## Parallel Thread Execution ISA Version 7.5

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 7.5

PTX ISA version 7.5 introduces the following new features:
• Debug information enhancements to support label difference and negative values in the .section debugging directive.
• Support for ignore-src operand on cp.async instruction.
• Extensions to the memory consistency model to introduce the following new concepts:
• A memory proxy as an abstract label for different methods of memory access.
• Virtual aliases as distinct memory addresses accessing the same physical memory location.
• Support for new fence.proxy and membar.proxy instructions to allow synchronization of memory accesses performed via virtual aliases.

### 1.4. Document Structure

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

## 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.

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

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. Grid of Cooperative Thread Arrays

There is a maximum number of threads that a CTA can contain. However, CTAs that execute the same kernel can be batched together into a grid of CTAs, 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 CTAs cannot communicate and synchronize with each other.

Multiple CTAs may execute concurrently and in parallel, or sequentially, depending on the platform. Each CTA has a unique CTA identifier (ctaid) within a grid of CTAs. Each grid of CTAs has a 1D, 2D , or 3D shape specified by the parameter nctaid. 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, %ctaid, %nctaid, and %gridid.

The host issues a succession of kernel invocations to the device. Each kernel is executed as a batch of threads organized as a grid of CTAs (Figure 1).

A cooperative thread array (CTA) is a set of concurrent threads that execute the same kernel program. A grid is a set of CTAs that execute independently.

### 2.3. Memory Hierarchy

PTX threads may access data from multiple memory spaces during their execution as illustrated by Figure 2. Each thread has a private local memory. Each thread block (CTA) has a shared memory visible to all threads of the block and with the same lifetime as the block. Finally, all threads have access to the same global memory.

The global, constant, and texture memory 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 2. 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 3. Hardware Model

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

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 3,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 and are not cached.

## 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.

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.

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

### 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.

### 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.

### 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.

### 4.6. 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.

### 4.6.1. 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

### 4.6.2. 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.

### 4.6.3. 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
>> << shifts
< > <= >= ordered comparisons
== != equal, not equal
& bitwise AND
^ bitwise XOR
| bitwise OR
&& logical AND
|| logical OR
Ternary ?: conditional right

### 4.6.4. 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.

### 4.6.5. 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.
.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.

.tex Global texture memory (deprecated).
Table 7. Properties of State Spaces
.sreg No No RO per-CTA
.const Yes Yes1 RO per-grid
.global Yes Yes1 R/W Context
.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-CTA
.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 instruction. Address may be taken via mov instruction.

3 Accessible via ld.param and st.param 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.

### 5.1.1. 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-, or 64-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, 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 different CTAs and different 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.

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. 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 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];
...
sub.u32      %n, %n, 1;
bra          Loop;
Done:
...
}

### 5.1.7. Shared State Space

The shared (.shared) state space is a per-CTA region of memory for threads in a CTA to share data. An address in shared memory can be read and written by any thread in a CTA. Use ld.shared and st.shared to access shared variables.

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.

### 5.2.1. 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
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.
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.

### 5.3. 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
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

### 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
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.

 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
 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 Attribute Directive: .attribute describes the .attribute directive.

### 5.4.8. Variable Attribute Directive: .attribute

#### .attribute

Variable attributes

#### Description

Used to specify special attributes of a variable.

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.

#### PTX ISA Notes

• Introduced in PTX ISA version 4.0.

#### Target ISA Notes

• .managed attribute requires sm_30 or higher.

#### Examples

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

## 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.

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

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. 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.

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;

If a memory instruction does not specify a state space, the operation is performed using generic addressing. The state spaces const, 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. 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, 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® architeture.

### 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 )
{
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 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.

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, the 64-bit 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 Programming Guide.

### 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. 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.

### 8.2.4. Packed Data-types

The packed data-type .f16x2 consists of two .f16 values accessed in adjacent memory locations. Memory operations on the packed data-type .f16x2 are modelled as a pair of equivalent memory operations with a scalar data-type .f16, executed in an unspecified order on each element of the packed data.

### 8.2.5. 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.cta, since no thread outside the same CTA 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.
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 or .volatile qualifier.
weak operation An ld or st instruction with a .weak qualifier.
synchronizing operation A bar instruction, fence operation, release operation or acquire operation.

### 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 three scopes:

Table 18. Scopes
Scope Description
.cta The set of all threads executing in the same CTA 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];

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];

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.

### 8.9.2. 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.sync or bar.red or bar.arrive operation synchronizes with a bar.sync or bar.red operation executed on the same barrier.
3. 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.

### 8.10.1. 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.

 .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.u32 %r0, [x]; R2: ld.global.relaxed.u32 %r1, [x]; IF %r0 == 1 THEN %r1 == 1

### 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
L1:  	...

### 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 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
b16 inv - chop chop inv - chop chop inv - chop chop - chop chop
b32 inv inv - chop inv inv - chop inv inv - chop inv - chop
b64 inv inv inv - inv inv inv - inv inv inv - inv inv -
s8 - chop chop chop - chop chop chop - chop chop chop inv inv inv
s16 inv - chop chop inv - chop chop inv - chop chop inv inv inv
s32 inv inv - chop inv inv - chop inv inv - chop inv inv inv
s64 inv inv inv - inv inv inv - inv inv inv - inv inv inv
u8 - chop chop chop - chop chop chop - chop chop chop inv inv inv
u16 inv - chop chop inv - chop chop inv - chop chop inv inv inv
u32 inv inv - chop inv inv - chop inv inv - chop inv inv inv
u64 inv inv inv - inv inv inv - inv inv inv - inv inv inv
f16 inv - chop chop inv inv inv inv inv inv inv inv - inv inv
f32 inv inv - chop inv inv inv inv inv inv inv inv inv - inv
f64 inv inv inv - 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.

1. Source register size must be of equal or greater size than the instruction-type size.
2. 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.
3. 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.
4. 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 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
b16 inv - zext zext inv - zext zext inv - zext zext - zext zext
b32 inv inv - zext inv inv - zext inv inv - zext inv - zext
b64 inv inv inv - inv inv inv - inv inv inv - inv inv -
s8 - sext sext sext - sext sext sext - sext sext sext inv inv inv
s16 inv - sext sext inv - sext sext inv - sext sext inv inv inv
s32 inv inv - sext inv inv - sext inv inv - sext inv inv inv
s64 inv inv inv - inv inv inv - inv inv inv - inv inv inv
u8 - zext zext zext - zext zext zext - zext zext zext inv inv inv
u16 inv - zext zext inv - zext zext inv - zext zext inv inv inv
u32 inv inv - zext inv inv - zext inv inv - zext inv inv inv
u64 inv inv inv - inv inv inv - inv inv inv - inv inv inv
f16 inv - zext zext inv inv inv inv inv inv inv inv - inv inv
f32 inv inv - zext inv inv inv inv inv inv inv inv inv - inv
f64 inv inv inv - 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.

1. Destination register size must be of equal or greater size than the instruction-type size.
2. 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.
3. 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.
4. 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:

• sub
• mul
• mul24
• div
• rem
• abs
• neg
• min
• max
• popc
• clz
• bfind
• fns
• brev
• bfe
• bfi
• dp4a
• dp2a

### 9.7.1.1. Integer Arithmetic Instructions: add

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

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

Performs addition 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
@p  add.u32     x,y,z;
add.sat.s32 c,c,1;

### 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{.hi,.lo,.wide}.type  d, a, b;

.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

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

##### Syntax
mad{.hi,.lo,.wide}.type  d, a, b, c;

.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{.hi,.lo}.type  d, a, b;

.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

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

##### Syntax
mad24{.hi,.lo}.type  d, a, b, c;

.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

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

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.type  d, a, b;

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

Store the minimum of a and b in d.

##### Semantics
d = (a < b) ? a : b; // Integer (signed and unsigned)
##### Notes

Signed and unsigned differ.

##### PTX ISA Notes

Introduced in PTX ISA version 1.0.

##### Target ISA Notes

Supported on all target architectures.

##### Examples
    min.s32  r0,a,b;
@p  min.u16  h,i,j;

### 9.7.1.13. Integer Arithmetic Instructions: max

##### max

Find the maximum of two values.

##### Syntax
max.type  d, a, b;

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

Store the maximum of a and b in d.

##### Semantics
d = (a > b) ? a : b; // Integer (signed and unsigned)
##### Notes

Signed and unsigned differ.

##### PTX ISA Notes

Introduced in PTX ISA version 1.0.

##### Target ISA Notes

Supported on all target architectures.

##### Examples
    max.u32  d,a,b;
max.s32  q,q,0;

### 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

##### 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) {
d = base;
}
} else {
pos = base;
count = |offset| - 1;
inc = (offset > 0) ? 1 : -1;

while ((pos >= 0) && (pos < 32)) {
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

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: 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;

### 9.7.1.22. 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:
• sub.cc, subc

### 9.7.2.1. Extended-Precision Arithmetic Instructions: add.cc

##### 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.u32     x4,y4,z4;

### 9.7.2.2. Extended-Precision Arithmetic Instructions: 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.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

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

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
// no carry-out
mad.lo.cc.u32   r1,r4,r7,r1;  // r1+=(r4*r7).[31:0], may carry-out
// 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


### 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
• sub
• mul
• fma
• 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

##### Syntax
add{.rnd}{.ftz}{.sat}.f32  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.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.

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

##### 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

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 .targetsm_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 .targetsm_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.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.

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.

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

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.NaN introduced 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.NaN requires 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.NaN introduced 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.NaN requires 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 2a.

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:

• 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

##### Syntax
add{.rnd}{.ftz}{.sat}.f16   d, a, b;

.rnd = { .rn };
##### Description

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

For .f16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then added in parallel to produce .f16x2 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.

##### Semantics
if (type == f16) {
d = a + b;
} else if (type == f16x2) {
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.

##### Target ISA Notes

Requires sm_53 or higher.

##### Examples
     // scalar f16 additions

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
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
add.f16x2       f2, f0, f1;     // SIMD f16x2 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;

.rnd = { .rn };
##### Description

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

For .f16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then subtracted in parallel to produce .f16x2 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.

##### Semantics
if (type == f16) {
d = a - b;
} else if (type == f16x2) {
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.

##### Target ISA Notes

Requires sm_53 or higher.

##### Examples
     // scalar f16 subtractions
sub.f16        d0, a0, b0;
sub.rn.f16     d1, a1, b1;

// 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 fp16 subtraction
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
sub.f16x2       f2, f0, f1;     // SIMD f16x2 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;

.rnd = { .rn };
##### Description

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

For .f16x2 instruction type, forms input vectors by half word values from source operands. Half-word operands are then multiplied in parallel to produce .f16x2 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.

##### Semantics
if (type == f16) {
d = a * b;
} else if (type == f16x2) {
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.

##### Target ISA Notes

Requires sm_53 or higher.

##### Examples
     // scalar f16 multiplications
mul.f16        d0, a0, b0;
mul.rn.f16     d1, a1, b1;

// 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 fp16 multiplication
ld.global.b32   f1, [addr + 4]; // load 32 bit which hold packed f16x2
mul.f16x2       f2, f0, f1;     // SIMD f16x2 multiplication

### 9.7.4.4. Half Precision Floating Point Instructions: fma

##### 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;

.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.
##### 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.

##### Target ISA Notes

Requires sm_53 or higher.

fma.relu.{f16, f16x2} and fma{.relu}.{bf16, bf16x2} require sm_80 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.bf16        d1, a1, b1, c1;
fma.rn.relu.bf16   d1, a1, b1, c1;

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
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

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


### 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

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.

##### 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