_group or cp.async.mbarrier.arrive. The asynchronous mbarrier arrive-on operation performed by a cp.async.mbarrier.arrive instruction is ordered with respect to the memory operations performed by all prior cp.async operations initiated by the same thread, but not to those of any other instruction issued by the thread. The implicit mbarrier complete-tx operation that is part of all variants of cp.async.bulk and cp.reduce.async.bulk instructions is ordered only with respect to the memory operations performed by the same asynchronous instruction, and in particular it does not transitively establish ordering with respect to prior instructions from the issuing thread.

8.9.2. Observation Order

Observation order relates a write W to a read R through an optional sequence of atomic read-modify-write operations.

A write W precedes a read R in observation order if:

1. R and W are morally strong and R reads the value written by W, or

2. For some atomic operation Z, W precedes Z and Z precedes R in observation order.

8.9.3. Fence-SC Order

The Fence-SC order is an acyclic partial order, determined at runtime, that relates every pair of morally strong fence.sc operations.

8.9.4. Memory synchronization

Synchronizing operations performed by different threads synchronize with each other at runtime as described here. The effect of such synchronization is to establish causality order across threads.

1. A fence.sc operation X synchronizes with a fence.sc operation Y if X precedes Y in the Fence-SC order.

2. A bar{.cta}.sync or bar{.cta}.red or bar{.cta}.arrive operation synchronizes with a bar{.cta}.sync or bar{.cta}.red operation executed on the same barrier.

3. A barrier.cluster.arrive operation synchronizes with a barrier.cluster.wait operation.

4. A release pattern X synchronizes with an acquire pattern Y, if a write operation in X precedes a read operation in Y in observation order, and the first operation in X and the last operation in Y are morally strong.

API synchronization

A synchronizes relation can also be established by certain CUDA APIs.

1. Completion of a task enqueued in a CUDA stream synchronizes with the start of the following task in the same stream, if any.

2. For purposes of the above, recording or waiting on a CUDA event in a stream, or causing a cross-stream barrier to be inserted due to cudaStreamLegacy, enqueues tasks in the associated streams even if there are no direct side effects. An event record task synchronizes with matching event wait tasks, and a barrier arrival task synchronizes with matching barrier wait tasks.

3. Start of a CUDA kernel synchronizes with start of all threads in the kernel. End of all threads in a kernel synchronize with end of the kernel.

4. Start of a CUDA graph synchronizes with start of all source nodes in the graph. Completion of all sink nodes in a CUDA graph synchronizes with completion of the graph. Completion of a graph node synchronizes with start of all nodes with a direct dependency.

5. Start of a CUDA API call to enqueue a task synchronizes with start of the task.

6. Completion of the last task queued to a stream, if any, synchronizes with return from cudaStreamSynchronize. Completion of the most recently queued matching event record task, if any, synchronizes with return from cudaEventSynchronize. Synchronizing a CUDA device or context behaves as if synchronizing all streams in the context, including ones that have been destroyed.

7. Returning cudaSuccess from an API to query a CUDA handle, such as a stream or event, behaves the same as return from the matching synchronization API.

In addition to establishing a synchronizes relation, the CUDA API synchronization mechanisms above also participate in proxy-preserved base causality order.

8.9.5. Causality Order

Causality order captures how memory operations become visible across threads through synchronizing operations. The axiom “Causality” uses this order to constrain the set of write operations from which a read operation may read a value.

Relations in the causality order primarily consist of relations in Base causality order¹ , which is a transitive order, determined at runtime.

Base causality order

An operation X precedes an operation Y in base causality order if:

1. X precedes Y in program order, or

2. X synchronizes with Y, or

3. For some operation Z,

   1. X precedes Z in program order and Z precedes Y in base causality order, or

   2. X precedes Z in base causality order and Z precedes Y in program order, or

   3. X precedes Z in base causality order and Z precedes Y in base causality order.

Proxy-preserved base causality order

A memory operation X precedes a memory operation Y in proxy-preserved base causality order if X precedes Y in base causality order, and:

1. X and Y are performed to the same address, using the generic proxy, or

2. X and Y are performed to the same address, using the same proxy, and by the same thread block, or

3. X and Y are aliases and there is an alias proxy fence along the base causality path from X to Y.

Causality order

Causality order combines base causality order with some non-transitive relations as follows:

An operation X precedes an operation Y in causality order if:

1. X precedes Y in proxy-preserved base causality order, or

2. For some operation Z, X precedes Z in observation order, and Z precedes Y in proxy-preserved base causality order.

¹ The transitivity of base causality order accounts for the “cumulativity” of synchronizing operations.

8.9.6. Coherence Order

There exists a partial transitive order that relates overlapping write operations, determined at runtime, called the coherence order¹. Two overlapping write operations are related in coherence order if they are morally strong or if they are related in causality order. Two overlapping writes are unrelated in coherence order if they are in a data-race, which gives rise to the partial nature of coherence order.

¹ Coherence order cannot be observed directly since it consists entirely of write operations. It may be observed indirectly by its use in constraining the set of candidate writes that a read operation may read from.

8.9.7. Communication Order

The communication order is a non-transitive order, determined at runtime, that relates write operations to other overlapping memory operations.

1. A write W precedes an overlapping read R in communication order if R returns the value of any byte that was written by W.

2. A write W precedes a write W’ in communication order if W precedes W’ in coherence order.

3. A read R precedes an overlapping write W in communication order if, for any byte accessed by both R and W, R returns the value written by a write W’ that precedes W in coherence order.

Communication order captures the visibility of memory operations — when a memory operation X1 precedes a memory operation X2 in communication order, X1 is said to be visible to X2.

8.10. Axioms

8.10.1. Coherence

If a write W precedes an overlapping write W’ in causality order, then W must precede W’ in coherence order.

8.10.2. Fence-SC

Fence-SC order cannot contradict causality order. For a pair of morally strong fence.sc operations F1 and F2, if F1 precedes F2 in causality order, then F1 must precede F2 in Fence-SC order.

8.10.3. Atomicity

Single-Copy Atomicity

Conflicting morally strong operations are performed with single-copy atomicity. When a read R and a write W are morally strong, then the following two communications cannot both exist in the same execution, for the set of bytes accessed by both R and W:

1. R reads any byte from W.

2. R reads any byte from any write W’ which precedes W in coherence order.

Atomicity of read-modify-write (RMW) operations

When an atomic operation A and a write W overlap and are morally strong, then the following two communications cannot both exist in the same execution, for the set of bytes accessed by both A and W:

1. A reads any byte from a write W’ that precedes W in coherence order.

2. A follows W in coherence order.

Litmus Test 1:

.global .u32 x = 0;
T1	T2
A1: atom.sys.inc.u32 %r0, [x];	A2: atom.sys.inc.u32 %r0, [x];
FINAL STATE: x == 2

Atomicity is guaranteed when the operations are morally strong.

Litmus Test 2:

.global .u32 x = 0;
T1	T2 (In a different CTA)
A1: atom.cta.inc.u32 %r0, [x];	A2: atom.gpu.inc.u32 %r0, [x];
FINAL STATE: x == 1 OR x == 2

Atomicity is not guaranteed if the operations are not morally strong.

8.10.4. No Thin Air

Values may not appear “out of thin air”: an execution cannot speculatively produce a value in such a way that the speculation becomes self-satisfying through chains of instruction dependencies and inter-thread communication. This matches both programmer intuition and hardware reality, but is necessary to state explicitly when performing formal analysis.

Litmus Test: Load Buffering

.global .u32 x = 0; .global .u32 y = 0;
T1	T2
A1: ld.global.u32 %r0, [x]; B1: st.global.u32 [y], %r0;	A2: ld.global.u32 %r1, [y]; B2: st.global.u32 [x], %r1;
FINAL STATE: x == 0 AND y == 0

The litmus test known as “LB” (Load Buffering) checks such forbidden values that may arise out of thin air. Two threads T1 and T2 each read from a first variable and copy the observed result into a second variable, with the first and second variable exchanged between the threads. If each variable is initially zero, the final result shall also be zero. If A1 reads from B2 and A2 reads from B1, then values passing through the memory operations in this example form a cycle: A1->B1->A2->B2->A1. Only the values x == 0 and y == 0 are allowed to satisfy this cycle. If any of the memory operations in this example were to speculatively associate a different value with the corresponding memory location, then such a speculation would become self-fulfilling, and hence forbidden.

8.10.5. Sequential Consistency Per Location

Within any set of overlapping memory operations that are pairwise morally strong, communication order cannot contradict program order, i.e., a concatenation of program order between overlapping operations and morally strong relations in communication order cannot result in a cycle. This ensures that each program slice of overlapping pairwise morally strong operations is strictly sequentially-consistent.

Litmus Test: CoRR

.global .u32 x = 0;
T1	T2
W1: st.global.relaxed.sys.u32 [x], 1;	R1: ld.global.relaxed.sys.u32 %r0, [x]; R2: ld.global.relaxed.sys.u32 %r1, [x];
IF %r0 == 1 THEN %r1 == 1

The litmus test “CoRR” (Coherent Read-Read), demonstrates one consequence of this guarantee. A thread T1 executes a write W1 on a location x, and a thread T2 executes two (or an infinite sequence of) reads R1 and R2 on the same location x. No other writes are executed on x, except the one modelling the initial value. The operations W1, R1 and R2 are pairwise morally strong. If R1 reads from W1, then the subsequent read R2 must also observe the same value. If R2 observed the initial value of x instead, then this would form a sequence of morally-strong relations R2->W1->R1 in communication order that contradicts the program order R1->R2 in thread T2. Hence R2 cannot read the initial value of x in such an execution.

8.10.6. Causality

Relations in communication order cannot contradict causality order. This constrains the set of candidate write operations that a read operation may read from:

1. If a read R precedes an overlapping write W in causality order, then R cannot read from W.

2. If a write W precedes an overlapping read R in causality order, then for any byte accessed by both R and W, R cannot read from any write W’ that precedes W in coherence order.

Litmus Test: Message Passing

.global .u32 data = 0; .global .u32 flag = 0;
T1	T2
W1: st.global.u32 [data], 1; F1: fence.sys; W2: st.global.relaxed.sys.u32 [flag], 1;	R1: ld.global.relaxed.sys.u32 %r0, [flag]; F2: fence.sys; R2: ld.global.u32 %r1, [data];
IF %r0 == 1 THEN %r1 == 1

The litmus test known as “MP” (Message Passing) represents the essence of typical synchronization algorithms. A vast majority of useful programs can be reduced to sequenced applications of this pattern.

Thread T1 first writes to a data variable and then to a flag variable while a second thread T2 first reads from the flag variable and then from the data variable. The operations on the flag are morally strong and the memory operations in each thread are separated by a fence, and these fences are morally strong.

If R1 observes W2, then the release pattern “F1; W2” synchronizes with the acquire pattern “R1; F2”. This establishes the causality order W1 -> F1 -> W2 -> R1 -> F2 -> R2. Then axiom causality guarantees that R2 cannot read from any write that precedes W1 in coherence order. In the absence of any other writes in this example, R2 must read from W1.

Litmus Test: CoWR

// These addresses are aliases .global .u32 data_alias_1; .global .u32 data_alias_2;

T1

W1: st.global.u32 [data_alias_1], 1; F1: fence.proxy.alias; R1: ld.global.u32 %r1, [data_alias_2];

%r1 == 1

Virtual aliases require an alias proxy fence along the synchronization path.

Litmus Test: Store Buffering

The litmus test known as “SB” (Store Buffering) demonstrates the sequential consistency enforced by the fence.sc. A thread T1 writes to a first variable, and then reads the value of a second variable, while a second thread T2 writes to the second variable and then reads the value of the first variable. The memory operations in each thread are separated by fence.sc instructions, and these fences are morally strong.

.global .u32 x = 0; .global .u32 y = 0;
T1	T2
W1: st.global.u32 [x], 1; F1: fence.sc.sys; R1: ld.global.u32 %r0, [y];	W2: st.global.u32 [y], 1; F2: fence.sc.sys; R2: ld.global.u32 %r1, [x];
%r0 == 1 OR %r1 == 1

In any execution, either F1 precedes F2 in Fence-SC order, or vice versa. If F1 precedes F2 in Fence-SC order, then F1 synchronizes with F2. This establishes the causality order in W1 -> F1 -> F2 -> R2. Axiom causality ensures that R2 cannot read from any write that precedes W1 in coherence order. In the absence of any other write to that variable, R2 must read from W1. Similarly, in the case where F2 precedes F1 in Fence-SC order, R1 must read from W2. If each fence.sc in this example were replaced by a fence.acq_rel instruction, then this outcome is not guaranteed. There may be an execution where the write from each thread remains unobserved from the other thread, i.e., an execution is possible, where both R1 and R2 return the initial value “0” for variables y and x respectively.

9. Instruction Set

9.1. Format and Semantics of Instruction Descriptions

This section describes each PTX instruction. In addition to the name and the format of the instruction, the semantics are described, followed by some examples that attempt to show several possible instantiations of the instruction.

9.2. PTX Instructions

PTX instructions generally have from zero to four operands, plus an optional guard predicate appearing after an @ symbol to the left of the opcode:

• @p   opcode;

• @p   opcode a;

• @p   opcode d, a;

• @p   opcode d, a, b;

• @p   opcode d, a, b, c;

For instructions that create a result value, the d operand is the destination operand, while a, b, and c are source operands.

The setp instruction writes two destination registers. We use a | symbol to separate multiple destination registers.

setp.lt.s32  p|q, a, b;  // p = (a < b); q = !(a < b);

For some instructions the destination operand is optional. A bit bucket operand denoted with an underscore (_) may be used in place of a destination register.

9.3. Predicated Execution

In PTX, predicate registers are virtual and have .pred as the type specifier. So, predicate registers can be declared as

.reg .pred p, q, r;

All instructions have an optional guard predicate which controls conditional execution of the instruction. The syntax to specify conditional execution is to prefix an instruction with @{!}p, where p is a predicate variable, optionally negated. Instructions without a guard predicate are executed unconditionally.

Predicates are most commonly set as the result of a comparison performed by the setp instruction.

As an example, consider the high-level code

if (i < n)
    j = j + 1;

This can be written in PTX as

      setp.lt.s32  p, i, n;    // p = (i < n)
@p    add.s32      j, j, 1;    // if i < n, add 1 to j

To get a conditional branch or conditional function call, use a predicate to control the execution of the branch or call instructions. To implement the above example as a true conditional branch, the following PTX instruction sequence might be used:

      setp.lt.s32  p, i, n;    // compare i to n
@!p   bra  L1;                 // if False, branch over
      add.s32      j, j, 1;
L1:     ...

9.3.1. Comparisons

9.3.1.1. Integer and Bit-Size Comparisons

The signed integer comparisons are the traditional eq (equal), ne (not-equal), lt (less-than), le (less-than-or-equal), gt (greater-than), and ge (greater-than-or-equal). The unsigned comparisons are eq, ne, lo (lower), ls (lower-or-same), hi (higher), and hs (higher-or-same). The bit-size comparisons are eq and ne; ordering comparisons are not defined for bit-size types.

Table 19 shows the operators for signed integer, unsigned integer, and bit-size types.

Table 19 Operators for Signed Integer, Unsigned Integer, and Bit-Size Types

Meaning	Signed Operator	Unsigned Operator	Bit-Size Operator
a == b	eq	eq	eq
a != b	ne	ne	ne
a < b	lt	lo	n/a
a <= b	le	ls	n/a
a > b	gt	hi	n/a
a >= b	ge	hs	n/a

9.3.1.2. Floating Point Comparisons

The ordered floating-point comparisons are eq, ne, lt, le, gt, and ge. If either operand is NaN, the result is False. Table 20 lists the floating-point comparison operators.

Table 20 Floating-Point Comparison Operators

Meaning	Floating-Point Operator
a == b && !isNaN(a) && !isNaN(b)	eq
a != b && !isNaN(a) && !isNaN(b)	ne
a < b && !isNaN(a) && !isNaN(b)	lt
a <= b && !isNaN(a) && !isNaN(b)	le
a > b && !isNaN(a) && !isNaN(b)	gt
a >= b && !isNaN(a) && !isNaN(b)	ge

To aid comparison operations in the presence of NaN values, unordered floating-point comparisons are provided: equ, neu, ltu, leu, gtu, and geu. If both operands are numeric values (not NaN), then the comparison has the same result as its ordered counterpart. If either operand is NaN, then the result of the comparison is True.

Table 21 lists the floating-point comparison operators accepting NaN values.

Table 21 Floating-Point Comparison Operators Accepting NaN

Meaning	Floating-Point Operator
a == b || isNaN(a) || isNaN(b)	equ
a != b || isNaN(a) || isNaN(b)	neu
a < b || isNaN(a) || isNaN(b)	ltu
a <= b || isNaN(a) || isNaN(b)	leu
a > b || isNaN(a) || isNaN(b)	gtu
a >= b || isNaN(a) || isNaN(b)	geu

To test for NaN values, two operators num (numeric) and nan (isNaN) are provided. num returns True if both operands are numeric values (not NaN), and nan returns True if either operand is NaN. Table 22 lists the floating-point comparison operators testing for NaN values.

Table 22 Floating-Point Comparison Operators Testing for NaN

Meaning	Floating-Point Operator
!isNaN(a) && !isNaN(b)	num
isNaN(a) || isNaN(b)	nan

9.3.2. Manipulating Predicates

Predicate values may be computed and manipulated using the following instructions: and, or, xor, not, and mov.

There is no direct conversion between predicates and integer values, and no direct way to load or store predicate register values. However, setp can be used to generate a predicate from an integer, and the predicate-based select (selp) instruction can be used to generate an integer value based on the value of a predicate; for example:

selp.u32 %r1,1,0,%p;    // convert predicate to 32-bit value

9.4. Type Information for Instructions and Operands

Typed instructions must have a type-size modifier. For example, the add instruction requires type and size information to properly perform the addition operation (signed, unsigned, float, different sizes), and this information must be specified as a suffix to the opcode.

Example

.reg .u16 d, a, b;

add.u16 d, a, b;    // perform a 16-bit unsigned add

Some instructions require multiple type-size modifiers, most notably the data conversion instruction cvt. It requires separate type-size modifiers for the result and source, and these are placed in the same order as the operands. For example:

.reg .u16 a;
.reg .f32 d;

cvt.f32.u16 d, a;   // convert 16-bit unsigned to 32-bit float

In general, an operand’s type must agree with the corresponding instruction-type modifier. The rules for operand and instruction type conformance are as follows:

• Bit-size types agree with any type of the same size.

• Signed and unsigned integer types agree provided they have the same size, and integer operands are silently cast to the instruction type if needed. For example, an unsigned integer operand used in a signed integer instruction will be treated as a signed integer by the instruction.

• Floating-point types agree only if they have the same size; i.e., they must match exactly.

Table 23 summarizes these type checking rules.

Table 23 Type Checking Rules

		Operand Type
		.bX	.sX	.uX	.fX
Instruction Type	.bX	okay	okay	okay	okay
	.sX	okay	okay	okay	invalid
	.uX	okay	okay	okay	invalid
	.fX	okay	invalid	invalid	okay

Note

Some operands have their type and size defined independently from the instruction type-size. For example, the shift amount operand for left and right shift instructions always has type .u32, while the remaining operands have their type and size determined by the instruction type.

Example

// 64-bit arithmetic right shift; shift amount 'b' is .u32
    shr.s64 d,a,b;

9.4.1. Operand Size Exceeding Instruction-Type Size

For convenience, ld, st, and cvt instructions permit source and destination data operands to be wider than the instruction-type size, so that narrow values may be loaded, stored, and converted using regular-width registers. For example, 8-bit or 16-bit values may be held directly in 32-bit or 64-bit registers when being loaded, stored, or converted to other types and sizes. The operand type checking rules are relaxed for bit-size and integer (signed and unsigned) instruction types; floating-point instruction types still require that the operand type-size matches exactly, unless the operand is of bit-size type.

When a source operand has a size that exceeds the instruction-type size, the source data is truncated (chopped) to the appropriate number of bits specified by the instruction type-size.

Table 24 summarizes the relaxed type-checking rules for source operands. Note that some combinations may still be invalid for a particular instruction; for example, the cvt instruction does not support .bX instruction types, so those rows are invalid for cvt.

Table 24 Relaxed Type-checking Rules for Source Operands

		Source Operand Type
		b8	b16	b32	b64	b128	s8	s16	s32	s64	u8	u16	u32	u64	f16	f32	f64
Instruction Type	b8	–	chop	chop	chop	chop	–	chop	chop	chop	–	chop	chop	chop	chop	chop	chop
	b16	inv	–	chop	chop	chop	inv	–	chop	chop	inv	–	chop	chop	–	chop	chop
	b32	inv	inv	–	chop	chop	inv	inv	–	chop	inv	inv	–	chop	inv	–	chop
	b64	inv	inv	inv	–	chop	inv	inv	inv	–	inv	inv	inv	–	inv	inv	–
	b128	inv	inv	inv	inv	–	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv
	s8	–	chop	chop	chop	chop	–	chop	chop	chop	–	chop	chop	chop	inv	inv	inv
	s16	inv	–	chop	chop	chop	inv	–	chop	chop	inv	–	chop	chop	inv	inv	inv
	s32	inv	inv	–	chop	chop	inv	inv	–	chop	inv	inv	–	chop	inv	inv	inv
	s64	inv	inv	inv	–	chop	inv	inv	inv	–	inv	inv	inv	–	inv	inv	inv
	u8	–	chop	chop	chop	chop	–	chop	chop	chop	–	chop	chop	chop	inv	inv	inv
	u16	inv	–	chop	chop	chop	inv	–	chop	chop	inv	–	chop	chop	inv	inv	inv
	u32	inv	inv	–	chop	chop	inv	inv	–	chop	inv	inv	–	chop	inv	inv	inv
	u64	inv	inv	inv	–	chop	inv	inv	inv	–	inv	inv	inv	–	inv	inv	inv
	f16	inv	–	chop	chop	chop	inv	inv	inv	inv	inv	inv	inv	inv	–	inv	inv
	f32	inv	inv	–	chop	chop	inv	inv	inv	inv	inv	inv	inv	inv	inv	–	inv
	f64	inv	inv	inv	–	chop	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv	–
Notes		chop = keep only low bits that fit; “–” = allowed, but no conversion needed; inv = invalid, parse error. Source register size must be of equal or greater size than the instruction-type size. Bit-size source registers may be used with any appropriately-sized instruction type. The data are truncated (“chopped”) to the instruction-type size and interpreted according to the instruction type. Integer source registers may be used with any appropriately-sized bit-size or integer instruction type. The data are truncated to the instruction-type size and interpreted according to the instruction type. Floating-point source registers can only be used with bit-size or floating-point instruction types. When used with a narrower bit-size instruction type, the data are truncated. When used with a floating-point instruction type, the size must match exactly.

When a destination operand has a size that exceeds the instruction-type size, the destination data is zero- or sign-extended to the size of the destination register. If the corresponding instruction type is signed integer, the data is sign-extended; otherwise, the data is zero-extended.

Table 25 summarizes the relaxed type-checking rules for destination operands.

Table 25 Relaxed Type-checking Rules for Destination Operands

		Destination Operand Type
		b8	b16	b32	b64	b128	s8	s16	s32	s64	u8	u16	u32	u64	f16	f32	f64
Instruction Type	b8	–	zext	zext	zext	zext	–	zext	zext	zext	–	zext	zext	zext	zext	zext	zext
	b16	inv	–	zext	zext	zext	inv	–	zext	zext	inv	–	zext	zext	–	zext	zext
	b32	inv	inv	–	zext	zext	inv	inv	–	zext	inv	inv	–	zext	inv	–	zext
	b64	inv	inv	inv	–	zext	inv	inv	inv	–	inv	inv	inv	–	inv	inv	–
	b128	inv	inv	inv	inv	–	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv
	s8	–	sext	sext	sext	sext	–	sext	sext	sext	–	sext	sext	sext	inv	inv	inv
	s16	inv	–	sext	sext	sext	inv	–	sext	sext	inv	–	sext	sext	inv	inv	inv
	s32	inv	inv	–	sext	sext	inv	inv	–	sext	inv	inv	–	sext	inv	inv	inv
	s64	inv	inv	inv	–	sext	inv	inv	inv	–	inv	inv	inv	–	inv	inv	inv
	u8	–	zext	zext	zext	zext	–	zext	zext	zext	–	zext	zext	zext	inv	inv	inv
	u16	inv	–	zext	zext	zext	inv	–	zext	zext	inv	–	zext	zext	inv	inv	inv
	u32	inv	inv	–	zext	zext	inv	inv	–	zext	inv	inv	–	zext	inv	inv	inv
	u64	inv	inv	inv	–	zext	inv	inv	inv	–	inv	inv	inv	–	inv	inv	inv
	f16	inv	–	zext	zext	zext	inv	inv	inv	inv	inv	inv	inv	inv	–	inv	inv
	f32	inv	inv	–	zext	zext	inv	inv	inv	inv	inv	inv	inv	inv	inv	–	inv
	f64	inv	inv	inv	–	zext	inv	inv	inv	inv	inv	inv	inv	inv	inv	inv	–
Notes		sext = sign-extend; zext = zero-extend; “–” = allowed, but no conversion needed; inv = invalid, parse error. Destination register size must be of equal or greater size than the instruction-type size. Bit-size destination registers may be used with any appropriately-sized instruction type. The data are sign-extended to the destination register width for signed integer instruction types, and are zero-extended to the destination register width otherwise. Integer destination registers may be used with any appropriately-sized bit-size or integer instruction type. The data are sign-extended to the destination register width for signed integer instruction types, and are zero-extended to the destination register width for bit-size an d unsigned integer instruction types. Floating-point destination registers can only be used with bit-size or floating-point instruction types. When used with a narrower bit-size instruction type, the data are zero-extended. When used with a floating-point instruction type, the size must match exactly.

9.5. Divergence of Threads in Control Constructs

Threads in a CTA execute together, at least in appearance, until they come to a conditional control construct such as a conditional branch, conditional function call, or conditional return. If threads execute down different control flow paths, the threads are called divergent. If all of the threads act in unison and follow a single control flow path, the threads are called uniform. Both situations occur often in programs.

A CTA with divergent threads may have lower performance than a CTA with uniformly executing threads, so it is important to have divergent threads re-converge as soon as possible. All control constructs are assumed to be divergent points unless the control-flow instruction is marked as uniform, using the .uni suffix. For divergent control flow, the optimizing code generator automatically determines points of re-convergence. Therefore, a compiler or code author targeting PTX can ignore the issue of divergent threads, but has the opportunity to improve performance by marking branch points as uniform when the compiler or author can guarantee that the branch point is non-divergent.

9.6. Semantics

The goal of the semantic description of an instruction is to describe the results in all cases in as simple language as possible. The semantics are described using C, until C is not expressive enough.

9.6.1. Machine-Specific Semantics of 16-bit Code

A PTX program may execute on a GPU with either a 16-bit or a 32-bit data path. When executing on a 32-bit data path, 16-bit registers in PTX are mapped to 32-bit physical registers, and 16-bit computations are promoted to 32-bit computations. This can lead to computational differences between code run on a 16-bit machine versus the same code run on a 32-bit machine, since the promoted computation may have bits in the high-order half-word of registers that are not present in 16-bit physical registers. These extra precision bits can become visible at the application level, for example, by a right-shift instruction.

At the PTX language level, one solution would be to define semantics for 16-bit code that is consistent with execution on a 16-bit data path. This approach introduces a performance penalty for 16-bit code executing on a 32-bit data path, since the translated code would require many additional masking instructions to suppress extra precision bits in the high-order half-word of 32-bit registers.

Rather than introduce a performance penalty for 16-bit code running on 32-bit GPUs, the semantics of 16-bit instructions in PTX is machine-specific. A compiler or programmer may chose to enforce portable, machine-independent 16-bit semantics by adding explicit conversions to 16-bit values at appropriate points in the program to guarantee portability of the code. However, for many performance-critical applications, this is not desirable, and for many applications the difference in execution is preferable to limiting performance.

9.7. Instructions

All PTX instructions may be predicated. In the following descriptions, the optional guard predicate is omitted from the syntax.

9.7.1. Integer Arithmetic Instructions

Integer arithmetic instructions operate on the integer types in register and constant immediate forms. The integer arithmetic instructions are:

• add

• sub

• mul

• mad

• mul24

• mad24

• sad

• div

• rem

• abs

• neg

• min

• max

• popc

• clz

• bfind

• fns

• brev

• bfe

• bfi

• bmsk

• szext

• dp4a

• dp2a

9.7.1.1. Integer Arithmetic Instructions: add

add

Add two values.

Syntax

add.type       d, a, b;
add{.sat}.s32  d, a, b;     // .sat applies only to .s32

.type = { .u16, .u32, .u64,
          .s16, .s32, .s64,
          .u16x2, .s16x2 };

Description

Performs addition and writes the resulting value into a destination register.

For .u16x2, .s16x2 instruction types, forms input vectors by half word values from source operands. Half-word operands are then added in parallel to produce .u16x2, .s16x2 result in destination.

Operands d, a and b have type .type. For instruction types .u16x2, .s16x2, operands d, a and b have type .b32.

Semantics

if (type == u16x2 || type == s16x2) {
    iA[0] = a[0:15];
    iA[1] = a[16:31];
    iB[0] = b[0:15];
    iB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = iA[i] + iB[i];
    }
} else {
    d = a + b;
}

Notes

Saturation modifier:

.sat

limits result to MININT..MAXINT (no overflow) for the size of the operation. Applies only to .s32 type.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

add.u16x2 and add.s16x2 introduced in PTX ISA version 8.0.

Target ISA Notes

Supported on all target architectures.

add.u16x2 and add.s16x2 require sm_90 or higher.

Examples

@p  add.u32     x,y,z;
    add.sat.s32 c,c,1;
    add.u16x2   u,v,w;

9.7.1.2. Integer Arithmetic Instructions: sub

sub

Subtract one value from another.

Syntax

sub.type       d, a, b;
sub{.sat}.s32  d, a, b;     // .sat applies only to .s32

.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Performs subtraction and writes the resulting value into a destination register.

Semantics

d = a - b;

Notes

Saturation modifier:

.sat

limits result to MININT..MAXINT (no overflow) for the size of the operation. Applies only to .s32 type.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

sub.s32 c,a,b;

9.7.1.3. Integer Arithmetic Instructions: mul

mul

Multiply two values.

Syntax

mul.mode.type  d, a, b;

.mode = { .hi, .lo, .wide };
.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Compute the product of two values.

Semantics

t = a * b;
n = bitwidth of type;
d = t;            // for .wide
d = t<2n-1..n>;   // for .hi variant
d = t<n-1..0>;    // for .lo variant

Notes

The type of the operation represents the types of the a and b operands. If .hi or .lo is specified, then d is the same size as a and b, and either the upper or lower half of the result is written to the destination register. If .wide is specified, then d is twice as wide as a and b to receive the full result of the multiplication.

The .wide suffix is supported only for 16- and 32-bit integer types.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

mul.wide.s16 fa,fxs,fys;   // 16*16 bits yields 32 bits
mul.lo.s16 fa,fxs,fys;     // 16*16 bits, save only the low 16 bits
mul.wide.s32 z,x,y;        // 32*32 bits, creates 64 bit result

9.7.1.4. Integer Arithmetic Instructions: mad

mad

Multiply two values, optionally extract the high or low half of the intermediate result, and add a third value.

Syntax

mad.mode.type  d, a, b, c;
mad.hi.sat.s32 d, a, b, c;

.mode = { .hi, .lo, .wide };
.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Multiplies two values, optionally extracts the high or low half of the intermediate result, and adds a third value. Writes the result into a destination register.

Semantics

t = a * b;
n = bitwidth of type;
d = t + c;           // for .wide
d = t<2n-1..n> + c;  // for .hi variant
d = t<n-1..0> + c;   // for .lo variant

Notes

The type of the operation represents the types of the a and b operands. If .hi or .lo is specified, then d and c are the same size as a and b, and either the upper or lower half of the result is written to the destination register. If .wide is specified, then d and c are twice as wide as a and b to receive the result of the multiplication.

The .wide suffix is supported only for 16-bit and 32-bit integer types.

Saturation modifier:

.sat

limits result to MININT..MAXINT (no overflow) for the size of the operation.

Applies only to .s32 type in .hi mode.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

@p  mad.lo.s32 d,a,b,c;
    mad.lo.s32 r,p,q,r;

9.7.1.5. Integer Arithmetic Instructions: mul24

mul24

Multiply two 24-bit integer values.

Syntax

mul24.mode.type  d, a, b;

.mode = { .hi, .lo };
.type = { .u32, .s32 };

Description

Compute the product of two 24-bit integer values held in 32-bit source registers, and return either the high or low 32-bits of the 48-bit result.

Semantics

t = a * b;
d = t<47..16>;    // for .hi variant
d = t<31..0>;     // for .lo variant

Notes

Integer multiplication yields a result that is twice the size of the input operands, i.e., 48-bits.

mul24.hi performs a 24x24-bit multiply and returns the high 32 bits of the 48-bit result.

mul24.lo performs a 24x24-bit multiply and returns the low 32 bits of the 48-bit result.

All operands are of the same type and size.

mul24.hi may be less efficient on machines without hardware support for 24-bit multiply.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

mul24.lo.s32 d,a,b;   // low 32-bits of 24x24-bit signed multiply.

9.7.1.6. Integer Arithmetic Instructions: mad24

mad24

Multiply two 24-bit integer values and add a third value.

Syntax

mad24.mode.type  d, a, b, c;
mad24.hi.sat.s32 d, a, b, c;

.mode = { .hi, .lo };
.type = { .u32, .s32 };

Description

Compute the product of two 24-bit integer values held in 32-bit source registers, and add a third, 32-bit value to either the high or low 32-bits of the 48-bit result. Return either the high or low 32-bits of the 48-bit result.

Semantics

t = a * b;
d = t<47..16> + c;   // for .hi variant
d = t<31..0> + c;    // for .lo variant

Notes

Integer multiplication yields a result that is twice the size of the input operands, i.e., 48-bits.

mad24.hi performs a 24x24-bit multiply and adds the high 32 bits of the 48-bit result to a third value.

mad24.lo performs a 24x24-bit multiply and adds the low 32 bits of the 48-bit result to a third value.

All operands are of the same type and size.

Saturation modifier:

.sat

limits result of 32-bit signed addition to MININT..MAXINT (no overflow). Applies only to .s32 type in .hi mode.

mad24.hi may be less efficient on machines without hardware support for 24-bit multiply.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

mad24.lo.s32 d,a,b,c;   // low 32-bits of 24x24-bit signed multiply.

9.7.1.7. Integer Arithmetic Instructions: sad

sad

Sum of absolute differences.

Syntax

sad.type  d, a, b, c;

.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Adds the absolute value of a-b to c and writes the resulting value into d.

Semantics

d = c + ((a<b) ? b-a : a-b);

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

sad.s32  d,a,b,c;
sad.u32  d,a,b,d;  // running sum

9.7.1.8. Integer Arithmetic Instructions: div

div

Divide one value by another.

Syntax

div.type  d, a, b;

.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Divides a by b, stores result in d.

Semantics

d = a / b;

Notes

Division by zero yields an unspecified, machine-specific value.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

div.s32  b,n,i;

9.7.1.9. Integer Arithmetic Instructions: rem

rem

The remainder of integer division.

Syntax

rem.type  d, a, b;

.type = { .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Divides a by b, store the remainder in d.

Semantics

d = a % b;

Notes

The behavior for negative numbers is machine-dependent and depends on whether divide rounds towards zero or negative infinity.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

rem.s32  x,x,8;    // x = x%8;

9.7.1.10. Integer Arithmetic Instructions: abs

abs

Absolute value.

Syntax

abs.type  d, a;

.type = { .s16, .s32, .s64 };

Description

Take the absolute value of a and store it in d.

Semantics

d = |a|;

Notes

Only for signed integers.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

abs.s32  r0,a;

9.7.1.11. Integer Arithmetic Instructions: neg

neg

Arithmetic negate.

Syntax

neg.type  d, a;

.type = { .s16, .s32, .s64 };

Description

Negate the sign of a and store the result in d.

Semantics

d = -a;

Notes

Only for signed integers.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

neg.s32  r0,a;

9.7.1.12. Integer Arithmetic Instructions: min

min

Find the minimum of two values.

Syntax

min.atype         d, a, b;
min{.relu}.btype  d, a, b;

.atype = { .u16, .u32, .u64,
           .u16x2, .s16, .s64 };
.btype = { .s16x2, .s32 };

Description

Store the minimum of a and b in d.

For .u16x2, .s16x2 instruction types, forms input vectors by half word values from source operands. Half-word operands are then processed in parallel to produce .u16x2, .s16x2 result in destination.

Operands d, a and b have the same type as the instruction type. For instruction types .u16x2, .s16x2, operands d, a and b have type .b32.

Semantics

if (type == u16x2 || type == s16x2) {
    iA[0] = a[0:15];
    iA[1] = a[16:31];
    iB[0] = b[0:15];
    iB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = (iA[i] < iB[i]) ? iA[i] : iB[i];
    }
} else {
    d = (a < b) ? a : b; // Integer (signed and unsigned)
}

Notes

Signed and unsigned differ.

Saturation modifier:

min.relu.{s16x2, s32} clamps the result to 0 if negative.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

min.u16x2, min{.relu}.s16x2 and min.relu.s32 introduced in PTX ISA version 8.0.

Target ISA Notes

Supported on all target architectures.

min.u16x2, min{.relu}.s16x2 and min.relu.s32 require sm_90 or higher.

Examples

    min.s32  r0,a,b;
@p  min.u16  h,i,j;
    min.s16x2.relu u,v,w;

9.7.1.13. Integer Arithmetic Instructions: max

max

Find the maximum of two values.

Syntax

max.atype         d, a, b;
max{.relu}.btype  d, a, b;

.atype = { .u16, .u32, .u64,
           .u16x2, .s16, .s64 };
.btype = { .s16x2, .s32 };

Description

Store the maximum of a and b in d.

For .u16x2, .s16x2 instruction types, forms input vectors by half word values from source operands. Half-word operands are then processed in parallel to produce .u16x2, .s16x2 result in destination.

Operands d, a and b have the same type as the instruction type. For instruction types .u16x2, .s16x2, operands d, a and b have type .b32.

Semantics

if (type == u16x2 || type == s16x2) {
    iA[0] = a[0:15];
    iA[1] = a[16:31];
    iB[0] = b[0:15];
    iB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = (iA[i] > iB[i]) ? iA[i] : iB[i];
    }
} else {
    d = (a > b) ? a : b; // Integer (signed and unsigned)
}

Notes

Signed and unsigned differ.

Saturation modifier:

max.relu.{s16x2, s32} clamps the result to 0 if negative.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

max.u16x2, max{.relu}.s16x2 and max.relu.s32 introduced in PTX ISA version 8.0.

Target ISA Notes

Supported on all target architectures.

max.u16x2, max{.relu}.s16x2 and max.relu.s32 require sm_90 or higher.

Examples

max.u32  d,a,b;
max.s32  q,q,0;
max.relu.s16x2 t,t,u;

9.7.1.14. Integer Arithmetic Instructions: popc

popc

Population count.

Syntax

popc.type  d, a;

.type = { .b32, .b64 };

Description

Count the number of one bits in a and place the resulting population count in 32-bit destination register d. Operand a has the instruction type and destination d has type .u32.

Semantics

.u32  d = 0;
while (a != 0) {
   if (a & 0x1)  d++;
   a = a >> 1;
}

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

popc requires sm_20 or higher.

Examples

popc.b32  d, a;
popc.b64  cnt, X;  // cnt is .u32

9.7.1.15. Integer Arithmetic Instructions: clz

clz

Count leading zeros.

Syntax

clz.type  d, a;

.type = { .b32, .b64 };

Description

Count the number of leading zeros in a starting with the most-significant bit and place the result in 32-bit destination register d. Operand a has the instruction type, and destination d has type .u32. For .b32 type, the number of leading zeros is between 0 and 32, inclusively. For.b64 type, the number of leading zeros is between 0 and 64, inclusively.

Semantics

.u32  d = 0;
if (.type == .b32)   { max = 32; mask = 0x80000000; }
else                 { max = 64; mask = 0x8000000000000000; }

while (d < max && (a&mask == 0) ) {
    d++;
    a = a << 1;
}

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

clz requires sm_20 or higher.

Examples

clz.b32  d, a;
clz.b64  cnt, X;  // cnt is .u32

9.7.1.16. Integer Arithmetic Instructions: bfind

bfind

Find most significant non-sign bit.

Syntax

bfind.type           d, a;
bfind.shiftamt.type  d, a;

.type = { .u32, .u64,
          .s32, .s64 };

Description

Find the bit position of the most significant non-sign bit in a and place the result in d. Operand a has the instruction type, and destination d has type .u32. For unsigned integers, bfind returns the bit position of the most significant 1. For signed integers, bfind returns the bit position of the most significant 0 for negative inputs and the most significant 1 for non-negative inputs.

If .shiftamt is specified, bfind returns the shift amount needed to left-shift the found bit into the most-significant bit position.

bfind returns 0xffffffff if no non-sign bit is found.

Semantics

msb = (.type==.u32 || .type==.s32) ? 31 : 63;
// negate negative signed inputs
if ( (.type==.s32 || .type==.s64) && (a & (1<<msb)) ) {
    a = ~a;
}
.u32  d = 0xffffffff;
for (.s32 i=msb; i>=0; i--) {
    if (a & (1<<i))  { d = i; break; }
}
if (.shiftamt && d != 0xffffffff)  { d = msb - d; }

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

bfind requires sm_20 or higher.

Examples

bfind.u32  d, a;
bfind.shiftamt.s64  cnt, X;  // cnt is .u32

9.7.1.17. Integer Arithmetic Instructions: fns

fns

Find the n-th set bit

Syntax

fns.b32 d, mask, base, offset;

Description

Given a 32-bit value mask and an integer value base (between 0 and 31), find the n-th (given by offset) set bit in mask from the base bit, and store the bit position in d. If not found, store 0xffffffff in d.

Operand mask has a 32-bit type. Operand base has .b32, .u32 or .s32 type. Operand offset has .s32 type. Destination d has type .b32.

Operand base must be <= 31, otherwise behavior is undefined.

Semantics

d = 0xffffffff;
if (offset == 0) {
    if (mask[base] == 1) {
        d = base;
    }
} else {
    pos = base;
    count = |offset| - 1;
    inc = (offset > 0) ? 1 : -1;

    while ((pos >= 0) && (pos < 32)) {
        if (mask[pos] == 1) {
            if (count == 0) {
              d = pos;
              break;
           } else {
               count = count – 1;
           }
        }
        pos = pos + inc;
    }
}

PTX ISA Notes

Introduced in PTX ISA version 6.0.

Target ISA Notes

fns requires sm_30 or higher.

Examples

fns.b32 d, 0xaaaaaaaa, 3, 1;   // d = 3
fns.b32 d, 0xaaaaaaaa, 3, -1;  // d = 3
fns.b32 d, 0xaaaaaaaa, 2, 1;   // d = 3
fns.b32 d, 0xaaaaaaaa, 2, -1;  // d = 1

9.7.1.18. Integer Arithmetic Instructions: brev

brev

Bit reverse.

Syntax

brev.type  d, a;

.type = { .b32, .b64 };

Description

Perform bitwise reversal of input.

Semantics

msb = (.type==.b32) ? 31 : 63;

for (i=0; i<=msb; i++) {
    d[i] = a[msb-i];
}

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

brev requires sm_20 or higher.

Examples

brev.b32  d, a;

9.7.1.19. Integer Arithmetic Instructions: bfe

bfe

Bit Field Extract.

Syntax

bfe.type  d, a, b, c;

.type = { .u32, .u64,
          .s32, .s64 };

Description

Extract bit field from a and place the zero or sign-extended result in d. Source b gives the bit field starting bit position, and source c gives the bit field length in bits.

Operands a and d have the same type as the instruction type. Operands b and c are type .u32, but are restricted to the 8-bit value range 0..255.

The sign bit of the extracted field is defined as:

.u32, .u64:

zero

.s32, .s64:

msb of input a if the extracted field extends beyond the msb of a msb of extracted field, otherwise

If the bit field length is zero, the result is zero.

The destination d is padded with the sign bit of the extracted field. If the start position is beyond the msb of the input, the destination d is filled with the replicated sign bit of the extracted field.

Semantics

msb = (.type==.u32 || .type==.s32) ? 31 : 63;
pos = b & 0xff;  // pos restricted to 0..255 range
len = c & 0xff;  // len restricted to 0..255 range

if (.type==.u32 || .type==.u64 || len==0)
    sbit = 0;
else
    sbit = a[min(pos+len-1,msb)];

d = 0;
for (i=0; i<=msb; i++) {
    d[i] = (i<len && pos+i<=msb) ? a[pos+i] : sbit;
}

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

bfe requires sm_20 or higher.

Examples

bfe.b32  d,a,start,len;

9.7.1.20. Integer Arithmetic Instructions: bfi

bfi

Bit Field Insert.

Syntax

bfi.type  f, a, b, c, d;

.type = { .b32, .b64 };

Description

Align and insert a bit field from a into b, and place the result in f. Source c gives the starting bit position for the insertion, and source d gives the bit field length in bits.

Operands a, b, and f have the same type as the instruction type. Operands c and d are type .u32, but are restricted to the 8-bit value range 0..255.

If the bit field length is zero, the result is b.

If the start position is beyond the msb of the input, the result is b.

Semantics

msb = (.type==.b32) ? 31 : 63;
pos = c & 0xff;  // pos restricted to 0..255 range
len = d & 0xff;  // len restricted to 0..255 range

f = b;
for (i=0; i<len && pos+i<=msb; i++) {
    f[pos+i] = a[i];
}

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

bfi requires sm_20 or higher.

Examples

bfi.b32  d,a,b,start,len;

9.7.1.21. Integer Arithmetic Instructions: szext

szext

Sign-extend or Zero-extend.

Syntax

szext.mode.type  d, a, b;

.mode = { .clamp, .wrap };
.type = { .u32, .s32 };

Description

Sign-extends or zero-extends an N-bit value from operand a where N is specified in operand b. The resulting value is stored in the destination operand d.

For the .s32 instruction type, the value in a is treated as an N-bit signed value and the most significant bit of this N-bit value is replicated up to bit 31. For the .u32 instruction type, the value in a is treated as an N-bit unsigned number and is zero-extended to 32 bits. Operand b is an unsigned 32-bit value.

If the value of N is 0, then the result of szext is 0. If the value of N is 32 or higher, then the result of szext depends upon the value of the .mode qualifier as follows:

• If .mode is .clamp, then the result is the same as the source operand a.

• If .mode is .wrap, then the result is computed using the wrapped value of N.

Semantics

b1        = b & 0x1f;
too_large = (b >= 32 && .mode == .clamp) ? true : false;
mask      = too_large ? 0 : (~0) << b1;
sign_pos  = (b1 - 1) & 0x1f;

if (b1 == 0 || too_large || .type != .s32) {
    sign_bit = false;
} else {
    sign_bit = (a >> sign_pos) & 1;
}
d = (a & ~mask) | (sign_bit ? mask | 0);

PTX ISA Notes

Introduced in PTX ISA version 7.6.

Target ISA Notes

szext requires sm_70 or higher.

Examples

szext.clamp.s32 rd, ra, rb;
szext.wrap.u32  rd, 0xffffffff, 0; // Result is 0.

9.7.1.22. Integer Arithmetic Instructions: bmsk

bmsk

Bit Field Mask.

Syntax

bmsk.mode.b32  d, a, b;

.mode = { .clamp, .wrap };

Description

Generates a 32-bit mask starting from the bit position specified in operand a, and of the width specified in operand b. The generated bitmask is stored in the destination operand d.

The resulting bitmask is 0 in the following cases:

• When the value of a is 32 or higher and .mode is .clamp.

• When either the specified value of b or the wrapped value of b (when .mode is specified as .wrap) is 0.

Semantics

a1    = a & 0x1f;
mask0 = (~0) << a1;
b1    = b & 0x1f;
sum   = a1 + b1;
mask1 = (~0) << sum;

sum-overflow          = sum >= 32 ? true : false;
bit-position-overflow = false;
bit-width-overflow    = false;

if (.mode == .clamp) {
    if (a >= 32) {
        bit-position-overflow = true;
        mask0 = 0;
    }
    if (b >= 32) {
        bit-width-overflow = true;
    }
}

if (sum-overflow || bit-position-overflow || bit-width-overflow) {
    mask1 = 0;
} else if (b1 == 0) {
    mask1 = ~0;
}
d = mask0 & ~mask1;

Notes

The bitmask width specified by operand b is limited to range 0..32 in .clamp mode and to range 0..31 in .wrap mode.

PTX ISA Notes

Introduced in PTX ISA version 7.6.

Target ISA Notes

bmsk requires sm_70 or higher.

Examples

bmsk.clamp.b32  rd, ra, rb;
bmsk.wrap.b32   rd, 1, 2; // Creates a bitmask of 0x00000006.

9.7.1.23. Integer Arithmetic Instructions: dp4a

dp4a

Four-way byte dot product-accumulate.

Syntax

dp4a.atype.btype  d, a, b, c;

.atype = .btype = { .u32, .s32 };

Description

Four-way byte dot product which is accumulated in 32-bit result.

Operand a and b are 32-bit inputs which hold 4 byte inputs in packed form for dot product.

Operand c has type .u32 if both .atype and .btype are .u32 else operand c has type .s32.

Semantics

d = c;

// Extract 4 bytes from a 32bit input and sign or zero extend
// based on input type.
Va = extractAndSignOrZeroExt_4(a, .atype);
Vb = extractAndSignOrZeroExt_4(b, .btype);

for (i = 0; i < 4; ++i) {
    d += Va[i] * Vb[i];
}

PTX ISA Notes

Introduced in PTX ISA version 5.0.

Target ISA Notes

Requires sm_61 or higher.

Examples

dp4a.u32.u32           d0, a0, b0, c0;
dp4a.u32.s32           d1, a1, b1, c1;

9.7.1.24. Integer Arithmetic Instructions: dp2a

dp2a

Two-way dot product-accumulate.

Syntax

dp2a.mode.atype.btype  d, a, b, c;

.atype = .btype = { .u32, .s32 };
.mode = { .lo, .hi };

Description

Two-way 16-bit to 8-bit dot product which is accumulated in 32-bit result.

Operand a and b are 32-bit inputs. Operand a holds two 16-bits inputs in packed form and operand b holds 4 byte inputs in packed form for dot product.

Depending on the .mode specified, either lower half or upper half of operand b will be used for dot product.

Operand c has type .u32 if both .atype and .btype are .u32 else operand c has type .s32.

Semantics

d = c;
// Extract two 16-bit values from a 32-bit input and sign or zero extend
// based on input type.
Va = extractAndSignOrZeroExt_2(a, .atype);

// Extract four 8-bit values from a 32-bit input and sign or zer extend
// based on input type.
Vb = extractAndSignOrZeroExt_4(b, .btype);

b_select = (.mode == .lo) ? 0 : 2;

for (i = 0; i < 2; ++i) {
    d += Va[i] * Vb[b_select + i];
}

PTX ISA Notes

Introduced in PTX ISA version 5.0.

Target ISA Notes

Requires sm_61 or higher.

Examples

dp2a.lo.u32.u32           d0, a0, b0, c0;
dp2a.hi.u32.s32           d1, a1, b1, c1;

9.7.2. Extended-Precision Integer Arithmetic Instructions

Instructions add.cc, addc, sub.cc, subc, mad.cc and madc reference an implicitly specified condition code register (CC) having a single carry flag bit (CC.CF) holding carry-in/carry-out or borrow-in/borrow-out. These instructions support extended-precision integer addition, subtraction, and multiplication. No other instructions access the condition code, and there is no support for setting, clearing, or testing the condition code. The condition code register is not preserved across calls and is mainly intended for use in straight-line code sequences for computing extended-precision integer addition, subtraction, and multiplication.

The extended-precision arithmetic instructions are:

• add.cc, addc

• sub.cc, subc

• mad.cc, madc

9.7.2.1. Extended-Precision Arithmetic Instructions: add.cc

add.cc

Add two values with carry-out.

Syntax

add.cc.type  d, a, b;

.type = { .u32, .s32, .u64, .s64 };

Description

Performs integer addition and writes the carry-out value into the condition code register.

Semantics

d = a + b;

carry-out written to CC.CF

Notes

No integer rounding modifiers.

No saturation.

Behavior is the same for unsigned and signed integers.

PTX ISA Notes

32-bit add.cc introduced in PTX ISA version 1.2.

64-bit add.cc introduced in PTX ISA version 4.3.

Target ISA Notes

32-bit add.cc is supported on all target architectures.

64-bit add.cc requires sm_20 or higher.

Examples

@p  add.cc.u32   x1,y1,z1;   // extended-precision addition of
@p  addc.cc.u32  x2,y2,z2;   // two 128-bit values
@p  addc.cc.u32  x3,y3,z3;
@p  addc.u32     x4,y4,z4;

9.7.2.2. Extended-Precision Arithmetic Instructions: addc

addc

Add two values with carry-in and optional carry-out.

Syntax

addc{.cc}.type  d, a, b;

.type = { .u32, .s32, .u64, .s64 };

Description

Performs integer addition with carry-in and optionally writes the carry-out value into the condition code register.

Semantics

d = a + b + CC.CF;

if .cc specified, carry-out written to CC.CF

Notes

No integer rounding modifiers.

No saturation.

Behavior is the same for unsigned and signed integers.

PTX ISA Notes

32-bit addc introduced in PTX ISA version 1.2.

64-bit addc introduced in PTX ISA version 4.3.

Target ISA Notes

32-bit addc is supported on all target architectures.

64-bit addc requires sm_20 or higher.

Examples

@p  add.cc.u32   x1,y1,z1;   // extended-precision addition of
@p  addc.cc.u32  x2,y2,z2;   // two 128-bit values
@p  addc.cc.u32  x3,y3,z3;
@p  addc.u32     x4,y4,z4;

9.7.2.3. Extended-Precision Arithmetic Instructions: sub.cc

sub.cc

Subtract one value from another, with borrow-out.

Syntax

sub.cc.type  d, a, b;

.type = { .u32, .s32, .u64, .s64 };

Description

Performs integer subtraction and writes the borrow-out value into the condition code register.

Semantics

d = a - b;

borrow-out written to CC.CF

Notes

No integer rounding modifiers.

No saturation.

Behavior is the same for unsigned and signed integers.

PTX ISA Notes

32-bit sub.cc introduced in PTX ISA version 1.2.

64-bit sub.cc introduced in PTX ISA version 4.3.

Target ISA Notes

32-bit sub.cc is supported on all target architectures.

64-bit sub.cc requires sm_20 or higher.

Examples

@p  sub.cc.u32   x1,y1,z1;   // extended-precision subtraction
@p  subc.cc.u32  x2,y2,z2;   // of two 128-bit values
@p  subc.cc.u32  x3,y3,z3;
@p  subc.u32     x4,y4,z4;

9.7.2.4. Extended-Precision Arithmetic Instructions: subc

subc

Subtract one value from another, with borrow-in and optional borrow-out.

Syntax

subc{.cc}.type  d, a, b;

.type = { .u32, .s32, .u64, .s64 };

Description

Performs integer subtraction with borrow-in and optionally writes the borrow-out value into the condition code register.

Semantics

d = a  - (b + CC.CF);

if .cc specified, borrow-out written to CC.CF

Notes

No integer rounding modifiers.

No saturation.

Behavior is the same for unsigned and signed integers.

PTX ISA Notes

32-bit subc introduced in PTX ISA version 1.2.

64-bit subc introduced in PTX ISA version 4.3.

Target ISA Notes

32-bit subc is supported on all target architectures.

64-bit subc requires sm_20 or higher.

Examples

@p  sub.cc.u32   x1,y1,z1;   // extended-precision subtraction
@p  subc.cc.u32  x2,y2,z2;   // of two 128-bit values
@p  subc.cc.u32  x3,y3,z3;
@p  subc.u32     x4,y4,z4;

9.7.2.5. Extended-Precision Arithmetic Instructions: mad.cc

mad.cc

Multiply two values, extract high or low half of result, and add a third value with carry-out.

Syntax

mad{.hi,.lo}.cc.type  d, a, b, c;

.type = { .u32, .s32, .u64, .s64 };

Description

Multiplies two values, extracts either the high or low part of the result, and adds a third value. Writes the result to the destination register and the carry-out from the addition into the condition code register.

Semantics

t = a * b;
d = t<63..32> + c;    // for .hi variant
d = t<31..0> + c;     // for .lo variant

carry-out from addition is written to CC.CF

Notes

Generally used in combination with madc and addc to implement extended-precision multi-word multiplication. See madc for an example.

PTX ISA Notes

32-bit mad.cc introduced in PTX ISA version 3.0.

64-bit mad.cc introduced in PTX ISA version 4.3.

Target ISA Notes

Requires target sm_20 or higher.

Examples

@p  mad.lo.cc.u32 d,a,b,c;
    mad.lo.cc.u32 r,p,q,r;

9.7.2.6. Extended-Precision Arithmetic Instructions: madc

madc

Multiply two values, extract high or low half of result, and add a third value with carry-in and optional carry-out.

Syntax

madc{.hi,.lo}{.cc}.type  d, a, b, c;

.type = { .u32, .s32, .u64, .s64 };

Description

Multiplies two values, extracts either the high or low part of the result, and adds a third value along with carry-in. Writes the result to the destination register and optionally writes the carry-out from the addition into the condition code register.

Semantics

t = a * b;
d = t<63..32> + c + CC.CF;     // for .hi variant
d = t<31..0> + c + CC.CF;      // for .lo variant

if .cc specified, carry-out from addition is written to CC.CF

Notes

Generally used in combination with mad.cc and addc to implement extended-precision multi-word multiplication. See example below.

PTX ISA Notes

32-bit madc introduced in PTX ISA version 3.0.

64-bit madc introduced in PTX ISA version 4.3.

Target ISA Notes

Requires target sm_20 or higher.

Examples

// extended-precision multiply:  [r3,r2,r1,r0] = [r5,r4] * [r7,r6]
mul.lo.u32     r0,r4,r6;      // r0=(r4*r6).[31:0], no carry-out
mul.hi.u32     r1,r4,r6;      // r1=(r4*r6).[63:32], no carry-out
mad.lo.cc.u32  r1,r5,r6,r1;   // r1+=(r5*r6).[31:0], may carry-out
madc.hi.u32    r2,r5,r6,0;    // r2 =(r5*r6).[63:32]+carry-in,
                              // no carry-out
mad.lo.cc.u32   r1,r4,r7,r1;  // r1+=(r4*r7).[31:0], may carry-out
madc.hi.cc.u32  r2,r4,r7,r2;  // r2+=(r4*r7).[63:32]+carry-in,
                              // may carry-out
addc.u32        r3,0,0;       // r3 = carry-in, no carry-out
mad.lo.cc.u32   r2,r5,r7,r2;  // r2+=(r5*r7).[31:0], may carry-out
madc.hi.u32     r3,r5,r7,r3;  // r3+=(r5*r7).[63:32]+carry-in

9.7.3. Floating-Point Instructions

Floating-point instructions operate on .f32 and .f64 register operands and constant immediate values. The floating-point instructions are:

• testp

• copysign

• add

• sub

• mul

• fma

• mad

• div

• abs

• neg

• min

• max

• rcp

• sqrt

• rsqrt

• sin

• cos

• lg2

• ex2

• tanh

Instructions that support rounding modifiers are IEEE-754 compliant. Double-precision instructions support subnormal inputs and results. Single-precision instructions support subnormal inputs and results by default for sm_20 and subsequent targets, and flush subnormal inputs and results to sign-preserving zero for sm_1x targets. The optional .ftz modifier on single-precision instructions provides backward compatibility with sm_1x targets by flushing subnormal inputs and results to sign-preserving zero regardless of the target architecture.

Single-precision add, sub, mul, and mad support saturation of results to the range [0.0, 1.0], with NaNs being flushed to positive zero. NaN payloads are supported for double-precision instructions (except for rcp.approx.ftz.f64 and rsqrt.approx.ftz.f64, which maps input NaNs to a canonical NaN). Single-precision instructions return an unspecified NaN. Note that future implementations may support NaN payloads for single-precision instructions, so PTX programs should not rely on the specific single-precision NaNs being generated.

Table 26 summarizes floating-point instructions in PTX.

Table 26 Summary of Floating-Point Instructions

Instruction	.rn	.rz	.rm	.rp	.ftz	.sat	Notes
{add,sub,mul}.rnd.f32	x	x	x	x	x	x	If no rounding modifier is specified, default is .rn and instructions may be folded into a multiply-add.
{add,sub,mul}.rnd.f64	x	x	x	x	n/a	n/a	If no rounding modifier is specified, default is .rn and instructions may be folded into a multiply-add.
mad.f32	n/a	n/a	n/a	n/a	x	x	.target sm_1x No rounding modifier.
{mad,fma}.rnd.f32	x	x	x	x	x	x	.target sm_20 or higher mad.f32 and fma.f32 are the same.
{mad,fma}.rnd.f64	x	x	x	x	n/a	n/a	mad.f64 and fma.f64 are the same.
div.full.f32	n/a	n/a	n/a	n/a	x	n/a	No rounding modifier.
{div,rcp,sqrt}.approx.f32	n/a	n/a	n/a	n/a	x	n/a	n/a
rcp.approx.ftz.f64	n/a	n/a	n/a	n/a	x	n/a	.target sm_20 or higher
{div,rcp,sqrt}.rnd.f32	x	x	x	x	x	n/a	.target sm_20 or higher
{div,rcp,sqrt}.rnd.f64	x	x	x	x	n/a	n/a	.target sm_20 or higher
{abs,neg,min,max}.f32	n/a	n/a	n/a	n/a	x	n/a
{abs,neg,min,max}.f64	n/a	n/a	n/a	n/a	n/a	n/a
rsqrt.approx.f32	n/a	n/a	n/a	n/a	x	n/a
rsqrt.approx.f64	n/a	n/a	n/a	n/a	n/a	n/a
rsqrt.approx.ftz.f64	n/a	n/a	n/a	n/a	x	n/a	.target sm_20 or higher
{sin,cos,lg2,ex2}.approx.f32	n/a	n/a	n/a	n/a	x	n/a
tanh.approx.f32	n/a	n/a	n/a	n/a	n/a	n/a	.target sm_75 or higher

9.7.3.1. Floating Point Instructions: testp

testp

Test floating-point property.

Syntax

testp.op.type  p, a;  // result is .pred

.op   = { .finite, .infinite,
          .number, .notanumber,
          .normal, .subnormal };
.type = { .f32, .f64 };

Description

testp tests common properties of floating-point numbers and returns a predicate value of 1 if True and 0 if False.

testp.finite

True if the input is not infinite or NaN

testp.infinite

True if the input is positive or negative infinity

testp.number

True if the input is not NaN

testp.notanumber

True if the input is NaN

testp.normal

True if the input is a normal number (not NaN, not infinity)

testp.subnormal

True if the input is a subnormal number (not NaN, not infinity)

As a special case, positive and negative zero are considered normal numbers.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

Requires sm_20 or higher.

Examples

testp.notanumber.f32  isnan, f0;
testp.infinite.f64    p, X;

9.7.3.2. Floating Point Instructions: copysign

copysign

Copy sign of one input to another.

Syntax

copysign.type  d, a, b;

.type = { .f32, .f64 };

Description

Copy sign bit of a into value of b, and return the result as d.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

Requires sm_20 or higher.

Examples

copysign.f32  x, y, z;
copysign.f64  A, B, C;

9.7.3.3. Floating Point Instructions: add

add

Add two values.

Syntax

add{.rnd}{.ftz}{.sat}.f32  d, a, b;
add{.rnd}.f64              d, a, b;

.rnd = { .rn, .rz, .rm, .rp };

Description

Performs addition and writes the resulting value into a destination register.

Semantics

d = a + b;

Notes

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

The default value of rounding modifier is .rn. Note that an add instruction with an explicit rounding modifier is treated conservatively by the code optimizer. An add instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/add sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

add.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

add.f64 supports subnormal numbers.

add.f32 flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

add.sat.f32 clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

add.f32 supported on all target architectures.

add.f64 requires sm_13 or higher.

Rounding modifiers have the following target requirements:

.rn, .rz

available for all targets

.rm, .rp

for add.f64, requires sm_13 or higher.

for add.f32, requires sm_20 or higher.

Examples

@p  add.rz.ftz.f32  f1,f2,f3;

9.7.3.4. Floating Point Instructions: sub

sub

Subtract one value from another.

Syntax

sub{.rnd}{.ftz}{.sat}.f32  d, a, b;
sub{.rnd}.f64              d, a, b;

.rnd = { .rn, .rz, .rm, .rp };

Description

Performs subtraction and writes the resulting value into a destination register.

Semantics

d = a - b;

Notes

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

The default value of rounding modifier is .rn. Note that a sub instruction with an explicit rounding modifier is treated conservatively by the code optimizer. A sub instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/sub sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

sub.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

sub.f64 supports subnormal numbers.

sub.f32 flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

sub.sat.f32 clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

sub.f32 supported on all target architectures.

sub.f64 requires sm_13 or higher.

Rounding modifiers have the following target requirements:

.rn, .rz

available for all targets

.rm, .rp

for sub.f64, requires sm_13 or higher.

for sub.f32, requires sm_20 or higher.

Examples

sub.f32 c,a,b;
sub.rn.ftz.f32  f1,f2,f3;

9.7.3.5. Floating Point Instructions: mul

mul

Multiply two values.

Syntax

mul{.rnd}{.ftz}{.sat}.f32  d, a, b;
mul{.rnd}.f64              d, a, b;

.rnd = { .rn, .rz, .rm, .rp };

Description

Compute the product of two values.

Semantics

d = a * b;

Notes

For floating-point multiplication, all operands must be the same size.

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

The default value of rounding modifier is .rn. Note that a mul instruction with an explicit rounding modifier is treated conservatively by the code optimizer. A mul instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/add and mul/sub sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

mul.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

mul.f64 supports subnormal numbers.

mul.f32 flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

mul.sat.f32 clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

mul.f32 supported on all target architectures.

mul.f64 requires sm_13 or higher.

Rounding modifiers have the following target requirements:

.rn, .rz

available for all targets

.rm, .rp

for mul.f64, requires sm_13 or higher.

for mul.f32, requires sm_20 or higher.

Examples

mul.ftz.f32 circumf,radius,pi  // a single-precision multiply

9.7.3.6. Floating Point Instructions: fma

fma

Fused multiply-add.

Syntax

fma.rnd{.ftz}{.sat}.f32  d, a, b, c;
fma.rnd.f64              d, a, b, c;

.rnd = { .rn, .rz, .rm, .rp };

Description

Performs a fused multiply-add with no loss of precision in the intermediate product and addition.

Semantics

d = a*b + c;

Notes

fma.f32 computes the product of a and b to infinite precision and then adds c to this product, again in infinite precision. The resulting value is then rounded to single precision using the rounding mode specified by .rnd.

fma.f64 computes the product of a and b to infinite precision and then adds c to this product, again in infinite precision. The resulting value is then rounded to double precision using the rounding mode specified by .rnd.

fma.f64 is the same as mad.f64.

Rounding modifiers (no default):

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

fma.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

fma.f64 supports subnormal numbers.

fma.f32 is unimplemented for sm_1x targets.

Saturation:

fma.sat.f32 clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

fma.f64 introduced in PTX ISA version 1.4.

fma.f32 introduced in PTX ISA version 2.0.

Target ISA Notes

fma.f32 requires sm_20 or higher.

fma.f64 requires sm_13 or higher.

Examples

    fma.rn.ftz.f32  w,x,y,z;
@p  fma.rn.f64      d,a,b,c;

9.7.3.7. Floating Point Instructions: mad

mad

Multiply two values and add a third value.

Syntax

mad{.ftz}{.sat}.f32      d, a, b, c;    // .target sm_1x
mad.rnd{.ftz}{.sat}.f32  d, a, b, c;    // .target sm_20
mad.rnd.f64              d, a, b, c;    // .target sm_13 and higher

.rnd = { .rn, .rz, .rm, .rp };

Description

Multiplies two values and adds a third, and then writes the resulting value into a destination register.

Semantics

d = a*b + c;

Notes

For .target sm_20 and higher:

• mad.f32 computes the product of a and b to infinite precision and then adds c to this product, again in infinite precision. The resulting value is then rounded to single precision using the rounding mode specified by .rnd.

• mad.f64 computes the product of a and b to infinite precision and then adds c to this product, again in infinite precision. The resulting value is then rounded to double precision using the rounding mode specified by .rnd.

• mad.{f32,f64} is the same as fma.{f32,f64}.

For .target sm_1x:

• mad.f32 computes the product of a and b at double precision, and then the mantissa is truncated to 23 bits, but the exponent is preserved. Note that this is different from computing the product with mul, where the mantissa can be rounded and the exponent will be clamped. The exception for mad.f32 is when c = +/-0.0, mad.f32 is identical to the result computed using separate mul and add instructions. When JIT-compiled for SM 2.0 devices, mad.f32 is implemented as a fused multiply-add (i.e., fma.rn.ftz.f32). In this case, mad.f32 can produce slightly different numeric results and backward compatibility is not guaranteed in this case.

• mad.f64 computes the product of a and b to infinite precision and then adds c to this product, again in infinite precision. The resulting value is then rounded to double precision using the rounding mode specified by .rnd. Unlike mad.f32, the treatment of subnormal inputs and output follows IEEE 754 standard.

• mad.f64 is the same as fma.f64.

Rounding modifiers (no default):

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

mad.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

mad.f64 supports subnormal numbers.

mad.f32 flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

mad.sat.f32 clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

In PTX ISA versions 1.4 and later, a rounding modifier is required for mad.f64.

Legacy mad.f64 instructions having no rounding modifier will map to mad.rn.f64.

In PTX ISA versions 2.0 and later, a rounding modifier is required for mad.f32 for sm_20 and higher targets.

Errata

mad.f32 requires a rounding modifier for sm_20 and higher targets. However for PTX ISA version 3.0 and earlier, ptxas does not enforce this requirement and mad.f32 silently defaults to mad.rn.f32. For PTX ISA version 3.1, ptxas generates a warning and defaults to mad.rn.f32, and in subsequent releases ptxas will enforce the requirement for PTX ISA version 3.2 and later.

Target ISA Notes

mad.f32 supported on all target architectures.

mad.f64 requires sm_13 or higher.

Rounding modifiers have the following target requirements:

• .rn,.rz,.rm,.rp for mad.f64, requires sm_13 or higher.

• .rn,.rz,.rm,.rp for mad.f32, requires sm_20 or higher.

Examples

@p  mad.f32  d,a,b,c;

9.7.3.8. Floating Point Instructions: div

div

Divide one value by another.

Syntax

div.approx{.ftz}.f32  d, a, b;  // fast, approximate divide
div.full{.ftz}.f32    d, a, b;  // full-range approximate divide
div.rnd{.ftz}.f32     d, a, b;  // IEEE 754 compliant rounding
div.rnd.f64           d, a, b;  // IEEE 754 compliant rounding

.rnd = { .rn, .rz, .rm, .rp };

Description

Divides a by b, stores result in d.

Semantics

d = a / b;

Notes

Fast, approximate single-precision divides:

• div.approx.f32 implements a fast approximation to divide, computed as d = a * (1/b). For |b| in [2^-126, 2¹²⁶], the maximum ulp error is 2. For 2¹²⁶ < |b| < 2¹²⁸, if a is infinity, div.approx.f32 returns NaN, otherwise it returns 0.

• div.full.f32 implements a relatively fast, full-range approximation that scales operands to achieve better accuracy, but is not fully IEEE 754 compliant and does not support rounding modifiers. The maximum ulp error is 2 across the full range of inputs.

• Subnormal inputs and results are flushed to sign-preserving zero. Fast, approximate division by zero creates a value of infinity (with same sign as a).

Divide with IEEE 754 compliant rounding:

Rounding modifiers (no default):

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

div.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

div.f64 supports subnormal numbers.

div.f32 flushes subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

div.f32 and div.f64 introduced in PTX ISA version 1.0.

Explicit modifiers .approx, .full, .ftz, and rounding introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, one of .approx, .full, or .rnd is required.

For PTX ISA versions 1.0 through 1.3, div.f32 defaults to div.approx.ftz.f32, and div.f64 defaults to div.rn.f64.

Target ISA Notes

div.approx.f32 and div.full.f32 supported on all target architectures.

div.rnd.f32 requires sm_20 or higher.

div.rn.f64 requires sm_13 or higher, or .target map_f64_to_f32.

div.{rz,rm,rp}.f64 requires sm_20 or higher.

Examples

div.approx.ftz.f32  diam,circum,3.14159;
div.full.ftz.f32    x, y, z;
div.rn.f64          xd, yd, zd;

9.7.3.9. Floating Point Instructions: abs

abs

Absolute value.

Syntax

abs{.ftz}.f32  d, a;
abs.f64        d, a;

Description

Take the absolute value of a and store the result in d.

Semantics

d = |a|;

Notes

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

abs.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

abs.f64 supports subnormal numbers.

abs.f32 flushes subnormal inputs and results to sign-preserving zero.

For abs.f32, NaN input yields unspecified NaN. For abs.f64, NaN input is passed through unchanged. Future implementations may comply with the IEEE 754 standard by preserving payload and modifying only the sign bit.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

abs.f32 supported on all target architectures.

abs.f64 requires sm_13 or higher.

Examples

abs.ftz.f32  x,f0;

9.7.3.10. Floating Point Instructions: neg

neg

Arithmetic negate.

Syntax

neg{.ftz}.f32  d, a;
neg.f64        d, a;

Description

Negate the sign of a and store the result in d.

Semantics

d = -a;

Notes

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

neg.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

neg.f64 supports subnormal numbers.

neg.f32 flushes subnormal inputs and results to sign-preserving zero.

NaN inputs yield an unspecified NaN. Future implementations may comply with the IEEE 754 standard by preserving payload and modifying only the sign bit.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

neg.f32 supported on all target architectures.

neg.f64 requires sm_13 or higher.

Examples

neg.ftz.f32  x,f0;

9.7.3.11. Floating Point Instructions: min

min

Find the minimum of two values.

Syntax

min{.ftz}{.NaN}{.xorsign.abs}.f32  d, a, b;
min.f64                            d, a, b;

Description

Store the minimum of a and b in d.

If .NaN modifier is specified, then the result is canonical NaN if either of the inputs is NaN.

If .abs modifier is specified, the magnitude of destination operand d is the minimum of absolute values of both the input arguments.

If .xorsign modifier is specified, the sign bit of destination d is equal to the XOR of the sign bits of both the inputs.

Modifiers .abs and .xorsign must be specified together and .xorsign considers the sign bit of both inputs before applying .abs operation.

If the result of min is NaN then the .xorsign and .abs modifiers will be ignored.

Semantics

if (.xorsign) {
    xorsign = getSignBit(a) ^ getSignBit(b);
    if (.abs) {
        a = |a|;
        b = |b|;
   }
}
if (isNaN(a) && isNaN(b))                 d = NaN;
else if (.NaN && (isNaN(a) || isNaN(b)))  d = NaN;
else if (isNaN(a))                        d = b;
else if (isNaN(b))                        d = a;
else                                      d = (a < b) ? a : b;
if (.xorsign && !isNaN(d)) {
    setSignBit(d, xorsign);
}

Notes

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

min.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

min.f64 supports subnormal numbers.

min.f32 flushes subnormal inputs and results to sign-preserving zero.

If values of both inputs are 0.0, then +0.0 > -0.0.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

min.NaNintroduced in PTX ISA version 7.0.

min.xorsign.abs introduced in PTX ISA version 7.2.

Target ISA Notes

min.f32 supported on all target architectures.

min.f64 requires sm_13 or higher.

min.NaNrequires sm_80 or higher.

min.xorsign.abs requires sm_86 or higher.

Examples

@p  min.ftz.f32  z,z,x;
    min.f64      a,b,c;
    // fp32 min with .NaN
    min.NaN.f32  f0,f1,f2;
    // fp32 min with .xorsign.abs
    min.xorsign.abs.f32 Rd, Ra, Rb;

9.7.3.12. Floating Point Instructions: max

max

Find the maximum of two values.

Syntax

max{.ftz}{.NaN}{.xorsign.abs}.f32  d, a, b;
max.f64                            d, a, b;

Description

Store the maximum of a and b in d.

If .NaN modifier is specified, the result is canonical NaN if either of the inputs is NaN.

If .abs modifier is specified, the magnitude of destination operand d is the maximum of absolute values of both the input arguments.

If .xorsign modifier is specified, the sign bit of destination d is equal to the XOR of the sign bits of both the inputs.

Modifiers .abs and .xorsign must be specified together and .xorsign considers the sign bit of both inputs before applying .abs operation.

If the result of max is NaN then the .xorsign and .abs modifiers will be ignored.

Semantics

if (.xorsign) {
    xorsign = getSignBit(a) ^ getSignBit(b);
    if (.abs) {
        a = |a|;
        b = |b|;
    }
}
if (isNaN(a) && isNaN(b))                 d = NaN;
else if (.NaN && (isNaN(a) || isNaN(b)))  d = NaN;
else if (isNaN(a))                        d = b;
else if (isNaN(b))                        d = a;
else                                      d = (a > b) ? a : b;
if (.xorsign && !isNaN(d)) {
    setSignBit(d, xorsign);
}

Notes

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

max.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

max.f64 supports subnormal numbers.

max.f32 flushes subnormal inputs and results to sign-preserving zero.

If values of both inputs are 0.0, then +0.0 > -0.0.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

max.NaNintroduced in PTX ISA version 7.0.

max.xorsign.abs introduced in PTX ISA version 7.2.

Target ISA Notes

max.f32 supported on all target architectures.

max.f64 requires sm_13 or higher.

max.NaNrequires sm_80 or higher.

max.xorsign.abs requires sm_86 or higher.

Examples

max.ftz.f32  f0,f1,f2;
max.f64      a,b,c;
// fp32 max with .NaN
max.NaN.f32  f0,f1,f2;
// fp32 max with .xorsign.abs
max.xorsign.abs.f32 Rd, Ra, Rb;

9.7.3.13. Floating Point Instructions: rcp

rcp

Take the reciprocal of a value.

Syntax

rcp.approx{.ftz}.f32  d, a;  // fast, approximate reciprocal
rcp.rnd{.ftz}.f32     d, a;  // IEEE 754 compliant rounding
rcp.rnd.f64           d, a;  // IEEE 754 compliant rounding

.rnd = { .rn, .rz, .rm, .rp };

Description

Compute 1/a, store result in d.

Semantics

d = 1 / a;

Notes

Fast, approximate single-precision reciprocal:

rcp.approx.f32 implements a fast approximation to reciprocal. The maximum absolute error is 2^-23.0 over the range 1.0-2.0.

Input	Result
-Inf	-0.0
-subnormal	-Inf
-0.0	-Inf
+0.0	+Inf
+subnormal	+Inf
+Inf	+0.0
NaN	NaN

Reciprocal with IEEE 754 compliant rounding:

Rounding modifiers (no default):

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

rcp.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

rcp.f64 supports subnormal numbers.

rcp.f32 flushes subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

rcp.f32 and rcp.f64 introduced in PTX ISA version 1.0. rcp.rn.f64 and explicit modifiers .approx and .ftz were introduced in PTX ISA version 1.4. General rounding modifiers were added in PTX ISA version 2.0.

For PTX ISA version 1.4 and later, one of .approx or .rnd is required.

For PTX ISA versions 1.0 through 1.3, rcp.f32 defaults to rcp.approx.ftz.f32, and rcp.f64 defaults to rcp.rn.f64.

Target ISA Notes

rcp.approx.f32 supported on all target architectures.

rcp.rnd.f32 requires sm_20 or higher.

rcp.rn.f64 requires sm_13 or higher, or .target map_f64_to_f32.

rcp.{rz,rm,rp}.f64 requires sm_20 or higher.

Examples

rcp.approx.ftz.f32  ri,r;
rcp.rn.ftz.f32      xi,x;
rcp.rn.f64          xi,x;

9.7.3.14. Floating Point Instructions: rcp.approx.ftz.f64

rcp.approx.ftz.f64

Compute a fast, gross approximation to the reciprocal of a value.

Syntax

rcp.approx.ftz.f64  d, a;

Description

Compute a fast, gross approximation to the reciprocal as follows:

1. extract the most-significant 32 bits of .f64 operand a in 1.11.20 IEEE floating-point format (i.e., ignore the least-significant 32 bits of a),

2. compute an approximate .f64 reciprocal of this value using the most-significant 20 bits of the mantissa of operand a,

3. place the resulting 32-bits in 1.11.20 IEEE floating-point format in the most-significant 32-bits of destination d,and

4. zero the least significant 32 mantissa bits of .f64 destination d.

Semantics

tmp = a[63:32]; // upper word of a, 1.11.20 format
d[63:32] = 1.0 / tmp;
d[31:0] = 0x00000000;

Notes

rcp.approx.ftz.f64 implements a fast, gross approximation to reciprocal.

Input a[63:32]	Result d[63:32]
-Inf	-0.0
-subnormal	-Inf
-0.0	-Inf
+0.0	+Inf
+subnormal	+Inf
+Inf	+0.0
NaN	NaN

Input NaNs map to a canonical NaN with encoding 0x7fffffff00000000.

Subnormal inputs and results are flushed to sign-preserving zero.

PTX ISA Notes

rcp.approx.ftz.f64 introduced in PTX ISA version 2.1.

Target ISA Notes

rcp.approx.ftz.f64 requires sm_20 or higher.

Examples

rcp.ftz.f64  xi,x;

9.7.3.15. Floating Point Instructions: sqrt

sqrt

Take the square root of a value.

Syntax

sqrt.approx{.ftz}.f32  d, a; // fast, approximate square root
sqrt.rnd{.ftz}.f32     d, a; // IEEE 754 compliant rounding
sqrt.rnd.f64           d, a; // IEEE 754 compliant rounding

.rnd = { .rn, .rz, .rm, .rp };

Description

Compute sqrt(a) and store the result in d.

Semantics

d = sqrt(a);

Notes

sqrt.approx.f32 implements a fast approximation to square root.

Input	Result
-Inf	NaN
-normal	NaN
-subnormal	-0.0
-0.0	-0.0
+0.0	+0.0
+subnormal	+0.0
+Inf	+Inf
NaN	NaN

Square root with IEEE 754 compliant rounding:

Rounding modifiers (no default):

.rn

mantissa LSB rounds to nearest even

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

sqrt.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

sqrt.f64 supports subnormal numbers.

sqrt.f32 flushes subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

sqrt.f32 and sqrt.f64 introduced in PTX ISA version 1.0. sqrt.rn.f64 and explicit modifiers .approx and .ftz were introduced in PTX ISA version 1.4. General rounding modifiers were added in PTX ISA version 2.0.

For PTX ISA version 1.4 and later, one of .approx or .rnd is required.

For PTX ISA versions 1.0 through 1.3, sqrt.f32 defaults to sqrt.approx.ftz.f32, and sqrt.f64 defaults to sqrt.rn.f64.

Target ISA Notes

sqrt.approx.f32 supported on all target architectures.

sqrt.rnd.f32 requires sm_20 or higher.

sqrt.rn.f64 requires sm_13 or higher, or .target map_f64_to_f32.

sqrt.{rz,rm,rp}.f64 requires sm_20 or higher.

Examples

sqrt.approx.ftz.f32  r,x;
sqrt.rn.ftz.f32      r,x;
sqrt.rn.f64          r,x;

9.7.3.16. Floating Point Instructions: rsqrt

rsqrt

Take the reciprocal of the square root of a value.

Syntax

rsqrt.approx{.ftz}.f32  d, a;
rsqrt.approx.f64        d, a;

Description

Compute 1/sqrt(a) and store the result in d.

Semantics

d = 1/sqrt(a);

Notes

rsqrt.approx implements an approximation to the reciprocal square root.

Input	Result
-Inf	NaN
-normal	NaN
-subnormal	-Inf
-0.0	-Inf
+0.0	+Inf
+subnormal	+Inf
+Inf	+0.0
NaN	NaN

The maximum absolute error for rsqrt.f32 is 2^-22.4 over the range 1.0-4.0.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

rsqrt.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

rsqrt.f64 supports subnormal numbers.

rsqrt.f32 flushes subnormal inputs and results to sign-preserving zero.

Note that rsqrt.approx.f64 is emulated in software and are relatively slow.

PTX ISA Notes

rsqrt.f32 and rsqrt.f64 were introduced in PTX ISA version 1.0. Explicit modifiers .approx and .ftz were introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, the .approx modifier is required.

For PTX ISA versions 1.0 through 1.3, rsqrt.f32 defaults to rsqrt.approx.ftz.f32, and rsqrt.f64 defaults to rsqrt.approx.f64.

Target ISA Notes

rsqrt.f32 supported on all target architectures.

rsqrt.f64 requires sm_13 or higher.

Examples

rsqrt.approx.ftz.f32  isr, x;
rsqrt.approx.f64      ISR, X;

9.7.3.17. Floating Point Instructions: rsqrt.approx.ftz.f64

rsqrt.approx.ftz.f64

Compute an approximation of the square root reciprocal of a value.

Syntax

rsqrt.approx.ftz.f64 d, a;

Description

Compute a double-precision (.f64) approximation of the square root reciprocal of a value. The least significant 32 bits of the double-precision (.f64) destination d are all zeros.

Semantics

tmp = a[63:32]; // upper word of a, 1.11.20 format
d[63:32] = 1.0 / sqrt(tmp);
d[31:0] = 0x00000000;

Notes

rsqrt.approx.ftz.f64 implements a fast approximation of the square root reciprocal of a value.

Input	Result
-Inf	NaN
-subnormal	-Inf
-0.0	-Inf
+0.0	+Inf
+subnormal	+Inf
+Inf	+0.0
NaN	NaN

Input NaNs map to a canonical NaN with encoding 0x7fffffff00000000.

Subnormal inputs and results are flushed to sign-preserving zero.

PTX ISA Notes

rsqrt.approx.ftz.f64 introduced in PTX ISA version 4.0.

Target ISA Notes

rsqrt.approx.ftz.f64 requires sm_20 or higher.

Examples

rsqrt.approx.ftz.f64 xi,x;

9.7.3.18. Floating Point Instructions: sin

sin

Find the sine of a value.

Syntax

sin.approx{.ftz}.f32  d, a;

Description

Find the sine of the angle a (in radians).

Semantics

d = sin(a);

Notes

sin.approx.f32 implements a fast approximation to sine.

Input	Result
-Inf	NaN
-subnormal	-0.0
-0.0	-0.0
+0.0	+0.0
+subnormal	+0.0
+Inf	NaN
NaN	NaN

The maximum absolute error is 2^-20.9 in quadrant 00.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

sin.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

Subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

sin.f32 introduced in PTX ISA version 1.0. Explicit modifiers .approx and .ftz introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, the .approx modifier is required.

For PTX ISA versions 1.0 through 1.3, sin.f32 defaults to sin.approx.ftz.f32.

Target ISA Notes

Supported on all target architectures.

Examples

sin.approx.ftz.f32  sa, a;

9.7.3.19. Floating Point Instructions: cos

cos

Find the cosine of a value.

Syntax

cos.approx{.ftz}.f32  d, a;

Description

Find the cosine of the angle a (in radians).

Semantics

d = cos(a);

Notes

cos.approx.f32 implements a fast approximation to cosine.

Input	Result
-Inf	NaN
-subnormal	+1.0
-0.0	+1.0
+0.0	+1.0
+subnormal	+1.0
+Inf	NaN
NaN	NaN

The maximum absolute error is 2^-20.9 in quadrant 00.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

cos.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

Subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

cos.f32 introduced in PTX ISA version 1.0. Explicit modifiers .approx and .ftz introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, the .approx modifier is required.

For PTX ISA versions 1.0 through 1.3, cos.f32 defaults to cos.approx.ftz.f32.

Target ISA Notes

Supported on all target architectures.

Examples

cos.approx.ftz.f32  ca, a;

9.7.3.20. Floating Point Instructions: lg2

lg2

Find the base-2 logarithm of a value.

Syntax

lg2.approx{.ftz}.f32  d, a;

Description

Determine the log₂ of a.

Semantics

d = log(a) / log(2);

Notes

lg2.approx.f32 implements a fast approximation to log₂(a).

Input	Result
-Inf	NaN
-subnormal	-Inf
-0.0	-Inf
+0.0	-Inf
+subnormal	-Inf
+Inf	+Inf
NaN	NaN

The maximum absolute error is 2^-22.6 for mantissa.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

lg2.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

Subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

lg2.f32 introduced in PTX ISA version 1.0. Explicit modifiers .approx and .ftz introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, the .approx modifier is required.

For PTX ISA versions 1.0 through 1.3, lg2.f32 defaults to lg2.approx.ftz.f32.

Target ISA Notes

Supported on all target architectures.

Examples

lg2.approx.ftz.f32  la, a;

9.7.3.21. Floating Point Instructions: ex2

ex2

Find the base-2 exponential of a value.

Syntax

ex2.approx{.ftz}.f32  d, a;

Description

Raise 2 to the power a.

Semantics

d = 2 ^ a;

Notes

ex2.approx.f32 implements a fast approximation to 2^a.

Input	Result
-Inf	+0.0
-subnormal	+1.0
-0.0	+1.0
+0.0	+1.0
+subnormal	+1.0
+Inf	+Inf
NaN	NaN

The maximum absolute error is 2^-22.5 for fraction in the primary range.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

ex2.ftz.f32 flushes subnormal inputs and results to sign-preserving zero.

sm_1x

Subnormal inputs and results to sign-preserving zero.

PTX ISA Notes

ex2.f32 introduced in PTX ISA version 1.0. Explicit modifiers .approx and .ftz introduced in PTX ISA version 1.4.

For PTX ISA version 1.4 and later, the .approx modifier is required.

For PTX ISA versions 1.0 through 1.3, ex2.f32 defaults to ex2.approx.ftz.f32.

Target ISA Notes

Supported on all target architectures.

Examples

ex2.approx.ftz.f32  xa, a;

9.7.3.22. Floating Point Instructions: tanh

tanh

Find the hyperbolic tangent of a value (in radians)

Syntax

tanh.approx.f32 d, a;

Description

Take hyperbolic tangent value of a.

The operands d and a are of type .f32.

Semantics

d = tanh(a);

Notes

tanh.approx.f32 implements a fast approximation to FP32 hyperbolic-tangent.

Results of tanh for various corner-case inputs are as follows:

Input	Result
-Inf	-1.0
-subnormal	Same as input
-0.0	-0.0
+0.0	+0.0
+subnormal	Same as input
+Inf	1.0
NaN	NaN

The subnormal numbers are supported.

Note

The subnormal inputs gets passed through to the output since the value of tanh(x) for small values of x is approximately the same as x.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

Target ISA Notes

Requires sm_75 or higher.

Examples

tanh.approx.f32 sa, a;

9.7.4. Half Precision Floating-Point Instructions

Half precision floating-point instructions operate on .f16 and .f16x2 register operands. The half precision floating-point instructions are:

• add

• sub

• mul

• fma

• neg

• abs

• min

• max

• tanh

• ex2

Half-precision add, sub, mul, and fma support saturation of results to the range [0.0, 1.0], with NaNs being flushed to positive zero. Half-precision instructions return an unspecified NaN.

9.7.4.1. Half Precision Floating Point Instructions: add

add

Add two values.

Syntax

add{.rnd}{.ftz}{.sat}.f16   d, a, b;
add{.rnd}{.ftz}{.sat}.f16x2 d, a, b;

add{.rnd}.bf16   d, a, b;
add{.rnd}.bf16x2 d, a, b;

.rnd = { .rn };

Description

Performs addition and writes the resulting value into a destination register.

For .f16x2 and .bf16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then added in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d, a and b have .f16 or .b16 type. For .f16x2 instruction type, operands d, a and b have .b32 type. For .bf16 instruction type, operands d, a, b have .b16 type. For .bf16x2 instruction type, operands d, a, b have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = a + b;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = fA[i] + fB[i];
    }
}

Notes

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

The default value of rounding modifier is .rn. Note that an add instruction with an explicit rounding modifier is treated conservatively by the code optimizer. An add instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/add sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

By default, subnormal numbers are supported. add.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

add.sat.{f16, f16x2} clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

add{.rnd}.bf16 and add{.rnd}.bf16x2 introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_53 or higher.

add{.rnd}.bf16 and add{.rnd}.bf16x2 requires sm_90 or higher.

Examples

// scalar f16 additions
add.f16        d0, a0, b0;
add.rn.f16     d1, a1, b1;
add.bf16       bd0, ba0, bb0;
add.rn.bf16    bd1, ba1, bb1;

// SIMD f16 addition
cvt.rn.f16.f32 h0, f0;
cvt.rn.f16.f32 h1, f1;
cvt.rn.f16.f32 h2, f2;
cvt.rn.f16.f32 h3, f3;
mov.b32  p1, {h0, h1};   // pack two f16 to 32bit f16x2
mov.b32  p2, {h2, h3};   // pack two f16 to 32bit f16x2
add.f16x2  p3, p1, p2;   // SIMD f16x2 addition

// SIMD bf16 addition
cvt.rn.bf16x2.f32 p4, f4, f5; // Convert two f32 into packed bf16x2
cvt.rn.bf16x2.f32 p5, f6, f7; // Convert two f32 into packed bf16x2
add.bf16x2  p6, p4, p5;       // SIMD bf16x2 addition

// SIMD fp16 addition
ld.global.b32   f0, [addr];     // load 32 bit which hold packed f16x2
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
add.f16x2       f2, f0, f1;     // SIMD f16x2 addition

ld.global.b32   f3, [addr + 8];  // load 32 bit which hold packed bf16x2
ld.global.b32   f4, [addr + 12]; // load 32 bit which hold packed bf16x2
add.bf16x2      f5, f3, f4;      // SIMD bf16x2 addition

9.7.4.2. Half Precision Floating Point Instructions: sub

sub

Subtract two values.

Syntax

sub{.rnd}{.ftz}{.sat}.f16   d, a, b;
sub{.rnd}{.ftz}{.sat}.f16x2 d, a, b;

sub{.rnd}.bf16   d, a, b;
sub{.rnd}.bf16x2 d, a, b;

.rnd = { .rn };

Description

Performs subtraction and writes the resulting value into a destination register.

For .f16x2 and .bf16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then subtracted in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d, a and b have .f16 or .b16 type. For .f16x2 instruction type, operands d, a and b have .b32 type. For .bf16 instruction type, operands d, a, b have .b16 type. For .bf16x2 instruction type, operands d, a, b have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = a - b;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = fA[i] - fB[i];
    }
}

Notes

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

The default value of rounding modifier is .rn. Note that a sub instruction with an explicit rounding modifier is treated conservatively by the code optimizer. A sub instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/sub sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

By default, subnormal numbers are supported. sub.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

sub.sat.{f16, f16x2} clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

sub{.rnd}.bf16 and sub{.rnd}.bf16x2 introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_53 or higher.

sub{.rnd}.bf16 and sub{.rnd}.bf16x2 requires sm_90 or higher.

Examples

// scalar f16 subtractions
sub.f16        d0, a0, b0;
sub.rn.f16     d1, a1, b1;
sub.bf16       bd0, ba0, bb0;
sub.rn.bf16    bd1, ba1, bb1;

// SIMD f16 subtraction
cvt.rn.f16.f32 h0, f0;
cvt.rn.f16.f32 h1, f1;
cvt.rn.f16.f32 h2, f2;
cvt.rn.f16.f32 h3, f3;
mov.b32  p1, {h0, h1};   // pack two f16 to 32bit f16x2
mov.b32  p2, {h2, h3};   // pack two f16 to 32bit f16x2
sub.f16x2  p3, p1, p2;   // SIMD f16x2 subtraction

// SIMD bf16 subtraction
cvt.rn.bf16x2.f32 p4, f4, f5; // Convert two f32 into packed bf16x2
cvt.rn.bf16x2.f32 p5, f6, f7; // Convert two f32 into packed bf16x2
sub.bf16x2  p6, p4, p5;       // SIMD bf16x2 subtraction

// SIMD fp16 subtraction
ld.global.b32   f0, [addr];     // load 32 bit which hold packed f16x2
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
sub.f16x2       f2, f0, f1;     // SIMD f16x2 subtraction

// SIMD bf16 subtraction
ld.global.b32   f3, [addr + 8];  // load 32 bit which hold packed bf16x2
ld.global.b32   f4, [addr + 12]; // load 32 bit which hold packed bf16x2
sub.bf16x2      f5, f3, f4;      // SIMD bf16x2 subtraction

9.7.4.3. Half Precision Floating Point Instructions: mul

mul

Multiply two values.

Syntax

mul{.rnd}{.ftz}{.sat}.f16   d, a, b;
mul{.rnd}{.ftz}{.sat}.f16x2 d, a, b;

mul{.rnd}.bf16   d, a, b;
mul{.rnd}.bf16x2 d, a, b;

.rnd = { .rn };

Description

Performs multiplication and writes the resulting value into a destination register.

For .f16x2 and .bf16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then multiplied in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d, a and b have .f16 or .b16 type. For .f16x2 instruction type, operands d, a and b have .b32 type. For .bf16 instruction type, operands d, a, b have .b16 type. For .bf16x2 instruction type, operands d, a, b have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = a * b;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = fA[i] * fB[i];
    }
}

Notes

Rounding modifiers:

.rn

mantissa LSB rounds to nearest even

The default value of rounding modifier is .rn. Note that a mul instruction with an explicit rounding modifier is treated conservatively by the code optimizer. A mul instruction with no rounding modifier defaults to round-to-nearest-even and may be optimized aggressively by the code optimizer. In particular, mul/add and mul/sub sequences with no rounding modifiers may be optimized to use fused-multiply-add instructions on the target device.

Subnormal numbers:

By default, subnormal numbers are supported. mul.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

mul.sat.{f16, f16x2} clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

mul{.rnd}.bf16 and mul{.rnd}.bf16x2 introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_53 or higher.

mul{.rnd}.bf16 and mul{.rnd}.bf16x2 requires sm_90 or higher.

Examples

// scalar f16 multiplications
mul.f16        d0, a0, b0;
mul.rn.f16     d1, a1, b1;
mul.bf16       bd0, ba0, bb0;
mul.rn.bf16    bd1, ba1, bb1;

// SIMD f16 multiplication
cvt.rn.f16.f32 h0, f0;
cvt.rn.f16.f32 h1, f1;
cvt.rn.f16.f32 h2, f2;
cvt.rn.f16.f32 h3, f3;
mov.b32  p1, {h0, h1};   // pack two f16 to 32bit f16x2
mov.b32  p2, {h2, h3};   // pack two f16 to 32bit f16x2
mul.f16x2  p3, p1, p2;   // SIMD f16x2 multiplication

// SIMD bf16 multiplication
cvt.rn.bf16x2.f32 p4, f4, f5; // Convert two f32 into packed bf16x2
cvt.rn.bf16x2.f32 p5, f6, f7; // Convert two f32 into packed bf16x2
mul.bf16x2  p6, p4, p5;       // SIMD bf16x2 multiplication

// SIMD fp16 multiplication
ld.global.b32   f0, [addr];     // load 32 bit which hold packed f16x2
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
mul.f16x2       f2, f0, f1;     // SIMD f16x2 multiplication

// SIMD bf16 multiplication
ld.global.b32   f3, [addr + 8];  // load 32 bit which hold packed bf16x2
ld.global.b32   f4, [addr + 12]; // load 32 bit which hold packed bf16x2
mul.bf16x2      f5, f3, f4;      // SIMD bf16x2 multiplication

9.7.4.4. Half Precision Floating Point Instructions: fma

fma

Fused multiply-add

Syntax

fma.rnd{.ftz}{.sat}.f16     d, a, b, c;
fma.rnd{.ftz}{.sat}.f16x2   d, a, b, c;
fma.rnd{.ftz}.relu.f16      d, a, b, c;
fma.rnd{.ftz}.relu.f16x2    d, a, b, c;
fma.rnd{.relu}.bf16         d, a, b, c;
fma.rnd{.relu}.bf16x2       d, a, b, c;
fma.rnd.oob.{relu}.type     d, a, b, c;

.rnd = { .rn };

Description

Performs a fused multiply-add with no loss of precision in the intermediate product and addition.

For .f16x2 and .bf16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then operated in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d, a, b and c have .f16 or .b16 type. For .f16x2 instruction type, operands d, a, b and c have .b32 type. For .bf16 instruction type, operands d, a, b and c have .b16 type. For .bf16x2 instruction type, operands d, a, b and c have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = a * b + c;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    fC[0] = c[0:15];
    fC[1] = c[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = fA[i] * fB[i] + fC[i];
    }
}

Notes

Rounding modifiers (default is .rn):

.rn

mantissa LSB rounds to nearest even

Subnormal numbers:

By default, subnormal numbers are supported. fma.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

Saturation modifier:

fma.sat.{f16, f16x2} clamps the result to [0.0, 1.0]. NaN results are flushed to +0.0f. fma.relu.{f16, f16x2, bf16, bf16x2} clamps the result to 0 if negative. NaN result is converted to canonical NaN.

Out Of Bounds modifier:

fma.oob.{f16, f16x2, bf16, bf16x2} clamps the result to 0 if either of the operands is OOB NaN (defined under Tensors) value. The test for the special NaN value and resultant forcing of the result to +0.0 is performed independently for each of the two SIMD operations.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

fma.relu.{f16, f16x2} and fma{.relu}.{bf16, bf16x2} introduced in PTX ISA version 7.0.

Support for modifier .oob introduced in PTX ISA version 8.1.

Target ISA Notes

Requires sm_53 or higher.

fma.relu.{f16, f16x2} and fma{.relu}.{bf16, bf16x2} require sm_80 or higher.

fma{.oob}.{f16, f16x2, bf16, bf16x2} requires sm_90 or higher.

Examples

// scalar f16 fused multiply-add
fma.rn.f16         d0, a0, b0, c0;
fma.rn.f16         d1, a1, b1, c1;
fma.rn.relu.f16    d1, a1, b1, c1;
fma.rn.oob.f16      d1, a1, b1, c1;
fma.rn.oob.relu.f16 d1, a1, b1, c1;

// scalar bf16 fused multiply-add
fma.rn.bf16        d1, a1, b1, c1;
fma.rn.relu.bf16   d1, a1, b1, c1;
fma.rn.oob.bf16       d1, a1, b1, c1;
fma.rn.oob.relu.bf16  d1, a1, b1, c1;

// SIMD f16 fused multiply-add
cvt.rn.f16.f32 h0, f0;
cvt.rn.f16.f32 h1, f1;
cvt.rn.f16.f32 h2, f2;
cvt.rn.f16.f32 h3, f3;
mov.b32  p1, {h0, h1}; // pack two f16 to 32bit f16x2
mov.b32  p2, {h2, h3}; // pack two f16 to 32bit f16x2
fma.rn.f16x2  p3, p1, p2, p2;   // SIMD f16x2 fused multiply-add
fma.rn.relu.f16x2  p3, p1, p2, p2; // SIMD f16x2 fused multiply-add with relu saturation mode
fma.rn.oob.f16x2  p3, p1, p2, p2; // SIMD f16x2 fused multiply-add with oob modifier
fma.rn.oob.relu.f16x2 p3, p1, p2, p2; // SIMD f16x2 fused multiply-add with oob modifier and relu saturation mode

// SIMD fp16 fused multiply-add
ld.global.b32   f0, [addr];     // load 32 bit which hold packed f16x2
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
fma.rn.f16x2    f2, f0, f1, f1; // SIMD f16x2 fused multiply-add

// SIMD bf16 fused multiply-add
fma.rn.bf16x2       f2, f0, f1, f1; // SIMD bf16x2 fused multiply-add
fma.rn.relu.bf16x2  f2, f0, f1, f1; // SIMD bf16x2 fused multiply-add with relu saturation mode
fma.rn.oob.bf16x2  f2, f0, f1, f1; // SIMD bf16x2 fused multiply-add with oob modifier
fma.rn.oob.relu.bf16x2  f2, f0, f1, f1; // SIMD bf16x2 fused multiply-add with oob modifier and relu saturation mode

9.7.4.5. Half Precision Floating Point Instructions: neg

neg

Arithmetic negate.

Syntax

neg{.ftz}.f16    d, a;
neg{.ftz}.f16x2  d, a;
neg.bf16         d, a;
neg.bf16x2       d, a;

Description

Negate the sign of a and store the result in d.

For .f16x2 and .bf16x2 instruction type, forms input vector by extracting half word values from the source operand. Half-word operands are then negated in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d and a have .f16 or .b16 type. For .f16x2 instruction type, operands d and a have .b32 type. For .bf16 instruction type, operands d and a have .b16 type. For .bf16x2 instruction type, operands d and a have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = -a;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = -fA[i];
    }
}

Notes

Subnormal numbers:

By default, subnormal numbers are supported. neg.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

NaN inputs yield an unspecified NaN. Future implementations may comply with the IEEE 754 standard by preserving payload and modifying only the sign bit.

PTX ISA Notes

Introduced in PTX ISA version 6.0.

neg.bf16 and neg.bf16x2 introduced in PTX ISA 7.0.

Target ISA Notes

Requires sm_53 or higher.

neg.bf16 and neg.bf16x2 requires architecture sm_80 or higher.

Examples

neg.ftz.f16  x,f0;
neg.bf16     x,b0;
neg.bf16x2   x1,b1;

9.7.4.6. Half Precision Floating Point Instructions: abs

abs

Absolute value

Syntax

abs{.ftz}.f16    d, a;
abs{.ftz}.f16x2  d, a;
abs.bf16         d, a;
abs.bf16x2       d, a;

Description

Take absolute value of a and store the result in d.

For .f16x2 and .bf16x2 instruction type, forms input vector by extracting half word values from the source operand. Absolute values of half-word operands are then computed in parallel to produce .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d and a have .f16 or .b16 type. For .f16x2 instruction type, operands d and a have .f16x2 or .b32 type. For .bf16 instruction type, operands d and a have .b16 type. For .bf16x2 instruction type, operands d and a have .b32 type.

Semantics

if (type == f16 || type == bf16) {
    d = |a|;
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    for (i = 0; i < 2; i++) {
         d[i] = |fA[i]|;
    }
}

Notes

Subnormal numbers:

By default, subnormal numbers are supported. abs.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

NaN inputs yield an unspecified NaN. Future implementations may comply with the IEEE 754 standard by preserving payload and modifying only the sign bit.

PTX ISA Notes

Introduced in PTX ISA version 6.5.

abs.bf16 and abs.bf16x2 introduced in PTX ISA 7.0.

Target ISA Notes

Requires sm_53 or higher.

abs.bf16 and abs.bf16x2 requires architecture sm_80 or higher.

Examples

abs.ftz.f16  x,f0;
abs.bf16     x,b0;
abs.bf16x2   x1,b1;

9.7.4.7. Half Precision Floating Point Instructions: min

min

Find the minimum of two values.

Syntax

min{.ftz}{.NaN}{.xorsign.abs}.f16      d, a, b;
min{.ftz}{.NaN}{.xorsign.abs}.f16x2    d, a, b;
min{.NaN}{.xorsign.abs}.bf16           d, a, b;
min{.NaN}{.xorsign.abs}.bf16x2         d, a, b;

Description

Store the minimum of a and b in d.

For .f16x2 and .bf16x2 instruction types, input vectors are formed with half-word values from source operands. Half-word operands are then processed in parallel to store .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d and a have .f16 or .b16 type. For .f16x2 instruction type, operands d and a have .f16x2 or .b32 type. For .bf16 instruction type, operands d and a have .b16 type. For .bf16x2 instruction type, operands d and a have .b32 type.

If .NaN modifier is specified, then the result is canonical NaN if either of the inputs is NaN.

If .abs modifier is specified, the magnitude of destination operand d is the minimum of absolute values of both the input arguments.

If .xorsign modifier is specified, the sign bit of destination d is equal to the XOR of the sign bits of both the inputs.

Modifiers .abs and .xorsign must be specified together and .xorsign considers the sign bit of both inputs before applying .abs operation.

If the result of min is NaN then the .xorsign and .abs modifiers will be ignored.

Semantics

if (type == f16 || type == bf16) {
    if (.xorsign) {
        xorsign = getSignBit(a) ^ getSignBit(b);
        if (.abs) {
            a = |a|;
            b = |b|;
        }
    }
    if (isNaN(a) && isNaN(b))              d = NaN;
    if (.NaN && (isNaN(a) || isNaN(b)))    d = NaN;
    else if (isNaN(a))                     d = b;
    else if (isNaN(b))                     d = a;
    else                                   d = (a < b) ? a : b;
    if (.xorsign && !isNaN(d)) {
         setSignBit(d, xorsign);
    }
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
        if (.xorsign) {
            xorsign = getSignBit(fA[i]) ^ getSignBit(fB[i]);
            if (.abs) {
               fA[i] = |fA[i]|;
               fB[i] = |fB[i]|;
           }
        }
        if (isNaN(fA[i]) && isNaN(fB[i]))              d[i] = NaN;
        if (.NaN && (isNaN(fA[i]) || isNaN(fB[i])))    d[i] = NaN;
        else if (isNaN(fA[i]))                         d[i] = fB[i];
        else if (isNaN(fB[i]))                         d[i] = fA[i];
        else                                           d[i] = (fA[i] < fB[i]) ? fA[i] : fB[i];
        if (.xorsign && !isNaN(d[i])) {
            setSignBit(d[i], xorsign);
        }
    }
}

Notes

Subnormal numbers:

By default, subnormal numbers are supported. min.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

If values of both inputs are 0.0, then +0.0 > -0.0.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

min.xorsign introduced in PTX ISA version 7.2.

Target ISA Notes

Requires sm_80 or higher.

min.xorsign.abs support requires sm_86 or higher.

Examples

min.ftz.f16       h0,h1,h2;
min.f16x2         b0,b1,b2;
// SIMD fp16 min with .NaN
min.NaN.f16x2     b0,b1,b2;
min.bf16          h0, h1, h2;
// SIMD bf16 min with NaN
min.NaN.bf16x2    b0, b1, b2;
// scalar bf16 min with xorsign.abs
min.xorsign.abs.bf16 Rd, Ra, Rb

9.7.4.8. Half Precision Floating Point Instructions: max

max

Find the maximum of two values.

Syntax

max{.ftz}{.NaN}{.xorsign.abs}.f16      d, a, b;
max{.ftz}{.NaN}{.xorsign.abs}.f16x2    d, a, b;
max{.NaN}{.xorsign.abs}.bf16           d, a, b;
max{.NaN}{.xorsign.abs}.bf16x2         d, a, b;

Description

Store the maximum of a and b in d.

For .f16x2 and .bf16x2 instruction types, input vectors are formed with half-word values from source operands. Half-word operands are then processed in parallel to store .f16x2 or .bf16x2 result in destination.

For .f16 instruction type, operands d and a have .f16 or .b16 type. For .f16x2 instruction type, operands d and a have .f16x2 or .b32 type. For .bf16 instruction type, operands d and a have .b16 type. For .bf16x2 instruction type, operands d and a have .b32 type.

If .NaN modifier is specified, the result is canonical NaN if either of the inputs is NaN.

If .abs modifier is specified, the magnitude of destination operand d is the maximum of absolute values of both the input arguments.

If .xorsign modifier is specified, the sign bit of destination d is equal to the XOR of the sign bits of both the inputs.

Modifiers .abs and .xorsign must be specified together and .xorsign considers the sign bit of both inputs before applying .abs operation.

If the result of max is NaN then the .xorsign and .abs modifiers will be ignored.

Semantics

if (type == f16 || type == bf16) {
    if (.xorsign) {
        xorsign = getSignBit(a) ^ getSignBit(b);
        if (.abs) {
            a = |a|;
            b = |b|;
        }
    }
    if (isNaN(a) && isNaN(b))              d = NaN;
    if (.NaN && (isNaN(a) || isNaN(b)))    d = NaN;
    else if (isNaN(a))                     d = b;
    else if (isNaN(b))                     d = a;
    else                                   d = (a > b) ? a : b;
    if (.xorsign && !isNaN(d)) {
         setSignBit(d, xorsign);
    }
} else if (type == f16x2 || type == bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    for (i = 0; i < 2; i++) {
        if (.xorsign) {
            xorsign = getSignBit(fA[i]) ^ getSignBit(fB[i]);
            if (.abs) {
                fA[i] = |fA[i]|;
                fB[i] = |fB[i]|;
            }
        }
        if (isNaN(fA[i]) && isNaN(fB[i]))              d[i] = NaN;
        if (.NaN && (isNaN(fA[i]) || isNaN(fB[i])))    d[i] = NaN;
        else if (isNaN(fA[i]))                         d[i] = fB[i];
        else if (isNaN(fB[i]))                         d[i] = fA[i];
        else                                           d[i] = (fA[i] > fB[i]) ? fA[i] : fB[i];
        if (.xorsign && !isNaN(fA[i])) {
            setSignBit(d[i], xorsign);
        }
    }
}

Notes

Subnormal numbers:

By default, subnormal numbers are supported. max.ftz.{f16, f16x2} flushes subnormal inputs and results to sign-preserving zero.

If values of both inputs are 0.0, then +0.0 > -0.0.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

max.xorsign.abs introduced in PTX ISA version 7.2.

Target ISA Notes

Requires sm_80 or higher.

max.xorsign.abs support requires sm_86 or higher.

Examples

max.ftz.f16       h0,h1,h2;
max.f16x2         b0,b1,b2;
// SIMD fp16 max with NaN
max.NaN.f16x2     b0,b1,b2;
// scalar f16 max with xorsign.abs
max.xorsign.abs.f16 Rd, Ra, Rb;
max.bf16          h0, h1, h2;
// scalar bf16 max and NaN
max.NaN.bf16x2    b0, b1, b2;
// SIMD bf16 max with xorsign.abs
max.xorsign.abs.bf16x2 Rd, Ra, Rb;

9.7.4.9. Half Precision Floating Point Instructions: tanh

tanh

Find the hyperbolic tangent of a value (in radians)

Syntax

tanh.approx.type d, a;

.type = {.f16, .f16x2, .bf16, .bf16x2}

Description

Take hyperbolic tangent value of a.

The type of operands d and a are as specified by .type.

For .f16x2 or .bf16x2 instruction type, each of the half-word operands are operated in parallel and the results are packed appropriately into a .f16x2 or .bf16x2.

Semantics

if (.type == .f16 || .type == .bf16) {
  d = tanh(a)
} else if (.type == .f16x2 || .type == .bf16x2) {
  fA[0] = a[0:15];
  fA[1] = a[16:31];
  d[0] = tanh(fA[0])
  d[1] = tanh(fA[1])
}

Notes

tanh.approx.{f16, f16x2, bf16, bf16x2} implements an approximate hyperbolic tangent in the target format.

Results of tanh for various corner-case inputs are as follows:

Input	Result
-Inf	-1.0
-0.0	-0.0
+0.0	+0.0
+Inf	1.0
NaN	NaN

The maximum absolute error for .f16 type is 2-10.987. The maximum absolute error for .bf16 type is 2-8.

The subnormal numbers are supported.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

tanh.approx.{bf16/bf16x2} introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_75 or higher.

tanh.approx.{bf16/bf16x2} requires sm_90 or higher.

Examples

tanh.approx.f16    h1, h0;
tanh.approx.f16x2  hd1, hd0;
tanh.approx.bf16   b1, b0;
tanh.approx.bf16x2 hb1, hb0;

9.7.4.10. Half Precision Floating Point Instructions: ex2

ex2

Find the base-2 exponent of input.

Syntax

ex2.approx.atype     d, a;
ex2.approx.ftz.btype d, a;

.atype = { .f16,  .f16x2}
.btype = { .bf16, .bf16x2}

Description

Raise 2 to the power a.

The type of operands d and a are as specified by .type.

For .f16x2 or .bf16x2 instruction type, each of the half-word operands are operated in parallel and the results are packed appropriately into a .f16x2 or .bf16x2.

Semantics

if (.type == .f16 || .type == .bf16) {
  d = 2 ^ a
} else if (.type == .f16x2 || .type == .bf16x2) {
  fA[0] = a[0:15];
  fA[1] = a[16:31];
  d[0] = 2 ^ fA[0]
  d[1] = 2 ^ fA[1]
}

Notes

ex2.approx.{f16, f16x2, bf16, bf16x2} implement a fast approximation to 2^a.

For the .f16 type, subnormal inputs are supported. ex2.approx.ftz.bf16 flushes subnormal inputs and results to sign-preserving zero.

Results of ex2.approx.ftz.bf16 for various corner-case inputs are as follows:

Input	Result
-Inf	+0.0
-subnormal	+1.0
-0.0	+1.0
+0.0	+1.0
+subnormal	+1.0
+Inf	+Inf
NaN	NaN

Results of ex2.approx.f16 for various corner-case inputs are as follows:

Input	Result
-Inf	+0.0
-0.0	+1.0
+0.0	+1.0
+Inf	+Inf
NaN	NaN

The maximum relative error for .f16 type is 2-9.9. The maximum relative error for .bf16 type is 2-7.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

ex2.approx.ftz.{bf16/bf16x2} introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_75 or higher.

ex2.approx.ftz.{bf16/bf16x2} requires sm_90 or higher.

Examples

ex2.approx.f16         h1, h0;
ex2.approx.f16x2       hd1, hd0;
ex2.approx.ftz.bf16    b1, b2;
ex2.approx.ftz.bf16x2  hb1, hb2;

9.7.5. Comparison and Selection Instructions

The comparison select instructions are:

• set

• setp

• selp

• slct

As with single-precision floating-point instructions, the set, setp, and slct instructions support subnormal numbers for sm_20 and higher targets and flush single-precision subnormal inputs to sign-preserving zero for sm_1x targets. The optional .ftz modifier provides backward compatibility with sm_1x targets by flushing subnormal inputs and results to sign-preserving zero regardless of the target architecture.

9.7.5.1. Comparison and Selection Instructions: set

set

Compare two numeric values with a relational operator, and optionally combine this result with a predicate value by applying a Boolean operator.

Syntax

set.CmpOp{.ftz}.dtype.stype         d, a, b;
set.CmpOp.BoolOp{.ftz}.dtype.stype  d, a, b, {!}c;

.CmpOp  = { eq, ne, lt, le, gt, ge, lo, ls, hi, hs,
            equ, neu, ltu, leu, gtu, geu, num, nan };
.BoolOp = { and, or, xor };
.dtype  = { .u32, .s32, .f32 };
.stype  = { .b16, .b32, .b64,
            .u16, .u32, .u64,
            .s16, .s32, .s64,
                  .f32, .f64 };

Description

Compares two numeric values and optionally combines the result with another predicate value by applying a Boolean operator. If this result is True, 1.0f is written for floating-point destination types, and 0xffffffff is written for integer destination types. Otherwise, 0x00000000 is written.

Operand dhas type .dtype; operands a and b have type .stype; operand c has type .pred.

Semantics

t = (a CmpOp b) ? 1 : 0;
if (isFloat(dtype))
    d = BoolOp(t, c) ? 1.0f : 0x00000000;
else
    d = BoolOp(t, c) ? 0xffffffff : 0x00000000;

Integer Notes

The signed and unsigned comparison operators are eq, ne, lt, le, gt, ge.

For unsigned values, the comparison operators lo, ls, hi, and hs for lower, lower-or-same, higher, and higher-or-same may be used instead of lt, le, gt, ge, respectively.

The untyped, bit-size comparisons are eq and ne.

Floating Point Notes

The ordered comparisons are eq, ne, lt, le, gt, ge. If either operand is NaN, the result is False.

To aid comparison operations in the presence of NaN values, unordered versions are included: equ, neu, ltu, leu, gtu, geu. If both operands are numeric values (not NaN), then these comparisons have the same result as their ordered counterparts. If either operand is NaN, then the result of these comparisons is True.

num returns True if both operands are numeric values (not NaN), and nan returns True if either operand is NaN.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

set.ftz.dtype.f32 flushes subnormal inputs to sign-preserving zero.

sm_1x

set.dtype.f64 supports subnormal numbers.

set.dtype.f32 flushes subnormal inputs to sign-preserving zero.

Modifier .ftz applies only to .f32 comparisons.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

set with .f64 source type requires sm_13 or higher.

Examples

@p  set.lt.and.f32.s32  d,a,b,r;
    set.eq.u32.u32      d,i,n;

9.7.5.2. Comparison and Selection Instructions: setp

setp

Compare two numeric values with a relational operator, and (optionally) combine this result with a predicate value by applying a Boolean operator.

Syntax

setp.CmpOp{.ftz}.type         p[|q], a, b;
setp.CmpOp.BoolOp{.ftz}.type  p[|q], a, b, {!}c;

.CmpOp  = { eq, ne, lt, le, gt, ge, lo, ls, hi, hs,
            equ, neu, ltu, leu, gtu, geu, num, nan };
.BoolOp = { and, or, xor };
.type   = { .b16, .b32, .b64,
            .u16, .u32, .u64,
            .s16, .s32, .s64,
                  .f32, .f64 };

Description

Compares two values and combines the result with another predicate value by applying a Boolean operator. This result is written to the first destination operand. A related value computed using the complement of the compare result is written to the second destination operand.

Applies to all numeric types. Operands a and b have type .type; operands p, q, and c have type .pred. The sink symbol ‘_’ may be used in place of any one of the destination operands.

Semantics

t = (a CmpOp b) ? 1 : 0;
p = BoolOp(t, c);
q = BoolOp(!t, c);

Integer Notes

The signed and unsigned comparison operators are eq, ne, lt, le, gt, ge.

For unsigned values, the comparison operators lo, ls, hi, and hs for lower, lower-or-same, higher, and higher-or-same may be used instead of lt, le, gt, ge, respectively.

The untyped, bit-size comparisons are eq and ne.

Floating Point Notes

The ordered comparisons are eq, ne, lt, le, gt, ge. If either operand is NaN, the result is False.

To aid comparison operations in the presence of NaN values, unordered versions are included: equ, neu, ltu, leu, gtu, geu. If both operands are numeric values (not NaN), then these comparisons have the same result as their ordered counterparts. If either operand is NaN, then the result of these comparisons is True.

num returns True if both operands are numeric values (not NaN), and nan returns True if either operand is NaN.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

setp.ftz.dtype.f32 flushes subnormal inputs to sign-preserving zero.

sm_1x

setp.dtype.f64 supports subnormal numbers.

setp.dtype.f32 flushes subnormal inputs to sign-preserving zero.

Modifier .ftz applies only to .f32 comparisons.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

setp with .f64 source type requires sm_13 or higher.

Examples

    setp.lt.and.s32  p|q,a,b,r;
@q  setp.eq.u32      p,i,n;

9.7.5.3. Comparison and Selection Instructions: selp

selp

Select between source operands, based on the value of the predicate source operand.

Syntax

selp.type d, a, b, c;

.type = { .b16, .b32, .b64,
          .u16, .u32, .u64,
          .s16, .s32, .s64,
                .f32, .f64 };

Description

Conditional selection. If c is True, a is stored in d, b otherwise. Operands d, a, and b must be of the same type. Operand c is a predicate.

Semantics

d = (c == 1) ? a : b;

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

selp.f64 requires sm_13 or higher.

Examples

    selp.s32  r0,r,g,p;
@q  selp.f32  f0,t,x,xp;

9.7.5.4. Comparison and Selection Instructions: slct

slct

Select one source operand, based on the sign of the third operand.

Syntax

slct.dtype.s32        d, a, b, c;
slct{.ftz}.dtype.f32  d, a, b, c;

.dtype = { .b16, .b32, .b64,
           .u16, .u32, .u64,
           .s16, .s32, .s64,
                 .f32, .f64 };

Description

Conditional selection. If c ≥ 0, a is stored in d, otherwise b is stored in d. Operands d, a, and b are treated as a bitsize type of the same width as the first instruction type; operand c must match the second instruction type (.s32 or .f32). The selected input is copied to the output without modification.

Semantics

d = (c >= 0) ? a : b;

Floating Point Notes

For .f32 comparisons, negative zero equals zero.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

slct.ftz.dtype.f32 flushes subnormal values of operand c to sign-preserving zero, and operand a is selected.

sm_1x

slct.dtype.f32 flushes subnormal values of operand c to sign-preserving zero, and operand a is selected.

Modifier .ftz applies only to .f32 comparisons.

If operand c is NaN, the comparison is unordered and operand b is selected.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

slct.f64 requires sm_13 or higher.

Examples

slct.u32.s32  x, y, z, val;
slct.ftz.u64.f32  A, B, C, fval;

9.7.6. Half Precision Comparison Instructions

The comparison instructions are:

• set

• setp

9.7.6.1. Half Precision Comparison Instructions: set

set

Compare two numeric values with a relational operator, and optionally combine this result with a predicate value by applying a Boolean operator.

Syntax

set.CmpOp{.ftz}.f16.stype            d, a, b;
set.CmpOp.BoolOp{.ftz}.f16.stype     d, a, b, {!}c;

set.CmpOp.bf16.stype                 d, a, b;
set.CmpOp.BoolOp.bf16.stype          d, a, b, {!}c;

set.CmpOp{.ftz}.dtype.f16            d, a, b;
set.CmpOp.BoolOp{.ftz}.dtype.f16     d, a, b, {!}c;
.dtype  = { .u16, .s16, .u32, .s32}

set.CmpOp.dtype.bf16                 d, a, b;
set.CmpOp.BoolOp.dtype.bf16          d, a, b, {!}c;
.dtype  = { .u16, .s16, .u32, .s32}

set.CmpOp{.ftz}.dtype.f16x2          d, a, b;
set.CmpOp.BoolOp{.ftz}.dtype.f16x2   d, a, b, {!}c;
.dtype  = { .f16x2, .u32, .s32}

set.CmpOp.dtype.bf16x2               d, a, b;
set.CmpOp.BoolOp.dtype.bf16x2        d, a, b, {!}c;
.dtype  = { .bf16x2, .u32, .s32}

.CmpOp  = { eq, ne, lt, le, gt, ge,
            equ, neu, ltu, leu, gtu, geu, num, nan };
.BoolOp = { and, or, xor };
.stype  = { .b16, .b32, .b64,
            .u16, .u32, .u64,
            .s16, .s32, .s64,
            .f16, .f32, .f64};

Description

Compares two numeric values and optionally combines the result with another predicate value by applying a Boolean operator.

Result of this computation is written in destination register in the following way:

• If result is True,

  • 0xffffffff is written for destination types .u32/.s32.

  • 0xffff is written for destination types .u16/.s16.

  • 1.0 in target precision floating point format is written for destination type .f16, .bf16.

• If result is False,

  • 0x0 is written for all integer destination types.

  • 0.0 in target precision floating point format is written for destination type .f16, .bf16.

If the source type is .f16x2 or .bf16x2 then result of individual operations are packed in the 32-bit destination operand.

Operand c has type .pred.

Semantics

if (stype == .f16x2 || stype == .bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    t[0]   = (fA[0] CmpOp fB[0]) ? 1 : 0;
    t[1]   = (fA[1] CmpOp fB[1]) ? 1 : 0;
    if (dtype == .f16x2 || stype == .bf16x2) {
        for (i = 0; i < 2; i++) {
            d[i] = BoolOp(t[i], c) ? 1.0 : 0.0;
        }
    } else {
        for (i = 0; i < 2; i++) {
            d[i] = BoolOp(t[i], c) ? 0xffff : 0;
        }
    }
} else if (dtype == .f16 || stype == .bf16) {
    t = (a CmpOp b) ? 1 : 0;
    d = BoolOp(t, c) ? 1.0 : 0.0;
} else  { // Integer destination type
    trueVal = (isU16(dtype) || isS16(dtype)) ?  0xffff : 0xffffffff;
    t = (a CmpOp b) ? 1 : 0;
    d = BoolOp(t, c) ? trueVal : 0;
}

Floating Point Notes

The ordered comparisons are eq, ne, lt, le, gt, ge. If either operand is NaN, the result is False.

To aid comparison operations in the presence of NaN values, unordered versions are included: equ, neu, ltu, leu, gtu, geu. If both operands are numeric values (not NaN), then these comparisons have the same result as their ordered counterparts. If either operand is NaN, then the result of these comparisons is True.

num returns True if both operands are numeric values (not NaN), and nan returns True if either operand is NaN.

Subnormal numbers:

By default, subnormal numbers are supported.

When .ftz modifier is specified then subnormal inputs and results are flushed to sign preserving zero.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

set.{u16, u32, s16, s32}.f16 and set.{u32, s32}.f16x2 are introduced in PTX ISA version 6.5.

set.{u16, u32, s16, s32}.bf16, set.{u32, s32, bf16x2}.bf16x2, set.bf16.{s16,u16,f16,b16,s32,u32,f32,b32,s64,u64,f64,b64} are introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_53 or higher.

set.{u16, u32, s16, s32}.bf16, set.{u32, s32, bf16x2}.bf16x2, set.bf16.{s16,u16,f16,b16,s32,u32,f32,b32,s64,u64,f64,b64} require sm_90 or higher.

Examples

set.lt.and.f16.f16  d,a,b,r;
set.eq.f16x2.f16x2  d,i,n;
set.eq.u32.f16x2    d,i,n;
set.lt.and.u16.f16  d,a,b,r;
set.ltu.or.bf16.f16    d,u,v,s;
set.equ.bf16x2.bf16x2  d,j,m;
set.geu.s32.bf16x2     d,j,m;
set.num.xor.s32.bf16   d,u,v,s;

9.7.6.2. Half Precision Comparison Instructions: setp

setp

Compare two numeric values with a relational operator, and optionally combine this result with a predicate value by applying a Boolean operator.

Syntax

setp.CmpOp{.ftz}.f16           p, a, b;
setp.CmpOp.BoolOp{.ftz}.f16    p, a, b, {!}c;

setp.CmpOp{.ftz}.f16x2         p|q, a, b;
setp.CmpOp.BoolOp{.ftz}.f16x2  p|q, a, b, {!}c;

setp.CmpOp.bf16                p, a, b;
setp.CmpOp.BoolOp.bf16         p, a, b, {!}c;

setp.CmpOp.bf16x2              p|q, a, b;
setp.CmpOp.BoolOp.bf16x2       p|q, a, b, {!}c;

.CmpOp  = { eq, ne, lt, le, gt, ge,
            equ, neu, ltu, leu, gtu, geu, num, nan };
.BoolOp = { and, or, xor };

Description

Compares two values and combines the result with another predicate value by applying a Boolean operator. This result is written to the destination operand.

Operand c, p and q has type .pred.

For instruction type .f16, operands a and b have type .b16 or .f16.

For instruction type .f16x2, operands a and b have type .b32.

For instruction type .bf16, operands a and b have type .b16.

For instruction type .bf16x2, operands a and b have type .b32.

Semantics

if (type == .f16 || type == .bf16) {
     t = (a CmpOp b) ? 1 : 0;
     p = BoolOp(t, c);
} else if (type == .f16x2 || type == .bf16x2) {
    fA[0] = a[0:15];
    fA[1] = a[16:31];
    fB[0] = b[0:15];
    fB[1] = b[16:31];
    t[0] = (fA[0] CmpOp fB[0]) ? 1 : 0;
    t[1] = (fA[1] CmpOp fB[1]) ? 1 : 0;
    p = BoolOp(t[0], c);
    q = BoolOp(t[1], c);
}

Floating Point Notes

The ordered comparisons are eq, ne, lt, le, gt, ge. If either operand is NaN, the result is False.

To aid comparison operations in the presence of NaN values, unordered versions are included: equ, neu, ltu, leu, gtu, geu. If both operands are numeric values (not NaN), then these comparisons have the same result as their ordered counterparts. If either operand is NaN, then the result of these comparisons is True.

num returns True if both operands are numeric values (not NaN), and nan returns True if either operand is NaN.

Subnormal numbers:

By default, subnormal numbers are supported.

setp.ftz.{f16,f16x2} flushes subnormal inputs to sign-preserving zero.

PTX ISA Notes

Introduced in PTX ISA version 4.2.

setp.{bf16/bf16x2} introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_53 or higher.

setp.{bf16/bf16x2} requires sm_90 or higher.

Examples

setp.lt.and.f16x2  p|q,a,b,r;
@q  setp.eq.f16    p,i,n;

setp.gt.or.bf16x2  u|v,c,d,s;
@q  setp.eq.bf16   u,j,m;

9.7.7. Logic and Shift Instructions

The logic and shift instructions are fundamentally untyped, performing bit-wise operations on operands of any type, provided the operands are of the same size. This permits bit-wise operations on floating point values without having to define a union to access the bits. Instructions and, or, xor, and not also operate on predicates.

The logical shift instructions are:

• and

• or

• xor

• not

• cnot

• lop3

• shf

• shl

• shr

9.7.7.1. Logic and Shift Instructions: and

and

Bitwise AND.

Syntax

and.type d, a, b;

.type = { .pred, .b16, .b32, .b64 };

Description

Compute the bit-wise and operation for the bits in a and b.

Semantics

d = a & b;

Notes

The size of the operands must match, but not necessarily the type.

Allowed types include predicate registers.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

and.b32  x,q,r;
and.b32  sign,fpvalue,0x80000000;

9.7.7.2. Logic and Shift Instructions: or

or

Biwise OR.

Syntax

or.type d, a, b;

.type = { .pred, .b16, .b32, .b64 };

Description

Compute the bit-wise or operation for the bits in a and b.

Semantics

d = a | b;

Notes

The size of the operands must match, but not necessarily the type.

Allowed types include predicate registers.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

or.b32  mask mask,0x00010001
or.pred  p,q,r;

9.7.7.3. Logic and Shift Instructions: xor

xor

Bitwise exclusive-OR (inequality).

Syntax

xor.type d, a, b;

.type = { .pred, .b16, .b32, .b64 };

Description

Compute the bit-wise exclusive-or operation for the bits in a and b.

Semantics

d = a ^ b;

Notes

The size of the operands must match, but not necessarily the type.

Allowed types include predicate registers.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

xor.b32  d,q,r;
xor.b16  d,x,0x0001;

9.7.7.4. Logic and Shift Instructions: not

not

Bitwise negation; one’s complement.

Syntax

not.type d, a;

.type = { .pred, .b16, .b32, .b64 };

Description

Invert the bits in a.

Semantics

d = ~a;

Notes

The size of the operands must match, but not necessarily the type.

Allowed types include predicates.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

not.b32  mask,mask;
not.pred  p,q;

9.7.7.5. Logic and Shift Instructions: cnot

cnot

C/C++ style logical negation.

Syntax

cnot.type d, a;

.type = { .b16, .b32, .b64 };

Description

Compute the logical negation using C/C++ semantics.

Semantics

d = (a==0) ? 1 : 0;

Notes

The size of the operands must match, but not necessarily the type.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Examples

cnot.b32 d,a;

9.7.7.6. Logic and Shift Instructions: lop3

lop3

Arbitrary logical operation on 3 inputs.

Syntax

lop3.b32 d, a, b, c, immLut;
lop3.BoolOp.b32 d|p, a, b, c, immLut, q;

.BoolOp   = { .or , .and };

Description

Compute bitwise logical operation on inputs a, b, c and store the result in destination d.

Optionally, .BoolOp can be specified to compute the predicate result p by performing a Boolean operation on the destination operand d with the predicate q in the following manner:

p = (d != 0) BoolOp q;

The sink symbol ‘_’ may be used in place of the destination operand d when .BoolOp qualifier is specified.

The logical operation is defined by a look-up table which, for 3 inputs, can be represented as an 8-bit value specified by operand immLut as described below. immLut is an integer constant that can take values from 0 to 255, thereby allowing up to 256 distinct logical operations on inputs a, b, c.

For a logical operation F(a, b, c) the value of immLut can be computed by applying the same operation to three predefined constant values as follows:

ta = 0xF0;
tb = 0xCC;
tc = 0xAA;

immLut = F(ta, tb, tc);

Examples:

If F = (a & b & c);
immLut = 0xF0 & 0xCC & 0xAA = 0x80

If F = (a | b | c);
immLut = 0xF0 | 0xCC | 0xAA = 0xFE

If F = (a & b & ~c);
immLut = 0xF0 & 0xCC & (~0xAA) = 0x40

If F = ((a & b | c) ^ a);
immLut = (0xF0 & 0xCC | 0xAA) ^ 0xF0 = 0x1A

The following table illustrates computation of immLut for various logical operations:

ta	tb	tc	Oper 0 (False)	Oper 1 (ta & tb & tc)	Oper 2 (ta & tb & ~tc)	…	Oper 254 (ta | tb | tc)	Oper 255 (True)
0	0	0	0	0	0	…	0	1
0	0	1	0	0	0		1	1
0	1	0	0	0	0		1	1
0	1	1	0	0	0		1	1
1	0	0	0	0	0		1	1
1	0	1	0	0	0		1	1
1	1	0	0	0	1		1	1
1	1	1	0	1	0		1	1
immLut			0x0	0x80	0x40	…	0xFE	0xFF

Semantics

F = GetFunctionFromTable(immLut); // returns the function corresponding to immLut value
d = F(a, b, c);
if (BoolOp specified) {
    p = (d != 0) BoolOp q;
}

PTX ISA Notes

Introduced in PTX ISA version 4.3.

Support for .BoolOp qualifier introduced in PTX ISA version 8.2.

Target ISA Notes

Requires sm_50 or higher.

Qualifier .BoolOp requires sm_70 or higher.

Examples

lop3.b32       d, a, b, c, 0x40;
lop3.or.b32  d|p, a, b, c, 0x3f, q;
lop3.and.b32 _|p, a, b, c, 0x3f, q;

9.7.7.7. Logic and Shift Instructions: shf

shf

Funnel shift.

Syntax

shf.l.mode.b32  d, a, b, c;  // left shift
shf.r.mode.b32  d, a, b, c;  // right shift

.mode = { .clamp, .wrap };

Description

Shift the 64-bit value formed by concatenating operands a and b left or right by the amount specified by the unsigned 32-bit value in c. Operand b holds bits 63:32 and operand a holds bits 31:0 of the 64-bit source value. The source is shifted left or right by the clamped or wrapped value in c. For shf.l, the most-significant 32-bits of the result are written into d; for shf.r, the least-significant 32-bits of the result are written into d.

Semantics

u32  n = (.mode == .clamp) ? min(c, 32) : c & 0x1f;
switch (shf.dir) {  // shift concatenation of [b, a]
    case shf.l:     // extract 32 msbs
           u32  d = (b << n)      | (a >> (32-n));
    case shf.r:     // extract 32 lsbs
           u32  d = (b << (32-n)) | (a >> n);
}

Notes

Use funnel shift for multi-word shift operations and for rotate operations. The shift amount is limited to the range 0..32 in clamp mode and 0..31 in wrap mode, so shifting multi-word values by distances greater than 32 requires first moving 32-bit words, then using shf to shift the remaining 0..31 distance.

To shift data sizes greater than 64 bits to the right, use repeated shf.r instructions applied to adjacent words, operating from least-significant word towards most-significant word. At each step, a single word of the shifted result is computed. The most-significant word of the result is computed using a shr.{u32,s32} instruction, which zero or sign fills based on the instruction type.

To shift data sizes greater than 64 bits to the left, use repeated shf.l instructions applied to adjacent words, operating from most-significant word towards least-significant word. At each step, a single word of the shifted result is computed. The least-significant word of the result is computed using a shl instruction.

Use funnel shift to perform 32-bit left or right rotate by supplying the same value for source arguments a and b.

PTX ISA Notes

Introduced in PTX ISA version 3.1.

Target ISA Notes

Requires sm_32 or higher.

Example

shf.l.clamp.b32  r3,r1,r0,16;

// 128-bit left shift; n < 32
// [r7,r6,r5,r4] = [r3,r2,r1,r0] << n
shf.l.clamp.b32  r7,r2,r3,n;
shf.l.clamp.b32  r6,r1,r2,n;
shf.l.clamp.b32  r5,r0,r1,n;
shl.b32          r4,r0,n;

// 128-bit right shift, arithmetic; n < 32
// [r7,r6,r5,r4] = [r3,r2,r1,r0] >> n
shf.r.clamp.b32  r4,r0,r1,n;
shf.r.clamp.b32  r5,r1,r2,n;
shf.r.clamp.b32  r6,r2,r3,n;
shr.s32          r7,r3,n;     // result is sign-extended

shf.r.clamp.b32  r1,r0,r0,n;  // rotate right by n; n < 32
shf.l.clamp.b32  r1,r0,r0,n;  // rotate left by n; n < 32

// extract 32-bits from [r1,r0] starting at position n < 32
shf.r.clamp.b32  r0,r0,r1,n;

9.7.7.8. Logic and Shift Instructions: shl

shl

Shift bits left, zero-fill on right.

Syntax

shl.type d, a, b;

.type = { .b16, .b32, .b64 };

Description

Shift a left by the amount specified by unsigned 32-bit value in b.

Semantics

d = a << b;

Notes

Shift amounts greater than the register width N are clamped to N.

The sizes of the destination and first source operand must match, but not necessarily the type. The b operand must be a 32-bit value, regardless of the instruction type.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Example

shl.b32  q,a,2;

9.7.7.9. Logic and Shift Instructions: shr

shr

Shift bits right, sign or zero-fill on left.

Syntax

shr.type d, a, b;

.type = { .b16, .b32, .b64,
          .u16, .u32, .u64,
          .s16, .s32, .s64 };

Description

Shift a right by the amount specified by unsigned 32-bit value in b. Signed shifts fill with the sign bit, unsigned and untyped shifts fill with 0.

Semantics

d = a >> b;

Notes

Shift amounts greater than the register width N are clamped to N.

The sizes of the destination and first source operand must match, but not necessarily the type. The b operand must be a 32-bit value, regardless of the instruction type.

Bit-size types are included for symmetry with shl.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Target ISA Notes

Supported on all target architectures.

Example

shr.u16  c,a,2;
shr.s32  i,i,1;
shr.b16  k,i,j;

9.7.8. Data Movement and Conversion Instructions

These instructions copy data from place to place, and from state space to state space, possibly converting it from one format to another. mov, ld, ldu, and st operate on both scalar and vector types. The isspacep instruction is provided to query whether a generic address falls within a particular state space window. The cvta instruction converts addresses between generic and const, global, local, or shared state spaces.

Instructions ld, st, suld, and sust support optional cache operations.

The Data Movement and Conversion Instructions are:

• mov

• shfl.sync

• prmt

• ld

• ldu

• st

• st.async

• multimem.ld_reduce, multimem.st, multimem.red

• prefetch, prefetchu

• isspacep

• cvta

• cvt

• cvt.pack

• cp.async

• cp.async.commit_group

• cp.async.wait_group, cp.async.wait_all

• cp.async.bulk

• cp.reduce.async.bulk

• cp.async.bulk.prefetch

• cp.async.bulk.tensor

• cp.reduce.async.bulk.tensor

• cp.async.bulk.prefetch.tensor

• cp.async.bulk.commit_group

• cp.async.bulk.wait_group

• tensormap.replace

9.7.8.1. Cache Operators

PTX ISA version 2.0 introduced optional cache operators on load and store instructions. The cache operators require a target architecture of sm_20 or higher.

Cache operators on load or store instructions are treated as performance hints only. The use of a cache operator on an ld or st instruction does not change the memory consistency behavior of the program.

For sm_20 and higher, the cache operators have the following definitions and behavior.

Table 27 Cache Operators for Memory Load Instructions

Operator	Meaning
.ca	Cache at all levels, likely to be accessed again. The default load instruction cache operation is ld.ca, which allocates cache lines in all levels (L1 and L2) with normal eviction policy. Global data is coherent at the L2 level, but multiple L1 caches are not coherent for global data. If one thread stores to global memory via one L1 cache, and a second thread loads that address via a second L1 cache with ld.ca, the second thread may get stale L1 cache data, rather than the data stored by the first thread. The driver must invalidate global L1 cache lines between dependent grids of parallel threads. Stores by the first grid program are then correctly fetched by the second grid program issuing default ld.ca loads cached in L1.
.cg	Cache at global level (cache in L2 and below, not L1). Use ld.cg to cache loads only globally, bypassing the L1 cache, and cache only in the L2 cache.
.cs	Cache streaming, likely to be accessed once. The ld.cs load cached streaming operation allocates global lines with evict-first policy in L1 and L2 to limit cache pollution by temporary streaming data that may be accessed once or twice. When ld.cs is applied to a Local window address, it performs the ld.lu operation.
.lu	Last use. The compiler/programmer may use ld.lu when restoring spilled registers and popping function stack frames to avoid needless write-backs of lines that will not be used again. The ld.lu instruction performs a load cached streaming operation (ld.cs) on global addresses.
.cv	Don’t cache and fetch again (consider cached system memory lines stale, fetch again). The ld.cv load operation applied to a global System Memory address invalidates (discards) a matching L2 line and re-fetches the line on each new load.

Table 28 Cache Operators for Memory Store Instructions

Operator	Meaning
.wb	Cache write-back all coherent levels. The default store instruction cache operation is st.wb, which writes back cache lines of coherent cache levels with normal eviction policy. If one thread stores to global memory, bypassing its L1 cache, and a second thread in a different SM later loads from that address via a different L1 cache with ld.ca, the second thread may get a hit on stale L1 cache data, rather than get the data from L2 or memory stored by the first thread. The driver must invalidate global L1 cache lines between dependent grids of thread arrays. Stores by the first grid program are then correctly missed in L1 and fetched by the second grid program issuing default ld.ca loads.
.cg	Cache at global level (cache in L2 and below, not L1). Use st.cg to cache global store data only globally, bypassing the L1 cache, and cache only in the L2 cache.
.cs	Cache streaming, likely to be accessed once. The st.cs store cached-streaming operation allocates cache lines with evict-first policy to limit cache pollution by streaming output data.
.wt	Cache write-through (to system memory). The st.wt store write-through operation applied to a global System Memory address writes through the L2 cache.

9.7.8.2. Cache Eviction Priority Hints

PTX ISA version 7.4 adds optional cache eviction priority hints on load and store instructions. Cache eviction priority requires target architecture sm_70 or higher.

Cache eviction priority on load or store instructions is treated as a performance hint. It is supported for .global state space and generic addresses where the address points to .global state space.

Table 29 Cache Eviction Priority Hints for Memory Load and Store Instructions

Cache Eviction Priority	Meaning
evict_normal	Cache data with normal eviction priority. This is the default eviction priority.
evict_first	Data cached with this priority will be first in the eviction priority order and will likely be evicted when cache eviction is required. This priority is suitable for streaming data.
evict_last	Data cached with this priority will be last in the eviction priority order and will likely be evicted only after other data with evict_normal or evict_first eviction priotity is already evicted. This priority is suitable for data that should remain persistent in cache.
evict_unchanged	Do not change eviction priority order as part of this operation.
no_allocate	Do not allocate data to cache. This priority is suitable for streaming data.

9.7.8.3. Data Movement and Conversion Instructions: mov

mov

Set a register variable with the value of a register variable or an immediate value. Take the non-generic address of a variable in global, local, or shared state space.

Syntax

mov.type  d, a;
mov.type  d, sreg;
mov.type  d, avar;       // get address of variable
mov.type  d, avar+imm;   // get address of variable with offset
mov.u32   d, fname;      // get address of device function
mov.u64   d, fname;      // get address of device function
mov.u32   d, kernel;     // get address of entry function
mov.u64   d, kernel;     // get address of entry function

.type = { .pred,
          .b16, .b32, .b64,
          .u16, .u32, .u64,
          .s16, .s32, .s64,
                .f32, .f64 };

Description

Write register d with the value of a.

Operand a may be a register, special register, variable with optional offset in an addressable memory space, or function name.

For variables declared in .const, .global, .local, and .shared state spaces, mov places the non-generic address of the variable (i.e., the address of the variable in its state space) into the destination register. The generic address of a variable in const, global, local, or shared state space may be generated by first taking the address within the state space with mov and then converting it to a generic address using the cvta instruction; alternately, the generic address of a variable declared in const, global, local, or shared state space may be taken directly using the cvta instruction.

Note that if the address of a device function parameter is moved to a register, the parameter will be copied onto the stack and the address will be in the local state space.

Semantics

d = a;
d = sreg;
d = &avar;        // address is non-generic; i.e., within the variable's declared state space
d = &avar+imm;

Notes

• Although only predicate and bit-size types are required, we include the arithmetic types for the programmer’s convenience: their use enhances program readability and allows additional type checking.

• When moving address of a kernel or a device function, only .u32 or .u64 instruction types are allowed. However, if a signed type is used, it is not treated as a compilation error. The compiler issues a warning in this case.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Taking the address of kernel entry functions requires PTX ISA version 3.1 or later. Kernel function addresses should only be used in the context of CUDA Dynamic Parallelism system calls. See the CUDA Dynamic Parallelism Programming Guide for details.

Target ISA Notes

mov.f64 requires sm_13 or higher.

Taking the address of kernel entry functions requires sm_35 or higher.

Examples

mov.f32  d,a;
mov.u16  u,v;
mov.f32  k,0.1;
mov.u32  ptr, A;        // move address of A into ptr
mov.u32  ptr, A[5];     // move address of A[5] into ptr
mov.u32  ptr, A+20;     // move address with offset into ptr
mov.u32  addr, myFunc;  // get address of device function 'myFunc'
mov.u64  kptr, main;    // get address of entry function 'main'

9.7.8.4. Data Movement and Conversion Instructions: mov

mov

Move vector-to-scalar (pack) or scalar-to-vector (unpack).

Syntax

mov.type  d, a;

.type = { .b16, .b32, .b64, .b128 };

Description

Write scalar register d with the packed value of vector register a, or write vector register d with the unpacked values from scalar register a.

When destination operand d is a vector register, the sink symbol '_' may be used for one or more elements provided that at least one element is a scalar register.

For bit-size types, mov may be used to pack vector elements into a scalar register or unpack sub-fields of a scalar register into a vector. Both the overall size of the vector and the size of the scalar must match the size of the instruction type.

Semantics

// pack two 8-bit elements into .b16
d = a.x | (a.y << 8)
// pack four 8-bit elements into .b32
d = a.x | (a.y << 8)  | (a.z << 16) | (a.w << 24)
// pack two 16-bit elements into .b32
d = a.x | (a.y << 16)
// pack four 16-bit elements into .b64
d = a.x | (a.y << 16)  | (a.z << 32) | (a.w << 48)
// pack two 32-bit elements into .b64
d = a.x | (a.y << 32)
// pack four 32-bit elements into .b128
d = a.x | (a.y << 32)  | (a.z << 64) | (a.w << 96)
// pack two 64-bit elements into .b128
d = a.x | (a.y << 64)

// unpack 8-bit elements from .b16
{ d.x, d.y } = { a[0..7], a[8..15] }
// unpack 8-bit elements from .b32
{ d.x, d.y, d.z, d.w }
        { a[0..7], a[8..15], a[16..23], a[24..31] }

// unpack 16-bit elements from .b32
{ d.x, d.y }  = { a[0..15], a[16..31] }
// unpack 16-bit elements from .b64
{ d.x, d.y, d.z, d.w } =
        { a[0..15], a[16..31], a[32..47], a[48..63] }

// unpack 32-bit elements from .b64
{ d.x, d.y } = { a[0..31], a[32..63] }

// unpack 32-bit elements from .b128
{ d.x, d.y, d.z, d.w } =
        { a[0..31], a[32..63], a[64..95], a[96..127] }
// unpack 64-bit elements from .b128
{ d.x, d.y } = { a[0..63], a[64..127] }

PTX ISA Notes

Introduced in PTX ISA version 1.0.

Support for .b128 type introduced in PTX ISA version 8.3.

Target ISA Notes

Supported on all target architectures.

Support for .b128 type requires sm_70 or higher.

Examples

mov.b32 %r1,{a,b};      // a,b have type .u16
mov.b64 {lo,hi}, %x;    // %x is a double; lo,hi are .u32
mov.b32 %r1,{x,y,z,w};  // x,y,z,w have type .b8
mov.b32 {r,g,b,a},%r1;  // r,g,b,a have type .u8
mov.b64 {%r1, _}, %x;   // %x is.b64, %r1 is .b32
mov.b128 {%b1, %b2}, %y;   // %y is.b128, %b1 and % b2 are .b64
mov.b128 %y, {%b1, %b2};   // %y is.b128, %b1 and % b2 are .b64

9.7.8.5. Data Movement and Conversion Instructions: shfl (deprecated)

shfl (deprecated)

Register data shuffle within threads of a warp.

Syntax

shfl.mode.b32  d[|p], a, b, c;

.mode = { .up, .down, .bfly, .idx };

Deprecation Note

The shfl instruction without a .sync qualifier is deprecated in PTX ISA version 6.0.

• Support for this instruction with .target lower than sm_70 may be removed in a future PTX ISA version.

Removal Note

Support for shfl instruction without a .sync qualifier is removed in PTX ISA version 6.4 for .targetsm_70 or higher.

Description

Exchange register data between threads of a warp.

Each thread in the currently executing warp will compute a source lane index j based on input operands b and c and the mode. If the computed source lane index j is in range, the thread will copy the input operand a from lane j into its own destination register d; otherwise, the thread will simply copy its own input a to destination d. The optional destination predicate p is set to True if the computed source lane is in range, and otherwise set to False.

Note that an out of range value of b may still result in a valid computed source lane index j. In this case, a data transfer occurs and the destination predicate p is True.

Note that results are undefined in divergent control flow within a warp, if an active thread sources a register from an inactive thread.

Operand b specifies a source lane or source lane offset, depending on the mode.

Operand c contains two packed values specifying a mask for logically splitting warps into sub-segments and an upper bound for clamping the source lane index.

Semantics

lane[4:0]  = [Thread].laneid;  // position of thread in warp
bval[4:0] = b[4:0];            // source lane or lane offset (0..31)
cval[4:0] = c[4:0];            // clamp value
mask[4:0] = c[12:8];

// get value of source register a if thread is active and
// guard predicate true, else unpredictable
if (isActive(Thread) && isGuardPredicateTrue(Thread)) {
    SourceA[lane] = a;
} else {
    // Value of SourceA[lane] is unpredictable for
    // inactive/predicated-off threads in warp
}
maxLane = (lane[4:0] & mask[4:0]) | (cval[4:0] & ~mask[4:0]);
minLane = (lane[4:0] & mask[4:0]);

switch (.mode) {
    case .up:    j = lane - bval; pval = (j >= maxLane); break;
    case .down:  j = lane + bval; pval = (j <= maxLane); break;
    case .bfly:  j = lane ^ bval; pval = (j <= maxLane); break;
    case .idx:   j = minLane  | (bval[4:0] & ~mask[4:0]);
                                 pval = (j <= maxLane); break;
}
if (!pval) j = lane;  // copy from own lane
d = SourceA[j];       // copy input a from lane j
if (dest predicate selected)
    p = pval;

PTX ISA Notes

Introduced in PTX ISA version 3.0.

Deprecated in PTX ISA version 6.0 in favor of shfl.sync.

Not supported in PTX ISA version 6.4 for .target sm_70 or higher.

Target ISA Notes

shfl requires sm_30 or higher.

shfl is not supported on sm_70 or higher starting PTX ISA version 6.4.

Examples

    // Warp-level INCLUSIVE PLUS SCAN:
    //
    // Assumes input in following registers:
    //     - Rx  = sequence value for this thread
    //
    shfl.up.b32  Ry|p, Rx, 0x1,  0x0;
@p  add.f32      Rx, Ry, Rx;
    shfl.up.b32  Ry|p, Rx, 0x2,  0x0;
@p  add.f32      Rx, Ry, Rx;
    shfl.up.b32  Ry|p, Rx, 0x4,  0x0;
@p  add.f32      Rx, Ry, Rx;
    shfl.up.b32  Ry|p, Rx, 0x8,  0x0;
@p  add.f32      Rx, Ry, Rx;
    shfl.up.b32  Ry|p, Rx, 0x10, 0x0;
@p  add.f32      Rx, Ry, Rx;


    // Warp-level INCLUSIVE PLUS REVERSE-SCAN:
    //
    // Assumes input in following registers:
    //     - Rx  = sequence value for this thread
    //
    shfl.down.b32  Ry|p, Rx, 0x1,  0x1f;
@p  add.f32        Rx, Ry, Rx;
    shfl.down.b32  Ry|p, Rx, 0x2,  0x1f;
@p  add.f32        Rx, Ry, Rx;
    shfl.down.b32  Ry|p, Rx, 0x4,  0x1f;
@p  add.f32        Rx, Ry, Rx;
    shfl.down.b32  Ry|p, Rx, 0x8,  0x1f;
@p  add.f32        Rx, Ry, Rx;
    shfl.down.b32  Ry|p, Rx, 0x10, 0x1f;
@p  add.f32        Rx, Ry, Rx;


    // BUTTERFLY REDUCTION:
    //
    // Assumes input in following registers:
    //     - Rx  = sequence value for this thread
    //
    shfl.bfly.b32  Ry, Rx, 0x10, 0x1f;   // no predicate dest
    add.f32        Rx, Ry, Rx;
    shfl.bfly.b32  Ry, Rx, 0x8,  0x1f;
    add.f32        Rx, Ry, Rx;
    shfl.bfly.b32  Ry, Rx, 0x4,  0x1f;
    add.f32        Rx, Ry, Rx;
    shfl.bfly.b32  Ry, Rx, 0x2,  0x1f;
    add.f32        Rx, Ry, Rx;
    shfl.bfly.b32  Ry, Rx, 0x1,  0x1f;
    add.f32        Rx, Ry, Rx;
    //
    // All threads now hold sum in Rx

9.7.8.6. Data Movement and Conversion Instructions: shfl.sync

shfl.sync

Register data shuffle within threads of a warp.

Syntax

shfl.sync.mode.b32  d[|p], a, b, c, membermask;

.mode = { .up, .down, .bfly, .idx };

Description

Exchange register data between threads of a warp.

shfl.sync will cause executing thread to wait until all non-exited threads corresponding to membermask have executed shfl.sync with the same qualifiers and same membermask value before resuming execution.

Operand membermask specifies a 32-bit integer which is a mask indicating threads participating in barrier where the bit position corresponds to thread’s laneid.

shfl.sync exchanges register data between threads in membermask.

Each thread in the currently executing warp will compute a source lane index j based on input operands b and c and the mode. If the computed source lane index j is in range, the thread will copy the input operand a from lane j into its own destination register d; otherwise, the thread will simply copy its own input a to destination d. The optional destination predicate p is set to True if the computed source lane is in range, and otherwise set to False.

Note that an out of range value of b may still result in a valid computed source lane index j. In this case, a data transfer occurs and the destination predicate p is True.

Note that results are undefined if a thread sources a register from an inactive thread or a thread that is not in membermask.

Operand b specifies a source lane or source lane offset, depending on the mode.

Operand c contains two packed values specifying a mask for logically splitting warps into sub-segments and an upper bound for clamping the source lane index.

The behavior of shfl.sync is undefined if the executing thread is not in the membermask.

Note

For .target sm_6x or below, all threads in membermask must execute the same shfl.sync instruction in convergence, and only threads belonging to some membermask can be active when the shfl.sync instruction is executed. Otherwise, the behavior is undefined.

Semantics

// wait for all threads in membermask to arrive
wait_for_specified_threads(membermask);

lane[4:0]  = [Thread].laneid;  // position of thread in warp
bval[4:0] = b[4:0];            // source lane or lane offset (0..31)
cval[4:0] = c[4:0];            // clamp value
segmask[4:0] = c[12:8];

// get value of source register a if thread is active and
// guard predicate true, else unpredictable
if (isActive(Thread) && isGuardPredicateTrue(Thread)) {
    SourceA[lane] = a;
} else {
    // Value of SourceA[lane] is unpredictable for
    // inactive/predicated-off threads in warp
}
maxLane = (lane[4:0] & segmask[4:0]) | (cval[4:0] & ~segmask[4:0]);
minLane = (lane[4:0] & segmask[4:0]);

switch (.mode) {
    case .up:    j = lane - bval; pval = (j >= maxLane); break;
    case .down:  j = lane + bval; pval = (j <= maxLane); break;
    case .bfly:  j = lane ^ bval; pval = (j <= maxLane); break;
    case .idx:   j = minLane  | (bval[4:0] & ~segmask[4:0]);
                                 pval = (j <= maxLane); break;
}
if (!pval) j = lane;  // copy from own lane
d = SourceA[j];       // copy input a from lane j
if (dest predicate selected)
    p = pval;

PTX ISA Notes

Introduced in PTX ISA version 6.0.

Target ISA Notes

Requires sm_30 or higher.

Examples

shfl.sync.up.b32  Ry|p, Rx, 0x1,  0x0, 0xffffffff;

9.7.8.7. Data Movement and Conversion Instructions: prmt

prmt

Permute bytes from register pair.

Syntax

prmt.b32{.mode}  d, a, b, c;

.mode = { .f4e, .b4e, .rc8, .ecl, .ecr, .rc16 };

Description

Pick four arbitrary bytes from two 32-bit registers, and reassemble them into a 32-bit destination register.

In the generic form (no mode specified), the permute control consists of four 4-bit selection values. The bytes in the two source registers are numbered from 0 to 7: {b, a} = {{b7, b6, b5, b4}, {b3, b2, b1, b0}}. For each byte in the target register, a 4-bit selection value is defined.

The 3 lsbs of the selection value specify which of the 8 source bytes should be moved into the target position. The msb defines if the byte value should be copied, or if the sign (msb of the byte) should be replicated over all 8 bits of the target position (sign extend of the byte value); msb=0 means copy the literal value; msb=1 means replicate the sign. Note that the sign extension is only performed as part of generic form.

Thus, the four 4-bit values fully specify an arbitrary byte permute, as a 16b permute code.

default mode	d.b3 source select	d.b2 source select	d.b1 source select	d.b0 source select
index	c[15:12]	c[11:8]	c[7:4]	c[3:0]

The more specialized form of the permute control uses the two lsb’s of operand c (which is typically an address pointer) to control the byte extraction.

mode	selector c[1:0]	d.b3 source	d.b2 source	d.b1 source	d.b0 source
f4e (forward 4 extract)	0	3	2	1	0
	1	4	3	2	1
	2	5	4	3	2
	3	6	5	4	3
b4e (backward 4 extract)	0	5	6	7	0
	1	6	7	0	1
	2	7	0	1	2
	3	0	1	2	3
rc8 (replicate 8)	0	0	0	0	0
	1	1	1	1	1
	2	2	2	2	2
	3	3	3	3	3
ecl (edge clamp left)	0	3	2	1	0
	1	3	2	1	1
	2	3	2	2	2
	3	3	3	3	3
ecr (edge clamp right)	0	0	0	0	0
	1	1	1	1	0
	2	2	2	1	0
	3	3	2	1	0
rc16 (replicate 16)	0	1	0	1	0
	1	3	2	3	2
	2	1	0	1	0
	3	3	2	3	2

Semantics

tmp64 = (b<<32) | a;  // create 8 byte source

if ( ! mode ) {
   ctl[0] = (c >>  0) & 0xf;
   ctl[1] = (c >>  4) & 0xf;
   ctl[2] = (c >>  8) & 0xf;
   ctl[3] = (c >> 12) & 0xf;
} else {
   ctl[0] = ctl[1] = ctl[2] = ctl[3] = (c >>  0) & 0x3;
}

tmp[07:00] = ReadByte( mode, ctl[0], tmp64 );
tmp[15:08] = ReadByte( mode, ctl[1], tmp64 );
tmp[23:16] = ReadByte( mode, ctl[2], tmp64 );
tmp[31:24] = ReadByte( mode, ctl[3], tmp64 );

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Target ISA Notes

prmt requires sm_20 or higher.

Examples

prmt.b32      r1, r2, r3, r4;
prmt.b32.f4e  r1, r2, r3, r4;

9.7.8.8. Data Movement and Conversion Instructions: ld

ld

Load a register variable from an addressable state space variable.

Syntax

ld{.weak}{.ss}{.cop}{.level::cache_hint}{.level::prefetch_size}{.vec}.type  d, [a]{.unified}{, cache-policy};

ld{.weak}{.ss}{.level::eviction_priority}{.level::cache_hint}{.level::prefetch_size}{.vec}.type  d, [a]{.unified}{, cache-policy};

ld.volatile{.ss}{.level::prefetch_size}{.vec}.type  d, [a];

ld.relaxed.scope{.ss}{.level::eviction_priority}{.level::cache_hint}{.level::prefetch_size}{.vec}.type  d, [a]{, cache-policy};

ld.acquire.scope{.ss}{.level::eviction_priority}{.level::cache_hint}{.level::prefetch_size}{.vec}.type  d, [a]{, cache-policy};

ld.mmio.relaxed.sys{.global}.type  d, [a];

.ss =                       { .const, .global, .local, .param{::entry, ::func}, .shared{::cta, ::cluster} };
.cop =                      { .ca, .cg, .cs, .lu, .cv };
.level::eviction_priority = { .L1::evict_normal, .L1::evict_unchanged,
                              .L1::evict_first, .L1::evict_last, .L1::no_allocate };
.level::cache_hint =        { .L2::cache_hint };
.level::prefetch_size =     { .L2::64B, .L2::128B, .L2::256B }
.scope =                    { .cta, .cluster, .gpu, .sys };
.vec =                      { .v2, .v4 };
.type =                     { .b8, .b16, .b32, .b64, .b128,
                              .u8, .u16, .u32, .u64,
                              .s8, .s16, .s32, .s64,
                              .f32, .f64 };

Description

Load register variable d from the location specified by the source address operand a in specified state space. If no state space is given, perform the load using Generic Addressing.

If no sub-qualifier is specified with .shared state space, then ::cta is assumed by default.

Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands

If no sub-qualifier is specified with .param state space, then :

• ::func is assumed when access is inside a device function.

• ::entry is assumed when accessing kernel function parameters from entry function. Otherwise, when accessing device function parameters or any other .param variables from entry function ::func is assumed by default.

For ld.param::entry instruction, operand a must be a kernel parameter address, otherwise behavior is undefined. For ld.param::func instruction, operand a must be a device function parameter address, otherwise behavior is undefined.

Instruction ld.param{::func} used for reading value returned from device function call cannot be predicated. See Parameter State Space and Function Declarations and Definitions for descriptions of the proper use of ld.param.

The .relaxed and .acquire qualifiers indicate memory synchronization as described in the Memory Consistency Model. The .scope qualifier indicates the set of threads with which an ld.relaxed or ld.acquire instruction can directly synchronize¹. The .weak qualifier indicates a memory instruction with no synchronization. The effects of this instruction become visible to other threads only when synchronization is established by other means.

The semantic details of .mmio qualifier are described in the Memory Consistency Model. Only .sys thread scope is valid for ld.mmio operation. The qualifiers .mmio and .relaxed must be specified together.

The .weak, .volatile, .relaxed and .acquire qualifiers are mutually exclusive. When none of these is specified, the .weak qualifier is assumed by default.

An ld.volatile operation is always performed and it will not be reordered with respect to other volatile operations to the same memory location. volatile and non-volatile load operations to the same memory location may be reordered. ld.volatile has the same memory synchronization semantics as ld.relaxed.sys.

The qualifiers .volatile, .relaxed and .acquire may be used only with .global and .shared spaces and with generic addressing, where the address points to .global or .shared space. Cache operations are not permitted with these qualifiers. The qualifier .mmio may be used only with .global space and with generic addressing, where the address points to .global space.

The optional qualifier .unified must be specified on operand a if a is the address of a variable declared with .unified attribute as described in Variable and Function Attribute Directive: .attribute.

The qualifier .level::eviction_priority specifies the eviction policy that will be used during memory access.

The .level::prefetch_size qualifier is a hint to fetch additional data of the specified size into the respective cache level.The sub-qualifier prefetch_size can be set to either of 64B, 128B, 256B thereby allowing the prefetch size to be 64 Bytes, 128 Bytes or 256 Bytes respectively.

The qualifier .level::prefetch_size may only be used with .global state space and with generic addressing where the address points to .global state space. If the generic address does not fall within the address window of the global memory, then the prefetching behavior is undefined.

The .level::prefetch_size qualifier is treated as a performance hint only.

When the optional argument cache-policy is specified, the qualifier .level::cache_hint is required. The 64-bit operand cache-policy specifies the cache eviction policy that may be used during the memory access.

The qualifiers .unified and .level::cache_hint are only supported for .global state space and for generic addressing where the address points to the .global state space.

cache-policy is a hint to the cache subsystem and may not always be respected. It is treated as a performance hint only, and does not change the memory consistency behavior of the program.

¹ This synchronization is further extended to other threads through the transitive nature of causality order, as described in the memory consistency model.

Semantics

d = a;             // named variable a
d = *(&a+immOff)   // variable-plus-offset
d = *a;            // register
d = *(a+immOff);   // register-plus-offset
d = *(immAddr);    // immediate address

Notes

Destination d must be in the .reg state space.

A destination register wider than the specified type may be used. The value loaded is sign-extended to the destination register width for signed integers, and is zero-extended to the destination register width for unsigned and bit-size types. See Table 25 for a description of these relaxed type-checking rules.

.f16 data may be loaded using ld.b16, and then converted to .f32 or .f64 using cvt or can be used in half precision floating point instructions.

.f16x2 data may be loaded using ld.b32 and then used in half precision floating point instructions.

PTX ISA Notes

ld introduced in PTX ISA version 1.0. ld.volatile introduced in PTX ISA version 1.1.

Generic addressing and cache operations introduced in PTX ISA version 2.0.

Support for scope qualifier, .relaxed, .acquire, .weak qualifiers introduced in PTX ISA version 6.0.

Support for generic addressing of .const space added in PTX ISA version 3.1.

Support for .level::eviction_priority, .level::prefetch_size and .level::cache_hint qualifiers introduced in PTX ISA version 7.4.

Support for .cluster scope qualifier introduced in PTX ISA version 7.8.

Support for ::cta and ::cluster sub-qualifiers introduced in PTX ISA version 7.8.

Support for .unified qualifier introduced in PTX ISA version 8.0.

Support for .mmio qualifier introduced in PTX ISA version 8.2.

Support for ::entry and ::func sub-qualifiers on .param space introduced in PTX ISA version 8.3.

Support for .b128 type introduced in PTX ISA version 8.3.

Support for .sys scope with .b128 type introduced in PTX ISA version 8.4.

Target ISA Notes

ld.f64 requires sm_13 or higher.

Support for scope qualifier, .relaxed, .acquire, .weak qualifiers require sm_70 or higher.

Generic addressing requires sm_20 or higher.

Cache operations require sm_20 or higher.

Support for .level::eviction_priority qualifier requires sm_70 or higher.

Support for .level::prefetch_size qualifier requires sm_75 or higher.

Support for .L2::256B and .L2::cache_hint qualifiers requires sm_80 or higher.

Support for .cluster scope qualifier requires sm_90 or higher.

Sub-qualifier ::cta requires sm_30 or higher.

Sub-qualifier ::cluster requires sm_90 or higher.

Support for .unified qualifier requires sm_90 or higher.

Support for .mmio qualifier requires sm_70 or higher.

Support for .b128 type requires sm_70 or higher.

Examples

ld.global.f32    d,[a];
ld.shared.v4.b32 Q,[p];
ld.const.s32     d,[p+4];
ld.local.b32     x,[p+-8]; // negative offset
ld.local.b64     x,[240];  // immediate address

ld.global.b16    %r,[fs];  // load .f16 data into 32-bit reg
cvt.f32.f16      %r,%r;    // up-convert f16 data to f32

ld.global.b32    %r0, [fs];     // load .f16x2 data in 32-bit reg
ld.global.b32    %r1, [fs + 4]; // load .f16x2 data in 32-bit reg
add.rn.f16x2     %d0, %r0, %r1; // addition of f16x2 data
ld.global.relaxed.gpu.u32 %r0, [gbl];
ld.shared.acquire.gpu.u32 %r1, [sh];
ld.global.relaxed.cluster.u32 %r2, [gbl];
ld.shared::cta.acquire.gpu.u32 %r2, [sh + 4];
ld.shared::cluster.u32 %r3, [sh + 8];
ld.global.mmio.relaxed.sys.u32 %r3, [gbl];

ld.global.f32    d,[ugbl].unified;
ld.b32           %r0, [%r1].unified;

ld.global.L1::evict_last.u32  d, [p];

ld.global.L2::64B.b32   %r0, [gbl]; // Prefetch 64B to L2
ld.L2::128B.f64         %r1, [gbl]; // Prefetch 128B to L2
ld.global.L2::256B.f64  %r2, [gbl]; // Prefetch 256B to L2

createpolicy.fractional.L2::evict_last.L2::evict_unchanged.b64 cache-policy, 1;
ld.global.L2::cache_hint.b64  x, [p], cache-policy;
ld.param::entry.b32 %rp1, [kparam1];

ld.global.b128   %r0, [gbl];   // 128-bit load

9.7.8.9. Data Movement and Conversion Instructions: ld.global.nc

ld.global.nc

Load a register variable from global state space via non-coherent cache.

Syntax

ld.global{.cop}.nc{.level::cache_hint}{.level::prefetch_size}.type                 d, [a]{, cache-policy};
ld.global{.cop}.nc{.level::cache_hint}{.level::prefetch_size}.vec.type             d, [a]{, cache-policy};

ld.global.nc{.level::eviction_priority}{.level::cache_hint}{.level::prefetch_size}.type      d, [a]{, cache-policy};
ld.global.nc{.level::eviction_priority}{.level::cache_hint}{.level::prefetch_size}.vec.type  d, [a]{, cache-policy};

.cop  =                     { .ca, .cg, .cs };     // cache operation
.level::eviction_priority = { .L1::evict_normal, .L1::evict_unchanged,
                              .L1::evict_first, .L1::evict_last, .L1::no_allocate};
.level::cache_hint =        { .L2::cache_hint };
.level::prefetch_size =     { .L2::64B, .L2::128B, .L2::256B }
.vec  =                     { .v2, .v4 };
.type =                     { .b8, .b16, .b32, .b64, .b128,
                              .u8, .u16, .u32, .u64,
                              .s8, .s16, .s32, .s64,
                              .f32, .f64 };

Description

Load register variable d from the location specified by the source address operand a in the global state space, and optionally cache in non-coherent read-only cache.

Note

On some architectures, the texture cache is larger, has higher bandwidth, and longer latency than the global memory cache. For applications with sufficient parallelism to cover the longer latency, ld.global.nc should offer better performance than ld.global on such architectures.

The address operand a may contain a generic address pointing to the .global state space. Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands

The qualifier .level::eviction_priority specifies the eviction policy that will be used during memory access.

The .level::prefetch_size qualifier is a hint to fetch additional data of the specified size into the respective cache level.The sub-qualifier prefetch_size can be set to either of 64B, 128B, 256B thereby allowing the prefetch size to be 64 Bytes, 128 Bytes or 256 Bytes respectively.

The .level::prefetch_size qualifier is treated as a performance hint only.

When the optional argument cache-policy is specified, the qualifier .level::cache_hint is required. The 64-bit operand cache-policy specifies the cache eviction policy that may be used during the memory access.

cache-policy is a hint to the cache subsystem and may not always be respected. It is treated as a performance hint only, and does not change the memory consistency behavior of the program.

Semantics

d = a;             // named variable a
d = *(&a+immOff)   // variable-plus-offset
d = *a;            // register
d = *(a+immOff);   // register-plus-offset
d = *(immAddr);    // immediate address

Notes

Destination d must be in the .reg state space.

A destination register wider than the specified type may be used. The value loaded is sign-extended to the destination register width for signed integers, and is zero-extended to the destination register width for unsigned and bit-size types.

.f16 data may be loaded using ld.b16, and then converted to .f32 or .f64 using cvt.

PTX ISA Notes

Introduced in PTX ISA version 3.1.

Support for .level::eviction_priority, .level::prefetch_size and .level::cache_hint qualifiers introduced in PTX ISA version 7.4.

Support for .b128 type introduced in PTX ISA version 8.3.

Target ISA Notes

Requires sm_32 or higher.

Support for .level::eviction_priority qualifier requires sm_70 or higher.

Support for .level::prefetch_size qualifier requires sm_75 or higher.

Support for .level::cache_hint qualifier requires sm_80 or higher.

Support for .b128 type requires sm_70 or higher.

Examples

ld.global.nc.f32           d, [a];
ld.gloal.nc.L1::evict_last.u32 d, [a];

createpolicy.fractional.L2::evict_last.b64 cache-policy, 0.5;
ld.global.nc.L2::cache_hint.f32  d, [a], cache-policy;

ld.global.nc.L2::64B.b32      d,  [a];     // Prefetch 64B to L2
ld.global.nc.L2::256B.f64     d,  [a];     // Prefetch 256B to L2

ld.global.nc.b128             d,  [a];

9.7.8.10. Data Movement and Conversion Instructions: ldu

ldu

Load read-only data from an address that is common across threads in the warp.

Syntax

ldu{.ss}.type      d, [a];       // load from address
ldu{.ss}.vec.type  d, [a];       // vec load from address

.ss   = { .global };             // state space
.vec  = { .v2, .v4 };
.type = { .b8, .b16, .b32, .b64, .b128,
          .u8, .u16, .u32, .u64,
          .s8, .s16, .s32, .s64,
                     .f32, .f64 };

Description

Load read-only data into register variable d from the location specified by the source address operand a in the global state space, where the address is guaranteed to be the same across all threads in the warp. If no state space is given, perform the load using Generic Addressing.

Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands

Semantics

d = a;             // named variable a
d = *(&a+immOff)   // variable-plus-offset
d = *a;            // register
d = *(a+immOff);   // register-plus-offset
d = *(immAddr);    // immediate address

Notes

Destination d must be in the .reg state space.

A destination register wider than the specified type may be used. The value loaded is sign-extended to the destination register width for signed integers, and is zero-extended to the destination register width for unsigned and bit-size types. See Table 25 for a description of these relaxed type-checking rules.

.f16 data may be loaded using ldu.b16, and then converted to .f32 or .f64 using cvtor can be used in half precision floating point instructions.

.f16x2 data may be loaded using ldu.b32 and then used in half precision floating point instructions.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Support for .b128 type introduced in PTX ISA version 8.3.

Target ISA Notes

ldu.f64 requires sm_13 or higher.

Support for .b128 type requires sm_70 or higher.

Examples

ldu.global.f32    d,[a];
ldu.global.b32    d,[p+4];
ldu.global.v4.f32 Q,[p];
ldu.global.b128   d,[a];

9.7.8.11. Data Movement and Conversion Instructions: st

st

Store data to an addressable state space variable.

Syntax

st{.weak}{.ss}{.cop}{.level::cache_hint}{.vec}.type   [a], b{, cache-policy};
st{.weak}{.ss}{.level::eviction_priority}{.level::cache_hint}{.vec}.type
                                                      [a], b{, cache-policy};
st.volatile{.ss}{.vec}.type                           [a], b;
st.relaxed.scope{.ss}{.level::eviction_priority}{.level::cache_hint}{.vec}.type
                                                      [a], b{, cache-policy};
st.release.scope{.ss}{.level::eviction_priority}{.level::cache_hint}{.vec}.type
                                                      [a], b{, cache-policy};
st.mmio.relaxed.sys{.global}.type         [a], b;

.ss =                       { .global, .local, .param{::func}, .shared{::cta, ::cluster} };
.level::eviction_priority = { .L1::evict_normal, .L1::evict_unchanged,
                              .L1::evict_first, .L1::evict_last, .L1::no_allocate };
.level::cache_hint =        { .L2::cache_hint };
.cop =                      { .wb, .cg, .cs, .wt };
.sem =                      { .relaxed, .release };
.scope =                    { .cta, .cluster, .gpu, .sys };
.vec =                      { .v2, .v4 };
.type =                     { .b8, .b16, .b32, .b64, .b128,
                              .u8, .u16, .u32, .u64,
                              .s8, .s16, .s32, .s64,
                              .f32, .f64 };

Description

Store the value of operand b in the location specified by the destination address operand a in specified state space. If no state space is given, perform the store using Generic Addressing. Stores to const memory are illegal.

If no sub-qualifier is specified with .shared state space, then ::cta is assumed by default.

Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands

If .param is specified without any sub-qualifiers then it defaults to .param::func.

Instruction st.param{::func} used for passing arguments to device function cannot be predicated. See Parameter State Space and Function Declarations and Definitions for descriptions of the proper use of st.param.

The qualifiers .relaxed and .release indicate memory synchronization as described in the Memory Consistency Model. The .scope qualifier indicates the set of threads with which an st.relaxed or st.release instruction can directly synchronize¹. The .weak qualifier indicates a memory instruction with no synchronization. The effects of this instruction become visible to other threads only when synchronization is established by other means.

The semantic details of .mmio qualifier are described in the Memory Consistency Model. Only .sys thread scope is valid for st.mmio operation. The qualifiers .mmio and .relaxed must be specified together.

The .weak, .volatile, .relaxed and .release qualifiers are mutually exclusive. When none of these is specified, the .weak qualifier is assumed by default.

An st.volatile operation is always performed and it will not be reordered with respect to other volatile operations to the same memory location. st.volatile has the same memory synchronization semantics as st.relaxed.sys.

The qualifiers .volatile, .relaxed and .release may be used only with .global and .shared spaces and with generic addressing, where the address points to .global or .shared space. Cache operations are not permitted with these qualifiers. The qualifier .mmio may be used only with .global space and with generic addressing, where the address points to .global space.

The qualifier .level::eviction_priority specifies the eviction policy that will be used during memory access.

When the optional argument cache-policy is specified, the qualifier .level::cache_hint is required. The 64-bit operand cache-policy specifies the cache eviction policy that may be used during the memory access.

The qualifier .level::cache_hint is only supported for .global state space and for generic addressing where the address points to the .global state space.

cache-policy is a hint to the cache subsystem and may not always be respected. It is treated as a performance hint only, and does not change the memory consistency behavior of the program.

¹ This synchronization is further extended to other threads through the transitive nature of causality order, as described in the memory consistency model.

Semantics

d = a;                // named variable d
*(&a+immOffset) = b;            // variable-plus-offset
*a = b;               // register
*(a+immOffset) = b;   // register-plus-offset
*(immAddr) = b;       // immediate address

Notes

Operand b must be in the .reg state space.

A source register wider than the specified type may be used. The lower n bits corresponding to the instruction-type width are stored to memory. See Table 24 for a description of these relaxed type-checking rules.

.f16 data resulting from a cvt instruction may be stored using st.b16.

.f16x2 data may be stored using st.b32.

PTX ISA Notes

st introduced in PTX ISA version 1.0. st.volatile introduced in PTX ISA version 1.1.

Generic addressing and cache operations introduced in PTX ISA version 2.0.

Support for scope qualifier, .relaxed, .release, .weak qualifiers introduced in PTX ISA version 6.0.

Support for .level::eviction_priority and .level::cache_hint qualifiers introduced in PTX ISA version 7.4.

Support for .cluster scope qualifier introduced in PTX ISA version 7.8.

Support for ::cta and ::cluster sub-qualifiers introduced in PTX ISA version 7.8.

Support for .mmio qualifier introduced in PTX ISA version 8.2.

Support for ::func sub-qualifier on .param space introduced in PTX ISA version 8.3.

Support for .b128 type introduced in PTX ISA version 8.3.

Support for .sys scope with .b128 type introduced in PTX ISA version 8.4.

Target ISA Notes

st.f64 requires sm_13 or higher.

Support for scope qualifier, .relaxed, .release, .weak qualifiers require sm_70 or higher.

Generic addressing requires sm_20 or higher.

Cache operations require sm_20 or higher.

Support for .level::eviction_priority qualifier requires sm_70 or higher.

Support for .level::cache_hint qualifier requires sm_80 or higher.

Support for .cluster scope qualifier requires sm_90 or higher.

Sub-qualifier ::cta requires sm_30 or higher.

Sub-qualifier ::cluster requires sm_90 or higher.

Support for .mmio qualifier requires sm_70 or higher.

Support for .b128 type requires sm_70 or higher.

Examples

st.global.f32    [a],b;
st.local.b32     [q+4],a;
st.global.v4.s32 [p],Q;
st.local.b32     [q+-8],a; // negative offset
st.local.s32     [100],r7; // immediate address

cvt.f16.f32      %r,%r;    // %r is 32-bit register
st.b16           [fs],%r;  // store lower
st.global.relaxed.sys.u32 [gbl], %r0;
st.shared.release.cta.u32 [sh], %r1;
st.global.relaxed.cluster.u32 [gbl], %r2;
st.shared::cta.release.cta.u32 [sh + 4], %r1;
st.shared::cluster.u32 [sh + 8], %r1;
st.global.mmio.relaxed.sys.u32 [gbl], %r1;

st.global.L1::no_allocate.f32 [p], a;

createpolicy.fractional.L2::evict_last.b64 cache-policy, 0.25;
st.global.L2::cache_hint.b32  [a], b, cache-policy;

st.param::func.b64 [param1], %rp1;

st.global.b128  [a], b;  // 128-bit store

9.7.8.12. Data Movement and Conversion Instructions: st.async

st.async

Asynchronous store operation on shared memory.

Syntax

st.async{.weak}{.ss}{.completion_mechanism}{.vec}.type [a], b, [mbar];

.ss   =                 { .shared::cluster };
.type =                 { .b32, .b64,
                          .u32, .u64,
                          .s32, .s64,
                          .f32, .f64 };
.vec  =                 { .v2, .v4 };
.completion_mechanism = { .mbarrier::complete_tx::bytes };

Description

st.async is a non-blocking instruction which initiates an asynchronous store operation that stores the value specified by source operand b to the destination memory location specified by operand a.

The modifier .completion_mechanism specifies that upon completion of the asynchronous operation, complete-tx operation, with completeCount argument equal to amount of data stored in bytes, will be performed on the mbarrier object specified by the operand mbar.

Operand a represents destination address and must be a register or of the form register + immOff as described in Addresses as Operands.

The shared memory addresses of destination operand a and the mbarrier object mbar, must meet all of the following conditions:

• They belong to the same CTA.

• They are different to the CTA of the executing thread but must be within the same cluster.

Otherwise, the behavior is undefined.

The state space of the address {.ss}, if specified, is applicable to both operands a and mbar. If not specified, then Generic Addressing is used for both a and mbar. If the generic addresses specified do not fall within the address window of .shared::cluster state space, then the behaviour is undefined.

The store operation in st.async is treated as a weak memory operation and the complete_tx operation on the mbarrier has .release semantics at the .cluster scope as described in the Memory Consistency Model.

PTX ISA Notes

Introduced in PTX ISA version 8.1.

Target ISA Notes

Requires sm_90 or higher.

Examples

st.async.shared::cluster.mbarrier::complete_tx::bytes.u32 [addr], b, [mbar_addr]

9.7.8.13. Data Movement and Conversion Instructions: multimem.ld_reduce, multimem.st, multimem.red

The multimem.* operations operate on multimem addresses and accesses all of the multiple memory locations which the multimem address points to.

Multimem addresses can only be accessed only by multimem.* operations. Accessing a multimem address with ld, st or any other memory operations results in undefined behavior.

Refer to CUDA programming guide for creation and management of the multimem addresses.

multimem.ld_reduce, multimem.st, multimem.red

Perform memory operations on the multimem address.

Syntax

// Integer type:

multimem.ld_reduce{.ldsem}{.scope}{.ss}.op.type      d, [a];
multimem.st{.stsem}{.scope}{.ss}.type                [a], b;
multimem.red{.redsem}{.scope}{.ss}.op.type           [a], b;

.ss =       { .global }
.ldsem =    { .weak, .relaxed, .acquire }
.stsem =    { .weak, .relaxed, .release }
.redsem =   { .relaxed, .release }
.scope =    { .cta, .cluster, .gpu, .sys }
.op  =      { .min, .max, .add, .and, .or, .xor }
.type =     { .b32, .b64,  .u32, .u64, .s32, .s64 }

// Floating point type:

multimem.ld_reduce{.ldsem}{.scope}{.ss}.op{.acc_prec}{.vec}.type    d, [a];
multimem.st{.stsem}{.scope}{.ss}{.vec}.type                         [a], b;
multimem.red{.redsem}{.scope}{.ss}.redop{.vec}.type                 [a], b;

.ss =       { .global }
.ldsem =    { .weak, .relaxed, .acquire }
.stsem =    { .weak, .relaxed, .release }
.redsem =   { .relaxed, .release }
.scope =    { .cta, .cluster, .gpu, .sys }
.op  =      { .min, .max, .add }
.redop  =   { .add }
.acc_prec = { .acc::f32 }
.vec =      { .v2, .v4, .v8 }
.type=      { .f16, .f16x2, .bf16, .bf16x2, .f32, .f64 }

Description

Instruction multimem.ld_reduce performs the following operations:

• load operation on the multimem address a, which involves loading of data from all of the multiple memory locations pointed to by the multimem address a,

• reduction operation specified by .op on the multiple data loaded from the multimem address a.

The result of the reduction operation in returned in register d.

Instruction multimem.st performs a store operation of the input operand b to all the memory locations pointed to by the multimem address a.

Instruction multimem.red performs a reduction operation on all the memory locations pointed to by the multimem address a, with operand b.

Instruction multimem.ld_reduce performs reduction on the values loaded from all the memory locations that the multimem address points to. In contrast, the multimem.red perform reduction on all the memory locations that the multimem address points to.

Address operand a must be a multimem address. Otherwise, the behavior is undefined. Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands.

If no state space is specified then Generic Addressing is used. If the address specified by a does not fall within the address window of .global state space then the behavior is undefined.

For floating-point type multi- operations, the size of the specified type along with .vec must equal either 32-bits or 64-bits or 128-bits. No other combinations of .vec and type are allowed. Type .f64 cannot be used with .vec qualifier.

The following table describes the valid combinations of .op and base type:

op	Base type
.add	.u32, .u64, .s32 .f16, .f16x2, .bf16, .bf16x2 .f32, .f64
.and, .or, .xor	.b32, .b64
.min, .max	.u32, .s32, .u64, .s644 .f16, .f16x2, .bf16, .bf16x2

For multimem.ld_reduce, the default precision of the intermediate accumulation is same as the specified type. Optionally for .f16, .f16x2, .bf16 and .bf16x2 types, .acc::f32 can be specified to change the precision of the intermediate accumulation to .f32.

Optional qualifiers .ldsem, .stsem and .redsem specify the memory synchronizing effect of the multimem.ld_reduce, multimem.st and multimem.red respectively, as described in Memory Consistency Model. If explicit semantics qualifiers are not specified, then multimem.ld_reduce and multimem.st default to .weak and multimem.red defaults to .relaxed.

The optional .scope qualifier specifies the set of threads that can directly observe the memory synchronizing effect of this operation, as described in Memory Consistency Model. If the .scope qualifier is not specified for multimem.red then .sys scope is assumed by default.

PTX ISA Notes

Introduced in PTX ISA version 8.1.

Support for .acc::f32 qualifier introduced in PTX ISA version 8.2.

Target ISA Notes

Requires sm_90 or higher.

Examples

multimem.ld_reduce.and.b32                    val1_b32, [addr1];
multimem.ld_reduce.acquire.gpu.global.add.u32 val2_u32, [addr2];

multimem.st.relaxed.gpu.b32                [addr3], val3_b32;
multimem.st.release.cta.global.u32         [addr4], val4_u32;

multimem.red.relaxed.gpu.max.f64           [addr5], val5_f64;
multimem.red.release.cta.global.add.v4.f32 [addr6], {val6, val7, val8, val9};
multimem.ld_reduce.add.acc::f32.v2.f16x2   {val_10, val_11}, [addr7];

9.7.8.14. Data Movement and Conversion Instructions: prefetch, prefetchu

prefetch, prefetchu

Prefetch line containing a generic address at a specified level of memory hierarchy, in specified state space.

Syntax

prefetch{.space}.level                    [a];   // prefetch to data cache
prefetch.global.level::eviction_priority  [a];   // prefetch to data cache

prefetchu.L1  [a];             // prefetch to uniform cache

prefetch{.tensormap_space}.tensormap [a];  // prefetch the tensormap

.space =                    { .global, .local };
.level =                    { .L1, .L2 };
.level::eviction_priority = { .L2::evict_last, .L2::evict_normal };
.tensormap_space =          { .const, .param };

Description

The prefetch instruction brings the cache line containing the specified address in global or local memory state space into the specified cache level.

If the .tensormap qualifier is specified then the prefetch instruction brings the cache line containing the specified address in the .const or .param memory state space for subsequent use by the cp.async.bulk.tensor instruction.

If no state space is given, the prefetch uses Generic Addressing.

Optionally, the eviction priority to be applied on the prefetched cache line can be specified by the modifier .level::eviction_priority.

Supported addressing modes for operand a and alignment requirements are described in Addresses as Operands

The prefetchu instruction brings the cache line containing the specified generic address into the specified uniform cache level.

A prefetch to a shared memory location performs no operation.

A prefetch into the uniform cache requires a generic address, and no operation occurs if the address maps to a const, local, or shared memory location.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

Support for .level::eviction_priority qualifier introduced in PTX ISA version 7.4.

Support for the .tensormap qualifier is introduced in PTX ISA version 8.0.

Target ISA Notes

prefetch and prefetchu require sm_20 or higher.

Support for .level::eviction_priority qualifier requires sm_80 or higher.

Support for the .tensormap qualifier requires sm_90 or higher.

Examples

prefetch.global.L1             [ptr];
prefetch.global.L2::evict_last [ptr];
prefetchu.L1  [addr];
prefetch.global.tensormap      [ptr];

9.7.8.15. Data Movement and Conversion Instructions: applypriority

applypriority

Apply the cache eviction priority to the specified address in the specified cache level.

Syntax

applypriority{.global}.level::eviction_priority  [a], size;

.level::eviction_priority = { .L2::evict_normal };

Description

The applypriority instruction applies the cache eviction priority specified by the .level::eviction_priority qualifier to the address range [a..a+size) in the specified cache level.

If no state space is specified then Generic Addressing is used. If the specified address does not fall within the address window of .global state space then the behavior is undefined.

The operand size is an integer constant that specifies the amount of data, in bytes, in the specified cache level on which the priority is to be applied. The only supported value for the size operand is 128.

Supported addressing modes for operand a are described in Addresses as Operands. a must be aligned to 128 bytes.

If the data pointed to by address a is not already present in the specified cache level, then the data will be prefetched before applying the specified priority.

PTX ISA Notes

Introduced in PTX ISA version 7.4.

Target ISA Notes

Requires sm_80 or higher.

Examples

applypriority.global.L2::evict_normal [ptr], 128;

9.7.8.16. Data Movement and Conversion Instructions: discard

discard

Invalidate the data in cache at the specified address and cache level.

Syntax

discard{.global}.level  [a], size;

.level = { .L2 };

Description

The discard instruction invalidates the data at the address range [a .. a + (size - 1)] in the cache level specified by the .level qualifier without writing back the data in the cache to the memory. Therefore after the discard operation, the data at the address range [a .. a+ (size - 1)] has undetermined value.

The operand size is an integer constant that specifies the amount of data, in bytes, in the cache level specified by the .level qualifier to be discarded. The only supported value for the size operand is 128.

If no state space is specified then Generic Addressing is used. If the specified address does not fall within the address window of .global state space then the behavior is undefined.

Supported addressing modes for address operand a are described in Addresses as Operands. a must be aligned to 128 bytes.

PTX ISA Notes

Introduced in PTX ISA version 7.4.

Target ISA Notes

Requires sm_80 or higher.

Examples

discard.global.L2 [ptr], 128;

9.7.8.17. Data Movement and Conversion Instructions: createpolicy

createpolicy

Create a cache eviction policy for the specified cache level.

Syntax

// Range-based policy
createpolicy.range{.global}.level::primary_priority{.level::secondary_priority}.b64
                                   cache-policy, [a], primary-size, total-size;

// Fraction-based policy
createpolicy.fractional.level::primary_priority{.level::secondary_priority}.b64
                                   cache-policy{, fraction};

// Converting the access property from CUDA APIs
createpolicy.cvt.L2.b64            cache-policy, access-property;

.level::primary_priority =   { .L2::evict_last, .L2::evict_normal,
                               .L2::evict_first, .L2::evict_unchanged };
.level::secondary_priority = { .L2::evict_first, .L2::evict_unchanged };

Description

The createpolicy instruction creates a cache eviction policy for the specified cache level in an opaque 64-bit register specified by the destination operand cache-policy. The cache eviction policy specifies how cache eviction priorities are applied to global memory addresses used in memory operations with .level::cache_hint qualifier.

There are two types of cache eviction policies:

• Range-based policy

  The cache eviction policy created using createpolicy.range specifies the cache eviction behaviors for the following three address ranges:

  • [a .. a + (primary-size - 1)] referred to as primary range.

  • [a + primary-size .. a + (total-size - 1)] referred to as trailing secondary range.

  • [a - (total-size - primary-size) .. (a - 1)] referred to as preceding secondary range.

  When a range-based cache eviction policy is used in a memory operation with .level::cache_hint qualifier, the eviction priorities are applied as follows:

  • If the memory address falls in the primary range, the eviction priority specified by .L2::primary_priority is applied.

  • If the memory address falls in any of the secondary ranges, the eviction priority specified by .L2::secondary_priority is applied.

  • If the memory address does not fall in either of the above ranges, then the applied eviction priority is unspecified.

  The 32-bit operand primary-size specifies the size, in bytes, of the primary range. The 32-bit operand total-size specifies the combined size, in bytes, of the address range including primary and secondary ranges. The value of primary-size must be less than or equal to the value of total-size. Maximum allowed value of total-size is 4GB.

  If .L2::secondary_priority is not specified, then it defaults to .L2::evict_unchanged.

  If no state space is specified then Generic Addressing is used. If the specified address does not fall within the address window of .global state space then the behavior is undefined.

• Fraction-based policy

  A memory operation with .level::cache_hint qualifier can use the fraction-based cache eviction policy to request the cache eviction priority specified by .L2:primary_priority to be applied to a fraction of cache accesses specified by the 32-bit floating point operand fraction. The remainder of the cache accesses get the eviction priority specified by .L2::secondary_priority. This implies that in a memory operation that uses a fraction-based cache policy, the memory access has a probability specified by the operand fraction of getting the cache eviction priority specified by .L2::primary_priority.

  The valid range of values for the operand fraction is (0.0,.., 1.0]. If the operand fraction is not specified, it defaults to 1.0.

  If .L2::secondary_priority is not specified, then it defaults to .L2::evict_unchanged.

The access property created using the CUDA APIs can be converted into cache eviction policy by the instruction createpolicy.cvt. The source operand access-property is a 64-bit opaque register. Refer to CUDA programming guide for more details.

PTX ISA Notes

Introduced in PTX ISA version 7.4.

Target ISA Notes

Requires sm_80 or higher.

Examples

createpolicy.fractional.L2::evict_last.b64                      policy, 1.0;
createpolicy.fractional.L2::evict_last.L2::evict_unchanged.b64  policy, 0.5;

createpolicy.range.L2::evict_last.L2::evict_first.b64
                                            policy, [ptr], 0x100000, 0x200000;

// access-prop is created by CUDA APIs.
createpolicy.cvt.L2.b64 policy, access-prop;

9.7.8.18. Data Movement and Conversion Instructions: isspacep

isspacep

Query whether a generic address falls within a specified state space window.

Syntax

isspacep.space  p, a;    // result is .pred

.space = { const, .global, .local, .shared{::cta, ::cluster}, .param{::entry} };

Description

Write predicate register p with 1 if generic address a falls within the specified state space window and with 0 otherwise. Destination p has type .pred; the source address operand must be of type .u32 or .u64.

isspacep.param{::entry} returns 1 if the generic address falls within the window of Kernel Function Parameters, otherwise returns 0. If .param is specified without any sub-qualifiers then it defaults to .param::entry.

isspacep.global returns 1 for Kernel Function Parameters as .param window is contained within the .global window.

If no sub-qualifier is specified with .shared state space, then ::cta is assumed by default.

Note

ispacep.shared::cluster will return 1 for every shared memory address that is accessible to the threads in the cluster, whereas ispacep.shared::cta will return 1 only if the address is of a variable declared in the executing CTA.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

isspacep.const introduced in PTX ISA version 3.1.

isspacep.param introduced in PTX ISA version 7.7.

Support for ::cta and ::cluster sub-qualifiers introduced in PTX ISA version 7.8.

Support for sub-qualifier ::entry on .param space introduced in PTX ISA version 8.3.

Target ISA Notes

isspacep requires sm_20 or higher.

isspacep.param{::entry} requires sm_70 or higher.

Sub-qualifier ::cta requires sm_30 or higher.

Sub-qualifier ::cluster requires sm_90 or higher.

Examples

isspacep.const           iscnst, cptr;
isspacep.global          isglbl, gptr;
isspacep.local           islcl,  lptr;
isspacep.shared          isshrd, sptr;
isspacep.param::entry    isparam, pptr;
isspacep.shared::cta     isshrdcta, sptr;
isspacep.shared::cluster ishrdany sptr;

9.7.8.19. Data Movement and Conversion Instructions: cvta

cvta

Convert address from .const, Kernel Function Parameters (.param), .global, .local, or .shared state space to generic, or vice-versa. Take the generic address of a variable declared in .const, Kernel Function Parameters (.param), .global, .local, or .shared state space.

Syntax

// convert const, global, local, or shared address to generic address
cvta.space.size  p, a;        // source address in register a
cvta.space.size  p, var;      // get generic address of var
cvta.space.size  p, var+imm;  // generic address of var+offset

// convert generic address to const, global, local, or shared address
cvta.to.space.size  p, a;

.space = { .const, .global, .local, .shared{::cta, ::cluster}, .param{::entry} };
.size  = { .u32, .u64 };

Description

Convert a const, Kernel Function Parameters (.param), global, local, or shared address to a generic address, or vice-versa. The source and destination addresses must be the same size. Use cvt.u32.u64 or cvt.u64.u32 to truncate or zero-extend addresses.

For variables declared in .const, Kernel Function Parameters (.param), .global, .local, or .shared state space, the generic address of the variable may be taken using cvta. The source is either a register or a variable defined in const, Kernel Function Parameters (.param), global, local, or shared memory with an optional offset.

When converting a generic address into a const, Kernel Function Parameters (.param), global, local, or shared address, the resulting address is undefined in cases where the generic address does not fall within the address window of the specified state space. A program may use isspacep to guard against such incorrect behavior.

For cvta with .shared state space, the address must belong to the space specified by ::cta or ::cluster sub-qualifier, otherwise the behavior is undefined. If no sub-qualifier is specified with .shared state space, then ::cta is assumed by default.

If .param is specified without any sub-qualifiers then it defaults to .param::entry.

PTX ISA Notes

Introduced in PTX ISA version 2.0.

cvta.const and cvta.to.const introduced in PTX ISA version 3.1.

cvta.param and cvta.to.param introduced in PTX ISA version 7.7.

Note: The current implementation does not allow generic pointers to const space variables in programs that contain pointers to constant buffers passed as kernel parameters.

Support for ::cta and ::cluster sub-qualifiers introduced in PTX ISA version 7.8.

Support for sub-qualifier ::entry on .param space introduced in PTX ISA version 8.3.

Target ISA Notes

cvta requires sm_20 or higher.

cvta.param{::entry} and cvta.to.param{::entry} requires sm_70 or higher.

Sub-qualifier ::cta requires sm_30 or higher.

Sub-qualifier ::cluster requires sm_90 or higher.

Examples

cvta.const.u32   ptr,cvar;
cvta.local.u32   ptr,lptr;
cvta.shared::cta.u32  p,As+4;
cvta.shared::cluster.u32 ptr, As;
cvta.to.global.u32  p,gptr;
cvta.param.u64   ptr,pvar;
cvta.to.param::entry.u64  epptr, ptr;

9.7.8.20. Data Movement and Conversion Instructions: cvt

cvt

Convert a value from one type to another.

Syntax

cvt{.irnd}{.ftz}{.sat}.dtype.atype         d, a;  // integer rounding
cvt{.frnd}{.ftz}{.sat}.dtype.atype         d, a;  // fp rounding
cvt.frnd2{.relu}{.satfinite}.f16.f32       d, a;
cvt.frnd2{.relu}{.satfinite}.f16x2.f32     d, a, b;
cvt.frnd2{.relu}{.satfinite}.bf16.f32      d, a;
cvt.frnd2{.relu}{.satfinite}.bf16x2.f32    d, a, b;
cvt.rna{.satfinite}.tf32.f32               d, a;
cvt.frnd2{.relu}.tf32.f32                  d, a;
cvt.rn.satfinite{.relu}.f8x2type.f32       d, a, b;
cvt.rn.satfinite{.relu}.f8x2type.f16x2     d, a;
cvt.rn.{.relu}.f16x2.f8x2type              d, a;

.irnd   = { .rni, .rzi, .rmi, .rpi };
.frnd   = { .rn,  .rz,  .rm,  .rp  };
.frnd2  = { .rn,  .rz };
.dtype = .atype = { .u8,   .u16, .u32, .u64,
                    .s8,   .s16, .s32, .s64,
                    .bf16, .f16, .f32, .f64 };
.f8x2type = { .e4m3x2, .e5m2x2 };

Description

Convert between different types and sizes.

For .f16x2 and .bf16x2 instruction type, two inputs a and b of .f32 type are converted into .f16 or .bf16 type and the converted values are packed in the destination register d, such that the value converted from input a is stored in the upper half of d and the value converted from input b is stored in the lower half of d

For .f16x2 instruction type, destination operand d has .f16x2 or .b32 type. For .bf16 instruction type, operand d has .b16 type. For .bf16x2 instruction type, operand d has .b32 type. For .tf32 instruction type, operand d has .b32 type.

When converting to .e4m3x2/.e5m2x2 data formats, the destination operand d has .b16 type. When converting two .f32 inputs to .e4m3x2/.e5m2x2, each input is converted to the specified format, and the converted values are packed in the destination operand d such that the value converted from input a is stored in the upper 8 bits of d and the value converted from input b is stored in the lower 8 bits of d. When converting an .f16x2 input to .e4m3x2/ .e5m2x2, each .f16 input from operand a is converted to the specified format. The converted values are packed in the destination operand d such that the value converted from the upper 16 bits of input a is stored in the upper 8 bits of d and the value converted from the lower 16 bits of input a is stored in the lower 8 bits of d.

When converting from .e4m3x2/.e5m2x2 to .f16x2, source operand a has .b16 type. Each 8-bit input value in operand a is converted to .f16 type. The converted values are packed in the destination operand d such that the value converted from the upper 8 bits of a is stored in the upper 16 bits of d and the value converted from the lower 8 bits of a is stored in the lower 16 bits of d.

Rounding modifier is mandatory in all of the following cases:

• float-to-float conversions, when destination type is smaller than source type

• All float-to-int conversions

• All int-to-float conversions

• All conversions involving .f16x2, .e4m3x2, .e5m2x2,.bf16x2 and .tf32 instruction types.

.satfinite modifier is only supported for conversions involving the following types:

• .e4m3x2 and .e5m2x2 destination types. .satfinite modifier is mandatory for such conversions.

• .f16, .bf16, .f16x2, .bf16x2 as destination types.

• .tf32 as destination type with rounding mode specified as round to nearest, ties away from zero.

Semantics

if (/* inst type is .f16x2 or .bf16x2 */) {
    d[31:16] = convert(a);
    d[15:0]  = convert(b);
} else {
    d = convert(a);
}

Integer Notes

Integer rounding is required for float-to-integer conversions, and for same-size float-to-float conversions where the value is rounded to an integer. Integer rounding is illegal in all other instances.

Integer rounding modifiers:

.rni

round to nearest integer, choosing even integer if source is equidistant between two integers

.rzi

round to nearest integer in the direction of zero

.rmi

round to nearest integer in direction of negative infinity

.rpi

round to nearest integer in direction of positive infinity

In float-to-integer conversion, NaN inputs are converted to 0.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported.

For cvt.ftz.dtype.f32 float-to-integer conversions and cvt.ftz.f32.f32 float-to-float conversions with integer rounding, subnormal inputs are flushed to sign-preserving zero. Modifier .ftz can only be specified when either .dtype or .atype is .f32 and applies only to single precision (.f32) inputs and results.

sm_1x

For cvt.ftz.dtype.f32 float-to-integer conversions and cvt.ftz.f32.f32 float-to-float conversions with integer rounding, subnormal inputs are flushed to sign-preserving zero. The optional .ftz modifier may be specified in these cases for clarity.

Note: In PTX ISA versions 1.4 and earlier, the cvt instruction did not flush single-precision subnormal inputs or results to zero if the destination type size was 64-bits. The compiler will preserve this behavior for legacy PTX code.

Saturation modifier:

.sat

For integer destination types, .sat limits the result to MININT..MAXINT for the size of the operation. Note that saturation applies to both signed and unsigned integer types.

The saturation modifier is allowed only in cases where the destination type’s value range is not a superset of the source type’s value range; i.e., the .sat modifier is illegal in cases where saturation is not possible based on the source and destination types.

For float-to-integer conversions, the result is clamped to the destination range by default; i.e, .sat is redundant.

Floating Point Notes

Floating-point rounding is required for float-to-float conversions that result in loss of precision, and for integer-to-float conversions. Floating-point rounding is illegal in all other instances.

Floating-point rounding modifiers:

.rn

mantissa LSB rounds to nearest even

.rna

mantissa LSB rounds to nearest, ties away from zero

.rz

mantissa LSB rounds towards zero

.rm

mantissa LSB rounds towards negative infinity

.rp

mantissa LSB rounds towards positive infinity

A floating-point value may be rounded to an integral value using the integer rounding modifiers (see Integer Notes). The operands must be of the same size. The result is an integral value, stored in floating-point format.

Subnormal numbers:

sm_20+

By default, subnormal numbers are supported. Modifier .ftz may be specified to flush single-precision subnormal inputs and results to sign-preserving zero. Modifier .ftz can only be specified when either .dtype or .atype is .f32 and applies only to single precision (.f32) inputs and results.

sm_1x

Single-precision subnormal inputs and results are flushed to sign-preserving zero. The optional .ftz modifier may be specified in these cases for clarity.

Note: In PTX ISA versions 1.4 and earlier, the cvt instruction did not flush single-precision subnormal inputs or results to zero if either source or destination type was .f64. The compiler will preserve this behavior for legacy PTX code. Specifically, if the PTX ISA version is 1.4 or earlier, single-precision subnormal inputs and results are flushed to sign-preserving zero only for cvt.f32.f16, cvt.f16.f32, and cvt.f32.f32 instructions.

Saturation modifier:

.sat:

For floating-point destination types, .sat limits the result to the range [0.0, 1.0]. NaN results are flushed to positive zero. Applies to .f16, .f32, and .f64 types.

.relu:

For .f16, .f16x2, .bf16, .bf16x2, .e4m3x2, .e5m2x2 and .tf32 destination types, .relu clamps the result to 0 if negative. NaN results are converted to canonical NaN.

.satfinite:

For .f16, .f16x2, .bf16, .bf16x2, .e4m3x2, .e5m2x2 and .tf32 destination formats, if the input value is NaN, then the result is NaN in the specified destination format. If the absolute value of input (ignoring sign) is greater than MAX_NORM of the specified destination format, then the result is sign-preserved MAX_NORM of the destination format.

Notes

A source register wider than the specified type may be used, except when the source operand has .bf16 or .bf16x2 format. The lower n bits corresponding to the instruction-type width are used in the conversion. See Operand Size Exceeding Instruction-Type Size for a description of these relaxed type-checking rules.

A destination register wider than the specified type may be used, except when the destination operand has .bf16, .bf16x2 or .tf32 format. The result of conversion is sign-extended to the destination register width for signed integers, and is zero-extended to the destination register width for unsigned, bit-size, and floating-point types. See Operand Size Exceeding Instruction-Type Size for a description of these relaxed type-checking rules.

For cvt.f32.bf16, NaN input yields unspecified NaN.

PTX ISA Notes

Introduced in PTX ISA version 1.0.

.relu modifier and {.f16x2, .bf16, .bf16x2, .tf32} destination formats introduced in PTX ISA version 7.0.

cvt.bf16.{u8/s8/u16/s16/u32/s32/u64/s64/f16/f64/bf16}, cvt.{u8/s8/u16/s16/u32/s32/u64/s64/f16/f64}.bf16, and cvt.tf32.f32.{relu}.{rn/rz} introduced in PTX ISA 7.8.

cvt with .e4m3x2/.e5m2x2 for sm_90 or higher introduced in PTX ISA version 7.8.

cvt.satfinite.{e4m3x2, e5m2x2}.{f32, f16x2} for sm_90 or higher introduced in PTX ISA version 7.8.

cvt with .e4m3x2/.e5m2x2 for sm_89 introduced in PTX ISA version 8.1.

cvt.satfinite.{e4m3x2, e5m2x2}.{f32, f16x2} for sm_89 introduced in PTX ISA version 8.1.

cvt.satfinite.{f16, bf16, f16x2, bf16x2, tf32}.f32 introduced in PTX ISA version 8.1.

Target ISA Notes

cvt to or from .f64 requires sm_13 or higher.

.relu modifier and {.f16x2, .bf16, .bf16x2, .tf32} destination formats require sm_80 or higher.

cvt.bf16.{u8/s8/u16/s16/u32/s32/u64/s64/f16/f64/bf16}, cvt.{u8/s8/u16/s16/u32/s32/u64/s64/f16/f64}.bf16, and cvt.tf32.f32.{relu}.{rn/rz} require sm_90 or higher.

cvt with .e4m3x2/.e5m2x2 requires sm89 or higher.

cvt.satfinite.{e4m3x2, e5m2x2}.{f32, f16x2} requires sm_89 or higher.

Examples

cvt.f32.s32 f,i;
cvt.s32.f64 j,r;     // float-to-int saturates by default
cvt.rni.f32.f32 x,y; // round to nearest int, result is fp
cvt.f32.f32 x,y;     // note .ftz behavior for sm_1x targets
cvt.rn.relu.f16.f32      b, f;        // result is saturated with .relu saturation mode
cvt.rz.f16x2.f32         b1, f, f1;   // convert two fp32 values to packed fp16 outputs
cvt.rn.relu.satfinite.f16x2.f32    b1, f, f1;   // convert two fp32 values to packed fp16 outputs with .relu saturation on each output
cvt.rn.bf16.f32          b, f;        // convert fp32 to bf16
cvt.rz.relu.satfinite.bf16.f3 2    b, f;        // convert fp32 to bf16 with .relu and .satfinite saturation
cvt.rz.satfinite.bf16x2.f32        b1, f, f1;   // convert two fp32 values to packed bf16 outputs
cvt.rn.relu.bf16x2.f32   b1, f, f1;   // convert two fp32 values to packed bf16 outputs with .relu saturation on each output
cvt.rna.satfinite.tf32.f32         b1, f;       // convert fp32 to tf32 format
cvt.rn.relu.tf32.f32     d, a;        // convert fp32 to tf32 format
cvt.f64.bf16.rp          f, b;        // convert bf16 to f64 format
cvt.bf16.f16.rz          b, f         // convert f16 to bf16 format
cvt.bf16.u64.rz          b, u         // convert u64 to bf16 format
cvt.s8.bf16.rpi          s, b         // convert bf16 to s8 format
cvt.bf16.bf16.rpi        b1, b2       // convert bf16 to corresponding int represented in bf16 format
cvt.rn.satfinite.e4m3x2.f32 d, a, b;  // convert a, b to .e4m3 and pack as .e4m3x2 output
cvt.rn.relu.satfinite.e5m2x2.f16x2 d, a; // unpack a and convert the values to .e5m2 outputs with .relu
                                         // saturation on each output and pack as .e5m2x2
cvt.rn.f16x2.e4m3x2 d, a;             // unpack a, convert two .e4m3 values to packed f16x2 output

9.7.8.21. Data Movement and Conversion Instructions: cvt.pack

cvt.pack

Convert two integer values from one integer type to another and pack the results.

Syntax

cvt.pack.sat.convertType.abType  d, a, b;
    .convertType  = { .u16, .s16 }
    .abType       = { .s32 }

cvt.pack.sat.convertType.abType.cType  d, a, b, c;
    .convertType  = { .u2, .s2, .u4, .s4, .u8, .s8 }
    .abType       = { .s32 }
    .cType        = { .b32 }

Description

Convert two 32-bit integers a and b into specified type and pack the results into d.

Destination d is an unsigned 32-bit integer. Source operands a and b are integers of type .abType and the source operand c is an integer of type .cType.

The inputs a and b are converted to values of type specified by .convertType with saturation and the results after conversion are packed into lower bits of d.

If operand c is specified then remaining bits of d are copied from lower bits of c.

Semantics

ta = a < MIN(convertType) ? MIN(convertType) : a;
ta = a > MAX(convertType) ? MAX(convertType) : a;
tb = b < MIN(convertType) ? MIN(convertType) : b;
tb = b > MAX(convertType) ? MAX(convertType) : b;

size = sizeInBits(convertType);
td = tb ;
for (i = size; i <= 2 * size - 1; i++) {
    td[i] = ta[i - size];
}

if (isU16(convertType) || isS16(convertType)) {
    d = td;
} else {
    for (i = 0; i < 2 * size; i++) {
        d[i] = td[i];
    }
    for (i = 2 * size; i <= 31; i++) {
        d[i] = c[i - 2 * size];
    }
}

.sat modifier limits the converted values to MIN(convertType)..MAX(convertedType) (no overflow) if the corresponding inputs are not in the range of datatype specified as .convertType.

PTX ISA Notes

Introduced in PTX ISA version 6.5.

Target ISA Notes

Requires sm_72 or higher.

Sub byte types (.u4/.s4 and .u2/.s2) requires sm_75 or higher.

Examples

cvt.pack.sat.s16.s32      %r1, %r2, %r3;           // 32-bit to 16-bit conversion
cvt.pack.sat.u8.s32.b32   %r4, %r5, %r6, 0;        // 32-bit to 8-bit conversion
cvt.pack.sat.u8.s32.b32   %r7, %r8, %r9, %r4;      // %r7 = { %r5, %r6, %r8, %r9 }
cvt.pack.sat.u4.s32.b32   %r10, %r12, %r13, %r14;  // 32-bit to 4-bit conversion
cvt.pack.sat.s2.s32.b32   %r15, %r16, %r17, %r18;  // 32-bits to 2-bit conversion

9.7.8.22. Data Movement and Conversion Instructions: mapa

mapa

Map the address of the shared variable in the target CTA.

Syntax

mapa{.space}.type          d, a, b;

// Maps shared memory address in register a into CTA b.
mapa.shared::cluster.type  d, a, b;

// Maps shared memory variable into CTA b.
mapa.shared::cluster.type  d, sh, b;

// Maps shared memory variable into CTA b.
mapa.shared::cluster.type  d, sh + imm, b;

// Maps generic address in register a into CTA b.
mapa.type                  d, a, b;

.space = { .shared::cluster }
.type  = { .u32, .u64 }

Description

Get address in the CTA specified by operand b which corresponds to the address specified by operand a.

Instruction type .type indicates the type of the destination operand d and the source operand a.

When space is .shared::cluster, source a is either a shared memory variable or a register containing a valid shared memory address and register d contains a shared memory address. When the optional qualifier .space is not specified, both a and d are registers containing generic addresses pointing to shared memory.

b is a 32-bit integer operand representing the rank of the target CTA.

Destination register d will hold an address in CTA b corresponding to operand a.

PTX ISA Notes

Introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_90 or higher.

Examples

mapa.shared::cluster.u64 d1, %reg1, cta;
mapa.shared::cluster.u32 d2, sh, 3;
mapa.u64                 d3, %reg2, cta;

9.7.8.23. Data Movement and Conversion Instructions: getctarank

getctarank

Generate the CTA rank of the address.

Syntax

getctarank{.space}.type d, a;

// Get cta rank from source shared memory address in register a.
getctarank.shared::cluster.type d, a;

// Get cta rank from shared memory variable.
getctarank.shared::cluster.type d, var;

// Get cta rank from shared memory variable+offset.
getctarank.shared::cluster.type d, var + imm;

// Get cta rank from generic address of shared memory variable in register a.
getctarank.type d, a;

.space = { .shared::cluster }
.type  = { .u32, .u64 }

Description

Write the destination register d with the rank of the CTA which contains the address specified in operand a.

Instruction type .type indicates the type of source operand a.

When space is .shared::cluster, source a is either a shared memory variable or a register containing a valid shared memory address. When the optional qualifier .space is not specified, a is a register containing a generic addresses pointing to shared memory. Destination d is always a 32-bit register which holds the rank of the CTA.

PTX ISA Notes

Introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_90 or higher.

Examples

getctarank.shared::cluster.u32 d1, addr;
getctarank.shared::cluster.u64 d2, sh + 4;
getctarank.u64                 d3, src;

9.7.8.24. Data Movement and Conversion Instructions: Asynchronous copy

An asynchronous copy operation performs the underlying operation asynchronously in the background, thus allowing the issuing threads to perform subsequent tasks.

An asynchronous copy operation can be a bulk operation that operates on a large amount of data, or a non-bulk operation that operates on smaller sized data. The amount of data handled by a bulk asynchronous operation must be a multiple of 16 bytes.

9.7.8.24.1. Completion Mechanisms for Asynchronous Copy Operations

A thread must explicitly wait for the completion of an asynchronous copy operation in order to access the result of the operation. Once an asynchronous copy operation is initiated, modifying the source memory location or reading from the destination memory location before the asynchronous operation completes, will cause unpredictable results.

This section describes two asynchronous copy operation completion mechanisms supported in PTX: Async-group mechanism and mbarrier-based mechanism.

Async-group mechanism

When using the async-group completion mechanism, the issuing thread specifies a group of asynchronous operations, called async-group, using a commit operation and tracks the completion of this group using a wait operation. The thread issuing the asynchronous operation must create separate async-groups for bulk and non-bulk asynchronous operations.

A commit operation creates a per-thread async-group containing all prior asynchronous operations initiated by the executing thread but none of the asynchronous operations following the commit operation. A committed asynchronous operation belongs to a single async-group.

When an async-group completes, all the asynchronous operations belonging to that group are complete and the executing thread that initiated the asynchronous operations can read the result of the asynchronous operations. All async-groups committed by an executing thread always complete in the order in which they were committed. There is no ordering between asynchronous operations within an async-group.

A typical pattern of using async-group as the completion mechanism is as follows:

• Initiate the asynchronous operations.

• Group the asynchronous operations into an async-group using a commit operation.

• Wait for the completion of the async-group using the wait operation.

• Once the async-group completes, access the results of all asynchronous operations in that async-group.

Mbarrier-based mechanism

A thread can track the completion of one or more asynchronous operations using the current phase of an mbarrier object. When the current phase of the mbarrier object is complete, it implies that all asynchronous operations tracked by this phase are complete, and all threads participating in that mbarrier object can access the result of the asynchronous operations.

The mbarrier object to be used for tracking the completion of an asynchronous operation can be either specified along with the asynchronous operation as part of its syntax, or as a separate operation. For a bulk asynchronous operation, the mbarrier object must be specified in the asynchronous operation, whereas for non-bulk operations, it can be specified after the asynchronous operation.

A typical pattern of using mbarrier-based completion mechanism is as follows:

• Initiate the asynchronous operations.

• Set up an mbarrier object to track the asynchronous operations in its current phase, either as part of the asynchronous operation or as a separate operation.

• Wait for the mbarrier object to complete its current phase using mbarrier.test_wait or mbarrier.try_wait.

• Once the mbarrier.test_wait or mbarrier.try_wait operation returns True, access the results of the asynchronous operations tracked by the mbarrier object.

9.7.8.24.2. Async Proxy

The cp{.reduce}.async.bulk operations are performed in the asynchronous proxy (or async proxy).

Accessing the same memory location across multiple proxies needs a cross-proxy fence. For the async proxy, fence.proxy.async should be used to synchronize memory between generic proxy and the async proxy.

The completion of a cp{.reduce}.async.bulk operation is followed by an implicit generic-async proxy fence. So the result of the asynchronous operation is made visible to the generic proxy as soon as its completion is observed. Async-group OR mbarrier-based completion mechanism must be used to wait for the completion of the cp{.reduce}.async.bulk instructions.

9.7.8.24.3. Data Movement and Conversion Instructions: cp.async

cp.async

Initiates an asynchronous copy operation from one state space to another.

Syntax

cp.async.ca.shared{::cta}.global{.level::cache_hint}{.level::prefetch_size}
                         [dst], [src], cp-size{, src-size}{, cache-policy} ;
cp.async.cg.shared{::cta}.global{.level::cache_hint}{.level::prefetch_size}
                         [dst], [src], 16{, src-size}{, cache-policy} ;
cp.async.ca.shared{::cta}.global{.level::cache_hint}{.level::prefetch_size}
                         [dst], [src], cp-size{, ignore-src}{, cache-policy} ;
cp.async.cg.shared{::cta}.global{.level::cache_hint}{.level::prefetch_size}
                         [dst], [src], 16{, ignore-src}{, cache-policy} ;

.level::cache_hint =     { .L2::cache_hint }
.level::prefetch_size =  { .L2::64B, .L2::128B, .L2::256B }
cp-size =                { 4, 8, 16 }

Description

cp.async is a non-blocking instruction which initiates an asynchronous copy operation of data from the location specified by source address operand src to the location specified by destination address operand dst. Operand src specifies a location in the global state space and dst specifies a location in the shared state space.

Operand cp-size is an integer constant which specifies the size of data in bytes to be copied to the destination dst. cp-size can only be 4, 8 and 16.

Instruction cp.async allows optionally specifying a 32-bit integer operand src-size. Operand src-size represents the size of the data in bytes to be copied from src to dst and must be less than cp-size. In such case, remaining bytes in destination dst are filled with zeros. Specifying src-size larger than cp-size results in undefined behavior.

The optional and non-immediate predicate argument ignore-src specifies whether the data from the source location src should be ignored completely. If the source data is ignored then zeros will be copied to destination dst. If the argument ignore-src is not specified then it defaults to False.

Supported alignment requirements and addressing modes for operand src and dst are described in Addresses as Operands.

The mandatory .async qualifier indicates that the cp instruction will initiate the memory copy operation asynchronously and control will return to the executing thread before the copy operation is complete. The executing thread can then use cp.async.wait_all or cp.async.wait_group or mbarrier instructions to wait for completion of the asynchronous copy operation. No other synchronization mechanisms described in Memory Consistency Model can be used to guarantee the completion of the asynchronous copy operations.

There is no ordering guarantee between two cp.async operations if they are not explicitly synchronized using cp.async.wait_all or cp.async.wait_group or mbarrier instructions.

As described in Cache Operators, the .cg qualifier indicates caching of data only at global level cache L2 and not at L1 whereas .ca qualifier indicates caching of data at all levels including L1 cache. Cache operator are treated as performance hints only.

cp.async is treated as a weak memory operation in the Memory Consistency Model.

The .level::prefetch_size qualifier is a hint to fetch additional data of the specified size into the respective cache level.The sub-qualifier prefetch_size can be set to either of 64B, 128B, 256B thereby allowing the prefetch size to be 64 Bytes, 128 Bytes or 256 Bytes respectively.

The qualifier .level::prefetch_size may only be used with .global state space and with generic addressing where the address points to .global state space. If the generic address does not fall within the address window of the global memory, then the prefetching behavior is undefined.

The .level::prefetch_size qualifier is treated as a performance hint only.

When the optional argument cache-policy is specified, the qualifier .level::cache_hint is required. The 64-bit operand cache-policy specifies the cache eviction policy that may be used during the memory access.

The qualifier .level::cache_hint is only supported for .global state space and for generic addressing where the address points to the .global state space.

cache-policy is a hint to the cache subsystem and may not always be respected. It is treated as a performance hint only, and does not change the memory consistency behavior of the program.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

Support for .level::cache_hint and .level::prefetch_size qualifiers introduced in PTX ISA version 7.4.

Support for ignore-src operand introduced in PTX ISA version 7.5.

Support for sub-qualifier ::cta introduced in PTX ISA version 7.8.

Target ISA Notes

Requires sm_80 or higher.

Sub-qualifier ::cta requires sm_30 or higher.

Examples

cp.async.ca.shared.global  [shrd],    [gbl + 4], 4;
cp.async.ca.shared::cta.global  [%r0 + 8], [%r1],     8;
cp.async.cg.shared.global  [%r2],     [%r3],     16;

cp.async.cg.shared.global.L2::64B   [%r2],      [%r3],     16;
cp.async.cg.shared.global.L2::128B  [%r0 + 16], [%r1],     16;
cp.async.cg.shared.global.L2::256B  [%r2 + 32], [%r3],     16;

createpolicy.fractional.L2::evict_last.L2::evict_unchanged.b64 cache-policy, 0.25;
cp.async.ca.shared.global.L2::cache_hint [%r2], [%r1], 4, cache-policy;

cp.async.ca.shared.global                   [shrd], [gbl], 4, p;
cp.async.cg.shared.global.L2::cache_hint   [%r0], [%r2], 16, q, cache-policy;

9.7.8.24.4. Data Movement and Conversion Instructions: cp.async.commit_group

cp.async.commit_group

Commits all prior initiated but uncommitted cp.async instructions into a cp.async-group.

Syntax

cp.async.commit_group ;

Description

cp.async.commit_group instruction creates a new cp.async-group per thread and batches all prior cp.async instructions initiated by the executing thread but not committed to any cp.async-group into the new cp.async-group. If there are no uncommitted cp.async instructions then cp.async.commit_group results in an empty cp.async-group.

An executing thread can wait for the completion of all cp.async operations in a cp.async-group using cp.async.wait_group.

There is no memory ordering guarantee provided between any two cp.async operations within the same cp.async-group. So two or more cp.async operations within a cp.async-group copying data to the same location results in undefined behavior.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

Target ISA Notes

Requires sm_80 or higher.

Examples

// Example 1:
cp.async.ca.shared.global [shrd], [gbl], 4;
cp.async.commit_group ; // Marks the end of a cp.async group

// Example 2:
cp.async.ca.shared.global [shrd1],   [gbl1],   8;
cp.async.ca.shared.global [shrd1+8], [gbl1+8], 8;
cp.async.commit_group ; // Marks the end of cp.async group 1

cp.async.ca.shared.global [shrd2],    [gbl2],    16;
cp.async.cg.shared.global [shrd2+16], [gbl2+16], 16;
cp.async.commit_group ; // Marks the end of cp.async group 2

9.7.8.24.5. Data Movement and Conversion Instructions: cp.async.wait_group / cp.async.wait_all

cp.async.wait_group/cp.async.wait_all

Wait for completion of prior asynchronous copy operations.

Syntax

cp.async.wait_group N;
cp.async.wait_all ;

Description

cp.async.wait_group instruction will cause executing thread to wait till only N or fewer of the most recent cp.async-groups are pending and all the prior cp.async-groups committed by the executing threads are complete. For example, when N is 0, the executing thread waits on all the prior cp.async-groups to complete. Operand N is an integer constant.

cp.async.wait_all is equivalent to :

cp.async.commit_group;
cp.async.wait_group 0;

An empty cp.async-group is considered to be trivially complete.

Writes performed by cp.async operations are made visible to the executing thread only after:

1. The completion of cp.async.wait_all or

2. The completion of cp.async.wait_group on the cp.async-group in which the cp.async belongs to or

3. mbarrier.test_wait returns True on an mbarrier object which is tracking the completion of the cp.async operation.

There is no ordering between two cp.async operations that are not synchronized with cp.async.wait_all or cp.async.wait_group or mbarrier objects.

cp.async.wait_group and cp.async.wait_all does not provide any ordering and visibility guarantees for any other memory operation apart from cp.async.

PTX ISA Notes

Introduced in PTX ISA version 7.0.

Target ISA Notes

Requires sm_80 or higher.

Examples

// Example of .wait_all:
cp.async.ca.shared.global [shrd1], [gbl1], 4;
cp.async.cg.shared.global [shrd2], [gbl2], 16;
cp.async.wait_all;  // waits for all prior cp.async to complete

// Example of .wait_group :
cp.async.ca.shared.global [shrd3], [gbl3], 8;
cp.async.commit_group;  // End of group 1

cp.async.cg.shared.global [shrd4], [gbl4], 16;
cp.async.commit_group;  // End of group 2

cp.async.cg.shared.global [shrd5], [gbl5], 16;
cp.async.commit_group;  // End of group 3

cp.async.wait_group 1;  // waits for group 1 and group 2 to complete

9.7.8.24.6. Data Movement and Conversion Instructions: cp.async.bulk

cp.async.bulk

Initiates an asynchronous copy operation from one state space to another.

Syntax

cp.async.bulk.dst.src.completion_mechanism{.multicast}{.level::cache_hint}
                      [dstMem], [srcMem], size, [mbar] {, ctaMask} {, cache-policy}

.dst =                  { .shared::cluster }
.src =                  { .global }
.completion_mechanism = { .mbarrier::complete_tx::bytes }
.level::cache_hint =    { .L2::cache_hint }
.multicast =            { .multicast::cluster  }


cp.async.bulk.dst.src.completion_mechanism [dstMem], [srcMem], size, [mbar]

.dst =                  { .shared::cluster }
.src =                  { .shared::cta }
.completion_mechanism = { .mbarrier::complete_tx::bytes }


cp.async.bulk.dst.src.completion_mechanism{.level::cache_hint} [dstMem], [srcMem], size{, cache-policy}

.dst =                  { .global }
.src =                  { .shared::cta }
.completion_mechanism = { .bulk_group }
.level::cache_hint =    { .L2::cache_hint }

Description

cp.async.bulk is a non-blocking instruction which initiates an asynchronous bulk-copy operation from the location specified by source address operand srcMem to the location specified by destination address operand dstMem.

The direction of bulk-copy is from the state space specified by the .src modifier to the state space specified by the .dst modifiers.

The 32-bit operand size specifies the amount of memory to be copied, in terms of number of bytes. size must be a multiple of 16. If the value is not a multiple of 16, then the behavior is undefined. The memory range [dstMem, dstMem + size - 1] must not overflow the destination memory space and the memory range [srcMem, srcMem + size - 1] must not overflow the source memory space. Otherwise, the behavior is undefined. The addresses dstMem and srcMem must be aligned to 16 bytes.

When the source of the copy is .shared::cta and the destination is .shared::cluster, the destination has to be in the shared memory of a different CTA within the cluster.

The modifier .completion_mechanism specifies the completion mechanism that is supported on the instruction variant. The completion mechanisms that are supported for different variants are summarized in the following table:

Completion mechanism	.dst	.src	Description
.mbarrier::...	.shared::cluster	.global	mbarrier based completion mechanism
	.shared::cluster	.shared::cta
.bulk_group	.global	.shared::cta	Bulk async-group based completion mechanism

The modifier .mbarrier::complete_tx::bytes specifies that the cp.async.bulk variant uses mbarrier based completion mechanism. The complete-tx operation, with completeCount argument equal to amount of data copied in bytes, will be performed on the mbarrier object specified by the operand mbar.

The modifier .bulk_group specifies that the cp.async.bulk variant uses bulk async-group based completion mechanism.

The optional modifier .multicast::cluster allows copying of data from global memory to shared memory of multiple CTAs in the cluster. Operand ctaMask specifies the destination CTAs in the cluster such that each bit position in the 16-bit ctaMask operand corresponds to the %ctaid of the destination CTA. The source data is multicast to the same CTA-relative offset as dstMem in the shared memory of each destination CTA. The mbarrier signal is also multicast to the same CTA-relative offset as mbar in the shared memory of the destination CTA.

When the optional argument cache-policy is specified, the qualifier .level::cache_hint is required. The 64-bit operand cache-policy specifies the cache eviction policy that may be used during the memory access.

cache-policy is a hint to the cache subsystem and may not always be respected. It is treated as a performance hint only, and does not change the memory consistency behavior of the program. The qualifier .level::cache_hint is only supported when at least one of the .src or .dst statespaces is .global state space.

The copy operation in cp.async.bulk is treated as a weak memory operation and the complete-tx operation on the mbarrier has .release semantics at the .cluster scope as described in the Memory Consistency Model.

Notes

.multicast::cluster qualifier is optimized for target architecture sm_90a and may have substantially reduced performance on other targets and hence .multicast::cluster is advised to be used with .target sm_90a.

PTX ISA Notes

Introduced in PTX ISA version 8.0.

Target ISA Notes

Requires sm_90 or higher.

.multicast::cluster qualifier advised to be used with .target sm_90a.

Examples

// .global -> .shared::cluster:
cp.async.bulk.shared::cluster.global.mbarrier::complete_tx::bytes [dstMem], [srcMem], size, [mbar];

cp.async.bulk.shared::cluster.global.mbarrier::complete_tx::bytes.multicast::cluster
                                             [dstMem], [srcMem], size, [mbar], ctaMask;

cp.async.bulk.shared::cluster.global.mbarrier::complete_tx::bytes.L2::cache_hint
                                             [dstMem], [srcMem], size, [mbar], cache-policy;


// .shared::cta -> .shared::cluster (strictly remote):
cp.async.bulk.shared::cluster.shared::cta.mbarrier::complete_tx::bytes [dstMem], [srcMem], size, [mbar];

// .shared::cta -> .global:
cp.async.bulk.global.shared::cta.bulk_group [dstMem], [srcMem], size;

cp.async.bulk.global.shared::cta.bulk_group.L2::cache_hint} [dstMem], [srcMem], size, cache-policy;

9.7.8.24.7. Data Movement and Conversion Instructions: cp.reduce.async.bulk

cp.reduce.async.bulk

Initiates an asynchronous reduction operation.

Syntax

cp.reduce.async.bulk.dst.src.completion_mechanism.redOp.type
              [dstMem], [srcMem], size, [mbar]

.dst =                  { .shared::cluster }
.src =                  { .shared::cta }
.completion_mechanism = { .mbarrier::complete_tx::bytes }
.redOp=                 { .and, .or, .xor,
                          .add, .inc, .dec,
                          .min, .max }
.type =                 { .b32, .u32, .s32, .b64, .u64 }


cp.reduce.async.bulk.dst.src.completion_mechanism{.level::cache_hint}.redOp.type
               [dstMem], [srcMem], size{, cache-policy}

.dst =                  { .global      }
.src =                  { .shared::cta }
.completion_mechanism = { .bulk_group }
.level::cache_hint    = { .L2::cache_hint }
.redOp=                 { .and, .or, .xor,
                          .add, .inc, .dec,
                          .min, .max }
.type =                 { .f16, .bf16, .b32, .u32, .s32, .b64, .u64, .s64, .f32, .f64 }


cp.reduce.async.bulk.dst.src.completion_mechanism{.level::cache_hint}.add.noftz.type
               [dstMem], [srcMem], size{, cache-policy}
.dst  =                 { .global }
.src  =                 { .shared::cta }
.completion_mechanism = { .bulk_group }
.type =                 { .f16, .bf16 }

Description

cp.reduce.async.bulk is a non-blocking instruction which initiates an asynchronous reduction operation on an array of memory locations specified by the destination address operand dstMem with the source array whose location is specified by the source address operand srcMem. The size of the source and the destination array must be the same and is specified by the operand size.

Each data element in the destination array is reduced inline with the corresponding data element in the source array with the reduction operation specified by the modifier .redOp. The type of each data element in the source and the destination array is specified by the modifier .type.

The source address operand srcMem is located in the state space specified by .src and the destination address operand dstMem is located in the state specified by the .dst.

The 32-bit operand size specifies the amount of memory to be copied from the source location and used in the reduction operation, in terms of number of bytes. size must be a multiple of 16. If the value is not a multiple of 16, then the behavior is undefined. The memory range [dstMem, dstMem + size - 1] must not overflow the destination memory space and the memory range [srcMem, srcMem + size - 1] must not overflow the source memory space. Otherwise, the behavior is undefined. The addresses dstMem and srcMem must be aligned to 16 bytes.

The operations supported by .redOp are classified as follows:

• The bit-size operations are .and, .or, and .xor.

• The integer operations are .add, .inc, .dec, .min, and .max. The .inc and .dec operations return a result in the range [0..x] where x is the value at the source state space.

• The floating point operation .add rounds to the nearest even. The current implementation of cp.reduce.async.bulk.add.f32 flushes subnormal inputs and results to sign-preserving zero. The cp.reduce.async.bulk.add.f16 and cp.reduce.async.bulk.add.bf16 operations require .noftz qualifier. It preserves input and result subnormals, and does not flush them to zero.

The following table describes the valid combinations of .redOp and element type:

.dst	.redOp	Element type
.shared::cluster	.add	.u32, .s32, .u64
	.min, .max	.u32, .s32
	.inc, .dec	.u32
	.and, .or, .xor	.b32
.global	.add	.u32, .s32</