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Programming Guide (PDF) - CUDA Toolkit v5.5 (older) - Last updated July 19, 2013 - Send Feedback

## Changes from Version 5.0

• Updated section CUDA C Runtime to mention that the CUDA runtime library can be statically linked.

• Mentioned in chapter Hardware Implementation that the NVIDIA GPU architecture uses a little-endian representation.

• Clarified in section SIMT Architecture the meaning of active and inactive threads within a warp.

• Added a sample code to Module that illustrates the new PTX linker.

## 1. Introduction

### 1.1. From Graphics Processing to General Purpose Parallel Computing

Driven by the insatiable market demand for realtime, high-definition 3D graphics, the programmable Graphic Processor Unit or GPU has evolved into a highly parallel, multithreaded, manycore processor with tremendous computational horsepower and very high memory bandwidth, as illustrated by Figure 1 and Figure 2.

Figure 1. Floating-Point Operations per Second for the CPU and GPU

Figure 2. Memory Bandwidth for the CPU and GPU

The reason behind the discrepancy in floating-point capability between the CPU and the GPU is that the GPU is specialized for compute-intensive, highly parallel computation - exactly what graphics rendering is about - and therefore designed such that more transistors are devoted to data processing rather than data caching and flow control, as schematically illustrated by Figure 3.

Figure 3. The GPU Devotes More Transistors to Data Processing

More specifically, 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.

### 1.2. CUDA™: A General-Purpose Parallel Computing Platform and Programming Model

In November 2006, NVIDIA introduced CUDA™, a general purpose parallel computing platform and programming model that leverages the parallel compute engine in NVIDIA GPUs to solve many complex computational problems in a more efficient way than on a CPU.

CUDA comes with a software environment that allows developers to use C as a high-level programming language. As illustrated by Figure 4, other languages, application programming interfaces, or directives-based approaches are supported, such as FORTRAN, DirectCompute, OpenACC.

Figure 4. GPU Computing Applications. CUDA is designed to support various languages and application programming interfaces.

### 1.3. A Scalable Programming Model

The advent of multicore CPUs and manycore GPUs means that mainstream processor chips are now parallel systems. Furthermore, their parallelism continues to scale with Moore's law. The challenge is to develop application software that transparently scales its parallelism to leverage the increasing number of processor cores, much as 3D graphics applications transparently scale their parallelism to manycore GPUs with widely varying numbers of cores.

The CUDA parallel programming model is designed to overcome this challenge while maintaining a low learning curve for programmers familiar with standard programming languages such as C.

At its core are three key abstractions - a hierarchy of thread groups, shared memories, and barrier synchronization - that are simply exposed to the programmer as a minimal set of language extensions.

These abstractions provide fine-grained data parallelism and thread parallelism, nested within coarse-grained data parallelism and task parallelism. They guide the programmer to partition the problem into coarse sub-problems that can be solved independently in parallel by blocks of threads, and each sub-problem into finer pieces that can be solved cooperatively in parallel by all threads within the block.

This decomposition preserves language expressivity by allowing threads to cooperate when solving each sub-problem, and at the same time enables automatic scalability. Indeed, each block of threads can be scheduled on any of the available multiprocessors within a GPU, in any order, concurrently or sequentially, so that a compiled CUDA program can execute on any number of multiprocessors as illustrated by Figure 5, and only the runtime system needs to know the physical multiprocessor count.

This scalable programming model allows the GPU architecture to span a wide market range by simply scaling the number of multiprocessors and memory partitions: from the high-performance enthusiast GeForce GPUs and professional Quadro and Tesla computing products to a variety of inexpensive, mainstream GeForce GPUs (see CUDA-Enabled GPUs for a list of all CUDA-enabled GPUs).

Figure 5. Automatic Scalability

Note: A GPU is built around an array of Streaming Multiprocessors (SMs) (see Hardware Implementation for more details). A multithreaded program is partitioned into blocks of threads that execute independently from each other, so that a GPU with more multiprocessors will automatically execute the program in less time than a GPU with fewer multiprocessors.

### 1.4. Document Structure

This document is organized into the following chapters:

## 2. Programming Model

This chapter introduces the main concepts behind the CUDA programming model by outlining how they are exposed in C. An extensive description of CUDA C is given in Programming Interface.

Full code for the vector addition example used in this chapter and the next can be found in the vectorAdd SDK code sample.

### 2.1. Kernels

CUDA C extends C by allowing the programmer to define C functions, called kernels, that, when called, are executed N times in parallel by N different CUDA threads, as opposed to only once like regular C functions.

A kernel is defined using the __global__ declaration specifier and the number of CUDA threads that execute that kernel for a given kernel call is specified using a new <<<...>>>execution configuration syntax (see C Language Extensions). Each thread that executes the kernel is given a unique thread ID that is accessible within the kernel through the built-in threadIdx variable.

As an illustration, the following sample code adds two vectors A and B of size N and stores the result into vector C:

```// Kernel definition
__global__ void VecAdd(float* A, float* B, float* C)
{
C[i] = A[i] + B[i];
}

int main()
{
...
// Kernel invocation with N threads
...
}```

For convenience, threadIdx is a 3-component vector, so that threads can be identified using a one-dimensional, two-dimensional, or three-dimensional thread index, forming a one-dimensional, two-dimensional, or three-dimensional thread block. This provides a natural way to invoke computation across the elements in a domain such as a vector, matrix, or volume.

The index of a thread and its thread ID relate to each other in a straightforward way: For a one-dimensional block, they are the same; for a two-dimensional block of size (Dx, Dy),the thread ID of a thread of index (x, y) is (x + y Dx); for a three-dimensional block of size (Dx, Dy, Dz), the thread ID of a thread of index (x, y, z) is (x + y Dx + z Dx Dy).

As an example, the following code adds two matrices A and B of size NxN and stores the result into matrix C:

```// Kernel definition
__global__ void MatAdd(float A[N][N], float B[N][N],
float C[N][N])
{
C[i][j] = A[i][j] + B[i][j];
}

int main()
{
...
// Kernel invocation with one block of N * N * 1 threads
int numBlocks = 1;
...
}```

There is a limit to the number of threads per block, since all threads of a block are expected to reside on the same processor core and must share the limited memory resources of that core. On current GPUs, a thread block may contain up to 1024 threads.

However, a kernel can be executed by multiple equally-shaped thread blocks, so that the total number of threads is equal to the number of threads per block times the number of blocks.

Blocks are organized into a one-dimensional, two-dimensional, or three-dimensional grid of thread blocks as illustrated by Figure 6. The number of thread blocks in a grid is usually dictated by the size of the data being processed or the number of processors in the system, which it can greatly exceed.

Figure 6. Grid of Thread Blocks

The number of threads per block and the number of blocks per grid specified in the <<<...>>> syntax can be of type int or dim3. Two-dimensional blocks or grids can be specified as in the example above.

Each block within the grid can be identified by a one-dimensional, two-dimensional, or three-dimensional index accessible within the kernel through the built-in blockIdx variable. The dimension of the thread block is accessible within the kernel through the built-in blockDim variable.

Extending the previous MatAdd() example to handle multiple blocks, the code becomes as follows.

```// Kernel definition
__global__ void MatAdd(float A[N][N], float B[N][N],
float C[N][N])
{
int i = blockIdx.x * blockDim.x + threadIdx.x;
int j = blockIdx.y * blockDim.y + threadIdx.y;
if (i < N && j < N)
C[i][j] = A[i][j] + B[i][j];
}

int main()
{
...
// Kernel invocation
...
}```

A thread block size of 16x16 (256 threads), although arbitrary in this case, is a common choice. The grid is created with enough blocks to have one thread per matrix element as before. For simplicity, this example assumes that the number of threads per grid in each dimension is evenly divisible by the number of threads per block in that dimension, although that need not be the case.

Thread blocks are required to execute independently: It must be possible to execute them in any order, in parallel or in series. This independence requirement allows thread blocks to be scheduled in any order across any number of cores as illustrated by Figure 1 4, enabling programmers to write code that scales with the number of cores.

Threads within a block can cooperate by sharing data through some shared memory and by synchronizing their execution to coordinate memory accesses. More precisely, one can specify synchronization points in the kernel by calling the __syncthreads() intrinsic function; __syncthreads() acts as a barrier at which all threads in the block must wait before any is allowed to proceed. Shared Memory gives an example of using shared memory.

For efficient cooperation, the shared memory is expected to be a low-latency memory near each processor core (much like an L1 cache) and __syncthreads() is expected to be lightweight.

### 2.3. Memory Hierarchy

CUDA threads may access data from multiple memory spaces during their execution as illustrated by Figure 7. Each thread has private local memory. Each thread block has shared memory visible to all threads of the block and with the same lifetime as the block. All threads have access to the same global memory.

There are also two additional read-only memory spaces accessible by all threads: the constant and texture memory spaces. The global, constant, and texture memory spaces are optimized for different memory usages (see Device Memory Accesses). Texture memory also offers different addressing modes, as well as data filtering, for some specific data formats (see Texture and Surface Memory).

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

Figure 7. Memory Hierarchy

### 2.4. Heterogeneous Programming

As illustrated by Figure 8, the CUDA programming model assumes that the CUDA threads execute on a physically separate device that operates as a coprocessor to the host running the C program. This is the case, for example, when the kernels execute on a GPU and the rest of the C program executes on a CPU.

The CUDA programming model also assumes that both the host and the device maintain their own separate memory spaces in DRAM, referred to as host memory and device memory, respectively. Therefore, a program manages the global, constant, and texture memory spaces visible to kernels through calls to the CUDA runtime (described in Programming Interface). This includes device memory allocation and deallocation as well as data transfer between host and device memory.

Figure 8. Heterogeneous Programming

Note: Serial code executes on the host while parallel code executes on the device.

### 2.5. Compute Capability

The compute capability of a device is defined by a major revision number and a minor revision number.

Devices with the same major revision number are of the same core architecture. The major revision number is 3 for devices based on the Kepler architecture, 2 for devices based on the Fermi architecture, and 1 for devices based on the Tesla architecture.

The minor revision number corresponds to an incremental improvement to the core architecture, possibly including new features.

CUDA-Enabled GPUs lists of all CUDA-enabled devices along with their compute capability. Compute Capabilities gives the technical specifications of each compute capability.

## 3. Programming Interface

CUDA C provides a simple path for users familiar with the C programming language to easily write programs for execution by the device.

It consists of a minimal set of extensions to the C language and a runtime library.

The core language extensions have been introduced in Programming Model. They allow programmers to define a kernel as a C function and use some new syntax to specify the grid and block dimension each time the function is called. A complete description of all extensions can be found in C Language Extensions. Any source file that contains some of these extensions must be compiled with nvcc as outlined in Compilation with NVCC.

The runtime is introduced in Compilation Workflow. It provides C functions that execute on the host to allocate and deallocate device memory, transfer data between host memory and device memory, manage systems with multiple devices, etc. A complete description of the runtime can be found in the CUDA reference manual.

The runtime is built on top of a lower-level C API, the CUDA driver API, which is also accessible by the application. The driver API provides an additional level of control by exposing lower-level concepts such as CUDA contexts - the analogue of host processes for the device - and CUDA modules - the analogue of dynamically loaded libraries for the device. Most applications do not use the driver API as they do not need this additional level of control and when using the runtime, context and module management are implicit, resulting in more concise code. The driver API is introduced in Driver API and fully described in the reference manual.

### Compilation with NVCC

Kernels can be written using the CUDA instruction set architecture, called PTX, which is described in the PTX reference manual. It is however usually more effective to use a high-level programming language such as C. In both cases, kernels must be compiled into binary code by nvcc to execute on the device.

nvcc is a compiler driver that simplifies the process of compiling C or PTX code: It provides simple and familiar command line options and executes them by invoking the collection of tools that implement the different compilation stages. This section gives an overview of nvcc workflow and command options. A complete description can be found in the nvcc user manual.

### 3.1.1.1. Offline Compilation

Source files compiled with nvcc can include a mix of host code (i.e., code that executes on the host) and device code (i.e., code that executes on the device). nvcc's basic workflow consists in separating device code from host code and then:

• compiling the device code into an assembly form (PTX code) and/or binary form (cubin object),
• and modifying the host code by replacing the <<<...>>> syntax introduced in Kernels (and described in more details in Execution Configuration) by the necessary CUDA C runtime function calls to load and launch each compiled kernel from the PTX code and/or cubin object.

The modified host code is output either as C code that is left to be compiled using another tool or as object code directly by letting nvcc invoke the host compiler during the last compilation stage.

Applications can then:

• Either link to the compiled host code (this is the most common case),
• Or ignore the modified host code (if any) and use the CUDA driver API (see Driver API) to load and execute the PTX code or cubin object.

### 3.1.1.2. Just-in-Time Compilation

Any PTX code loaded by an application at runtime is compiled further to binary code by the device driver. This is called just-in-time compilation. Just-in-time compilation increases application load time, but allows the application to benefit from any new compiler improvements coming with each new device driver. It is also the only way for applications to run on devices that did not exist at the time the application was compiled, as detailed in Application Compatibility.

When the device driver just-in-time compiles some PTX code for some application, it automatically caches a copy of the generated binary code in order to avoid repeating the compilation in subsequent invocations of the application. The cache - referred to as compute cache - is automatically invalidated when the device driver is upgraded, so that applications can benefit from the improvements in the new just-in-time compiler built into the device driver.

Environment variables are available to control just-in-time compilation as described in CUDA Environment Variables

### 3.1.2. Binary Compatibility

Binary code is architecture-specific. A cubin object is generated using the compiler option -code that specifies the targeted architecture: For example, compiling with -code=sm_13 produces binary code for devices of compute capability 1.3 (see Compute Capability for a description of the compute capability). Binary compatibility is guaranteed from one minor revision to the next one, but not from one minor revision to the previous one or across major revisions. In other words, a cubin object generated for compute capability X.y is only guaranteed to execute on devices of compute capability X.z where z≥y.

### 3.1.3. PTX Compatibility

Some PTX instructions are only supported on devices of higher compute capabilities. For example, atomic instructions on global memory are only supported on devices of compute capability 1.1 and above; double-precision instructions are only supported on devices of compute capability 1.3 and above. The -arch compiler option specifies the compute capability that is assumed when compiling C to PTX code. So, code that contains double-precision arithmetic, for example, must be compiled with -arch=sm_13 (or higher compute capability), otherwise double-precision arithmetic will get demoted to single-precision arithmetic.

PTX code produced for some specific compute capability can always be compiled to binary code of greater or equal compute capability.

### 3.1.4. Application Compatibility

To execute code on devices of specific compute capability, an application must load binary or PTX code that is compatible with this compute capability as described in Binary Compatibility and PTX Compatibility. In particular, to be able to execute code on future architectures with higher compute capability (for which no binary code can be generated yet), an application must load PTX code that will be just-in-time compiled for these devices (see Just-in-Time Compilation).

Which PTX and binary code gets embedded in a CUDA C application is controlled by the -arch and -code compiler options or the -gencode compiler option as detailed in the nvcc user manual. For example,

```nvcc x.cu
-gencode arch=compute_10,code=sm_10
-gencode arch=compute_11,code=\'compute_11,sm_11\'```

embeds binary code compatible with compute capability 1.0 (first -gencode option) and PTX and binary code compatible with compute capability 1.1 (second -gencode option).

Host code is generated to automatically select at runtime the most appropriate code to load and execute, which, in the above example, will be:

• 1.0 binary code for devices with compute capability 1.0,
• 1.1 binary code for devices with compute capability 1.1, 1.2, 1.3,
• binary code obtained by compiling 1.1 PTX code for devices with compute capabilities 2.0 and higher.

x.cu can have an optimized code path that uses atomic operations, for example, which are only supported in devices of compute capability 1.1 and higher. The __CUDA_ARCH__ macro can be used to differentiate various code paths based on compute capability. It is only defined for device code. When compiling with -arch=compute_11 for example, __CUDA_ARCH__ is equal to 110.

Applications using the driver API must compile code to separate files and explicitly load and execute the most appropriate file at runtime.

The nvcc user manual lists various shorthand for the -arch, -code, and -gencode compiler options. For example, -arch=sm_13 is a shorthand for -arch=compute_13-code=compute_13,sm_13 (which is the same as -gencodearch=compute_13,code=\'compute_13,sm_13\').

### 3.1.5. C/C++ Compatibility

The front end of the compiler processes CUDA source files according to C++ syntax rules. Full C++ is supported for the host code. However, only a subset of C++ is fully supported for the device code as described in C/C++ Language Support.

### 3.1.6. 64-Bit Compatibility

The 64-bit version of nvcc compiles device code in 64-bit mode (i.e., pointers are 64-bit). Device code compiled in 64-bit mode is only supported with host code compiled in 64-bit mode.

Similarly, the 32-bit version of nvcc compiles device code in 32-bit mode and device code compiled in 32-bit mode is only supported with host code compiled in 32-bit mode.

The 32-bit version of nvcc can compile device code in 64-bit mode also using the -m64 compiler option.

The 64-bit version of nvcc can compile device code in 32-bit mode also using the -m32 compiler option.

### 3.2. CUDA C Runtime

The runtime is implemented in the cudart library, which is linked to the application, either statically via cudart.lib or libcudart.a, or dynamically via cudart.dll or libcudart.so. Applications that require cudart.dll and/or cudart.so for dynamic linking typically include them as part of the application installation package.

All its entry points are prefixed with cuda.

As mentioned in Heterogeneous Programming, the CUDA programming model assumes a system composed of a host and a device, each with their own separate memory. Device Memory gives an overview of the runtime functions used to manage device memory.

Shared Memory illustrates the use of shared memory, introduced in Thread Hierarchy, to maximize performance.

Page-Locked Host Memory introduces page-locked host memory that is required to overlap kernel execution with data transfers between host and device memory.

Asynchronous Concurrent Execution describes the concepts and API used to enable asynchronous concurrent execution at various levels in the system.

Multi-Device System shows how the programming model extends to a system with multiple devices attached to the same host.

Error Checking describes how to properly check the errors generated by the runtime.

Call Stack mentions the runtime functions used to manage the CUDA C call stack.

Texture and Surface Memory presents the texture and surface memory spaces that provide another way to access device memory; they also expose a subset of the GPU texturing hardware.

Graphics Interoperability introduces the various functions the runtime provides to interoperate with the two main graphics APIs, OpenGL and Direct3D.

### 3.2.1. Initialization

There is no explicit initialization function for the runtime; it initializes the first time a runtime function is called (more specifically any function other than functions from the device and version management sections of the reference manual). One needs to keep this in mind when timing runtime function calls and when interpreting the error code from the first call into the runtime.

During initialization, the runtime creates a CUDA context for each device in the system (see Context for more details on CUDA contexts). This context is the primary context for this device and it is shared among all the host threads of the application. This all happens under the hood and the runtime does not expose the primary context to the application.

When a host thread calls cudaDeviceReset(), this destroys the primary context of the device the host thread currently operates on (i.e., the current device as defined in Device Selection). The next runtime function call made by any host thread that has this device as current will create a new primary context for this device.

### 3.2.2. Device Memory

As mentioned in Heterogeneous Programming, the CUDA programming model assumes a system composed of a host and a device, each with their own separate memory. Kernels operate out of device memory, so the runtime provides functions to allocate, deallocate, and copy device memory, as well as transfer data between host memory and device memory.

Device memory can be allocated either as linear memory or as CUDA arrays.

CUDA arrays are opaque memory layouts optimized for texture fetching. They are described in Texture and Surface Memory.

Linear memory exists on the device in a 32-bit address space for devices of compute capability 1.x and 40-bit address space of devices of higher compute capability, so separately allocated entities can reference one another via pointers, for example, in a binary tree.

Linear memory is typically allocated using cudaMalloc() and freed using cudaFree() and data transfer between host memory and device memory are typically done using cudaMemcpy(). In the vector addition code sample of Kernels, the vectors need to be copied from host memory to device memory:

```// Device code
__global__ void VecAdd(float* A, float* B, float* C, int N)
{
int i = blockDim.x * blockIdx.x + threadIdx.x;
if (i < N)
C[i] = A[i] + B[i];
}

// Host code
int main()
{
int N = ...;
size_t size = N * sizeof(float);

// Allocate input vectors h_A and h_B in host memory
float* h_A = (float*)malloc(size);
float* h_B = (float*)malloc(size);

// Initialize input vectors
...

// Allocate vectors in device memory
float* d_A;
cudaMalloc(&d_A, size);
float* d_B;
cudaMalloc(&d_B, size);
float* d_C;
cudaMalloc(&d_C, size);

// Copy vectors from host memory to device memory
cudaMemcpy(d_A, h_A, size, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size, cudaMemcpyHostToDevice);

// Invoke kernel
int blocksPerGrid =

// Copy result from device memory to host memory
// h_C contains the result in host memory
cudaMemcpy(h_C, d_C, size, cudaMemcpyDeviceToHost);

// Free device memory
cudaFree(d_A);
cudaFree(d_B);
cudaFree(d_C);

// Free host memory
...
}```

Linear memory can also be allocated through cudaMallocPitch() and cudaMalloc3D(). These functions are recommended for allocations of 2D or 3D arrays as it makes sure that the allocation is appropriately padded to meet the alignment requirements described in Device Memory Accesses, therefore ensuring best performance when accessing the row addresses or performing copies between 2D arrays and other regions of device memory (using the cudaMemcpy2D() and cudaMemcpy3D() functions). The returned pitch (or stride) must be used to access array elements. The following code sample allocates a width x height 2D array of floating-point values and shows how to loop over the array elements in device code:

```// Host code
int width = 64, height = 64;
float* devPtr;
size_t pitch;
cudaMallocPitch(&devPtr, &pitch,
width * sizeof(float), height);
MyKernel<<<100, 512>>>(devPtr, pitch, width, height);

// Device code
__global__ void MyKernel(float* devPtr,
size_t pitch, int width, int height)
{
for (int r = 0; r < height; ++r) {
float* row = (float*)((char*)devPtr + r * pitch);
for (int c = 0; c > width; ++c) {
float element = row[c];
}
}
}```

The following code sample allocates a width x height x depth 3D array of floating-point values and shows how to loop over the array elements in device code:

```// Host code
int width = 64, height = 64, depth = 64;
cudaExtent extent = make_cudaExtent(width * sizeof(float),
height, depth);
cudaPitchedPtr devPitchedPtr;
cudaMalloc3D(&devPitchedPtr, extent);
MyKernel<<<100, 512>>>(devPitchedPtr, width, height, depth);

// Device code
__global__ void MyKernel(cudaPitchedPtr devPitchedPtr,
int width, int height, int depth)
{
char* devPtr = devPitchedPtr.ptr;
size_t pitch = devPitchedPtr.pitch;
size_t slicePitch = pitch * height;
for (int z = 0; z < depth; ++z) {
char* slice = devPtr + z * slicePitch;
for (int y = 0; y < height; ++y) {
float* row = (float*)(slice + y * pitch);
for (int x = 0; x < width; ++x) {
float element = row[x];
}
}
}
}```

The reference manual lists all the various functions used to copy memory between linear memory allocated with cudaMalloc(), linear memory allocated with cudaMallocPitch() or cudaMalloc3D(), CUDA arrays, and memory allocated for variables declared in global or constant memory space.

The following code sample illustrates various ways of accessing global variables via the runtime API:

```__constant__ float constData[256];
float data[256];
cudaMemcpyToSymbol(constData, data, sizeof(data));
cudaMemcpyFromSymbol(data, constData, sizeof(data));

__device__ float devData;
float value = 3.14f;
cudaMemcpyToSymbol(devData, &value, sizeof(float));

__device__ float* devPointer;
float* ptr;
cudaMalloc(&ptr, 256 * sizeof(float));
cudaMemcpyToSymbol(devPointer, &ptr, sizeof(ptr));```

cudaGetSymbolAddress() is used to retrieve the address pointing to the memory allocated for a variable declared in global memory space. The size of the allocated memory is obtained through cudaGetSymbolSize().

### 3.2.3. Shared Memory

As detailed in Variable Type Qualifiers shared memory is allocated using the __shared__ qualifier.

Shared memory is expected to be much faster than global memory as mentioned in Thread Hierarchy and detailed in Shared Memory. Any opportunity to replace global memory accesses by shared memory accesses should therefore be exploited as illustrated by the following matrix multiplication example.

The following code sample is a straightforward implementation of matrix multiplication that does not take advantage of shared memory. Each thread reads one row of A and one column of B and computes the corresponding element of C as illustrated in Figure 9. A is therefore read B.width times from global memory and B is read A.height times.

```// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.width + col)
typedef struct {
int width;
int height;
float* elements;
} Matrix;

#define BLOCK_SIZE 16

// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);

// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix B, Matrix C)
{
// Load A and B to device memory
Matrix d_A;
d_A.width = A.width; d_A.height = A.height;
size_t size = A.width * A.height * sizeof(float);
cudaMalloc(&d_A.elements, size);
cudaMemcpy(d_A.elements, A.elements, size,
cudaMemcpyHostToDevice);
Matrix d_B;
d_B.width = B.width; d_B.height = B.height;
size = B.width * B.height * sizeof(float);
cudaMalloc(&d_B.elements, size);
cudaMemcpy(d_B.elements, B.elements, size,
cudaMemcpyHostToDevice);

// Allocate C in device memory
Matrix d_C;
d_C.width = C.width; d_C.height = C.height;
size = C.width * C.height * sizeof(float);
cudaMalloc(&d_C.elements, size);

// Invoke kernel
dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);

// Read C from device memory
cudaMemcpy(C.elements, Cd.elements, size,
cudaMemcpyDeviceToHost);

// Free device memory
cudaFree(d_A.elements);
cudaFree(d_B.elements);
cudaFree(d_C.elements);
}

// Matrix multiplication kernel called by MatMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
// Each thread computes one element of C
// by accumulating results into Cvalue
float Cvalue = 0;
int row = blockIdx.y * blockDim.y + threadIdx.y;
int col = blockIdx.x * blockDim.x + threadIdx.x;
for (int e = 0; e < A.width; ++e)
Cvalue += A.elements[row * A.width + e]
* B.elements[e * B.width + col];
C.elements[row * C.width + col] = Cvalue;
}```
Figure 9. Matrix Multiplication without Shared Memory

The following code sample is an implementation of matrix multiplication that does take advantage of shared memory. In this implementation, each thread block is responsible for computing one square sub-matrix Csub of C and each thread within the block is responsible for computing one element of Csub. As illustrated in Figure 10, Csub is equal to the product of two rectangular matrices: the sub-matrix of A of dimension (A.width, block_size) that has the same row indices as Csub, and the sub-matrix of B of dimension (block_size, A.width )that has the same column indices as Csub. In order to fit into the device's resources, these two rectangular matrices are divided into as many square matrices of dimension block_size as necessary and Csub is computed as the sum of the products of these square matrices. Each of these products is performed by first loading the two corresponding square matrices from global memory to shared memory with one thread loading one element of each matrix, and then by having each thread compute one element of the product. Each thread accumulates the result of each of these products into a register and once done writes the result to global memory.

By blocking the computation this way, we take advantage of fast shared memory and save a lot of global memory bandwidth since A is only read (B.width / block_size) times from global memory and B is read (A.height / block_size) times.

The Matrix type from the previous code sample is augmented with a stride field, so that sub-matrices can be efficiently represented with the same type. __device__ functions (see __device__) are used to get and set elements and build any sub-matrix from a matrix.

```// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.stride + col)
typedef struct {
int width;
int height;
int stride;
float* elements;
} Matrix;

// Get a matrix element
__device__ float GetElement(const Matrix A, int row, int col)
{
return A.elements[row * A.stride + col];
}

// Set a matrix element
__device__ void SetElement(Matrix A, int row, int col,
float value)
{
A.elements[row * A.stride + col] = value;
}

// Get the BLOCK_SIZExBLOCK_SIZE sub-matrix Asub of A that is
// located col sub-matrices to the right and row sub-matrices down
// from the upper-left corner of A
__device__ Matrix GetSubMatrix(Matrix A, int row, int col)
{
Matrix Asub;
Asub.width    = BLOCK_SIZE;
Asub.height   = BLOCK_SIZE;
Asub.stride   = A.stride;
Asub.elements = &A.elements[A.stride * BLOCK_SIZE * row
+ BLOCK_SIZE * col];
return Asub;
}

#define BLOCK_SIZE 16

// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);

// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix B, Matrix C)
{
// Load A and B to device memory
Matrix d_A;
d_A.width = d_A.stride = A.width; d_A.height = A.height;
size_t size = A.width * A.height * sizeof(float);
cudaMalloc(&d_A.elements, size);
cudaMemcpy(d_A.elements, A.elements, size,
cudaMemcpyHostToDevice);
Matrix d_B;
d_B.width = d_B.stride = B.width; d_B.height = B.height;
size = B.width * B.height * sizeof(float);
cudaMalloc(&d_B.elements, size);
cudaMemcpy(d_B.elements, B.elements, size,
cudaMemcpyHostToDevice);

// Allocate C in device memory
Matrix d_C;
d_C.width = d_C.stride = C.width; d_C.height = C.height;
size = C.width * C.height * sizeof(float);
cudaMalloc(&d_C.elements, size);

// Invoke kernel
dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);

// Read C from device memory
cudaMemcpy(C.elements, d_C.elements, size,
cudaMemcpyDeviceToHost);

// Free device memory
cudaFree(d_A.elements);
cudaFree(d_B.elements);
cudaFree(d_C.elements);
}

// Matrix multiplication kernel called by MatMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
// Block row and column
int blockRow = blockIdx.y;
int blockCol = blockIdx.x;

// Each thread block computes one sub-matrix Csub of C
Matrix Csub = GetSubMatrix(C, blockRow, blockCol);

// Each thread computes one element of Csub
// by accumulating results into Cvalue
float Cvalue = 0;

// Thread row and column within Csub

// Loop over all the sub-matrices of A and B that are
// required to compute Csub
// Multiply each pair of sub-matrices together
// and accumulate the results
for (int m = 0; m < (A.width / BLOCK_SIZE); ++m) {

// Get sub-matrix Asub of A
Matrix Asub = GetSubMatrix(A, blockRow, m);

// Get sub-matrix Bsub of B
Matrix Bsub = GetSubMatrix(B, m, blockCol);

// Shared memory used to store Asub and Bsub respectively
__shared__ float As[BLOCK_SIZE][BLOCK_SIZE];
__shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];

// Load Asub and Bsub from device memory to shared memory
As[row][col] = GetElement(Asub, row, col);
Bs[row][col] = GetElement(Bsub, row, col);

// Synchronize to make sure the sub-matrices are loaded
// before starting the computation

// Multiply Asub and Bsub together
for (int e = 0; e < BLOCK_SIZE; ++e)
Cvalue += As[row][e] * Bs[e][col];

// Synchronize to make sure that the preceding
// sub-matrices of A and B in the next iteration
}

// Write Csub to device memory
// Each thread writes one element
SetElement(Csub, row, col, Cvalue);
}```
Figure 10. Matrix Multiplication with Shared Memory

### 3.2.4. Page-Locked Host Memory

The runtime provides functions to allow the use of page-locked (also known as pinned) host memory (as opposed to regular pageable host memory allocated by malloc()):

• cudaHostAlloc() and cudaFreeHost() allocate and free page-locked host memory;
• cudaHostRegister() page-locks a range of memory allocated by malloc() (see reference manual for limitations).

Using page-locked host memory has several benefits:

• Copies between page-locked host memory and device memory can be performed concurrently with kernel execution for some devices as mentioned in Asynchronous Concurrent Execution.
• On some devices, page-locked host memory can be mapped into the address space of the device, eliminating the need to copy it to or from device memory as detailed in Mapped Memory.
• On systems with a front-side bus, bandwidth between host memory and device memory is higher if host memory is allocated as page-locked and even higher if in addition it is allocated as write-combining as described in Write-Combining Memory.

Page-locked host memory is a scarce resource however, so allocations in page-locked memory will start failing long before allocations in pageable memory. In addition, by reducing the amount of physical memory available to the operating system for paging, consuming too much page-locked memory reduces overall system performance.

The simple zero-copy SDK sample comes with a detailed document on the page-locked memory APIs.

### 3.2.4.1. Portable Memory

A block of page-locked memory can be used in conjunction with any device in the system (see Multi-Device System for more details on multi-device systems), but by default, the benefits of using page-locked memory described above are only available in conjunction with the device that was current when the block was allocated (and with all devices sharing the same unified address space, if any, as described in Unified Virtual Address Space). To make these advantages available to all devices, the block needs to be allocated by passing the flag cudaHostAllocPortable to cudaHostAlloc() or page-locked by passing the flag cudaHostRegisterPortable to cudaHostRegister().

### 3.2.4.2. Write-Combining Memory

By default page-locked host memory is allocated as cacheable. It can optionally be allocated as write-combining instead by passing flag cudaHostAllocWriteCombined to cudaHostAlloc(). Write-combining memory frees up the host's L1 and L2 cache resources, making more cache available to the rest of the application. In addition, write-combining memory is not snooped during transfers across the PCI Express bus, which can improve transfer performance by up to 40%.

Reading from write-combining memory from the host is prohibitively slow, so write-combining memory should in general be used for memory that the host only writes to.

### 3.2.4.3. Mapped Memory

On devices of compute capability greater than 1.0, a block of page-locked host memory can also be mapped into the address space of the device by passing flag cudaHostAllocMapped to cudaHostAlloc() or by passing flag cudaHostRegisterMapped to cudaHostRegister(). Such a block has therefore in general two addresses: one in host memory that is returned by cudaHostAlloc() or malloc(), and one in device memory that can be retrieved using cudaHostGetDevicePointer() and then used to access the block from within a kernel. The only exception is for pointers allocated with cudaHostAlloc() and when a unified address space is used for the host and the device as mentioned in Unified Virtual Address Space.

Accessing host memory directly from within a kernel has several advantages:

• There is no need to allocate a block in device memory and copy data between this block and the block in host memory; data transfers are implicitly performed as needed by the kernel;
• There is no need to use streams (see Concurrent Data Transfers) to overlap data transfers with kernel execution; the kernel-originated data transfers automatically overlap with kernel execution.

Since mapped page-locked memory is shared between host and device however, the application must synchronize memory accesses using streams or events (see Asynchronous Concurrent Execution) to avoid any potential read-after-write, write-after-read, or write-after-write hazards.

To be able to retrieve the device pointer to any mapped page-locked memory, page-locked memory mapping must be enabled by calling cudaSetDeviceFlags() with the cudaDeviceMapHost flag before any other CUDA call is performed. Otherwise, cudaHostGetDevicePointer() will return an error.

cudaHostGetDevicePointer() also returns an error if the device does not support mapped page-locked host memory. Applications may query this capability by checking the canMapHostMemory device property (see Device Enumeration), which is equal to 1 for devices that support mapped page-locked host memory.

Note that atomic functions (see Atomic Functions) operating on mapped page-locked memory are not atomic from the point of view of the host or other devices.

### 3.2.5.1. Concurrent Execution between Host and Device

In order to facilitate concurrent execution between host and device, some function calls are asynchronous: Control is returned to the host thread before the device has completed the requested task. These are:

• Kernel launches;
• Memory copies between two addresses to the same device memory;
• Memory copies from host to device of a memory block of 64 KB or less;
• Memory copies performed by functions that are suffixed with Async;
• Memory set function calls.

Programmers can globally disable asynchronous kernel launches for all CUDA applications running on a system by setting the CUDA_LAUNCH_BLOCKING environment variable to 1. This feature is provided for debugging purposes only and should never be used as a way to make production software run reliably.

Kernel launches are synchronous in the following cases:
• The application is run via a debugger or memory checker (cuda-gdb, cuda-memcheck, Nsight) on a device of compute capability 1.x;
• Hardware counters are collected via a profiler (Nsight, Visual Profiler).

### 3.2.5.2. Overlap of Data Transfer and Kernel Execution

Some devices of compute capability 1.1 and higher can perform copies between page-locked host memory and device memory concurrently with kernel execution. Applications may query this capability by checking the asyncEngineCount device property (see Device Enumeration), which is greater than zero for devices that support it. For devices of compute capability 1.x, this capability is only supported for memory copies that do not involve CUDA arrays or 2D arrays allocated through cudaMallocPitch() (see Device Memory).

### Concurrent Kernel Execution

Some devices of compute capability 2.x and higher can execute multiple kernels concurrently. Applications may query this capability by checking the concurrentKernels device property (see Device Enumeration), which is equal to 1 for devices that support it.

The maximum number of kernel launches that a device can execute concurrently is 32 on devices of compute capability 3.5 and 16 on devices of lower compute capability.

A kernel from one CUDA context cannot execute concurrently with a kernel from another CUDA context.

Kernels that use many textures or a large amount of local memory are less likely to execute concurrently with other kernels.

### 3.2.5.4. Concurrent Data Transfers

Some devices of compute capability 2.x and higher can perform a copy from page-locked host memory to device memory concurrently with a copy from device memory to page-locked host memory.

Applications may query this capability by checking the asyncEngineCount device property (see Device Enumeration), which is equal to 2 for devices that support it.

### 3.2.5.5. Streams

Applications manage concurrency through streams. A stream is a sequence of commands (possibly issued by different host threads) that execute in order. Different streams, on the other hand, may execute their commands out of order with respect to one another or concurrently; this behavior is not guaranteed and should therefore not be relied upon for correctness (e.g., inter-kernel communication is undefined).

### 3.2.5.5.1. Creation and Destruction

A stream is defined by creating a stream object and specifying it as the stream parameter to a sequence of kernel launches and host <-> device memory copies. The following code sample creates two streams and allocates an array hostPtr of float in page-locked memory.

```cudaStream_t stream[2];
for (int i = 0; i < 2; ++i)
cudaStreamCreate(&stream[i]);
float* hostPtr;
cudaMallocHost(&hostPtr, 2 * size);```

Each of these streams is defined by the following code sample as a sequence of one memory copy from host to device, one kernel launch, and one memory copy from device to host:

```for (int i = 0; i < 2; ++i) {
cudaMemcpyAsync(inputDevPtr + i * size, hostPtr + i * size,
size, cudaMemcpyHostToDevice, stream[i]);
MyKernel <<<100, 512, 0, stream[i]>>>
(outputDevPtr + i * size, inputDevPtr + i * size, size);
cudaMemcpyAsync(hostPtr + i * size, outputDevPtr + i * size,
size, cudaMemcpyDeviceToHost, stream[i]);
}```

Each stream copies its portion of input array hostPtr to array inputDevPtr in device memory, processes inputDevPtr on the device by calling MyKernel(), and copies the result outputDevPtr back to the same portion of hostPtr. Overlapping Behavior describes how the streams overlap in this example depending on the capability of the device. Note that hostPtr must point to page-locked host memory for any overlap to occur.

Streams are released by calling cudaStreamDestroy().

```for (int i = 0; i < 2; ++i)
cudaStreamDestroy(stream[i]);```

cudaStreamDestroy() waits for all preceding commands in the given stream to complete before destroying the stream and returning control to the host thread.

### 3.2.5.5.2. Default Stream

Kernel launches and host <-> device memory copies that do not specify any stream parameter, or equivalently that set the stream parameter to zero, are issued to the default stream. They are therefore executed in order.

### 3.2.5.5.3. Explicit Synchronization

There are various ways to explicitly synchronize streams with each other.

cudaDeviceSynchronize() waits until all preceding commands in all streams of all host threads have completed.

cudaStreamSynchronize()takes a stream as a parameter and waits until all preceding commands in the given stream have completed. It can be used to synchronize the host with a specific stream, allowing other streams to continue executing on the device.

cudaStreamWaitEvent()takes a stream and an event as parameters (see Events for a description of events)and makes all the commands added to the given stream after the call to cudaStreamWaitEvent()delay their execution until the given event has completed. The stream can be 0, in which case all the commands added to any stream after the call to cudaStreamWaitEvent()wait on the event.

cudaStreamQuery()provides applications with a way to know if all preceding commands in a stream have completed.

To avoid unnecessary slowdowns, all these synchronization functions are usually best used for timing purposes or to isolate a launch or memory copy that is failing.

### 3.2.5.5.4. Implicit Synchronization

Two commands from different streams cannot run concurrently if any one of the following operations is issued in-between them by the host thread:

• a page-locked host memory allocation,
• a device memory allocation,
• a device memory set,
• a memory copy between two addresses to the same device memory,
• any CUDA command to the default stream,
• a switch between the L1/shared memory configurations described in Compute Capability 2.x.

For devices that support concurrent kernel execution and are of compute capability 3.0 or lower, any operation that requires a dependency check to see if a streamed kernel launch is complete:

• Can start executing only when all thread blocks of all prior kernel launches from any stream in the CUDA context have started executing;
• Blocks all later kernel launches from any stream in the CUDA context until the kernel launch being checked is complete.

Operations that require a dependency check include any other commands within the same stream as the launch being checked and any call to cudaStreamQuery() on that stream. Therefore, applications should follow these guidelines to improve their potential for concurrent kernel execution:

• All independent operations should be issued before dependent operations,
• Synchronization of any kind should be delayed as long as possible.

### 3.2.5.5.5. Overlapping Behavior

The amount of execution overlap between two streams depends on the order in which the commands are issued to each stream and whether or not the device supports overlap of data transfer and kernel execution (see Overlap of Data Transfer and Kernel Execution), concurrent kernel execution (see Concurrent Kernel Execution), and/or concurrent data transfers (see Concurrent Data Transfers).

For example, on devices that do not support concurrent data transfers, the two streams of the code sample of Creation and Destruction do not overlap at all because the memory copy from host to device is issued to stream[1] after the memory copy from device to host is issued to stream[0], so it can only start once the memory copy from device to host issued to stream[0] has completed. If the code is rewritten the following way (and assuming the device supports overlap of data transfer and kernel execution)

```for (int i = 0; i < 2; ++i)
cudaMemcpyAsync(inputDevPtr + i * size, hostPtr + i * size,
size, cudaMemcpyHostToDevice, stream[i]);
for (int i = 0; i < 2; ++i)
MyKernel<<<100, 512, 0, stream[i]>>>
(outputDevPtr + i * size, inputDevPtr + i * size, size);
for (int i = 0; i < 2; ++i)
cudaMemcpyAsync(hostPtr + i * size, outputDevPtr + i * size,
size, cudaMemcpyDeviceToHost, stream[i]);```

then the memory copy from host to device issued to stream[1] overlaps with the kernel launch issued to stream[0].

On devices that do support concurrent data transfers, the two streams of the code sample of Creation and Destruction do overlap: The memory copy from host to device issued to stream[1] overlaps with the memory copy from device to host issued to stream[0] and even with the kernel launch issued to stream[0] (assuming the device supports overlap of data transfer and kernel execution). However, for devices of compute capability 3.0 or lower, the kernel executions cannot possibly overlap because the second kernel launch is issued to stream[1] after the memory copy from device to host is issued to stream[0], so it is blocked until the first kernel launch issued to stream[0] is complete as per Implicit Synchronization. If the code is rewritten as above, the kernel executions overlap (assuming the device supports concurrent kernel execution) since the second kernel launch is issued to stream[1] before the memory copy from device to host is issued to stream[0]. In that case however, the memory copy from device to host issued to stream[0] only overlaps with the last thread blocks of the kernel launch issued to stream[1] as per Implicit Synchronization, which can represent only a small portion of the total execution time of the kernel.

### 3.2.5.5.6. Callbacks

The runtime provides a way to insert a callback at any point into a stream via cudaStreamAddCallback(). A callback is a function that is executed on the host once all commands issued to the stream before the callback have completed. Callbacks in stream 0 are executed once all preceding tasks and commands issued in all streams before the callback have completed.

The following code sample adds the callback function MyCallback to each of two streams after issuing a host-to-device memory copy, a kernel launch and a device-to-host memory copy into each stream. The callback will begin execution on the host after each of the device-to-host memory copies completes.

```void CUDART_CB MyCallback(cudaStream_t stream, cudaError_t status, void *data){
printf("Inside callback %d\n", (int)data);
}
...
for (int i = 0; i < 2; ++i) {
cudaMemcpyAsync(devPtrIn[i], hostPtr[i], size, cudaMemcpyHostToDevice, stream[i]);
MyKernel<<<100, 512, 0, stream[i]>>>(devPtrOut[i], devPtrIn[i], size);
cudaMemcpyAsync(hostPtr[i], devPtrOut[i], size, cudaMemcpyDeviceToHost, stream[i]);
}
```

The commands that are issued in a stream (or all commands issued to any stream if the callback is issued to stream 0) after a callback do not start executing before the callback has completed. The last parameter of cudaStreamAddCallback() is reserved for future use.

A callback must not make CUDA API calls (directly or indirectly), as it might end up waiting on itself if it makes such a call leading to a deadlock.

### 3.2.5.6. Events

The runtime also provides a way to closely monitor the device's progress, as well as perform accurate timing, by letting the application asynchronously record events at any point in the program and query when these events are completed. An event has completed when all tasks - or optionally, all commands in a given stream - preceding the event have completed. Events in stream zero are completed after all preceding tasks and commands in all streams are completed.

### 3.2.5.6.1. Creation and Destruction

The following code sample creates two events:

```cudaEvent_t start, stop;
cudaEventCreate(&start);
cudaEventCreate(&stop);```

They are destroyed this way:

```cudaEventDestroy(start);
cudaEventDestroy(stop);```

### 3.2.5.6.2. Elapsed Time

The events created in Creation and Destruction can be used to time the code sample of Creation and Destruction the following way:

```cudaEventRecord(start, 0);
for (int i = 0; i < 2; ++i) {
cudaMemcpyAsync(inputDev + i * size, inputHost + i * size,
size, cudaMemcpyHostToDevice, stream[i]);
MyKernel<<<100, 512, 0, stream[i]>>>
(outputDev + i * size, inputDev + i * size, size);
cudaMemcpyAsync(outputHost + i * size, outputDev + i * size,
size, cudaMemcpyDeviceToHost, stream[i]);
}
cudaEventRecord(stop, 0);
cudaEventSynchronize(stop);
float elapsedTime;
cudaEventElapsedTime(&elapsedTime, start, stop);```

### 3.2.5.7. Synchronous Calls

When a synchronous function is called, control is not returned to the host thread before the device has completed the requested task. Whether the host thread will then yield, block, or spin can be specified by calling cudaSetDeviceFlags()with some specific flags (see reference manual for details) before any other CUDA call is performed by the host thread.

### 3.2.6.1. Device Enumeration

A host system can have multiple devices. The following code sample shows how to enumerate these devices, query their properties, and determine the number of CUDA-enabled devices.

```int deviceCount;
cudaGetDeviceCount(&deviceCount);
int device;
for (device = 0; device < deviceCount; ++device) {
cudaGetDeviceProperties(&deviceProp, device);
printf("Device %d has compute capability %d.%d.\n",
device, deviceProp.major, deviceProp.minor);
}```

### 3.2.6.2. Device Selection

A host thread can set the device it operates on at any time by calling cudaSetDevice(). Device memory allocations and kernel launches are made on the currently set device; streams and events are created in association with the currently set device. If no call to cudaSetDevice() is made, the current device is device 0.

The following code sample illustrates how setting the current device affects memory allocation and kernel execution.

```size_t size = 1024 * sizeof(float);
cudaSetDevice(0);            // Set device 0 as current
float* p0;
cudaMalloc(&p0, size);       // Allocate memory on device 0
MyKernel<<<1000, 128>>>(p0); // Launch kernel on device 0
cudaSetDevice(1);            // Set device 1 as current
float* p1;
cudaMalloc(&p1, size);       // Allocate memory on device 1
MyKernel<<<1000, 128>>>(p1); // Launch kernel on device 1```

### 3.2.6.3. Stream and Event Behavior

A kernel launch or memory copy will fail if it is issued to a stream that is not associated to the current device as illustrated in the following code sample.

```cudaSetDevice(0);               // Set device 0 as current
cudaStream_t s0;
cudaStreamCreate(&s0);          // Create stream s0 on device 0
MyKernel<<<100, 64, 0, s0>>>(); // Launch kernel on device 0 in s0
cudaSetDevice(1);               // Set device 1 as current
cudaStream_t s1;
cudaStreamCreate(&s1);          // Create stream s1 on device 1
MyKernel<<<100, 64, 0, s1>>>(); // Launch kernel on device 1 in s1

// This kernel launch will fail:
MyKernel<<<100, 64, 0, s0>>>(); // Launch kernel on device 1 in s0```

cudaEventRecord() will fail if the input event and input stream are associated to different devices.

cudaEventElapsedTime() will fail if the two input events are associated to different devices.

cudaEventSynchronize() and cudaEventQuery() will succeed even if the input event is associated to a device that is different from the current device.

cudaStreamWaitEvent() will succeed even if the input stream and input event are associated to different devices. cudaStreamWaitEvent() can therefore be used to synchronize multiple devices with each other.

Each device has its own default stream (see Default Stream), so commands issued to the default stream of a device may execute out of order or concurrently with respect to commands issued to the default stream of any other device.

### 3.2.6.4. Peer-to-Peer Memory Access

When the application is run as a 64-bit process, devices of compute capability 2.0 and higher from the Tesla series may address each other's memory (i.e., a kernel executing on one device can dereference a pointer to the memory of the other device). This peer-to-peer memory access feature is supported between two devices if cudaDeviceCanAccessPeer() returns true for these two devices.

Peer-to-peer memory access must be enabled between two devices by calling cudaDeviceEnablePeerAccess() as illustrated in the following code sample.

A unified address space is used for both devices (see Unified Virtual Address Space), so the same pointer can be used to address memory from both devices as shown in the code sample below.

```cudaSetDevice(0);                   // Set device 0 as current
float* p0;
size_t size = 1024 * sizeof(float);
cudaMalloc(&p0, size);              // Allocate memory on device 0
MyKernel<<<1000, 128>>>(p0);        // Launch kernel on device 0
cudaSetDevice(1);                   // Set device 1 as current
cudaDeviceEnablePeerAccess(0, 0);   // Enable peer-to-peer access
// with device 0

// Launch kernel on device 1
// This kernel launch can access memory on device 0 at address p0
MyKernel<<<1000, 128>>>(p0);```

### 3.2.6.5. Peer-to-Peer Memory Copy

Memory copies can be performed between the memories of two different devices.

When a unified address space is used for both devices (see Unified Virtual Address Space), this is done using the regular memory copy functions mentioned in Device Memory.

Otherwise, this is done using cudaMemcpyPeer(), cudaMemcpyPeerAsync(), cudaMemcpy3DPeer(), or cudaMemcpy3DPeerAsync() as illustrated in the following code sample.

```cudaSetDevice(0);                   // Set device 0 as current
float* p0;
size_t size = 1024 * sizeof(float);
cudaMalloc(&p0, size);              // Allocate memory on device 0
cudaSetDevice(1);                   // Set device 1 as current
float* p1;
cudaMalloc(&p1, size);              // Allocate memory on device 1
cudaSetDevice(0);                   // Set device 0 as current
MyKernel<<<1000, 128>>>(p0);        // Launch kernel on device 0
cudaSetDevice(1);                   // Set device 1 as current
cudaMemcpyPeer(p1, 1, p0, 0, size); // Copy p0 to p1
MyKernel<<<1000, 128>>>(p1);        // Launch kernel on device 1```

A copy between the memories of two different devices

• does not start until all commands previously issued to either device have completed and
• runs to completion before any asynchronous commands (see Asynchronous Concurrent Execution) issued after the copy to either device can start.

Note that if peer-to-peer access is enabled between two devices via cudaDeviceEnablePeerAccess() as described in Peer-to-Peer Memory Access, peer-to-peer memory copy between these two devices no longer needs to be staged through the host and is therefore faster.

### 3.2.7. Unified Virtual Address Space

When the application is run as a 64-bit process, a single address space is used for the host and all the devices of compute capability 2.0 and higher. This address space is used for all allocations made in host memory via cudaHostAlloc()and in any of the device memories via cudaMalloc*(). Which memory a pointer points to - host memory or any of the device memories - can be determined from the value of the pointer using cudaPointerGetAttributes(). As a consequence:

• When copying from or to the memory of one of the devices for which the unified address space is used, the cudaMemcpyKind parameter of cudaMemcpy*() becomes useless and can be set to cudaMemcpyDefault;
• Allocations via cudaHostAlloc() are automatically portable (see Portable Memory) across all the devices for which the unified address space is used, and pointers returned by cudaHostAlloc() can be used directly from within kernels running on these devices (i.e., there is no need to obtain a device pointer via cudaHostGetDevicePointer() as described in Mapped Memory.

Applications may query if the unified address space is used for a particular device by checking that the unifiedAddressing device property (see Device Enumeration) is equal to 1.

### 3.2.8. Interprocess Communication

Any device memory pointer or event handle created by a host thread can be directly referenced by any other thread within the same process. It is not valid outside this process however, and therefore cannot be directly referenced by threads belonging to a different process.

To share device memory pointers and events across processes, an application must use the Inter Process Communication API, which is described in detail in the reference manual. The IPC API is only supported for 64-bit processes on Linux and for devices of compute capability 2.0 and higher.

Using this API, an application can get the IPC handle for a given device memory pointer using cudaIpcGetMemHandle(), pass it to another process using standard IPC mechanisms (e.g., interprocess shared memory or files), and use cudaIpcOpenMemHandle() to retrieve a device pointer from the IPC handle that is a valid pointer within this other process. Event handles can be shared using similar entry points.

An example of using the IPC API is where a single master process generates a batch of input data, making the data available to multiple slave processes without requiring regeneration or copying.

### 3.2.9. Error Checking

All runtime functions return an error code, but for an asynchronous function (see Asynchronous Concurrent Execution), this error code cannot possibly report any of the asynchronous errors that could occur on the device since the function returns before the device has completed the task; the error code only reports errors that occur on the host prior to executing the task, typically related to parameter validation; if an asynchronous error occurs, it will be reported by some subsequent unrelated runtime function call.

The only way to check for asynchronous errors just after some asynchronous function call is therefore to synchronize just after the call by calling cudaDeviceSynchronize() (or by using any other synchronization mechanisms described in Asynchronous Concurrent Execution) and checking the error code returned by cudaDeviceSynchronize().

The runtime maintains an error variable for each host thread that is initialized to cudaSuccess and is overwritten by the error code every time an error occurs (be it a parameter validation error or an asynchronous error). cudaPeekAtLastError() returns this variable. cudaGetLastError() returns this variable and resets it to cudaSuccess.

Kernel launches do not return any error code, so cudaPeekAtLastError() or cudaGetLastError() must be called just after the kernel launch to retrieve any pre-launch errors. To ensure that any error returned by cudaPeekAtLastError() or cudaGetLastError() does not originate from calls prior to the kernel launch, one has to make sure that the runtime error variable is set to cudaSuccess just before the kernel launch, for example, by calling cudaGetLastError() just before the kernel launch. Kernel launches are asynchronous, so to check for asynchronous errors, the application must synchronize in-between the kernel launch and the call to cudaPeekAtLastError() or cudaGetLastError().

Note that cudaErrorNotReady that may be returned by cudaStreamQuery() and cudaEventQuery() is not considered an error and is therefore not reported by cudaPeekAtLastError() or cudaGetLastError().

### 3.2.10. Call Stack

On devices of compute capability 2.x and higher, the size of the call stack can be queried using cudaDeviceGetLimit() and set using cudaDeviceSetLimit().

When the call stack overflows, the kernel call fails with a stack overflow error if the application is run via a CUDA debugger (cuda-gdb, Nsight) or an unspecified launch error, otherwise.

### 3.2.11. Texture and Surface Memory

CUDA supports a subset of the texturing hardware that the GPU uses for graphics to access texture and surface memory. Reading data from texture or surface memory instead of global memory can have several performance benefits as described in Device Memory Accesses.

There are two different APIs to access texture and surface memory:

• The texture reference API that is supported on all devices,
• The texture object API that is only supported on devices of compute capability 3.x.

The texture reference API has limitations that the texture object API does not have. They are mentioned in Texture Reference API.

### 3.2.11.1. Texture Memory

Texture memory is read from kernels using the device functions described in Texture Functions. The process of reading a texture calling one of these functions is called a texture fetch. Each texture fetch specifies a parameter called a texture object for the texture object API or a texture reference for the texture reference API.

The texture object or the texture reference specifies:

• The texture, which is the piece of texture memory that is fetched. Texture objects are created at runtime and the texture is specified when creating the texture object as described in Texture Object API. Texture references are created at compile time and the texture is specified at runtime by bounding the texture reference to the texture through runtime functions as described in Texture Reference API; several distinct texture references might be bound to the same texture or to textures that overlap in memory. A texture can be any region of linear memory or a CUDA array (described in CUDA Arrays).
• Its dimensionality that specifies whether the texture is addressed as a one dimensional array using one texture coordinate, a two-dimensional array using two texture coordinates, or a three-dimensional array using three texture coordinates. Elements of the array are called texels, short for texture elements. The texture width, height, and depth refer to the size of the array in each dimension. Table 12 lists the maximum texture width, height, and depth depending on the compute capability of the device.
• The type of a texel, which is restricted to the basic integer and single-precision floating-point types and any of the 1-, 2-, and 4-component vector types defined in char, short, int, long, longlong, float, double that are derived from the basic integer and single-precision floating-point types.
• The read mode, which is equal to cudaReadModeNormalizedFloat or cudaReadModeElementType. If it is cudaReadModeNormalizedFloat and the type of the texel is a 16-bit or 8-bit integer type, the value returned by the texture fetch is actually returned as floating-point type and the full range of the integer type is mapped to [0.0, 1.0] for unsigned integer type and [-1.0, 1.0] for signed integer type; for example, an unsigned 8-bit texture element with the value 0xff reads as 1. If it is cudaReadModeElementType, no conversion is performed.
• Whether texture coordinates are normalized or not. By default, textures are referenced (by the functions of Texture Functions) using floating-point coordinates in the range [0, N-1] where N is the size of the texture in the dimension corresponding to the coordinate. For example, a texture that is 64x32 in size will be referenced with coordinates in the range [0, 63] and [0, 31] for the x and y dimensions, respectively. Normalized texture coordinates cause the coordinates to be specified in the range [0.0, 1.0-1/N] instead of [0, N-1], so the same 64x32 texture would be addressed by normalized coordinates in the range [0, 1-1/N] in both the x and y dimensions. Normalized texture coordinates are a natural fit to some applications' requirements, if it is preferable for the texture coordinates to be independent of the texture size.
• The addressing mode. It is valid to call the device functions of Section B.8 with coordinates that are out of range. The addressing mode defines what happens in that case. The default addressing mode is to clamp the coordinates to the valid range: [0, N) for non-normalized coordinates and [0.0, 1.0) for normalized coordinates. If the border mode is specified instead, texture fetches with out-of-range texture coordinates return zero. For normalized coordinates, the warp mode and the mirror mode are also available. When using the wrap mode, each coordinate x is converted to frac(x)=x floor(x) where floor(x) is the largest integer not greater than x. When using the mirror mode, each coordinate x is converted to frac(x) if floor(x) is even and 1-frac(x) if floor(x) is odd. The addressing mode is specified as an array of size three whose first, second, and third elements specify the addressing mode for the first, second, and third texture coordinates, respectively; the addressing mode are cudaAddressModeBorder, cudaAddressModeClamp, cudaAddressModeWrap, and cudaAddressModeMirror; cudaAddressModeWrap and cudaAddressModeMirror are only supported for normalized texture coordinates
• The filtering mode which specifies how the value returned when fetching the texture is computed based on the input texture coordinates. Linear texture filtering may be done only for textures that are configured to return floating-point data. It performs low-precision interpolation between neighboring texels. When enabled, the texels surrounding a texture fetch location are read and the return value of the texture fetch is interpolated based on where the texture coordinates fell between the texels. Simple linear interpolation is performed for one-dimensional textures, bilinear interpolation for two-dimensional textures, and trilinear interpolation for three-dimensional textures. Texture Fetching gives more details on texture fetching. The filtering mode is equal to cudaFilterModePoint or cudaFilterModeLinear. If it is cudaFilterModePoint, the returned value is the texel whose texture coordinates are the closest to the input texture coordinates. If it is cudaFilterModeLinear, the returned value is the linear interpolation of the two (for a one-dimensional texture), four (for a two dimensional texture), or eight (for a three dimensional texture) texels whose texture coordinates are the closest to the input texture coordinates. cudaFilterModeLinear is only valid for returned values of floating-point type.

Texture Object API introduces the texture object API.

Texture Reference API introduces the texture reference API.

16-Bit Floating-Point Textures explains how to deal with 16-bit floating-point textures.

Textures can also be layered as described in Layered Textures.

Cubemap Textures and Cubemap Layered Textures describe a special type of texture, the cubemap texture.

Texture Gather describes a special texture fetch, texture gather.

### 3.2.11.1.1. Texture Object API

A texture object is created using cudaCreateTextureObject() from a resource description of type struct cudaResourceDesc, which specifies the texture, and from a texture description defined as such:

```struct cudaTextureDesc
{
enum cudaTextureFilterMode  filterMode;
int                         sRGB;
int                         normalizedCoords;
unsigned int                maxAnisotropy;
enum cudaTextureFilterMode  mipmapFilterMode;
float                       mipmapLevelBias;
float                       minMipmapLevelClamp;
float                       maxMipmapLevelClamp;
};```
• filterMode specifies the filter mode;
• normalizedCoords specifies whether texture coordinates are normalized or not;
• See reference manual for sRGB, maxAnisotropy, mipmapFilterMode, mipmapLevelBias, minMipmapLevelClamp, and maxMipmapLevelClamp.

The following code sample applies some simple transformation kernel to a texture.

```// Simple transformation kernel
__global__ void transformKernel(float* output,
cudaTextureObject_t texObj,
int width, int height,
float theta)
{
// Calculate normalized texture coordinates
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

float u = x / (float)width;
float v = y / (float)height;

// Transform coordinates
u -= 0.5f;
v -= 0.5f;
float tu = u * cosf(theta) - v * sinf(theta) + 0.5f;
float tv = v * cosf(theta) + u * sinf(theta) + 0.5f;

// Read from texture and write to global memory
output[y * width + x] = tex2D<float>(texObj, tu, tv);
}

// Host code
int main()
{
// Allocate CUDA array in device memory
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc(32, 0, 0, 0,
cudaChannelFormatKindFloat);
cudaArray* cuArray;
cudaMallocArray(&cuArray, &channelDesc, width, height);

// Copy to device memory some data located at address h_data
// in host memory
cudaMemcpyToArray(cuArray, 0, 0, h_data, size,
cudaMemcpyHostToDevice);

// Specify texture
struct cudaResourceDesc resDesc;
memset(&resDesc, 0, sizeof(resDesc));
resDesc.resType = cudaResourceTypeArray;
resDesc.res.array.array = cuArray;

// Specify texture object parameters
struct cudaTextureDesc texDesc;
memset(&texDesc, 0, sizeof(texDesc));
texDesc.filterMode       = cudaFilterModeLinear;
texDesc.normalizedCoords = 1;

// Create texture object
cudaTextureObject_t texObj = 0;
cudaCreateTextureObject(&texObj, &resDesc, &texDesc, NULL);

// Allocate result of transformation in device memory
float* output;
cudaMalloc(&output, width * height * sizeof(float));

// Invoke kernel
dim3 dimBlock(16, 16);
dim3 dimGrid((width  + dimBlock.x - 1) / dimBlock.x,
(height + dimBlock.y - 1) / dimBlock.y);
transformKernel<<<dimGrid, dimBlock>>>(output,
texObj, width, height,
angle);

// Destroy texture object

// Free device memory
cudaFreeArray(cuArray);
cudaFree(output);

return 0;
}```

### 3.2.11.1.2. Texture Reference API

Some of the attributes of a texture reference are immutable and must be known at compile time; they are specified when declaring the texture reference. A texture reference is declared at file scope as a variable of type texture:

`texture<DataType, Type, ReadMode> texRef;`

where:

• DataType specifies the type of the texel;
• Type specifies the type of the texture reference and is equal to cudaTextureType1D, cudaTextureType2D, or cudaTextureType3D, for a one-dimensional, two-dimensional, or three-dimensional texture, respectively, or cudaTextureType1DLayered or cudaTextureType2DLayered for a one-dimensional or two-dimensional layered texture respectively; Type is an optional argument which defaults to cudaTextureType1D;

A texture reference can only be declared as a static global variable and cannot be passed as an argument to a function.

The other attributes of a texture reference are mutable and can be changed at runtime through the host runtime. As explained in the reference manual, the runtime API has a low-level C-style interface and a high-level C++-style interface. The texture type is defined in the high-level API as a structure publicly derived from the textureReference type defined in the low-level API as such:

```struct textureReference {
int                          normalized;
enum cudaTextureFilterMode   filterMode;
struct cudaChannelFormatDesc channelDesc;
int                          sRGB;
unsigned int                 maxAnisotropy;
enum cudaTextureFilterMode   mipmapFilterMode;
float                        mipmapLevelBias;
float                        minMipmapLevelClamp;
float                        maxMipmapLevelClamp;
}```
• normalized specifies whether texture coordinates are normalized or not;
• filterMode specifies the filtering mode;
• channelDesc describes the format of the texel; it must match the DataType argument of the texture reference declaration; channelDesc is of the following type:

```struct cudaChannelFormatDesc {
int x, y, z, w;
enum cudaChannelFormatKind f;
};```

where x, y, z, and w are equal to the number of bits of each component of the returned value and f is:

• cudaChannelFormatKindSigned if these components are of signed integer type,
• cudaChannelFormatKindUnsigned if they are of unsigned integer type,
• cudaChannelFormatKindFloat if they are of floating point type.
• See reference manual for sRGB, maxAnisotropy, mipmapFilterMode, mipmapLevelBias, minMipmapLevelClamp, and maxMipmapLevelClamp.

normalized, addressMode, and filterMode may be directly modified in host code.

Before a kernel can use a texture reference to read from texture memory, the texture reference must be bound to a texture using cudaBindTexture() or cudaBindTexture2D() for linear memory, or cudaBindTextureToArray() for CUDA arrays. cudaUnbindTexture() is used to unbind a texture reference. Once a texture reference has been unbound, it can be safely rebound to another array, even if kernels that use the previously bound texture have not completed. It is recommended to allocate two-dimensional textures in linear memory using cudaMallocPitch() and use the pitch returned by cudaMallocPitch() as input parameter to cudaBindTexture2D().

The following code samples bind a 2D texture reference to linear memory pointed to by devPtr:

• Using the low-level API:

```texture<float, cudaTextureType2D,
textureReference* texRefPtr;
cudaGetTextureReference(&texRefPtr, &texRef);
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc<float>();
size_t offset;
cudaBindTexture2D(&offset, texRefPtr, devPtr, &channelDesc,
width, height, pitch);```
• Using the high-level API:

```texture<float, cudaTextureType2D,
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc<float>();
size_t offset;
cudaBindTexture2D(&offset, texRef, devPtr, channelDesc,
width, height, pitch);```

The following code samples bind a 2D texture reference to a CUDA array cuArray:

• Using the low-level API:

```texture<float, cudaTextureType2D,
textureReference* texRefPtr;
cudaGetTextureReference(&texRefPtr, &texRef);
cudaChannelFormatDesc channelDesc;
cudaGetChannelDesc(&channelDesc, cuArray);
cudaBindTextureToArray(texRef, cuArray, &channelDesc);```
• Using the high-level API:

```texture<float, cudaTextureType2D,
texture<float, cudaTextureType2D,
cudaBindTextureToArray(texRef, cuArray);```

The format specified when binding a texture to a texture reference must match the parameters specified when declaring the texture reference; otherwise, the results of texture fetches are undefined.

There is a limit to the number of textures that can be bound to a kernel as specified in Table 12.

The following code sample applies some simple transformation kernel to a texture.

```// 2D float texture

// Simple transformation kernel
__global__ void transformKernel(float* output,
int width, int height,
float theta)
{
// Calculate normalized texture coordinates
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

float u = x / (float)width;
float v = y / (float)height;

// Transform coordinates
u -= 0.5f;
v -= 0.5f;
float tu = u * cosf(theta) - v * sinf(theta) + 0.5f;
float tv = v * cosf(theta) + u * sinf(theta) + 0.5f;

// Read from texture and write to global memory
output[y * width + x] = tex2D(texRef, tu, tv);
}

// Host code
int main()
{
// Allocate CUDA array in device memory
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc(32, 0, 0, 0,
cudaChannelFormatKindFloat);
cudaArray* cuArray;
cudaMallocArray(&cuArray, &channelDesc, width, height);

// Copy to device memory some data located at address h_data
// in host memory
cudaMemcpyToArray(cuArray, 0, 0, h_data, size,
cudaMemcpyHostToDevice);

// Set texture reference parameters
texRef.filterMode     = cudaFilterModeLinear;
texRef.normalized     = true;

// Bind the array to the texture reference
cudaBindTextureToArray(texRef, cuArray, channelDesc);

// Allocate result of transformation in device memory
float* output;
cudaMalloc(&output, width * height * sizeof(float));

// Invoke kernel
dim3 dimBlock(16, 16);
dim3 dimGrid((width  + dimBlock.x - 1) / dimBlock.x,
(height + dimBlock.y - 1) / dimBlock.y);
transformKernel<<<dimGrid, dimBlock>>>(output, width, height,
angle);

// Free device memory
cudaFreeArray(cuArray);
cudaFree(output);

return 0;
}
```

### 3.2.11.1.3. 16-Bit Floating-Point Textures

The 16-bit floating-point or half format supported by CUDA arrays is the same as the IEEE 754-2008 binary2 format.

CUDA C does not support a matching data type, but provides intrinsic functions to convert to and from the 32-bit floating-point format via the unsigned short type: __float2half_rn(float) and __half2float(unsigned short). These functions are only supported in device code. Equivalent functions for the host code can be found in the OpenEXR library, for example.

16-bit floating-point components are promoted to 32 bit float during texture fetching before any filtering is performed.

A channel description for the 16-bit floating-point format can be created by calling one of the cudaCreateChannelDescHalf*() functions.

### 3.2.11.1.4. Layered Textures

A one-dimensional or two-dimensional layered texture (also known as texture array in Direct3D and array texture in OpenGL) is a texture made up of a sequence of layers, all of which are regular textures of same dimensionality, size, and data type.

A one-dimensional layered texture is addressed using an integer index and a floating-point texture coordinate; the index denotes a layer within the sequence and the coordinate addresses a texel within that layer. A two-dimensional layered texture is addressed using an integer index and two floating-point texture coordinates; the index denotes a layer within the sequence and the coordinates address a texel within that layer.

A layered texture can only be a CUDA array by calling cudaMalloc3DArray() with the cudaArrayLayered flag (and a height of zero for one-dimensional layered texture).

Layered textures are fetched using the device functions described in tex1DLayered(), tex1DLayered(), tex2DLayered(), and tex2DLayered(). Texture filtering (see Texture Fetching) is done only within a layer, not across layers.

Layered textures are only supported on devices of compute capability 2.0 and higher.

### 3.2.11.1.5. Cubemap Textures

A cubemap texture is a special type of two-dimensional layered texture that has six layers representing the faces of a cube:

• The width of a layer is equal to its height.
• The cubemap is addressed using three texture coordinates x, y, and z that are interpreted as a direction vector emanating from the center of the cube and pointing to one face of the cube and a texel within the layer corresponding to that face. More specifically, the face is selected by the coordinate with largest magnitude m and the corresponding layer is addressed using coordinates (s/m+1)/2 and (t/m+1)/2 where s and t are defined in Table 1.
Table 1. Cubemap Fetch
face m s t
|x| > |y| and |x| > |z| x > 0 0 x -z -y
x < 0 1 -x z -y
|y| > |x| and |y| > |z| y > 0 2 y x z
y < 0 3 -y x -z
|z| > |x| and |z| > |y| z > 0 4 z x -y
z < 0 5 -z -x -y

A layered texture can only be a CUDA array by calling cudaMalloc3DArray() with the cudaArrayCubemap flag.

Cubemap textures are fetched using the device function described in texCubemap() and texCubemap().

Cubemap textures are only supported on devices of compute capability 2.0 and higher.

### 3.2.11.1.6. Cubemap Layered Textures

A cubemap layered texture is a layered texture whose layers are cubemaps of same dimension.

A cubemap layered texture is addressed using an integer index and three floating-point texture coordinates; the index denotes a cubemap within the sequence and the coordinates address a texel within that cubemap.

A layered texture can only be a CUDA array by calling cudaMalloc3DArray() with the cudaArrayLayered and cudaArrayCubemap flags.

Cubemap layered textures are fetched using the device function described in texCubemapLayered() and texCubemapLayered(). Texture filtering (see Texture Fetching) is done only within a layer, not across layers.

Cubemap layered textures are only supported on devices of compute capability 2.0 and higher.

### 3.2.11.1.7. Texture Gather

Texture gather is a special texture fetch that is available for two-dimensional textures only. It is performed by the tex2Dgather() function, which has the same parameters as tex2D(), plus an additional comp parameter equal to 0, 1, 2, or 3 (see tex2Dgather() and tex2Dgather()). It returns four 32-bit numbers that correspond to the value of the component comp of each of the four texels that would have been used for bilinear filtering during a regular texture fetch. For example, if these texels are of values (253, 20, 31, 255), (250, 25, 29, 254), (249, 16, 37, 253), (251, 22, 30, 250), and comp is 2, tex2Dgather() returns (31, 29, 37, 30).

Texture gather is only supported for CUDA arrays created with the cudaArrayTextureGather flag and of width and height less than the maximum specified in Table 12 for texture gather, which is smaller than for regular texture fetch.

Texture gather is only supported on devices of compute capability 2.0 and higher.

### 3.2.11.2. Surface Memory

For devices of compute capability 2.0 and higher, a CUDA array (described in Cubemap Surfaces), created with the cudaArraySurfaceLoadStore flag, can be read and written via a surface object or surface reference using the functions described in Surface Functions.

Table 12 lists the maximum surface width, height, and depth depending on the compute capability of the device.

### 3.2.11.2.1. Surface Object API

A surface object is created using cudaCreateSurfaceObject() from a resource description of type struct cudaResourceDesc.

The following code sample applies some simple transformation kernel to a texture.

```// Simple copy kernel
__global__ void copyKernel(cudaSurfaceObject_t inputSurfObj,
cudaSurfaceObject_t outputSurfObj,
int width, int height)
{
// Calculate surface coordinates
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;
if (x < width && y < height) {
uchar4 data;
surf2Dread(&data,  inputSurfObj, x * 4, y);
// Write to output surface
surf2Dwrite(data, outputSurfObj, x * 4, y);
}
}

// Host code
int main()
{
// Allocate CUDA arrays in device memory
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc(8, 8, 8, 8,
cudaChannelFormatKindUnsigned);
cudaArray* cuInputArray;
cudaMallocArray(&cuInputArray, &channelDesc, width, height,
cudaArray* cuOutputArray;
cudaMallocArray(&cuOutputArray, &channelDesc, width, height,

// Copy to device memory some data located at address h_data
// in host memory
cudaMemcpyToArray(cuInputArray, 0, 0, h_data, size,
cudaMemcpyHostToDevice);

// Specify surface
struct cudaResourceDesc resDesc;
memset(&resDesc, 0, sizeof(resDesc));
resDesc.resType = cudaResourceTypeArray;

// Create the surface objects
resDesc.res.array.array = cuInputArray;
cudaSurfaceObject_t inputSurfObj = 0;
cudaCreateSurfaceObject(&inputSurfObj, &resDesc);
resDesc.res.array.array = cuOutputArray;
cudaSurfaceObject_t outputSurfObj = 0;
cudaCreateSurfaceObject(&outputSurfObj, &resDesc);

// Invoke kernel
dim3 dimBlock(16, 16);
dim3 dimGrid((width  + dimBlock.x - 1) / dimBlock.x,
(height + dimBlock.y - 1) / dimBlock.y);
copyKernel<<<dimGrid, dimBlock>>>(inputSurfObj,
outputSurfObj,
width, height);

// Destroy surface objects

// Free device memory
cudaFreeArray(cuInputArray);
cudaFreeArray(cuOutputArray);

return 0;
}```

### 3.2.11.2.2. B.9.2. Surface Reference API

A surface reference is declared at file scope as a variable of type surface:

`surface<void, Type> surfRef;`

where Type specifies the type of the surface reference and is equal to cudaSurfaceType1D, cudaSurfaceType2D, cudaSurfaceType3D, cudaSurfaceTypeCubemap, cudaSurfaceType1DLayered, cudaSurfaceType2DLayered, or cudaSurfaceTypeCubemapLayered; Type is an optional argument which defaults to cudaSurfaceType1D. A surface reference can only be declared as a static global variable and cannot be passed as an argument to a function.

Before a kernel can use a surface reference to access a CUDA array, the surface reference must be bound to the CUDA array using cudaBindSurfaceToArray().

The following code samples bind a surface reference to a CUDA array cuArray:

• Using the low-level API:

```surface<void, cudaSurfaceType2D> surfRef;
surfaceReference* surfRefPtr;
cudaGetSurfaceReference(&surfRefPtr, "surfRef");
cudaChannelFormatDesc channelDesc;
cudaGetChannelDesc(&channelDesc, cuArray);
cudaBindSurfaceToArray(surfRef, cuArray, &channelDesc);```
• Using the high-level API:

```surface<void, cudaSurfaceType2D> surfRef;
cudaBindSurfaceToArray(surfRef, cuArray);```

A CUDA array must be read and written using surface functions of matching dimensionality and type and via a surface reference of matching dimensionality; otherwise, the results of reading and writing the CUDA array are undefined.

Unlike texture memory, surface memory uses byte addressing. This means that the x-coordinate used to access a texture element via texture functions needs to be multiplied by the byte size of the element to access the same element via a surface function. For example, the element at texture coordinate x of a one-dimensional floating-point CUDA array bound to a texture reference texRef and a surface reference surfRef is read using tex1d(texRef, x) via texRef, but surf1Dread(surfRef, 4*x) via surfRef. Similarly, the element at texture coordinate x and y of a two-dimensional floating-point CUDA array bound to a texture reference texRef and a surface reference surfRef is accessed using tex2d(texRef, x, y) via texRef, but surf2Dread(surfRef, 4*x, y) via surfRef (the byte offset of the y-coordinate is internally calculated from the underlying line pitch of the CUDA array).

The following code sample applies some simple transformation kernel to a texture.

```// 2D surfaces
surface<void, 2> inputSurfRef;
surface<void, 2> outputSurfRef;

// Simple copy kernel
__global__ void copyKernel(int width, int height)
{
// Calculate surface coordinates
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;
if (x < width && y < height) {
uchar4 data;
surf2Dread(&data,  inputSurfRef, x * 4, y);
// Write to output surface
surf2Dwrite(data, outputSurfRef, x * 4, y);
}
}

// Host code
int main()
{
// Allocate CUDA arrays in device memory
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc(8, 8, 8, 8,
cudaChannelFormatKindUnsigned);
cudaArray* cuInputArray;
cudaMallocArray(&cuInputArray, &channelDesc, width, height,
cudaArray* cuOutputArray;
cudaMallocArray(&cuOutputArray, &channelDesc, width, height,

// Copy to device memory some data located at address h_data
// in host memory
cudaMemcpyToArray(cuInputArray, 0, 0, h_data, size,
cudaMemcpyHostToDevice);

// Bind the arrays to the surface references
cudaBindSurfaceToArray(inputSurfRef, cuInputArray);
cudaBindSurfaceToArray(outputSurfRef, cuOutputArray);

// Invoke kernel
dim3 dimBlock(16, 16);
dim3 dimGrid((width  + dimBlock.x - 1) / dimBlock.x,
(height + dimBlock.y - 1) / dimBlock.y);
copyKernel<<<dimGrid, dimBlock>>>(width, height);

// Free device memory
cudaFreeArray(cuInputArray);
cudaFreeArray(cuOutputArray);

return 0;
}```

### 3.2.11.2.3. Cubemap Surfaces

Cubemap surfaces are accessed usingsurfCubemapread() and surfCubemapwrite() (surfCubemapread and surfCubemapwrite) as a two-dimensional layered surface, i.e., using an integer index denoting a face and two floating-point texture coordinates addressing a texel within the layer corresponding to this face. Faces are ordered as indicated in Table 1.

### 3.2.11.2.4. Cubemap Layered Surfaces

Cubemap layered surfaces are accessed using surfCubemapLayeredread() and surfCubemapLayeredwrite() (surfCubemapLayeredread() and surfCubemapLayeredwrite()) as a two-dimensional layered surface, i.e., using an integer index denoting a face of one of the cubemaps and two floating-point texture coordinates addressing a texel within the layer corresponding to this face. Faces are ordered as indicated in Table 1, so index ((2 * 6) + 3), for example, accesses the fourth face of the third cubemap.

### 3.2.11.3. CUDA Arrays

CUDA arrays are opaque memory layouts optimized for texture fetching. They are one dimensional, two dimensional, or three-dimensional and composed of elements, each of which has 1, 2 or 4 components that may be signed or unsigned 8 , 16 or 32 bit integers, 16 bit floats, or 32 bit floats. CUDA arrays are only accessible by kernels through texture fetching as described in Texture Memory or surface reading and writing as described in Surface Memory .

The texture and surface memory is cached (see Device Memory Accesses) and within the same kernel call, the cache is not kept coherent with respect to global memory writes and surface memory writes, so any texture fetch or surface read to an address that has been written to via a global write or a surface write in the same kernel call returns undefined data. In other words, a thread can safely read some texture or surface memory location only if this memory location has been updated by a previous kernel call or memory copy, but not if it has been previously updated by the same thread or another thread from the same kernel call.

### 3.2.12. Graphics Interoperability

Some resources from OpenGL and Direct3D may be mapped into the address space of CUDA, either to enable CUDA to read data written by OpenGL or Direct3D, or to enable CUDA to write data for consumption by OpenGL or Direct3D.

A resource must be registered to CUDA before it can be mapped using the functions mentioned in OpenGL Interoperability and Direct3D Interoperability. These functions return a pointer to a CUDA graphics resource of type struct cudaGraphicsResource. Registering a resource is potentially high-overhead and therefore typically called only once per resource. A CUDA graphics resource is unregistered using cudaGraphicsUnregisterResource().

Once a resource is registered to CUDA, it can be mapped and unmapped as many times as necessary using cudaGraphicsMapResources() and cudaGraphicsUnmapResources(). cudaGraphicsResourceSetMapFlags() can be called to specify usage hints (write-only, read-only) that the CUDA driver can use to optimize resource management.

A mapped resource can be read from or written to by kernels using the device memory address returned by cudaGraphicsResourceGetMappedPointer() for buffers and cudaGraphicsSubResourceGetMappedArray() for CUDA arrays.

Accessing a resource through OpenGL or Direct3D while it is mapped to CUDA produces undefined results. OpenGL Interoperability and Direct3D Interoperability give specifics for each graphics API and some code samples. SLI Interoperability gives specifics for when the system is in SLI mode.

### 3.2.12.1. OpenGL Interoperability

Interoperability with OpenGL requires that the CUDA device be specified by cudaGLSetGLDevice() before any other runtime calls. Note that cudaSetDevice() and cudaGLSetGLDevice() are mutually exclusive.

The OpenGL resources that may be mapped into the address space of CUDA are OpenGL buffer, texture, and renderbuffer objects.

A buffer object is registered using cudaGraphicsGLRegisterBuffer(). In CUDA, it appears as a device pointer and can therefore be read and written by kernels or via cudaMemcpy() calls.

A texture or renderbuffer object is registered using cudaGraphicsGLRegisterImage(). In CUDA, it appears as a CUDA array. Kernels can read from the array by binding it to a texture or surface reference. They can also write to it via the surface write functions if the resource has been registered with the cudaGraphicsRegisterFlagsSurfaceLoadStore flag. The array can also be read and written via cudaMemcpy2D() calls. cudaGraphicsGLRegisterImage() supports all texture formats with 1, 2, or 4 components and an internal type of float (e.g., GL_RGBA_FLOAT32), normalized integer (e.g., GL_RGBA8, GL_INTENSITY16), and unnormalized integer (e.g., GL_RGBA8UI) (please note that since unnormalized integer formats require OpenGL 3.0, they can only be written by shaders, not the fixed function pipeline).

The OpenGL context whose resources are being shared has to be current to the host thread making any OpenGL interoperability API calls.

The following code sample uses a kernel to dynamically modify a 2D width x height grid of vertices stored in a vertex buffer object:

```GLuint positionsVBO;
struct cudaGraphicsResource* positionsVBO_CUDA;

int main()
{
// Initialize OpenGL and GLUT for device 0
// and make the OpenGL context current
...
glutDisplayFunc(display);

// Explicitly set device 0
cudaGLSetGLDevice(0);

// Create buffer object and register it with CUDA
glGenBuffers(1, &positionsVBO);
glBindBuffer(GL_ARRAY_BUFFER, positionsVBO);
unsigned int size = width * height * 4 * sizeof(float);
glBufferData(GL_ARRAY_BUFFER, size, 0, GL_DYNAMIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, 0);
cudaGraphicsGLRegisterBuffer(&positionsVBO_CUDA,
positionsVBO,

// Launch rendering loop
glutMainLoop();

...
}

void display()
{
// Map buffer object for writing from CUDA
float4* positions;
cudaGraphicsMapResources(1, &positionsVBO_CUDA, 0);
size_t num_bytes;
cudaGraphicsResourceGetMappedPointer((void**)&positions,
&num_bytes,
positionsVBO_CUDA));

// Execute kernel
dim3 dimBlock(16, 16, 1);
dim3 dimGrid(width / dimBlock.x, height / dimBlock.y, 1);
createVertices<<<dimGrid, dimBlock>>>(positions, time,
width, height);

// Unmap buffer object
cudaGraphicsUnmapResources(1, &positionsVBO_CUDA, 0);

// Render from buffer object
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glBindBuffer(GL_ARRAY_BUFFER, positionsVBO);
glVertexPointer(4, GL_FLOAT, 0, 0);
glEnableClientState(GL_VERTEX_ARRAY);
glDrawArrays(GL_POINTS, 0, width * height);
glDisableClientState(GL_VERTEX_ARRAY);

// Swap buffers
glutSwapBuffers();
glutPostRedisplay();
}

void deleteVBO()
{
cudaGraphicsUnregisterResource(positionsVBO_CUDA);
glDeleteBuffers(1, &positionsVBO);
}

__global__ void createVertices(float4* positions, float time,
unsigned int width, unsigned int height)
{
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

// Calculate uv coordinates
float u = x / (float)width;
float v = y / (float)height;
u = u * 2.0f - 1.0f;
v = v * 2.0f - 1.0f;

// calculate simple sine wave pattern
float freq = 4.0f;
float w = sinf(u * freq + time)
* cosf(v * freq + time) * 0.5f;

// Write positions
positions[y * width + x] = make_float4(u, w, v, 1.0f);
}```

On Windows and for Quadro GPUs, cudaWGLGetDevice() can be used to retrieve the CUDA device associated to the handle returned by wglEnumGpusNV(). Quadro GPUs offer higher performance OpenGL interoperability than GeForce and Tesla GPUs in a multi-GPU configuration where OpenGL rendering is performed on the Quadro GPU and CUDA computations are performed on other GPUs in the system.

### 3.2.12.2. Direct3D Interoperability

Direct3D interoperability is supported for Direct3D 9, Direct3D 10, and Direct3D 11.

A CUDA context may interoperate with only one Direct3D device at a time and the CUDA context and Direct3D device must be created on the same GPU. In addition the following considerations must be taken when creating the device: Direct3D 9 devices must be created with DeviceType set to D3DDEVTYPE_HAL and BehaviorFlags with the D3DCREATE_HARDWARE_VERTEXPROCESSING flag. Direct3D 10 and Direct3D 11 devices must be created with DriverType set to D3D_DRIVER_TYPE_HARDWARE.

A set of calls is also available to allow the creation of CUDA contexts with interoperability with Direct3D devices that use NVIDIA SLI in AFR (Alternate Frame Rendering) mode: cudaD3D[9|10|11]GetDevices(). A call to cudaD3D[9|10|11]GetDevices()can be used to obtain a list of CUDA device handles that can be passed as the (optional) last parameter to cudaD3D[9|10|11]SetDirect3DDevice().

The application has the choice to either create multiple CPU threads, each using a different CUDA context, or a single CPU thread using multiple CUDA context. If using separate CPU threads for each GPU each of the CUDA contexts would be created by the CUDA runtime by calling in a separate CPU thread cudaD3D[9|10|11]SetDirect3DDevice() using one of the CUDA device handles returned by cudaD3D[9|10|11]GetDevices().

If using a single CPU thread the CUDA contexts would have to be created using the CUDA driver API context creation functions for interoperability with Direct3D devices that use NVIDIA SLI (cuD3D[9|10|11]CtxCreateOnDevice()). The application relies on the interoperability between CUDA driver and runtime APIs (Interoperability between Runtime and Driver APIs), which allows it to call cuCtxPushCurrent() and cuCtxPopCurrent() to change the CUDA context active at a given time.

The Direct3D resources that may be mapped into the address space of CUDA are Direct3D buffers, textures, and surfaces. These resources are registered using cudaGraphicsD3D9RegisterResource(), cudaGraphicsD3D10RegisterResource(), and cudaGraphicsD3D11RegisterResource().

The following code sample uses a kernel to dynamically modify a 2D width x height grid of vertices stored in a vertex buffer object.

### 3.2.12.2.1. Direct3D 9 Version

```IDirect3D9* D3D;
IDirect3DDevice9* device;
struct CUSTOMVERTEX {
FLOAT x, y, z;
DWORD color;
};
IDirect3DVertexBuffer9* positionsVB;
struct cudaGraphicsResource* positionsVB_CUDA;

int main()
{
// Initialize Direct3D
D3D = Direct3DCreate9(D3D_SDK_VERSION);

int dev;
== cudaSuccess)
break;
}

// Create device
...
D3DCREATE_HARDWARE_VERTEXPROCESSING,
&params, &device);

// Register device with CUDA

// Create vertex buffer and register it with CUDA
unsigned int size = width * height * sizeof(CUSTOMVERTEX);
device->CreateVertexBuffer(size, 0, D3DFVF_CUSTOMVERTEX,
D3DPOOL_DEFAULT, &positionsVB, 0);
cudaGraphicsD3D9RegisterResource(&positionsVB_CUDA,
positionsVB,
cudaGraphicsRegisterFlagsNone);
cudaGraphicsResourceSetMapFlags(positionsVB_CUDA,

// Launch rendering loop
while (...) {
...
Render();
...
}
...
}

void Render()
{
// Map vertex buffer for writing from CUDA
float4* positions;
cudaGraphicsMapResources(1, &positionsVB_CUDA, 0);
size_t num_bytes;
cudaGraphicsResourceGetMappedPointer((void**)&positions,
&num_bytes,
positionsVB_CUDA));

// Execute kernel
dim3 dimBlock(16, 16, 1);
dim3 dimGrid(width / dimBlock.x, height / dimBlock.y, 1);
createVertices<<<dimGrid, dimBlock>>>(positions, time,
width, height);

// Unmap vertex buffer
cudaGraphicsUnmapResources(1, &positionsVB_CUDA, 0);

// Draw and present
...
}

void releaseVB()
{
cudaGraphicsUnregisterResource(positionsVB_CUDA);
positionsVB->Release();
}

__global__ void createVertices(float4* positions, float time,
unsigned int width, unsigned int height)
{
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

// Calculate uv coordinates
float u = x / (float)width;
float v = y / (float)height;
u = u * 2.0f - 1.0f;
v = v * 2.0f - 1.0f;

// Calculate simple sine wave pattern
float freq = 4.0f;
float w = sinf(u * freq + time)
* cosf(v * freq + time) * 0.5f;

// Write positions
positions[y * width + x] =
make_float4(u, w, v, __int_as_float(0xff00ff00));
}```

### 3.2.12.2.2. Direct3D 10 Version

```ID3D10Device* device;
struct CUSTOMVERTEX {
FLOAT x, y, z;
DWORD color;
};
ID3D10Buffer* positionsVB;
struct cudaGraphicsResource* positionsVB_CUDA;

int main()
{
IDXGIFactory* factory;
CreateDXGIFactory(__uuidof(IDXGIFactory), (void**)&factory);
for (unsigned int i = 0; !adapter; ++i) {
break;
int dev;
break;
}
factory->Release();

// Create swap chain and device
...
D3D10_DRIVER_TYPE_HARDWARE, 0,
D3D10_CREATE_DEVICE_DEBUG,
D3D10_SDK_VERSION,
&swapChainDesc, &swapChain,
&device);

// Register device with CUDA

// Create vertex buffer and register it with CUDA
unsigned int size = width * height * sizeof(CUSTOMVERTEX);
D3D10_BUFFER_DESC bufferDesc;
bufferDesc.Usage          = D3D10_USAGE_DEFAULT;
bufferDesc.ByteWidth      = size;
bufferDesc.BindFlags      = D3D10_BIND_VERTEX_BUFFER;
bufferDesc.CPUAccessFlags = 0;
bufferDesc.MiscFlags      = 0;
device->CreateBuffer(&bufferDesc, 0, &positionsVB);
cudaGraphicsD3D10RegisterResource(&positionsVB_CUDA,
positionsVB,
cudaGraphicsRegisterFlagsNone);
cudaGraphicsResourceSetMapFlags(positionsVB_CUDA,

// Launch rendering loop
while (...) {
...
Render();
...
}
...
}

void Render()
{
// Map vertex buffer for writing from CUDA
float4* positions;
cudaGraphicsMapResources(1, &positionsVB_CUDA, 0);
size_t num_bytes;
cudaGraphicsResourceGetMappedPointer((void**)&positions,
&num_bytes,
positionsVB_CUDA));

// Execute kernel
dim3 dimBlock(16, 16, 1);
dim3 dimGrid(width / dimBlock.x, height / dimBlock.y, 1);
createVertices<<<dimGrid, dimBlock>>>(positions, time,
width, height);

// Unmap vertex buffer
cudaGraphicsUnmapResources(1, &positionsVB_CUDA, 0);

// Draw and present
...
}

void releaseVB()
{
cudaGraphicsUnregisterResource(positionsVB_CUDA);
positionsVB->Release();
}

__global__ void createVertices(float4* positions, float time,
unsigned int width, unsigned int height)
{
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

// Calculate uv coordinates
float u = x / (float)width;
float v = y / (float)height;
u = u * 2.0f - 1.0f;
v = v * 2.0f - 1.0f;

// Calculate simple sine wave pattern
float freq = 4.0f;
float w = sinf(u * freq + time)
* cosf(v * freq + time) * 0.5f;

// Write positions
positions[y * width + x] =
make_float4(u, w, v, __int_as_float(0xff00ff00));
}```

### 3.2.12.2.3. Direct3D 11 Version

```ID3D11Device* device;
struct CUSTOMVERTEX {
FLOAT x, y, z;
DWORD color;
};
ID3D11Buffer* positionsVB;
struct cudaGraphicsResource* positionsVB_CUDA;

int main()
{
IDXGIFactory* factory;
CreateDXGIFactory(__uuidof(IDXGIFactory), (void**)&factory);
for (unsigned int i = 0; !adapter; ++i) {
break;
int dev;
break;
}
factory->Release();

// Create swap chain and device
...
D3D11_DRIVER_TYPE_HARDWARE,
0,
D3D11_CREATE_DEVICE_DEBUG,
featureLevels, 3,
D3D11_SDK_VERSION,
&swapChainDesc, &swapChain,
&device,
&featureLevel,
&deviceContext);

// Register device with CUDA

// Create vertex buffer and register it with CUDA
unsigned int size = width * height * sizeof(CUSTOMVERTEX);
D3D11_BUFFER_DESC bufferDesc;
bufferDesc.Usage          = D3D11_USAGE_DEFAULT;
bufferDesc.ByteWidth      = size;
bufferDesc.BindFlags      = D3D11_BIND_VERTEX_BUFFER;
bufferDesc.CPUAccessFlags = 0;
bufferDesc.MiscFlags      = 0;
device->CreateBuffer(&bufferDesc, 0, &positionsVB);
cudaGraphicsD3D11RegisterResource(&positionsVB_CUDA,
positionsVB,
cudaGraphicsRegisterFlagsNone);
cudaGraphicsResourceSetMapFlags(positionsVB_CUDA,

// Launch rendering loop
while (...) {
...
Render();
...
}
...
}

void Render()
{
// Map vertex buffer for writing from CUDA
float4* positions;
cudaGraphicsMapResources(1, &positionsVB_CUDA, 0);
size_t num_bytes;
cudaGraphicsResourceGetMappedPointer((void**)&positions,
&num_bytes,
positionsVB_CUDA));

// Execute kernel
dim3 dimBlock(16, 16, 1);
dim3 dimGrid(width / dimBlock.x, height / dimBlock.y, 1);
createVertices<<<dimGrid, dimBlock>>>(positions, time,
width, height);

// Unmap vertex buffer
cudaGraphicsUnmapResources(1, &positionsVB_CUDA, 0);

// Draw and present
...
}

void releaseVB()
{
cudaGraphicsUnregisterResource(positionsVB_CUDA);
positionsVB->Release();
}

__global__ void createVertices(float4* positions, float time,
unsigned int width, unsigned int height)
{
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;

// Calculate uv coordinates
float u = x / (float)width;
float v = y / (float)height;
u = u * 2.0f - 1.0f;
v = v * 2.0f - 1.0f;

// Calculate simple sine wave pattern
float freq = 4.0f;
float w = sinf(u * freq + time)
* cosf(v * freq + time) * 0.5f;

// Write positions
positions[y * width + x] =
make_float4(u, w, v, __int_as_float(0xff00ff00));
}```

### 3.2.12.3. SLI Interoperability

In a system with multiple GPUs, all CUDA-enabled GPUs are accessible via the CUDA driver and runtime as separate devices. There are however special considerations as described below when the system is in SLI mode.

First, an allocation in one CUDA device on one GPU will consume memory on other GPUs that are part of the SLI configuration of the Direct3D or OpenGL device. Because of this, allocations may fail earlier than otherwise expected.

Second, applications have to create multiple CUDA contexts, one for each GPU in the SLI configuration and deal with the fact that a different GPU is used for rendering by the Direct3D or OpenGL device at every frame. The application can use the cudaD3D[9|10|11]GetDevices() for Direct3D and cudaGLGetDevices() for OpenGL set of calls to identify the CUDA device handle(s) for the device(s) that are performing the rendering in the current and next frame. Given this information the application will typically map Direct3D or OpenGL resources to the CUDA context corresponding to the CUDA device returned by cudaD3D[9|10|11]GetDevices() or cudaGLGetDevices() when the deviceList parameter is set to CU_D3D10_DEVICE_LIST_CURRENT_FRAME or cudaGLDeviceListCurrentFrame.

See Direct3D Interoperability and OpenGL Interoperability for details on how the CUDA runtime interoperate with Direct3D and OpenGL, respectively.

### 3.3. Versioning and Compatibility

There are two version numbers that developers should care about when developing a CUDA application: The compute capability that describes the general specifications and features of the compute device (see Compute Capability) and the version of the CUDA driver API that describes the features supported by the driver API and runtime.

The version of the driver API is defined in the driver header file as CUDA_VERSION. It allows developers to check whether their application requires a newer device driver than the one currently installed. This is important, because the driver API is backward compatible, meaning that applications, plug-ins, and libraries (including the C runtime) compiled against a particular version of the driver API will continue to work on subsequent device driver releases as illustrated in Figure 11. The driver API is not forward compatible, which means that applications, plug-ins, and libraries (including the C runtime) compiled against a particular version of the driver API will not work on previous versions of the device driver.

It is important to note that mixing and matching versions is not supported; specifically:

• All applications, plug-ins, and libraries on a system must use the same version of the CUDA driver API, since only one version of the CUDA device driver can be installed on a system.
• All plug-ins and libraries used by an application must use the same version of the runtime.
• All plug-ins and libraries used by an application must use the same version of any libraries that use the runtime (such as CUFFT, CUBLAS, ...).
Figure 11. The Driver API Is Backward, but Not Forward Compatible

### 3.4. Compute Modes

On Tesla solutions running Windows Server 2008 and later or Linux, one can set any device in a system in one of the three following modes using NVIDIA's System Management Interface (nvidia-smi), which is a tool distributed as part of the driver:

• Default compute mode: Multiple host threads can use the device (by calling cudaSetDevice() on this device, when using the runtime API, or by making current a context associated to the device, when using the driver API) at the same time.
• Exclusive-process compute mode: Only one CUDA context may be created on the device across all processes in the system and that context may be current to as many threads as desired within the process that created that context.
• Exclusive-process-and-thread compute mode: Only one CUDA context may be created on the device across all processes in the system and that context may only be current to one thread at a time.
• Prohibited compute mode: No CUDA context can be created on the device.

This means, in particular, that a host thread using the runtime API without explicitly calling cudaSetDevice() might be associated with a device other than device 0 if device 0 turns out to be in the exclusive-process mode and used by another process, or in the exclusive-process-and-thread mode and used by another thread, or in prohibited mode. cudaSetValidDevices() can be used to set a device from a prioritized list of devices.

Applications may query the compute mode of a device by checking the computeMode device property (see Device Enumeration).

### 3.5. Mode Switches

GPUs that have a display output dedicate some DRAM memory to the so-called primary surface, which is used to refresh the display device whose output is viewed by the user. When users initiate a mode switch of the display by changing the resolution or bit depth of the display (using NVIDIA control panel or the Display control panel on Windows), the amount of memory needed for the primary surface changes. For example, if the user changes the display resolution from 1280x1024x32-bit to 1600x1200x32-bit, the system must dedicate 7.68 MB to the primary surface rather than 5.24 MB. (Full-screen graphics applications running with anti-aliasing enabled may require much more display memory for the primary surface.) On Windows, other events that may initiate display mode switches include launching a full-screen DirectX application, hitting Alt+Tab to task switch away from a full-screen DirectX application, or hitting Ctrl+Alt+Del to lock the computer.

If a mode switch increases the amount of memory needed for the primary surface, the system may have to cannibalize memory allocations dedicated to CUDA applications. Therefore, a mode switch results in any call to the CUDA runtime to fail and return an invalid context error.

### 3.6. Tesla Compute Cluster Mode for Windows

Using NVIDIA's System Management Interface (nvidia-smi), the Windows device driver can be put in TCC (Tesla Compute Cluster) mode for devices of the Tesla and Quadro Series of compute capability 2.0 and higher.

This mode has the following primary benefits:

• It makes it possible to use these GPUs in cluster nodes with non-NVIDIA integrated graphics;
• It makes these GPUs available via Remote Desktop, both directly and via cluster management systems that rely on Remote Desktop;
• It makes these GPUs available to applications running as a Windows service (i.e., in Session 0).

However, the TCC mode removes support for any graphics functionality.

## 4. Hardware Implementation

The NVIDIA GPU architecture is built around a scalable array of multithreaded Streaming Multiprocessors (SMs). When a CUDA program on the host CPU 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, and multiple thread blocks can execute concurrently on one multiprocessor. As thread blocks terminate, new blocks are launched on the vacated multiprocessors.

A multiprocessor is designed to execute hundreds of threads concurrently. To manage such a large amount of threads, it employs a unique architecture called SIMT (Single-Instruction, Multiple-Thread) that is described in SIMT Architecture. The instructions are pipelined to leverage instruction-level parallelism within a single thread, as well as thread-level parallelism extensively through simultaneous hardware multithreading as detailed in Hardware Multithreading. Unlike CPU cores they are issued in order however and there is no branch prediction and no speculative execution.

SIMT Architecture and Hardware Multithreading describe the architecture features of the streaming multiprocessor that are common to all devices. Compute Capability 1.x, Compute Capability 2.x, and Compute Capability 3.x provide the specifics for devices of compute capabilities 1.x, 2.x, and 3.x, respectively.

The NVIDIA GPU architecture uses a little-endian representation.

### 4.1. SIMT Architecture

The multiprocessor creates, manages, schedules, and executes threads in groups of 32 parallel threads called warps. Individual threads composing a warp start together at the same program address, but they have their own instruction address counter and register state and are therefore free to branch and execute independently. The term warp originates from weaving, the first parallel thread technology. A half-warp is either the first or second half of a warp. A quarter-warp is either the first, second, third, or fourth quarter of a warp.

When a multiprocessor is given one or more thread blocks to execute, it partitions them into warps and each warp gets scheduled by a warp scheduler for execution. The way a block is partitioned into warps is always the same; each warp contains threads of consecutive, increasing thread IDs with the first warp containing thread 0. Thread Hierarchy describes how thread IDs relate to thread indices in the block.

A warp executes one common instruction at a time, so full efficiency is realized when all 32 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 disjoint code paths.

The 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.

### Notes

The threads of a warp that are on that warp's current execution path are called the active threads, whereas threads not on the current path are inactive (disabled). Threads can be inactive because they have exited earlier than other threads of their warp, or because they are on a different branch path than the branch path currently executed by the warp, or because they are the last threads of a block whose number of threads is not a multiple of the warp size.

If a non-atomic instruction executed by a warp writes to the same location in global or shared memory for more than one of the threads of the warp, the number of serialized writes that occur to that location varies depending on the compute capability of the device (see Compute Capability 1.x, Compute Capability 2.x, and Compute Capability 3.x), and which thread performs the final write is undefined.

If an atomic instruction executed by a warp reads, modifies, and writes to the same location in global memory for more than one of the threads of the warp, each read/modify/write to that location occurs and they are all serialized, but the order in which they occur is undefined.

The execution context (program counters, registers, etc.) for each warp processed by a multiprocessor is maintained on-chip during the entire lifetime of the warp. Therefore, switching from one execution context to another has no cost, and at every instruction issue time, a warp scheduler selects a warp that has threads ready to execute its next instruction (the active threads of the warp) and issues the instruction to those threads.

In particular, each multiprocessor has a set of 32-bit registers that are partitioned among the warps, and a parallel data cache or shared memory that is partitioned among the thread blocks.

The number of blocks and warps that can reside and be processed together on the multiprocessor for a given kernel depends on the amount of registers and shared memory used by the kernel and the amount of registers and shared memory available on the multiprocessor. There are also a maximum number of resident blocks and a maximum number of resident warps per multiprocessor. These limits as well the amount of registers and shared memory available on the multiprocessor are a function of the compute capability of the device and are given in Appendix F. If there are not enough registers or shared memory available per multiprocessor to process at least one block, the kernel will fail to launch.

The total number of warps in a block is as follows:

$\text{ceil}\left(\frac{T}{{W}_{size}},1\right)$

• T is the number of threads per block,
• Wsize is the warp size, which is equal to 32,
• ceil(x, y) is equal to x rounded up to the nearest multiple of y.

The total number of registers and total amount of shared memory allocated for a block are documented in the CUDA Occupancy Calculator provided in CUDA Software Development Kit.

## 5. Performance Guidelines

### 5.1. Overall Performance Optimization Strategies

Performance optimization revolves around three basic strategies:

• Maximize parallel execution to achieve maximum utilization;
• Optimize memory usage to achieve maximum memory throughput;
• Optimize instruction usage to achieve maximum instruction throughput.

Which strategies will yield the best performance gain for a particular portion of an application depends on the performance limiters for that portion; optimizing instruction usage of a kernel that is mostly limited by memory accesses will not yield any significant performance gain, for example. Optimization efforts should therefore be constantly directed by measuring and monitoring the performance limiters, for example using the CUDA profiler. Also, comparing the floating-point operation throughput or memory throughput - whichever makes more sense - of a particular kernel to the corresponding peak theoretical throughput of the device indicates how much room for improvement there is for the kernel.

### 5.2. Maximize Utilization

To maximize utilization the application should be structured in a way that it exposes as much parallelism as possible and efficiently maps this parallelism to the various components of the system to keep them busy most of the time.

### 5.2.1. Application Level

At a high level, the application should maximize parallel execution between the host, the devices, and the bus connecting the host to the devices, by using asynchronous functions calls and streams as described in Asynchronous Concurrent Execution. It should assign to each processor the type of work it does best: serial workloads to the host; parallel workloads to the devices.

For the parallel workloads, at points in the algorithm where parallelism is broken because some threads need to synchronize in order to share data with each other, there are two cases: Either these threads belong to the same block, in which case they should use __syncthreads() and share data through shared memory within the same kernel invocation, or they belong to different blocks, in which case they must share data through global memory using two separate kernel invocations, one for writing to and one for reading from global memory. The second case is much less optimal since it adds the overhead of extra kernel invocations and global memory traffic. Its occurrence should therefore be minimized by mapping the algorithm to the CUDA programming model in such a way that the computations that require inter-thread communication are performed within a single thread block as much as possible.

### 5.2.2. Device Level

At a lower level, the application should maximize parallel execution between the multiprocessors of a device.

For devices of compute capability 1.x, only one kernel can execute on a device at one time, so the kernel should be launched with at least as many thread blocks as there are multiprocessors in the device.

For devices of compute capability 2.x and higher, multiple kernels can execute concurrently on a device, so maximum utilization can also be achieved by using streams to enable enough kernels to execute concurrently as described in Asynchronous Concurrent Execution.

### 5.2.3. Multiprocessor Level

At an even lower level, the application should maximize parallel execution between the various functional units within a multiprocessor.

As described in Hardware Multithreading, a GPU multiprocessor relies on thread-level parallelism to maximize utilization of its functional units. Utilization is therefore directly linked to the number of resident warps. At every instruction issue time, a warp scheduler selects a warp that is ready to execute its next instruction, if any, and issues the instruction to the active threads of the warp. The number of clock cycles it takes for a warp to be ready to execute its next instruction is called the latency, and full utilization is achieved when all warp schedulers always have some instruction to issue for some warp at every clock cycle during that latency period, or in other words, when latency is completely "hidden". The number of instructions required to hide a latency of L clock cycles depends on the respective throughputs of these instructions (see Arithmetic Instructions for the throughputs of various arithmetic instructions); assuming maximum throughput for all instructions, it is:

• L/4 (rounded up to nearest integer) for devices of compute capability 1.x since a multiprocessor issues one instruction per warp over four clock cycles, as mentioned in Compute Capability 1.x,
• L for devices of compute capability 2.0 since a multiprocessor issues one instruction per warp over two clock cycles for two warps at a time, as mentioned in Compute Capability 2.x,
• 2L for devices of compute capability 2.1 since a multiprocessor issues a pair of instructions per warp over two clock cycles for two warps at a time, as mentioned in Compute Capability 2.x,
• 8L for devices of compute capability 3.x since a multiprocessor issues a pair of instructions per warp over one clock cycle for four warps at a time, as mentioned in Compute Capability 3.x.

For devices of compute capability 2.0, the two instructions issued every other cycle are for two different warps. For devices of compute capability 2.1, the four instructions issued every other cycle are two pairs for two different warps, each pair being for the same warp.

For devices of compute capability 3.x, the eight instructions issued every cycle are four pairs for four different warps, each pair being for the same warp.

The most common reason a warp is not ready to execute its next instruction is that the instruction's input operands are not available yet.

If all input operands are registers, latency is caused by register dependencies, i.e., some of the input operands are written by some previous instruction(s) whose execution has not completed yet. In the case of a back-to-back register dependency (i.e., some input operand is written by the previous instruction), the latency is equal to the execution time of the previous instruction and the warp schedulers must schedule instructions for different warps during that time. Execution time varies depending on the instruction, but it is typically about 22 clock cycles for devices of compute capability 1.x and 2.x and about 11 clock cycles for devices of compute capability 3.x, which translates to 6 warps for devices of compute capability 1.x, 22 warps for devices of compute capability 2.x, and 44 warps for devices of compute capability 3.x and higher (still assuming that warps execute instructions with maximum throughput, otherwise fewer warps are needed). For devices of compute capability 2.1 and higher, this is also assuming enough instruction-level parallelism so that schedulers are always able to issue pairs of instructions for each warp.

If some input operand resides in off-chip memory, the latency is much higher: 400 to 800 clock cycles for devices of compute capability 1.x and 2.x and about 200 to 400 clock cycles for devices of compute capability 3.x. The number of warps required to keep the warp schedulers busy during such high latency periods depends on the kernel code and its degree of instruction-level parallelism. In general, more warps are required if the ratio of the number of instructions with no off-chip memory operands (i.e., arithmetic instructions most of the time) to the number of instructions with off-chip memory operands is low (this ratio is commonly called the arithmetic intensity of the program). For example, assume this ratio is 30, also assume the latencies are 600 cycles on devices of compute capability 1.x and 2.x and 300 cycles on devices of compute capability 3.x. Then about 5 warps are required for devices of compute capability 1.x, about 20 for devices of compute capability 2.x and about 40 for devices of compute capability 3.x (with the same assumptions as in the previous paragraph).

Another reason a warp is not ready to execute its next instruction is that it is waiting at some memory fence (Memory Fence Functions) or synchronization point (Memory Fence Functions). A synchronization point can force the multiprocessor to idle as more and more warps wait for other warps in the same block to complete execution of instructions prior to the synchronization point. Having multiple resident blocks per multiprocessor can help reduce idling in this case, as warps from different blocks do not need to wait for each other at synchronization points.

The number of blocks and warps residing on each multiprocessor for a given kernel call depends on the execution configuration of the call (Execution Configuration), the memory resources of the multiprocessor, and the resource requirements of the kernel as described in Hardware Multithreading. To assist programmers in choosing thread block size based on register and shared memory requirements, the CUDA Software Development Kit provides a spreadsheet, called the CUDA Occupancy Calculator, where occupancy is defined as the ratio of the number of resident warps to the maximum number of resident warps (given in Compute Capabilities for various compute capabilities).

Register, local, shared, and constant memory usages are reported by the compiler when compiling with the -ptxas-options=-v option.

The total amount of shared memory required for a block is equal to the sum of the amount of statically allocated shared memory, the amount of dynamically allocated shared memory, and for devices of compute capability 1.x, the amount of shared memory used to pass the kernel's arguments (see __noinline__ and __forceinline__).

The number of registers used by a kernel can have a significant impact on the number of resident warps. For example, for devices of compute capability 1.2, if a kernel uses 16 registers and each block has 512 threads and requires very little shared memory, then two blocks (i.e., 32 warps) can reside on the multiprocessor since they require 2x512x16 registers, which exactly matches the number of registers available on the multiprocessor. But as soon as the kernel uses one more register, only one block (i.e., 16 warps) can be resident since two blocks would require 2x512x17 registers, which are more registers than are available on the multiprocessor. Therefore, the compiler attempts to minimize register usage while keeping register spilling (see Device Memory Accesses) and the number of instructions to a minimum. Register usage can be controlled using the maxrregcount compiler option or launch bounds as described in Launch Bounds.

Each double variable (on devices that supports native double precision, i.e., devices of compute capability 1.2 and higher) and each long long variable uses two registers. However, devices of compute capability 1.2 and higher have at least twice as many registers per multiprocessor as devices with lower compute capability.

The effect of execution configuration on performance for a given kernel call generally depends on the kernel code. Experimentation is therefore recommended. Applications can also parameterize execution configurations based on register file size and shared memory size, which depends on the compute capability of the device, as well as on the number of multiprocessors and memory bandwidth of the device, all of which can be queried using the runtime (see reference manual).

The number of threads per block should be chosen as a multiple of the warp size to avoid wasting computing resources with under-populated warps as much as possible.

### 5.3. Maximize Memory Throughput

The first step in maximizing overall memory throughput for the application is to minimize data transfers with low bandwidth.

That means minimizing data transfers between the host and the device, as detailed in Data Transfer between Host and Device, since these have much lower bandwidth than data transfers between global memory and the device.

That also means minimizing data transfers between global memory and the device by maximizing use of on-chip memory: shared memory and caches (i.e., L1/L2 caches available on devices of compute capability 2.x and higher, texture cache and constant cache available on all devices).

Shared memory is equivalent to a user-managed cache: The application explicitly allocates and accesses it. As illustrated in CUDA C Runtime, a typical programming pattern is to stage data coming from device memory into shared memory; in other words, to have each thread of a block:

• Load data from device memory to shared memory,
• Synchronize with all the other threads of the block so that each thread can safely read shared memory locations that were populated by different threads,
• Process the data in shared memory,
• Synchronize again if necessary to make sure that shared memory has been updated with the results,
• Write the results back to device memory.

For some applications (e.g., for which global memory access patterns are data-dependent), a traditional hardware-managed cache is more appropriate to exploit data locality. As mentioned in Compute Capability 2.x, for devices of compute capability 2.x and higher, the same on-chip memory is used for both L1 and shared memory, and how much of it is dedicated to L1 versus shared memory is configurable for each kernel call.

The throughput of memory accesses by a kernel can vary by an order of magnitude depending on access pattern for each type of memory. The next step in maximizing memory throughput is therefore to organize memory accesses as optimally as possible based on the optimal memory access patterns described in Device Memory Accesses. This optimization is especially important for global memory accesses as global memory bandwidth is low, so non-optimal global memory accesses have a higher impact on performance.

### 5.3.1. Data Transfer between Host and Device

Applications should strive to minimize data transfer between the host and the device. One way to accomplish this is to move more code from the host to the device, even if that means running kernels with low parallelism computations. Intermediate data structures may be created in device memory, operated on by the device, and destroyed without ever being mapped by the host or copied to host memory.

Also, because of the overhead associated with each transfer, batching many small transfers into a single large transfer always performs better than making each transfer separately.

On systems with a front-side bus, higher performance for data transfers between host and device is achieved by using page-locked host memory as described in Page-Locked Host Memory.

In addition, when using mapped page-locked memory (Mapped Memory), there is no need to allocate any device memory and explicitly copy data between device and host memory. Data transfers are implicitly performed each time the kernel accesses the mapped memory. For maximum performance, these memory accesses must be coalesced as with accesses to global memory (see Device Memory Accesses). Assuming that they are and that the mapped memory is read or written only once, using mapped page-locked memory instead of explicit copies between device and host memory can be a win for performance.

On integrated systems where device memory and host memory are physically the same, any copy between host and device memory is superfluous and mapped page-locked memory should be used instead. Applications may query a device is integrated by checking that the integrated device property (see Device Enumeration) is equal to 1.

### 5.3.2. Device Memory Accesses

An instruction that accesses addressable memory (i.e., global, local, shared, constant, or texture memory) might need to be re-issued multiple times depending on the distribution of the memory addresses across the threads within the warp. How the distribution affects the instruction throughput this way is specific to each type of memory and described in the following sections. For example, for global memory, as a general rule, the more scattered the addresses are, the more reduced the throughput is.

#### Global Memory

Global memory resides in device memory and device memory is accessed via 32-, 64-, or 128-byte memory transactions. These memory transactions must be naturally aligned: Only the 32-, 64-, or 128-byte segments of device memory that are aligned to their size (i.e., whose first address is a multiple of their size) can be read or written by memory transactions.

When a warp executes an instruction that accesses global memory, it coalesces the memory accesses of the threads within the warp into one or more of these memory transactions depending on the size of the word accessed by each thread and the distribution of the memory addresses across the threads. In general, the more transactions are necessary, the more unused words are transferred in addition to the words accessed by the threads, reducing the instruction throughput accordingly. For example, if a 32-byte memory transaction is generated for each thread's 4-byte access, throughput is divided by 8.

How many transactions are necessary and how much throughput is ultimately affected varies with the compute capability of the device. For devices of compute capability 1.0 and 1.1, the requirements on the distribution of the addresses across the threads to get any coalescing at all are very strict. They are much more relaxed for devices of higher compute capabilities. For devices of compute capability 2.x and higher, the memory transactions are cached, so data locality is exploited to reduce impact on throughput. Compute Capability 1.x, Compute Capability 2.x, and Compute Capability 3.x give more details on how global memory accesses are handled for various compute capabilities.

To maximize global memory throughput, it is therefore important to maximize coalescing by:

#### Size and Alignment Requirement

Global memory instructions support reading or writing words of size equal to 1, 2, 4, 8, or 16 bytes. Any access (via a variable or a pointer) to data residing in global memory compiles to a single global memory instruction if and only if the size of the data type is 1, 2, 4, 8, or 16 bytes and the data is naturally aligned (i.e., its address is a multiple of that size).

If this size and alignment requirement is not fulfilled, the access compiles to multiple instructions with interleaved access patterns that prevent these instructions from fully coalescing. It is therefore recommended to use types that meet this requirement for data that resides in global memory.

The alignment requirement is automatically fulfilled for the built-in types of char, short, int, long, longlong, float, double like float2 or float4.

For structures, the size and alignment requirements can be enforced by the compiler using the alignment specifiers __align__(8) or __align__(16), such as

```struct __align__(8) {
float x;
float y;
};```

or

```struct __align__(16) {
float x;
float y;
float z;
};```

Any address of a variable residing in global memory or returned by one of the memory allocation routines from the driver or runtime API is always aligned to at least 256 bytes.

Reading non-naturally aligned 8-byte or 16-byte words produces incorrect results (off by a few words), so special care must be taken to maintain alignment of the starting address of any value or array of values of these types. A typical case where this might be easily overlooked is when using some custom global memory allocation scheme, whereby the allocations of multiple arrays (with multiple calls to cudaMalloc() or cuMemAlloc()) is replaced by the allocation of a single large block of memory partitioned into multiple arrays, in which case the starting address of each array is offset from the block's starting address.

#### Two-Dimensional Arrays

A common global memory access pattern is when each thread of index (tx,ty) uses the following address to access one element of a 2D array of width width, located at address BaseAddress of type type* (where type meets the requirement described in Maximize Utilization):

`BaseAddress + width * ty + tx`

For these accesses to be fully coalesced, both the width of the thread block and the width of the array must be a multiple of the warp size (or only half the warp size for devices of compute capability 1.x).

In particular, this means that an array whose width is not a multiple of this size will be accessed much more efficiently if it is actually allocated with a width rounded up to the closest multiple of this size and its rows padded accordingly. The cudaMallocPitch() and cuMemAllocPitch() functions and associated memory copy functions described in the reference manual enable programmers to write non-hardware-dependent code to allocate arrays that conform to these constraints.

#### Local Memory

Local memory accesses only occur for some automatic variables as mentioned in Variable Type Qualifiers. Automatic variables that the compiler is likely to place in local memory are:

• Arrays for which it cannot determine that they are indexed with constant quantities,
• Large structures or arrays that would consume too much register space,
• Any variable if the kernel uses more registers than available (this is also known as register spilling).

Inspection of the PTX assembly code (obtained by compiling with the -ptx or-keep option) will tell if a variable has been placed in local memory during the first compilation phases as it will be declared using the .local mnemonic and accessed using the ld.local and st.local mnemonics. Even if it has not, subsequent compilation phases might still decide otherwise though if they find it consumes too much register space for the targeted architecture: Inspection of the cubin object using cuobjdump will tell if this is the case. Also, the compiler reports total local memory usage per kernel (lmem) when compiling with the --ptxas-options=-v option. Note that some mathematical functions have implementation paths that might access local memory.

The local memory space resides in device memory, so local memory accesses have same high latency and low bandwidth as global memory accesses and are subject to the same requirements for memory coalescing as described in Device Memory Accesses. Local memory is however organized such that consecutive 32-bit words are accessed by consecutive thread IDs. Accesses are therefore fully coalesced as long as all threads in a warp access the same relative address (e.g., same index in an array variable, same member in a structure variable).

On devices of compute capability 2.x and higher, local memory accesses are always cached in L1 and L2 in the same way as global memory accesses (see Compute Capability 2.x).

#### Shared Memory

Because it is on-chip, shared memory has much higher bandwidth and much lower latency than local or global memory.

To achieve high bandwidth, shared memory is divided into equally-sized memory modules, called banks, which can be accessed simultaneously. Any memory read or write request made of n addresses that fall in n distinct memory banks can therefore be serviced simultaneously, yielding an overall bandwidth that is n times as high as the bandwidth of a single module.

However, if two addresses of a memory request fall in the same memory bank, there is a bank conflict and the access has to be serialized. The hardware splits a memory request with bank conflicts into as many separate conflict-free requests as necessary, decreasing throughput by a factor equal to the number of separate memory requests. If the number of separate memory requests is n, the initial memory request is said to cause n-way bank conflicts.

To get maximum performance, it is therefore important to understand how memory addresses map to memory banks in order to schedule the memory requests so as to minimize bank conflicts. This is described in Compute Capability 1.x,Compute Capability 2.x, Compute Capability 3.x for devices of compute capability 1.x, 2.x, and 3.x, respectively.

#### Constant Memory

The constant memory space resides in device memory and is cached in the constant cache mentioned in Compute Capability 1.x and Compute Capability 2.x.

For devices of compute capability 1.x, a constant memory request for a warp is first split into two requests, one for each half-warp, that are issued independently.

A request is then split into as many separate requests as there are different memory addresses in the initial request, decreasing throughput by a factor equal to the number of separate requests.

The resulting requests are then serviced at the throughput of the constant cache in case of a cache hit, or at the throughput of device memory otherwise.

#### Texture and Surface Memory

The texture and surface memory spaces reside in device memory and are cached in texture cache, so a texture fetch or surface read costs one memory read from device memory only on a cache miss, otherwise it just costs one read from texture cache. The texture cache is optimized for 2D spatial locality, so threads of the same warp that read texture or surface addresses that are close together in 2D will achieve best performance. Also, it is designed for streaming fetches with a constant latency; a cache hit reduces DRAM bandwidth demand but not fetch latency.

Reading device memory through texture or surface fetching present some benefits that can make it an advantageous alternative to reading device memory from global or constant memory:

• If the memory reads do not follow the access patterns that global or constant memory reads must follow to get good performance, higher bandwidth can be achieved providing that there is locality in the texture fetches or surface reads;
• Addressing calculations are performed outside the kernel by dedicated units;
• Packed data may be broadcast to separate variables in a single operation;
• 8-bit and 16-bit integer input data may be optionally converted to 32 bit floating-point values in the range [0.0, 1.0] or [-1.0, 1.0] (see Texture Memory).

### 5.4. Maximize Instruction Throughput

To maximize instruction throughput the application should:

• Minimize the use of arithmetic instructions with low throughput; this includes trading precision for speed when it does not affect the end result, such as using intrinsic instead of regular functions (intrinsic functions are listed in Intrinsic Functions), single-precision instead of double-precision, or flushing denormalized numbers to zero;
• Minimize divergent warps caused by control flow instructions as detailed in Control Flow Instructions
• Reduce the number of instructions, for example, by optimizing out synchronization points whenever possible as described in Synchronization Instruction or by using restricted pointers as described in __restrict__.

In this section, throughputs are given in number of operations per clock cycle per multiprocessor. For a warp size of 32, one instruction corresponds to 32 operations, so if N is the number of operations per clock cycle, the instruction throughput is N/32 instructions per clock cycle.

All throughputs are for one multiprocessor. They must be multiplied by the number of multiprocessors in the device to get throughput for the whole device.

### 5.4.1. Arithmetic Instructions

Table 2 gives the throughputs of the arithmetic instructions that are natively supported in hardware for devices of various compute capabilities.

Table 2. Throughput of Native Arithmetic Instructions. (Number of Operations per Clock Cycle per Multiprocessor)
Compute Capability

1.0

1.1

1.2

1.3 2.0 2.1 3.0 3.5
32-bit floating-point reciprocal, reciprocal square root, base-2 logarithm (__log2f), base 2 exponential (exp2f), sine (__sinf), cosine (__cosf) 2 2 4 8 32 32
32-bit integer add, extended-precision add, subtract, extended-precision subtract, compare, minimum, maximum 10 10 32 48 160 160
32-bit integer multiply, multiply-add, extended-precision multiply-add, sum of absolute difference, population count, count of leading zeros, most significant non-sign bit Multiple instructions Multiple instructions 16 16 32 32
24-bit integer multiply (__[u]mul24) 8 8 Multiple instructions Multiple instructions Multiple instructions Multiple instructions
32-bit integer absolute value, negate 8 8 16 16 32 32
32-bit integer shift 8 8 16 16 32 64(*)
32-bit integer bit reverse, bit field extract/insert Multiple instructions Multiple instructions 16 16 32 32
32-bit bitwise AND, OR, XOR 8 8 32 48 160 160
Warp shuffle N/A N/A N/A N/A 32 32
SIMD video instructions vabsdiff2 and vabsdiff2 N/A N/A N/A N/A 160 160
All other SIMD video instructions N/A N/A 16 16 32 32
Type conversions from 8-bit and 16-bit integer to 32-bit types 8 8 16 16 128 128
Type conversions from and to 64-bit types Multiple instructions 1 16(*) 4 8 32
All other type conversions 8 8 16 16 32 32
(*) Throughput is lower for GeForce GPUs.

Other instructions and functions are implemented on top of the native instructions. The implementation may be different for devices of different compute capabilities, and the number of native instructions after compilation may fluctuate with every compiler version. For complicated functions, there can be multiple code paths depending on input. cuobjdump can be used to inspect a particular implementation in a cubin object.

The implementation of some functions are readily available on the CUDA header files (math_functions.h, device_functions.h, ...).

In general, code compiled with -ftz=true (denormalized numbers are flushed to zero) tends to have higher performance than code compiled with -ftz=false. Similarly, code compiled with -prec div=false (less precise division) tends to have higher performance code than code compiled with -prec div=true, and code compiled with -prec-sqrt=false (less precise square root) tends to have higher performance than code compiled with -prec-sqrt=true. The nvcc user manual describes these compilation flags in more details.

#### Single-Precision Floating-Point Addition and Multiplication Intrinsics

__fadd_r[d,u], __fsub_r[d,u], __fmul_r[d,u], and __fmaf_r[n,z,d,u] (see Intrinsic Functions) compile to tens of instructions for devices of compute capability 1.x, but map to a single native instruction for devices of compute capability 2.x and higher.

#### Single-Precision Floating-Point Division

__fdividef(x, y) (see Intrinsic Functions) provides faster single-precision floating-point division than the division operator.

#### Single-Precision Floating-Point Reciprocal Square Root

To preserve IEEE-754 semantics the compiler can optimize 1.0/sqrtf() into rsqrtf() only when both reciprocal and square root are approximate, (i.e., with -prec-div=false and -prec-sqrt=false). It is therefore recommended to invoke rsqrtf() directly where desired.

#### Single-Precision Floating-Point Square Root

Single-precision floating-point square root is implemented as a reciprocal square root followed by a reciprocal instead of a reciprocal square root followed by a multiplication so that it gives correct results for 0 and infinity.

#### Sine and Cosine

sinf(x), cosf(x), tanf(x), sincosf(x), and corresponding double-precision instructions are much more expensive and even more so if the argument x is large in magnitude.

More precisely, the argument reduction code (see Mathematical Functions for implementation) comprises two code paths referred to as the fast path and the slow path, respectively.

The fast path is used for arguments sufficiently small in magnitude and essentially consists of a few multiply-add operations. The slow path is used for arguments large in magnitude and consists of lengthy computations required to achieve correct results over the entire argument range.

At present, the argument reduction code for the trigonometric functions selects the fast path for arguments whose magnitude is less than 48039.0f for the single-precision functions, and less than 2147483648.0 for the double-precision functions.

As the slow path requires more registers than the fast path, an attempt has been made to reduce register pressure in the slow path by storing some intermediate variables in local memory, which may affect performance because of local memory high latency and bandwidth (see Device Memory Accesses). At present, 28 bytes of local memory are used by single-precision functions, and 44 bytes are used by double-precision functions. However, the exact amount is subject to change.

Due to the lengthy computations and use of local memory in the slow path, the throughput of these trigonometric functions is lower by one order of magnitude when the slow path reduction is required as opposed to the fast path reduction.

#### Integer Arithmetic

On devices of compute capability 1.x, 32-bit integer multiplication is implemented using multiple instructions as it is not natively supported. 24-bit integer multiplication is natively supported however via the __[u]mul24 intrinsic. Using __[u]mul24 instead of the 32-bit multiplication operator whenever possible usually improves performance for instruction bound kernels. It can have the opposite effect however in cases where the use of __[u]mul24 inhibits compiler optimizations.

On devices of compute capability 2.x and beyond, 32-bit integer multiplication is natively supported, but 24-bit integer multiplication is not. __[u]mul24 is therefore implemented using multiple instructions and should not be used.

Integer division and modulo operation are costly: tens of instructions on devices of compute capability 1.x, below 20 instructions on devices of compute capability 2.x and higher. They can be replaced with bitwise operations in some cases: If n is a power of 2, (i/n) is equivalent to (i>>log2(n)) and (i%n) is equivalent to (i&(n-1)); the compiler will perform these conversions if n is literal.

__brev, __brevll, __popc, and __popcll compile to tens of instructions for devices of compute capability 1.x, but __brev and __popc map to a single instruction for devices of compute capability 2.x and higher and __brevll and __popcll to just a few.

__clz, __clzll, __ffs, and __ffsll compile to fewer instructions for devices of compute capability 2.x and higher than for devices of compute capability 1.x.

#### Type Conversion

Sometimes, the compiler must insert conversion instructions, introducing additional execution cycles. This is the case for:

• Functions operating on variables of type char or short whose operands generally need to be converted to int,
• Double-precision floating-point constants (i.e., those constants defined without any type suffix) used as input to single-precision floating-point computations (as mandated by C/C++ standards).

This last case can be avoided by using single-precision floating-point constants, defined with an f suffix such as 3.141592653589793f, 1.0f, 0.5f.

### 5.4.2. Control Flow Instructions

Any flow control instruction (if, switch, do, for, while) can significantly impact the effective instruction throughput by causing threads of the same warp to diverge (i.e., to follow different execution paths). If this happens, the different executions paths have to be serialized, increasing the total number of instructions executed for this warp. When all the different execution paths have completed, the threads converge back to the same execution path.

To obtain best performance in cases where the control flow depends on the thread ID, the controlling condition should be written so as to minimize the number of divergent warps. This is possible because the distribution of the warps across the block is deterministic as mentioned in SIMT Architecture. A trivial example is when the controlling condition only depends on (threadIdx / warpSize) where warpSize is the warp size. In this case, no warp diverges since the controlling condition is perfectly aligned with the warps.

Sometimes, the compiler may unroll loops or it may optimize out if or switch statements by using branch predication instead, as detailed below. In these cases, no warp can ever diverge. The programmer can also control loop unrolling using the #pragma unroll directive (see #pragma unroll).

When using branch predication none of the instructions whose execution depends on the controlling condition gets skipped. Instead, each of them is associated with a per-thread condition code or predicate that is set to true or false based on the controlling condition and although each of these instructions gets scheduled for execution, only the instructions with a true predicate are actually executed. Instructions with a false predicate do not write results, and also do not evaluate addresses or read operands.

The compiler replaces a branch instruction with predicated instructions only if the number of instructions controlled by the branch condition is less or equal to a certain threshold: If the compiler determines that the condition is likely to produce many divergent warps, this threshold is 7, otherwise it is 4.

### 5.4.3. Synchronization Instruction

Throughput for __syncthreads() is 8 operations per clock cycle for devices of compute capability 1.x, 16 operations per clock cycle for devices of compute capability 2.x, and 128 operations per clock cycle for devices of compute capability 3.x.

Note that __syncthreads() can impact performance by forcing the multiprocessor to idle as detailed in Device Memory Accesses.

## A. CUDA-Enabled GPUs

http://developer.nvidia.com/cuda-gpus lists all CUDA-enabled devices with their compute capability.

The compute capability, number of multiprocessors, clock frequency, total amount of device memory, and other properties can be queried using the runtime (see reference manual).

## B. C Language Extensions

### B.1. Function Type Qualifiers

Function type qualifiers specify whether a function executes on the host or on the device and whether it is callable from the host or from the device.

### B.1.1. __device__

The __device__ qualifier declares a function that is:

• Executed on the device,
• Callable from the device only.

### B.1.2. __global__

The __global__ qualifier declares a function as being a kernel. Such a function is:

• Executed on the device,
• Callable from the host,
• Callable from the device for devices of compute capability 3.x (see CUDA Dynamic Parallelism for more details).

__global__ functions must have void return type.

Any call to a __global__ function must specify its execution configuration as described in Execution Configuration.

A call to a __global__ function is asynchronous, meaning it returns before the device has completed its execution.

### B.1.3. __host__

The __host__ qualifier declares a function that is:

• Executed on the host,
• Callable from the host only.

It is equivalent to declare a function with only the __host__ qualifier or to declare it without any of the __host__, __device__, or __global__ qualifier; in either case the function is compiled for the host only.

The __global__ and __host__ qualifiers cannot be used together.

The __device__ and __host__ qualifiers can be used together however, in which case the function is compiled for both the host and the device. The __CUDA_ARCH__ macro introduced in Application Compatibility can be used to differentiate code paths between host and device:

```__host__ __device__ func()
{
#if __CUDA_ARCH__ >= 300
// Device code path for compute capability 3.x
#elif __CUDA_ARCH__ >= 200
// Device code path for compute capability 2.x
#elif __CUDA_ARCH__ >= 100
// Device code path for compute capability 1.x
#elif !defined(__CUDA_ARCH__)
// Host code path
#endif
}```

### B.1.4. __noinline__ and __forceinline__

When compiling code for devices of compute capability 1.x, a __device__ function is always inlined by default. When compiling code for devices of compute capability 2.x and higher, a __device__ function is only inlined when deemed appropriate by the compiler.

The __noinline__ function qualifier can be used as a hint for the compiler not to inline the function if possible. The function body must still be in the same file where it is called. For devices of compute capability 1.x, the compiler will not honor the __noinline__ qualifier for functions with pointer parameters and for functions with large parameter lists. For devices of compute capability 2.x and higher, the compiler will always honor the __noinline__ qualifier.

The __forceinline__ function qualifier can be used to force the compiler to inline the function.

### B.2. Variable Type Qualifiers

Variable type qualifiers specify the memory location on the device of a variable.

An automatic variable declared in device code without any of the __device__, __shared__ and __constant__ qualifiers described in this section generally resides in a register. However in some cases the compiler might choose to place it in local memory, which can have adverse performance consequences as detailed in Device Memory Accesses.

### B.2.1. __device__

The __device__ qualifier declares a variable that resides on the device.

At most one of the other type qualifiers defined in the next three sections may be used together with __device__ to further specify which memory space the variable belongs to. If none of them is present, the variable:

• Resides in global memory space,
• Has the lifetime of an application,
• Is accessible from all the threads within the grid and from the host through the runtime library (cudaGetSymbolAddress() / cudaGetSymbolSize() / cudaMemcpyToSymbol() / cudaMemcpyFromSymbol()).

### B.2.2. __constant__

The __constant__ qualifier, optionally used together with __device__, declares a variable that:

• Resides in constant memory space,
• Has the lifetime of an application,
• Is accessible from all the threads within the grid and from the host through the runtime library (cudaGetSymbolAddress() / cudaGetSymbolSize() / cudaMemcpyToSymbol() / cudaMemcpyFromSymbol()).

### B.2.3. __shared__

The __shared__ qualifier, optionally used together with __device__, declares a variable that:

• Resides in the shared memory space of a thread block,
• Has the lifetime of the block,
• Is only accessible from all the threads within the block.

When declaring a variable in shared memory as an external array such as

```extern __shared__ float shared[];
```

the size of the array is determined at launch time (see Execution Configuration). All variables declared in this fashion, start at the same address in memory, so that the layout of the variables in the array must be explicitly managed through offsets. For example, if one wants the equivalent of

```short array0[128];
float array1[64];
int   array2[256];
```

in dynamically allocated shared memory, one could declare and initialize the arrays the following way:

```extern __shared__ float array[];
__device__ void func()      // __device__ or __global__ function
{
short* array0 = (short*)array;
float* array1 = (float*)&array0[128];
int*   array2 =   (int*)&array1[64];
}```

Note that pointers need to be aligned to the type they point to, so the following code, for example, does not work since array1 is not aligned to 4 bytes.

```extern __shared__ float array[];
__device__ void func()      // __device__ or __global__ function
{
short* array0 = (short*)array;
float* array1 = (float*)&array0[127];
}```

Alignment requirements for the built-in vector types are listed in Table 3.

### B.2.4. __restrict__

nvcc supports restricted pointers via the __restrict__ keyword.

Restricted pointers were introduced in C99 to alleviate the aliasing problem that exists in C-type languages, and which inhibits all kind of optimization from code re-ordering to common sub-expression elimination.

Here is an example subject to the aliasing issue, where use of restricted pointer can help the compiler to reduce the number of instructions:

```void foo(const float* a,
const float* b,
float* c)
{
c[0] = a[0] * b[0];
c[1] = a[0] * b[0];
c[2] = a[0] * b[0] * a[1];
c[3] = a[0] * a[1];
c[4] = a[0] * b[0];
c[5] = b[0];
...
}```

In C-type languages, the pointers a, b, and c may be aliased, so any write through c could modify elements of a or b. This means that to guarantee functional correctness, the compiler cannot load a[0] and b[0] into registers, multiply them, and store the result to both c[0] and c[1], because the results would differ from the abstract execution model if, say, a[0] is really the same location as c[0]. So the compiler cannot take advantage of the common sub-expression. Likewise, the compiler cannot just reorder the computation of c[4] into the proximity of the computation of c[0] and c[1] because the preceding write to c[3] could change the inputs to the computation of c[4].

By making a, b, and c restricted pointers, the programmer asserts to the compiler that the pointers are in fact not aliased, which in this case means writes through c would never overwrite elements of a or b. This changes the function prototype as follows:

```void foo(const float* __restrict__ a,
const float* __restrict__ b,
float* __restrict__ c);
```

Note that all pointer arguments need to be made restricted for the compiler optimizer to derive any benefit. With the __restrict__ keywords added, the compiler can now reorder and do common sub-expression elimination at will, while retaining functionality identical with the abstract execution model:

```void foo(const float* __restrict__ a,
const float* __restrict__ b,
float* __restrict__ c)
{
float t0 = a[0];
float t1 = b[0];
float t2 = t0 * t2;
float t3 = a[1];
c[0] = t2;
c[1] = t2;
c[4] = t2;
c[2] = t2 * t3;
c[3] = t0 * t3;
c[5] = t1;
...
}
```

The effects here are a reduced number of memory accesses and reduced number of computations. This is balanced by an increase in register pressure due to "cached" loads and common sub-expressions.

Since register pressure is a critical issue in many CUDA codes, use of restricted pointers can have negative performance impact on CUDA code, due to reduced occupancy.

### B.3.1. char, short, int, long, longlong, float, double

These are vector types derived from the basic integer and floating-point types. They are structures and the 1st, 2nd, 3rd, and 4th components are accessible through the fields x, y, z, and w, respectively. They all come with a constructor function of the form make_<type name>; for example,
```int2 make_int2(int x, int y);
```
which creates a vector of type int2 with value(x, y).

In host code, the alignment requirement of a vector type is equal to the alignment requirement of its base type. This is not always the case in device code as detailed in Table 3.

Table 3. Alignment Requirements in Device Code
Type Alignment
char1, uchar1 1
char2, uchar2 2
char3, uchar3 1
char4, uchar4 4
short1, ushort1 2
short2, ushort2 4
short3, ushort3 2
short4, ushort4 8
int1, uint1 4
int2, uint2 8
int3, uint3 4
int4, uint4 16
long1, ulong1 4 if sizeof(long) is equal to sizeof(int) 8, otherwise
long2, ulong2 8 if sizeof(long) is equal to sizeof(int), 16, otherwise
long3, ulong3 4 if sizeof(long) is equal to sizeof(int), 8, otherwise
long4, ulong4 16
longlong1, ulonglong1 8
longlong2, ulonglong2 16
float1 4
float2 8
float3 4
float4 16
double1 8
double2 16

### B.3.2. dim3

This type is an integer vector type based on uint3 that is used to specify dimensions. When defining a variable of type dim3, any component left unspecified is initialized to 1.

### B.4. Built-in Variables

Built-in variables specify the grid and block dimensions and the block and thread indices. They are only valid within functions that are executed on the device.

### B.4.1. gridDim

This variable is of type dim3 (see dim3) and contains the dimensions of the grid.

### B.4.2. blockIdx

This variable is of type uint3 (see char, short, int, long, longlong, float, double) and contains the block index within the grid.

### B.4.3. blockDim

This variable is of type dim3 (see dim3) and contains the dimensions of the block.

This variable is of type uint3 (see char, short, int, long, longlong, float, double ) and contains the thread index within the block.

### B.4.5. warpSize

This variable is of type int and contains the warp size in threads (see SIMT Architecture for the definition of a warp).

### B.5. Memory Fence Functions

The CUDA programming model assumes a device with a weakly-ordered memory model, that is:
• The order in which a CUDA thread writes data to shared memory, global memory, page-locked host memory, or the memory of a peer device is not necessarily the order in which the data is observed being written by another CUDA or host thread;
• The order in which a CUDA thread reads data from shared memory, global memory, page-locked host memory, or the memory of a peer device is not necessarily the order in which the read instructions appear in the program for instructions that are independent of each other.
For example, if thread 0 executes writeXY() and thread 1 executes readXY() as defined in the following code sample
```__device__ int X = 1, Y = 2;
__device__ void writeXY()
{
X = 10;
Y = 20;
}

{
int A = X;
int B = Y;
}
```
it is possible that A ends up equal to 1 and B equal to 20 for thread 1:
• either because at the time thread 1 reads X and Y, thread 0's write to Y has happened from thread 1's perspective, but thread 0's write to X has not,
In a strongly-ordered memory model, the only possibilities would be:
• A equal to 1 and B equal to 2 (thread 0's writes to X and Y happen after thread 1's read of X and Y),
• A equal to 10 and B equal to 2 (thread 0's write to X happens before thread 1's read of X and thread 0's write to Y happens after thread 1's read of Y),
• A equal to 10 and B equal to 20 (thread 0's writes to X and Y happen before thread 1's read of X and Y),

Memory fence functions can be used to enforce some ordering:

`void __threadfence_block();`
ensures that:
• All writes to shared and global memory made by the calling thread before the call to __threadfence_block() are observed by all threads in the block of the calling thread as occurring before all writes to shared memory and global memory made by the calling thread after the call to __threadfence_block();
`void __threadfence();`

acts as __threadfence_block() for all threads in the block of the calling thread and also ensures that all writes to global memory made by the calling thread before the call to __threadfence() are observed by all threads in the device as occurring before all writes to global memory made by the calling thread after the call to __threadfence().

`void __threadfence_system();`
acts as __threadfence_block() for all threads in the block of the calling thread and also ensures that:
• All writes to global memory, page-locked host memory, and the memory of a peer device made by the calling thread before the call to __threadfence_system() are observed by all threads in the device, host threads, and all threads in peer devices as occurring before all writes to global memory, page-locked host memory, and the memory of a peer device made by the calling thread after the call to __threadfence_system().
• All reads from shared memory, global memory, page-locked host memory, and the memory of a peer device made by the calling thread before the call to __threadfence_system() are performed before all reads from shared memory, global memory, page-locked host memory, and the memory of a peer device made by the calling thread after the call to __threadfence_system().

__threadfence_system() is only supported by devices of compute capability 2.x and higher.

In the previous code sample, inserting a fence function call between X = 10; and Y = 20; and between int A = X; and int B = Y; would ensure that for thread 1, A will always be equal to 10 if B is equal to 20. If thread 0 and 1 belong to the same block, it is enough to use __threadfence_block(). If thread 0 and 1 do not belong to the same block, __threadfence() must be used if they are CUDA threads from the same device and __threadfence_system() must be used if they are CUDA threads from two different devices.

A common use case is when threads consume some data produced by other threads as illustrated by the following code sample of a kernel that computes the sum of an array of N numbers in one call. Each block first sums a subset of the array and stores the result in global memory. When all blocks are done, the last block done reads each of these partial sums from global memory and sums them to obtain the final result. In order to determine which block is finished last, each block atomically increments a counter to signal that it is done with computing and storing its partial sum (see Atomic Functions about atomic functions). The last block is the one that receives the counter value equal to gridDim.x-1. If no fence is placed between storing the partial sum and incrementing the counter, the counter might increment before the partial sum is stored and therefore, might reach gridDim.x-1 and let the last block start reading partial sums before they have been actually updated in memory.

```__device__ unsigned int count = 0;
__shared__ bool isLastBlockDone;
__global__ void sum(const float* array, unsigned int N,
float* result)
{
// Each block sums a subset of the input array
float partialSum = calculatePartialSum(array, N);

// Thread 0 of each block stores the partial sum
// to global memory
result[blockIdx.x] = partialSum;

// last block will read its correct partial sum

// Thread 0 of each block signals that it is done
unsigned int value = atomicInc(&count, gridDim.x);

// Thread 0 of each block determines if its block is
// the last block to be done
isLastBlockDone = (value == (gridDim.x - 1));
}

// the correct value of isLastBlockDone

if (isLastBlockDone) {

// The last block sums the partial sums
// stored in result[0 .. gridDim.x-1]
float totalSum = calculateTotalSum(result);

// Thread 0 of last block stores total sum
// to global memory and resets count so that
// next kernel call works properly
result[0] = totalSum;
count = 0;
}
}
}```

### B.6. Synchronization Functions

`void __syncthreads();`

waits until all threads in the thread block have reached this point and all global and shared memory accesses made by these threads prior to __syncthreads() are visible to all threads in the block.

__syncthreads() is used to coordinate communication between the threads of the same block. When some threads within a block access the same addresses in shared or global memory, there are potential read-after-write, write-after-read, or write-after-write hazards for some of these memory accesses. These data hazards can be avoided by synchronizing threads in-between these accesses.

__syncthreads() is allowed in conditional code but only if the conditional evaluates identically across the entire thread block, otherwise the code execution is likely to hang or produce unintended side effects.

Devices of compute capability 2.x and higher support three variations of __syncthreads() described below.

`int __syncthreads_count(int predicate);`

is identical to __syncthreads() with the additional feature that it evaluates predicate for all threads of the block and returns the number of threads for which predicate evaluates to non-zero.

`int __syncthreads_and(int predicate);`

is identical to __syncthreads() with the additional feature that it evaluates predicate for all threads of the block and returns non-zero if and only if predicate evaluates to non-zero for all of them.

`int __syncthreads_or(int predicate);`

is identical to __syncthreads() with the additional feature that it evaluates predicate for all threads of the block and returns non-zero if and only if predicate evaluates to non-zero for any of them.

### B.7. Mathematical Functions

The reference manual lists all C/C++ standard library mathematical functions that are supported in device code and all intrinsic functions that are only supported in device code.

Mathematical Functions provides accuracy information for some of these functions when relevant.

### B.8. Texture Functions

Texture objects are described in Texture Object API

Texture references are described in Texture Reference API

Texture fetching is described in Texture Fetching.

### B.8.1.1. tex1Dfetch()

```template<class T>
T tex1Dfetch(cudaTextureObject_t texObj, int x);
```

fetches the region of linear memory specified by the one-dimensional texture object texObj using integer texture coordinate x. tex1Dfetch() only works with non-normalized coordinates, so only the border and clamp addressing modes are supported. It does not perform any texture filtering. For integer types, it may optionally promote the integer to single-precision floating point.

### B.8.1.2. tex1D()

```template<class T>
T tex1D(cudaTextureObject_t texObj, float x);
template<class T>
T tex1D(cudaTextureObject_t texObj, float x);
```

fetches the CUDA array specified by the one-dimensional texture object texObj using texture coordinate x.

### B.8.1.3. tex2D()

```template<class T>
T tex2D(cudaTextureObject_t texObj, float x, float y);
```

fetches the CUDA array or the region of linear memory specified by the two-dimensional texture object texObj using texture coordinates x and y.

### B.8.2.4. tex3D()

```template<class T>
T tex3D(cudaTextureObject_t texObj, float x, float y, float z);
```

fetches the CUDA array specified by the three-dimensional texture object texObj using texture coordinates x, y, and z.

### B.8.1.5. tex1DLayered()

```template<class T>
T tex1DLayered(cudaTextureObject_t texObj, float x, int layer);
```

fetches the CUDA array specified by the one-dimensional texture object texObj using texture coordinate x and index layer, as described in Layered Textures

### B.8.1.6. tex2DLayered()

```template<class T>
T tex2DLayered(cudaTextureObject_t texObj,
float x, float y, int layer);
```

fetches the CUDA array specified by the two-dimensional texture object texObj using texture coordinates x and y, and index layer, as described in Layered Textures.

### B.8.1.7. texCubemap()

```template<class T>
T texCubemap(cudaTextureObject_t texObj, float x, float y, float z);
```

fetches the CUDA array specified by the three-dimensional texture object texObj using texture coordinates x, y, and z, as described in Section Cubemap Textures.

### B.8.1.8. texCubemapLayered()

```template<class T>
T texCubemapLayered(cudaTextureObject_t texObj,
float x, float y, float z, int layer);
```

fetches the CUDA array specified by the cubemap layered texture object texObj using texture coordinates x, y, and z, and index layer, as described in Cubemap Layered Textures.

### B.8.1.9. tex2Dgather()

```template<class T>
T tex2Dgather(cudaTextureObject_t texObj,
float x, float y, int comp = 0);
```

fetches the CUDA array specified by the 2D texture object texObj using texture coordinates x and y and the comp parameter as described in Texture Gather.

### B.8.2.1. tex1Dfetch()

```template<class DataType>
Type tex1Dfetch(
texture<DataType, cudaTextureType1D,
int x);

float tex1Dfetch(
texture<unsigned char, cudaTextureType1D,
int x);

float tex1Dfetch(
texture<signed char, cudaTextureType1D,
int x);

float tex1Dfetch(
texture<unsigned short, cudaTextureType1D,
int x);

float tex1Dfetch(
texture<signed short, cudaTextureType1D,
int x);```

fetches the region of linear memory bound to the one-dimensional texture reference texRef using integer texture coordinate x. tex1Dfetch() only works with non-normalized coordinates, so only the border and clamp addressing modes are supported. It does not perform any texture filtering. For integer types, it may optionally promote the integer to single-precision floating point.

Besides the functions shown above, 2-, and 4-tuples are supported; for example:

```float4 tex1Dfetch(
texture<uchar4, cudaTextureType1D,
int x);```

fetches the region of linear memory bound to texture reference texRef using texture coordinate x.

### B.8.2.2. tex1D()

```template<class DataType, enum cudaTextureReadMode readMode>
float x);```

fetches the CUDA array bound to the one-dimensional texture reference texRef using texture coordinate x. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.3. tex2D()

```template<class DataType, enum cudaTextureReadMode readMode>
float x, float y);```

fetches the CUDA array or the region of linear memory bound to the two-dimensional texture reference texRef using texture coordinates x and y. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### tex3D()

```template<class DataType, enum cudaTextureReadMode readMode>
float x, float y, float z);```

fetches the CUDA array bound to the three-dimensional texture reference texRef using texture coordinates x, y, and z. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.5. tex1DLayered()

```template<class DataType, enum cudaTextureReadMode readMode>
Type tex1DLayered(
float x, int layer);```

fetches the CUDA array bound to the one-dimensional layered texture reference texRef using texture coordinate x and index layer, as described in Layered Textures. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.6. tex2DLayered()

```template<class DataType, enum cudaTextureReadMode readMode>
Type tex2DLayered(
float x, float y, int layer);```

fetches the CUDA array bound to the two-dimensional layered texture reference texRef using texture coordinates x and y, and index layer, as described in Texture Memory. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.7. texCubemap()

```template<class DataType, enum cudaTextureReadMode readMode>
Type texCubemap(
float x, float y, float z);```

fetches the CUDA array bound to the cubemap texture reference texRef using texture coordinates x, y, and z, as described in Cubemap Textures. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.8. texCubemapLayered()

```template<class DataType, enum cudaTextureReadMode readMode>
Type texCubemapLayered(
float x, float y, float z, int layer);```

fetches the CUDA array bound to the cubemap layered texture reference texRef using texture coordinates x, y, and z, and index layer, as described in Cubemap Layered Textures. Type is equal to DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case Type is equal to the matching floating-point type.

### B.8.2.9. tex2Dgather()

```template<class DataType, enum cudaTextureReadMode readMode>
Type tex2Dgather(
float x, float y, int comp = 0);```

fetches the CUDA array bound to the 2D texture reference texRef using texture coordinates x and y and the comp parameter as described in Texture Gather. Type is a 4-component vector type. It is based on the base type of DataType except when readMode is equal to cudaReadModeNormalizedFloat (see Texture Reference API), in which case it is always float4.

### B.9. Surface Functions

Surface functions are only supported by devices of compute capability 2.0 and higher.

Surface objects are described in described in Surface Object API

Surface references are described in Surface Reference API.

In the sections below, boundaryMode specifies the boundary mode, that is how out-of-range surface coordinates are handled; it is equal to either cudaBoundaryModeClamp, in which case out-of-range coordinates are clamped to the valid range, or cudaBoundaryModeZero, in which case out-of-range reads return zero and out-of-range writes are ignored, or cudaBoundaryModeTrap, in which case out-of-range accesses cause the kernel execution to fail.

### B.9.1. Surface Object API

```template<class T>
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the one-dimensional surface object surfObj using coordinate x.

### B.9.1.2. surf1Dwrite

```template<class T>
void surf1Dwrite(T data,
cudaSurfaceObject_t surfObj,
int x,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the one-dimensional surface object surfObj at coordinate x.

```template<class T>
int x, int y,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int y,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the two-dimensional surface object surfObj using coordinates x and y.

### B.9.2.4. surf2Dwrite()

```template<class T>
void surf2Dwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int y,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the two-dimensional surface object surfObj at coordinate x and y.

```template<class T>
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the three-dimensional surface object surfObj using coordinates x, y, and z.

### B.9.1.6. surf3Dwrite()

```template<class T>
void surf3Dwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the three-dimensional object surfObj at coordinate x, y, and z.

```template<class T>
cudaSurfaceObject_t surfObj,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the one-dimensional layered surface object surfObj using coordinate x and index layer.

### B.9.1.8. surf1DLayeredwrite()

```template<class Type>
void surf1DLayeredwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the two-dimensional layered surface object surfObj at coordinate x and index layer.

```template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the two-dimensional layered surface object surfObj using coordinate x and y, and index layer.

### B.9.1.10. surf2DLayeredwrite()

```template<class T>
void surf2DLayeredwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the one-dimensional layered surface object surfObj at coordinate x and y, and index layer.

```template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the cubemap surface object surfObj using coordinate x and y, and face index face.

### B.9.1.12. surfCubemapwrite()

```template<class T>
void surfCubemapwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the cubemap object surfObj at coordinate x and y, and face index face.

```template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);
template<class T>
cudaSurfaceObject_t surfObj,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);
```
reads the CUDA array specified by the cubemap layered surface object surfObj using coordinate x and y, and index layerFace.

### B.9.2.14. surfCubemapLayeredwrite()

```template<class T>
void surfCubemapLayeredwrite(T data,
cudaSurfaceObject_t surfObj,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);
```
writes value data to the CUDA array specified by the cubemap layered object surfObj at coordinate x and y, and index layerFace.

### Surface Reference API

A surface reference is declared at file scope as a variable of type surface:

`surface<void, Type> surfRef;`

where Type specifies the type of the surface reference and is equal to cudaSurfaceType1D, cudaSurfaceType2D, cudaSurfaceType3D, cudaSurfaceTypeCubemap, cudaSurfaceType1DLayered, cudaSurfaceType2DLayered, or cudaSurfaceTypeCubemapLayered; Type is an optional argument which defaults to cudaSurfaceType1D. A surface reference can only be declared as a static global variable and cannot be passed as an argument to a function.

Before a kernel can use a surface reference to access a CUDA array, the surface reference must be bound to the CUDA array using cudaBindSurfaceToArray().

The following code samples bind a surface reference to a CUDA array cuArray:

• Using the low-level API:

```surface<void, cudaSurfaceType2D> surfRef;
surfaceReference* surfRefPtr;
cudaGetSurfaceReference(&surfRefPtr, "surfRef");
cudaChannelFormatDesc channelDesc;
cudaGetChannelDesc(&channelDesc, cuArray);
cudaBindSurfaceToArray(surfRef, cuArray, &channelDesc);```
• Using the high-level API:

```surface<void, cudaSurfaceType2D> surfRef;
cudaBindSurfaceToArray(surfRef, cuArray);```

A CUDA array must be read and written using surface functions of matching dimensionality and type and via a surface reference of matching dimensionality; otherwise, the results of reading and writing the CUDA array are undefined.

Unlike texture memory, surface memory uses byte addressing. This means that the x-coordinate used to access a texture element via texture functions needs to be multiplied by the byte size of the element to access the same element via a surface function. For example, the element at texture coordinate x of a one-dimensional floating-point CUDA array bound to a texture reference texRef and a surface reference surfRef is read using tex1d(texRef, x) via texRef, but surf1Dread(surfRef, 4*x) via surfRef. Similarly, the element at texture coordinate x and y of a two-dimensional floating-point CUDA array bound to a texture reference texRef and a surface reference surfRef is accessed using tex2d(texRef, x, y) via texRef, but surf2Dread(surfRef, 4*x, y) via surfRef (the byte offset of the y-coordinate is internally calculated from the underlying line pitch of the CUDA array).

The following code sample applies some simple transformation kernel to a texture.

```// 2D surfaces
surface<void, 2> inputSurfRef;
surface<void, 2> outputSurfRef;

// Simple copy kernel
__global__ void copyKernel(int width, int height)
{
// Calculate surface coordinates
unsigned int x = blockIdx.x * blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y * blockDim.y + threadIdx.y;
if (x < width && y < height) {
uchar4 data;
surf2Dread(&data,  inputSurfRef, x * 4, y);
// Write to output surface
surf2Dwrite(data, outputSurfRef, x * 4, y);
}
}

// Host code
int main()
{
// Allocate CUDA arrays in device memory
cudaChannelFormatDesc channelDesc =
cudaCreateChannelDesc(8, 8, 8, 8,
cudaChannelFormatKindUnsigned);
cudaArray* cuInputArray;
cudaMallocArray(&cuInputArray, &channelDesc, width, height,
cudaArray* cuOutputArray;
cudaMallocArray(&cuOutputArray, &channelDesc, width, height,

// Copy to device memory some data located at address h_data
// in host memory
cudaMemcpyToArray(cuInputArray, 0, 0, h_data, size,
cudaMemcpyHostToDevice);

// Bind the arrays to the surface references
cudaBindSurfaceToArray(inputSurfRef, cuInputArray);
cudaBindSurfaceToArray(outputSurfRef, cuOutputArray);

// Invoke kernel
dim3 dimBlock(16, 16);
dim3 dimGrid((width  + dimBlock.x - 1) / dimBlock.x,
(height + dimBlock.y - 1) / dimBlock.y);
copyKernel<<<dimGrid, dimBlock>>>(width, height);

// Free device memory
cudaFreeArray(cuInputArray);
cudaFreeArray(cuOutputArray);

return 0;
}```

```template<class Type>
int x,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceType1D> surfRef,
int x,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the one-dimensional surface reference surfRef using coordinate x.

### B.9.2.2. surf1Dwrite

```template<class Type>
void surf1Dwrite(Type data,
surface<void, cudaSurfaceType1D> surfRef,
int x,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the one-dimensional surface reference surfRef at coordinate x.

```template<class Type>
int x, int y,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceType2D> surfRef,
int x, int y,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the two-dimensional surface reference surfRef using coordinates x and y.

### surf2Dwrite()

```template<class Type>
void surf3Dwrite(Type data,
surface<void, cudaSurfaceType3D> surfRef,
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the two-dimensional surface reference surfRef at coordinate x and y.

```template<class Type>
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceType3D> surfRef,
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the three-dimensional surface reference surfRef using coordinates x, y, and z.

### B.9.2.6. surf3Dwrite()

```template<class Type>
void surf3Dwrite(Type data,
surface<void, cudaSurfaceType3D> surfRef,
int x, int y, int z,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the three-dimensional surface reference surfRef at coordinate x, y, and z.

```template<class Type>
surface<void, cudaSurfaceType1DLayered> surfRef,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceType1DLayered> surfRef,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the one-dimensional layered surface reference surfRef using coordinate x and index layer.

### B.9.2.8. surf1DLayeredwrite()

```template<class Type>
void surf1DLayeredwrite(Type data,
surface<void, cudaSurfaceType1DLayered> surfRef,
int x, int layer,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the two-dimensional layered surface reference surfRef at coordinate x and index layer.

```template<class Type>
surface<void, cudaSurfaceType2DLayered> surfRef,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceType2DLayered> surfRef,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the two-dimensional layered surface reference surfRef using coordinate x and y, and index layer.

### B.9.2.10. surf2DLayeredwrite()

```template<class Type>
void surf2DLayeredwrite(Type data,
surface<void, cudaSurfaceType2DLayered> surfRef,
int x, int y, int layer,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the one-dimensional layered surface reference surfRef at coordinate x and y, and index layer.

```template<class Type>
surface<void, cudaSurfaceTypeCubemap> surfRef,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceTypeCubemap> surfRef,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the cubemap surface reference surfRef using coordinate x and y, and face index face.

### B.9.2.12. surfCubemapwrite()

```template<class Type>
void surfCubemapwrite(Type data,
surface<void, cudaSurfaceTypeCubemap> surfRef,
int x, int y, int face,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the cubemap reference surfRef at coordinate x and y, and face index face.

```template<class Type>
surface<void, cudaSurfaceTypeCubemapLayered> surfRef,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);
template<class Type>
surface<void, cudaSurfaceTypeCubemapLayered> surfRef,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);```
reads the CUDA array bound to the cubemap layered surface reference surfRef using coordinate x and y, and index layerFace.

### surfCubemapLayeredwrite()

```template<class Type>
void surfCubemapLayeredwrite(Type data,
surface<void, cudaSurfaceTypeCubemapLayered> surfRef,
int x, int y, int layerFace,
boundaryMode = cudaBoundaryModeTrap);```
writes value data to the CUDA array bound to the cubemap layered reference surfRef at coordinate x and y, and index layerFace.

The read-only data cache load function is only supported by devices of compute capability 3.5 and higher.

`T __ldg(const T* address);`
returns the data of type T located at address address, where T is char, short, int, long longunsigned char, unsigned short, unsigned int, unsigned long long, int2, int4, uint2, uint4, float, float2, float4, double, or double2. The operation is cached in the read-only data cache (see Global Memory).

### B.11. Time Function

```clock_t clock();
long long int clock64();```
when executed in device code, returns the value of a per-multiprocessor counter that is incremented every clock cycle. Sampling this counter at the beginning and at the end of a kernel, taking the difference of the two samples, and recording the result per thread provides a measure for each thread of the number of clock cycles taken by the device to completely execute the thread, but not of the number of clock cycles the device actually spent executing thread instructions. The former number is greater that the latter since threads are time sliced.

### B.12. Atomic Functions

An atomic function performs a read-modify-write atomic operation on one 32-bit or 64-bit word residing in global or shared memory. For example, atomicAdd() reads a word at some address in global or shared memory, adds a number to it, and writes the result back to the same address. The operation is atomic in the sense that it is guaranteed to be performed without interference from other threads. In other words, no other thread can access this address until the operation is complete. Atomic functions can only be used in device functions and atomic functions operating on mapped page-locked memory (Mapped Memory) are not atomic from the point of view of the host or other devices.

As mentioned in Table 11, the support for atomic operations varies with the compute capability:

• Atomic functions are only available for devices of compute capability 1.1 and higher.
• Atomic functions operating on 32-bit integer values in shared memory and atomic functions operating on 64-bit integer values in global memory are only available for devices of compute capability 1.2 and higher.
• Atomic functions operating on 64-bit integer values in shared memory are only available for devices of compute capability 2.x and higher.
• Only atomicExch() and atomicAdd() can operate on 32-bit floating-point values:
• in global memory for atomicExch() and devices of compute capability 1.1 and higher.
• in shared memory for atomicExch() and devices of compute capability 1.2 and higher.
• in global and shared memory for atomicAdd() and devices of compute capability 2.x and higher.

Note however that any atomic operation can be implemented based on atomicCAS() (Compare And Swap). For example, atomicAdd() for double-precision floating-point numbers can be implemented as follows:

```__device__ double atomicAdd(double* address, double val)
{
unsigned long long int* address_as_ull =
unsigned long long int old = *address_as_ull, assumed;
do {
assumed = old;
__double_as_longlong(val +
__longlong_as_double(assumed)));
} while (assumed != old);
return __longlong_as_double(old);
}```

### B.12.1. Arithmetic Functions

```int atomicAdd(int* address, int val);
unsigned int val);
unsigned long long int val);

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes (old + val), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The floating-point version of atomicAdd() is only supported by devices of compute capability 2.x and higher.

### B.12.1.2. atomicSub()

```int atomicSub(int* address, int val);
unsigned int val);
```
reads the 32-bit word old located at the address address in global or shared memory, computes (old - val), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

### B.12.1.3. atomicExch()

```int atomicExch(int* address, int val);
unsigned int val);
unsigned long long int atomicExch(unsigned long long int* address,
unsigned long long int val);

reads the 32-bit or 64-bit word old located at the address address in global or shared memory and stores val back to memory at the same address. These two operations are performed in one atomic transaction. The function returns old.

### B.12.1.4. atomicMin()

```int atomicMin(int* address, int val);
unsigned int val);
unsigned long long int atomicMin(unsigned long long int* address,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes the minimum of old and val, and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The 64-bit version of atomicMin() is only supported by devices of compute capability 3.5 and higher.

### B.12.1.5. atomicMax()

```int atomicMax(int* address, int val);
unsigned int val);
unsigned long long int atomicMax(unsigned long long int* address,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes the maximum of old and val, and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The 64-bit version of atomicMax() is only supported by devices of compute capability 3.5 and higher.

### B.12.1.6. atomicInc()

```unsigned int atomicInc(unsigned int* address,
unsigned int val);```

reads the 32-bit word old located at the address address in global or shared memory, computes ((old >= val) ? 0 : (old+1)), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

### B.12.1.7. atomicDec()

```unsigned int atomicDec(unsigned int* address,
unsigned int val);```

reads the 32-bit word old located at the address address in global or shared memory, computes (((old == 0) | (old > val)) ? val : (old-1) ), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

### B.12.1.8. atomicCAS()

```int atomicCAS(int* address, int compare, int val);
unsigned int compare,
unsigned int val);
unsigned long long int atomicCAS(unsigned long long int* address,
unsigned long long int compare,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes (old == compare ? val : old) , and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old (Compare And Swap).

### B.12.2.1. atomicAnd()

```int atomicAnd(int* address, int val);
unsigned int val);
unsigned long long int atomicAnd(unsigned long long int* address,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes (old & val), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The 64-bit version of atomicAnd() is only supported by devices of compute capability 3.5 and higher.

### B.12.2.2. atomicOr()

```int atomicOr(int* address, int val);
unsigned int val);
unsigned long long int atomicOr(unsigned long long int* address,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes (old | val), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The 64-bit version of atomicOr() is only supported by devices of compute capability 3.5 and higher.

### atomicXor()

```int atomicXor(int* address, int val);
unsigned int val);
unsigned long long int atomicXor(unsigned long long int* address,
unsigned long long int val);```

reads the 32-bit or 64-bit word old located at the address address in global or shared memory, computes (old ^ val), and stores the result back to memory at the same address. These three operations are performed in one atomic transaction. The function returns old.

The 64-bit version of atomicXor() is only supported by devices of compute capability 3.5 and higher.

### B.13. Warp Vote Functions

```int __all(int predicate);
int __any(int predicate);
unsigned int __ballot(int predicate);
```

The warp vote functions allow the threads of a given warp to perform a reduction-and-broadcast operation. These functions take as input an integer predicate from each thread in the warp and compare those values with zero. The results of the comparisons are combined (reduced) across the active threads of the warp in one of the following ways, broadcasting a single return value to each participating thread:

__all(predicate):
Evaluate predicate for all active threads of the warp and return non-zero if and only if predicate evaluates to non-zero for all of them. Supported by devices of compute capability 1.2 and higher.
__any(predicate):
Evaluate predicate for all active threads of the warp and return non-zero if and only if predicate evaluates to non-zero for any of them. Supported by devices of compute capability 1.2 and higher.
__ballot(predicate):
Evaluate predicate for all active threads of the warp and return an integer whose Nth bit is set if and only if predicate evaluates to non-zero for the Nth thread of the warp and the Nth thread is active. Supported by devices of compute capability 2.0 and higher.

### Notes

For each of these warp vote operations, the result excludes threads that are inactive (e.g., due to warp divergence). Inactive threads are represented by 0 bits in the value returned by __ballot() and are not considered in the reductions performed by __all() and __any().

### B.14. Warp Shuffle Functions

__shfl, __shfl_up, __shfl_down, __shfl_xor exchange a variable between threads within a warp.

They are only supported by devices of compute capability 3.x (see SIMT Architecture for the definition of a warp).

### B.14.1. Synopsis

```int __shfl(int var, int srcLane, int width=warpSize);
int __shfl_up(int var, unsigned int delta, int width=warpSize);
int __shfl_down(int var, unsigned int delta, int width=warpSize);
int __shfl_xor(int var, int laneMask, int width=warpSize);

float __shfl(float var, int srcLane, int width=warpSize);
float __shfl_up(float var, unsigned int delta,
int width=warpSize);
float __shfl_down(float var, unsigned int delta,
int width=warpSize);
float __shfl_xor(float var, int laneMask, int width=warpSize);
```

### Description

The __shfl() intrinsics permit exchanging of a variable between threads within a warp without use of shared memory. The exchange occurs simultaneously for all active threads within the warp, moving 4 bytes of data per thread. Exchange of 8-byte quantities must be broken into two separate invocations of __shfl().

Threads within a warp are referred to as lanes, and for devices of compute capability 3.x may have an index between 0 and warpSize-1 (inclusive). Four source-lane addressing modes are supported:

__shfl()
Direct copy from indexed lane
__shfl_up()
Copy from a lane with lower ID relative to caller
__shfl_down()
Copy from a lane with higher ID relative to caller
__shfl_xor()
Copy from a lane based on bitwise XOR of own lane ID

Threads may only read data from another thread which is actively participating in the __shfl() command. If the target thread is inactive, the retrieved value is undefined.

All the __shfl() intrinsics take an optional width parameter which permits sub-division of the warp into segments - for example to exchange data between 4 groups of 8 lanes in a SIMD manner. If width is less than warpSize then each subsection of the warp behaves as a separate entity with a starting logical lane ID of 0. A thread may only exchange data with others in its own subsection. width must have a value which is a power of 2 so that the warp can be subdivided equally; results are undefined if width is not a power of 2, or is a number greater than warpSize.

__shfl() returns the value of var held by the thread whose ID is given by srcLane. If srcLane is outside the range [0:width-1], then the thread's own value of var is returned.

__shfl_up() calculates a source lane ID by subtracting delta from the caller's lane ID. The value of var held by the resulting lane ID is returned: in effect, var is shifted up the warp by delta lanes. The source lane index will not wrap around the value of width, so effectively the lower delta lanes will be unchanged.

__shfl_down() calculates a source lane ID by adding delta to the caller's lane ID. The value of var held by the resulting lane ID is returned: this has the effect of shifting var down the warp by delta lanes. As for __shfl_up(), the ID number of the source lane will not wrap around the value of width and so the upper delta lanes will remain unchanged.

__shfl_xor() calculates a source line ID by performing a bitwise XOR of the caller's lane ID with laneMask: the value of var held by the resulting lane ID is returned. If the resulting lane ID falls outside the range permitted by width, the thread's own value of var is returned. This mode implements a butterfly addressing pattern such as is used in tree reduction and broadcast.

### B.14.3. Return Value

All __shfl() intrinsics return the 4-byte word referenced by var from the source lane ID as an unsigned integer. If the source lane ID is out of range or the source thread has exited, the calling thread's own var is returned.

### B.14.4. Notes

All __shfl() intrinsics share the same semantics with respect to code motion as the vote intrinsics __any() and __all().

Threads may only read data from another thread which is actively participating in the __shfl() command. If the target thread is inactive, the retrieved value is undefined.

width must be a power-of-2 (i.e., 2, 4, 8, 16 or 32). Results are unspecified for other values.

Types other than int or float must first be cast in order to use the __shfl() intrinsics.

### B.14.5.1. Broadcast of a single value across a warp

```      __global__ void bcast(int arg) {
int laneId = threadIdx.x & 0x1f;
int value;
if (laneId == 0)        // Note unused variable for
value = arg;        // all threads except lane 0
value = __shfl(value, 0);   // Get "value" from lane 0
if (value != arg)
}

void main() {
bcast<<< 1, 32 >>>(1234);
}```

### B.14.5.2. Inclusive plus-scan across sub-partitions of 8 threads

```__global__ void scan4() {
// Seed sample starting value (inverse of lane ID)
int value = 31 - laneId;

// Loop to accumulate scan within my partition.
// Scan requires log2(n) == 3 steps for 8 threads
// It works by an accumulated sum up the warp
// by 1, 2, 4, 8 etc. steps.
for (int i=1; i<=4; i*=2) {
// Note: shfl requires all threads being
// accessed to be active. Therefore we do
// the __shfl unconditionally so that we
// sum, and then conditionally assign the result.
int n = __shfl_up(value, i, 8);
if (laneId >= i)
value += n;
}

}

void main() {
scan4<<< 1, 32 >>>();
}
```

### B.14.5.3. Reduction across a warp

```__global__ void warpReduce() {
// Seed starting value as inverse lane ID
int value = 31 - laneId;

// Use XOR mode to perform butterfly reduction
for (int i=16; i>=1; i/=2)
value += __shfl_xor(value, i, 32);

// "value" now contains the sum across all threads
}

void main() {
warpReduce<<< 1, 32 >>>();
}
```

### B.15. Profiler Counter Function

Each multiprocessor has a set of sixteen hardware counters that an application can increment with a single instruction by calling the __prof_trigger() function.

`[void __prof_trigger(int counter);`

increments by one per warp the per-multiprocessor hardware counter of index counter. Counters 8 to 15 are reserved and should not be used by applications.

The value of counters 0, 1, ..., 7 can be obtained via nvprof by nvprof --events prof_trigger_0x where x is 0, 1, ..., 7. The value of those counters for the first multiprocessor can also be obtained via the old CUDA command-line profiler by listing prof_trigger_00, prof_trigger_01, ..., prof_trigger_07 , etc. in the profiler.conf file (see the profiler manual for more details). All counters are reset before each kernel launch (note that when collecting counters, kernel launches are synchronous as mentioned in Concurrent Execution between Host and Device).

### B.16. Assertion

Assertion is only supported by devices of compute capability 2.x and higher. It is not supported on MacOS, regardless of the device, and loading a module that references the assert function on Mac OS will fail.

`void assert(int expression);`

stops the kernel execution if expression is equal to zero. If the program is run within a debugger, this triggers a breakpoint and the debugger can be used to inspect the current state of the device. Otherwise, each thread for which expression is equal to zero prints a message to stderr after synchronization with the host via cudaDeviceSynchronize(), cudaStreamSynchronize(), or cudaEventSynchronize(). The format of this message is as follows:

```<filename>:<line number>:<function>:
block: [blockId.x,blockId.x,blockIdx.z],
Assertion `<expression>` failed.```

Any subsequent host-side synchronization calls made for the same device will return cudaErrorAssert. No more commands can be sent to this device until cudaDeviceReset() is called to reinitialize the device.

If expression is different from zero, the kernel execution is unaffected.

For example, the following program from source file test.cu

```#include <assert.h>

// assert() is only supported
// for devices of compute capability 2.0 and higher
#if defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 200)
#undef  assert
#define assert(arg)
#endif

__global__ void testAssert(void)
{
int is_one = 1;
int should_be_one = 0;

// This will have no effect
assert(is_one);

// This will halt kernel execution
assert(should_be_one);
}

int main(int argc, char* argv[])
{
testAssert<<<1,1>>>();
return 0;
}```

will output:

`test.cu:19: void testAssert(): block: [0,0,0], thread: [0,0,0] Assertion `should_be_one` failed.`

Assertions are for debugging purposes. They can affect performance and it is therefore recommended to disable them in production code. They can be disabled at compile time by defining the NDEBUG preprocessor macro before including assert.h. Note that expression should not be an expression with side effects (something like (++i > 0), for example), otherwise disabling the assertion will affect the functionality of the code.

### B.17. Formatted Output

Formatted output is only supported by devices of compute capability 2.x and higher.

`int printf(const char *format[, arg, ...]);`

prints formatted output from a kernel to a host-side output stream.

The in-kernel printf() function behaves in a similar way to the standard C-library printf() function, and the user is referred to the host system's manual pages for a complete description of printf() behavior. In essence, the string passed in as format is output to a stream on the host, with substitutions made from the argument list wherever a format specifier is encountered. Supported format specifiers are listed below.

The printf() command is executed as any other device-side function: per-thread, and in the context of the calling thread. From a multi-threaded kernel, this means that a straightforward call to printf() will be executed by every thread, using that thread's data as specified. Multiple versions of the output string will then appear at the host stream, once for each thread which encountered the printf().

It is up to the programmer to limit the output to a single thread if only a single output string is desired (see Examples for an illustrative example).

Unlike the C-standard printf(), which returns the number of characters printed, CUDA's printf() returns the number of arguments parsed. If no arguments follow the format string, 0 is returned. If the format string is NULL, -1 is returned. If an internal error occurs, -2 is returned.

### B.17.1. Format Specifiers

As for standard printf(), format specifiers take the form: %[flags][width][.precision][size]type

The following fields are supported (see widely-available documentation for a complete description of all behaviors):

• Flags: `#' ` ' `0' `+' `-'
• Width: `*' `0-9'
• Precision: `0-9'
• Size: `h' `l' `ll'
• Type: `%cdiouxXpeEfgGaAs'

Note that CUDA's printf()will accept any combination of flag, width, precision, size and type, whether or not overall they form a valid format specifier. In other words, "%hd" will be accepted and printf will expect a double-precision variable in the corresponding location in the argument list.

### B.17.2. Limitations

Final formatting of the printf() output takes place on the host system. This means that the format string must be understood by the host-system's compiler and C library. Every effort has been made to ensure that the format specifiers supported by CUDA's printf function form a universal subset from the most common host compilers, but exact behavior will be host-OS-dependent.

As described in Format Specifiers, printf() will accept all combinations of valid flags and types. This is because it cannot determine what will and will not be valid on the host system where the final output is formatted. The effect of this is that output may be undefined if the program emits a format string which contains invalid combinations.

The printf() command can accept at most 32 arguments in addition to the format string. Additional arguments beyond this will be ignored, and the format specifier output as-is.

Owing to the differing size of the long type on 64-bit Windows platforms (four bytes on 64-bit Windows platforms, eight bytes on other 64-bit platforms), a kernel which is compiled on a non-Windows 64-bit machine but then run on a win64 machine will see corrupted output for all format strings which include "%ld". It is recommended that the compilation platform matches the execution platform to ensure safety.

The output buffer for printf() is set to a fixed size before kernel launch (see Associated Host-Side API). It is circular and if more output is produced during kernel execution than can fit in the buffer, older output is overwritten. It is flushed only when one of these actions is performed:

• Kernel launch via <<<>>> or cuLaunchKernel() (at the start of the launch, and if the CUDA_LAUNCH_BLOCKING environment variable is set to 1, at the end of the launch as well),
• Synchronization via cudaDeviceSynchronize(), cuCtxSynchronize(), cudaStreamSynchronize(), cuStreamSynchronize(), cudaEventSynchronize(), or cuEventSynchronize(),
• Memory copies via any blocking version of cudaMemcpy*() or cuMemcpy*(),
• Context destruction via cudaDeviceReset() or cuCtxDestroy().

Note that the buffer is not flushed automatically when the program exits. The user must call cudaDeviceReset() or cuCtxDestroy() explicitly, as shown in the examples below.

Internally printf() uses a shared data structure and so it is possible that calling printf() might change the order of execution of threads. In particular, a thread which calls printf() might take a longer execution path than one which does not call printf(), and that path length is dependent upon the parameters of the printf(). Note, however, that CUDA makes no guarantees of thread execution order except at explicit __syncthreads() barriers, so it is impossible to tell whether execution order has been modified by printf() or by other scheduling behaviour in the hardware.

### B.17.3. Associated Host-Side API

The following API functions get and set the size of the buffer used to transfer the printf() arguments and internal metadata to the host (default is 1 megabyte):

### B.17.4. Examples

The following code sample:
```#include "stdio.h"

// printf() is only supported
// for devices of compute capability 2.0 and higher
#if defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 200)
# error printf is only supported on devices of compute capability 2.0 and higher, please compile with -arch=sm_20 or higher
#endif

__global__ void helloCUDA(float f)
{
}

int main()
{
helloCUDA<<<1, 5>>>(1.2345f);
return 0;
}```

will output:

```Hello thread 2, f=1.2345

Notice how each thread encounters the printf() command, so there are as many lines of output as there were threads launched in the grid. As expected, global values (i.e., float f) are common between all threads, and local values (i.e., threadIdx.x) are distinct per-thread.

The following code sample:
```#include "stdio.h"

// printf() is only supported
// for devices of compute capability 2.0 and higher
#if defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 200)
# error printf is only supported on devices of compute capability 2.0 and higher, please compile with -arch=sm_20 or higher
#endif

__global__ void helloCUDA(float f)
{
}

int main()
{
helloCUDA<<<1, 5>>>(1.2345f);
return 0;
}```

will output:

`Hello thread 0, f=1.2345`

Self-evidently, the if() statement limits which threads will call printf, so that only a single line of output is seen.

### B.18. Dynamic Global Memory Allocation and Operations

Dynamic global memory allocation and operations are only supported by devices of compute capability 2.x and higher.

```void* malloc(size_t size);
void free(void* ptr);```

allocate and free memory dynamically from a fixed-size heap in global memory.

`void* memcpy(void* dest, const void* src, size_t size);`

copy size bytes from the memory location pointed by src to the memory location pointed by dest.

`void* memset(void* ptr, int value, size_t size);`

set size bytes of memory block pointed by ptr to value (interpreted as an unsigned char).

The CUDA in-kernel malloc() function allocates at least size bytes from the device heap and returns a pointer to the allocated memory or NULL if insufficient memory exists to fulfill the request. The returned pointer is guaranteed to be aligned to a 16-byte boundary.

The CUDA in-kernel free() function deallocates the memory pointed to by ptr, which must have been returned by a previous call to malloc(). If ptr is NULL, the call to free() is ignored. Repeated calls to free() with the same ptr has undefined behavior.

The memory allocated by a given CUDA thread via malloc() remains allocated for the lifetime of the CUDA context, or until it is explicitly released by a call to free(). It can be used by any other CUDA threads even from subsequent kernel launches. Any CUDA thread may free memory allocated by another thread, but care should be taken to ensure that the same pointer is not freed more than once.

### B.18.1. Heap Memory Allocation

The device memory heap has a fixed size that must be specified before any program using malloc() or free() is loaded into the context. A default heap of eight megabytes is allocated if any program uses malloc() without explicitly specifying the heap size.

The following API functions get and set the heap size:

The heap size granted will be at least size bytes. cuCtxGetLimit()and cudaDeviceGetLimit() return the currently requested heap size.

The actual memory allocation for the heap occurs when a module is loaded into the context, either explicitly via the CUDA driver API (see Module), or implicitly via the CUDA runtime API (see CUDA C Runtime). If the memory allocation fails, the module load will generate a CUDA_ERROR_SHARED_OBJECT_INIT_FAILED error.

Heap size cannot be changed once a module load has occurred and it does not resize dynamically according to need.

Memory reserved for the device heap is in addition to memory allocated through host-side CUDA API calls such as cudaMalloc().

### B.18.2. Interoperability with Host Memory API

Memory allocated via malloc() cannot be freed using the runtime (i.e., by calling any of the free memory functions from Device Memory).

Similarly, memory allocated via the runtime (i.e., by calling any of the memory allocation functions from Device Memory) cannot be freed via free().

### Examples

The following code sample:

```  #include <stdlib.h>
#include <stdio.h>

__global__ void mallocTest()
{
size_t size = 123;
char* ptr = (char*)malloc(size);
memset(ptr, 0, size);
free(ptr);
}

int main()
{
// Set a heap size of 128 megabytes. Note that this must
// be done before any kernel is launched.
mallocTest<<<1, 5>>>();
return 0;
}```

will output:

```Thread 0 got pointer: 00057020

Notice how each thread encounters the malloc() and memset() commands and so receives and initializes its own allocation. (Exact pointer values will vary: these are illustrative.)

### B.18.3.2. Per Thread Block Allocation

```      #include <stdlib.h>

__global__ void mallocTest()
{
__shared__ int* data;

// The first thread in the block does the allocation and initialization
// and then shares the pointer with all other threads through shared memory,
// so that access can easily be coalesced.
// 64 bytes per thread are allocated.
size_t size = blockDim.x * 64;
data = (int*)malloc(size);
memset(data, 0, size);
}

// Check for failure
if (data == NULL)
return;

// Threads index into the memory, ensuring coalescence
int* ptr = data;
for (int i = 0; i < 64; ++i)

// Ensure all threads complete before freeing

// Only one thread may free the memory!
free(data);
}

int main()
{
mallocTest<<<10, 128>>>();
return 0;
}```

### B.18.3.3. Allocation Persisting Between Kernel Launches

```#include <stdlib.h>
#include <stdio.h>

#define NUM_BLOCKS 20

__device__ int* dataptr[NUM_BLOCKS]; // Per-block pointer

__global__ void allocmem()
{
// Only the first thread in the block does the allocation
// since we want only one allocation per block.
dataptr[blockIdx.x] = (int*)malloc(blockDim.x * 4);

// Check for failure
if (dataptr[blockIdx.x] == NULL)
return;

// Zero the data with all threads in parallel
}

// Simple example: store thread ID into each element
__global__ void usemem()
{
int* ptr = dataptr[blockIdx.x];
if (ptr != NULL)
}

// Print the content of the buffer before freeing it
__global__ void freemem()
{
int* ptr = dataptr[blockIdx.x];
if (ptr != NULL)
printf("Block %d, Thread %d: final value = %d\n",

// Only free from one thread!
free(ptr);
}

int main()
{

// Allocate memory
allocmem<<< NUM_BLOCKS, 10 >>>();

// Use memory
usemem<<< NUM_BLOCKS, 10 >>>();
usemem<<< NUM_BLOCKS, 10 >>>();
usemem<<< NUM_BLOCKS, 10 >>>();

// Free memory
freemem<<< NUM_BLOCKS, 10 >>>();

return 0;
}```

### B.19. Execution Configuration

Any call to a __global__ function must specify the execution configuration for that call. The execution configuration defines the dimension of the grid and blocks that will be used to execute the function on the device, as well as the associated stream (see CUDA C Runtime for a description of streams).

The execution configuration is specified by inserting an expression of the form <<< Dg, Db, Ns, S >>> between the function name and the parenthesized argument list, where:

• Dg is of type dim3 (see dim3) and specifies the dimension and size of the grid, such that Dg.x * Dg.y * Dg.z equals the number of blocks being launched; Dg.z must be equal to 1 for devices of compute capability 1.x;
• Db is of type dim3 (see dim3) and specifies the dimension and size of each block, such that Db.x * Db.y * Db.z equals the number of threads per block;
• Ns is of type size_t and specifies the number of bytes in shared memory that is dynamically allocated per block for this call in addition to the statically allocated memory; this dynamically allocated memory is used by any of the variables declared as an external array as mentioned in __shared__; Ns is an optional argument which defaults to 0;
• S is of type cudaStream_t and specifies the associated stream; S is an optional argument which defaults to 0.

As an example, a function declared as

`__global__ void Func(float* parameter);`

must be called like this:

`Func<<< Dg, Db, Ns >>>(parameter);`

The arguments to the execution configuration are evaluated before the actual function arguments. For devices of compute capability 1.x, they are passed via shared memory to the device.

The function call will fail if Dg or Db are greater than the maximum sizes allowed for the device as specified in Compute Capabilities, or if Ns is greater than the maximum amount of shared memory available on the device, minus the amount of shared memory required for static allocation. For devices of compute capability 1.x, the execution configuration and the function arguments also consume shared memory.

### B.20. Launch Bounds

As discussed in detail in Multiprocessor Level, the fewer registers a kernel uses, the more threads and thread blocks are likely to reside on a multiprocessor, which can improve performance.

Therefore, the compiler uses heuristics to minimize register usage while keeping register spilling (see Device Memory Accesses) and instruction count to a minimum. An application can optionally aid these heuristics by providing additional information to the compiler in the form of launch bounds that are specified using the __launch_bounds__() qualifier in the definition of a __global__ function:

```__global__ void
MyKernel(...)
{
...
}```
• maxThreadsPerBlock specifies the maximum number of threads per block with which the application will ever launch MyKernel(); it compiles to the .maxntidPTX directive;
• minBlocksPerMultiprocessor is optional and specifies the desired minimum number of resident blocks per multiprocessor; it compiles to the .minnctapersmPTX directive.

If launch bounds are specified, the compiler first derives from them the upper limit L on the number of registers the kernel should use to ensure that minBlocksPerMultiprocessor blocks (or a single block if minBlocksPerMultiprocessor is not specified) of maxThreadsPerBlock threads can reside on the multiprocessor (see Hardware Multithreading for the relationship between the number of registers used by a kernel and the number of registers allocated per block). The compiler then optimizes register usage in the following way:

• If the initial register usage is higher than L, the compiler reduces it further until it becomes less or equal to L, usually at the expense of more local memory usage and/or higher number of instructions;
• If the initial register usage is lower than L
• If maxThreadsPerBlock is specified and minBlocksPerMultiprocessor is not, the compiler uses maxThreadsPerBlock to determine the register usage thresholds for the transitions between n and n+1 resident blocks (i.e., when using one less register makes room for an additional resident block as in the example of Multiprocessor Level) and then applies similar heuristics as when no launch bounds are specified;
• If both minBlocksPerMultiprocessor and maxThreadsPerBlock are specified, the compiler may increase register usage as high as L to reduce the number of instructions and better hide single thread instruction latency.

A kernel will fail to launch if it is executed with more threads per block than its launch bound maxThreadsPerBlock.

Optimal launch bounds for a given kernel will usually differ across major architecture revisions. The sample code below shows how this is typically handled in device code using the __CUDA_ARCH__ macro introduced in Application Compatibility

```#define THREADS_PER_BLOCK          256
#if __CUDA_ARCH__ >= 200
#define MY_KERNEL_MIN_BLOCKS   3
#else
#define MY_KERNEL_MIN_BLOCKS   2
#endif

// Device code
__global__ void
MyKernel(...)
{
...
}```

In the common case where MyKernel is invoked with the maximum number of threads per block (specified as the first parameter of __launch_bounds__()), it is tempting to use MY_KERNEL_MAX_THREADS as the number of threads per block in the execution configuration:

```// Host code

This will not work however since __CUDA_ARCH__ is undefined in host code as mentioned in Application Compatibility, so MyKernel will launch with 256 threads per block even when __CUDA_ARCH__ is greater or equal to 200. Instead the number of threads per block should be determined:

• Either at compile time using a macro that does not depend on __CUDA_ARCH__, for example
```// Host code
• Or at runtime based on the compute capability
```// Host code
cudaGetDeviceProperties(&deviceProp, device);
(deviceProp.major >= 2 ?

Register usage is reported by the --ptxas options=-v compiler option. The number of resident blocks can be derived from the occupancy reported by the CUDA profiler (see Device Memory Accessesfor a definition of occupancy).

Register usage can also be controlled for all __global__ functions in a file using the maxrregcount compiler option. The value of maxrregcount is ignored for functions with launch bounds.

### B.21. #pragma unroll

By default, the compiler unrolls small loops with a known trip count. The #pragma unroll directive however can be used to control unrolling of any given loop. It must be placed immediately before the loop and only applies to that loop. It is optionally followed by a number that specifies how many times the loop must be unrolled.

For example, in this code sample:

```#pragma unroll 5
for (int i = 0; i < n; ++i)```

the loop will be unrolled 5 times. The compiler will also insert code to ensure correctness (in the example above, to ensure that there will only be n iterations if n is less than 5, for example). It is up to the programmer to make sure that the specified unroll number gives the best performance.

#pragma unroll 1 will prevent the compiler from ever unrolling a loop.

If no number is specified after #pragma unroll, the loop is completely unrolled if its trip count is constant, otherwise it is not unrolled at all.

### B.22. SIMD Video Instructions

PTX ISA version 3.0 includes SIMD (Single Instruction, Multiple Data) video instructions which operate on pairs of 16-bit values and quads of 8-bit values. These are available on devices of compute capability 3.0.

The SIMD video instructions are:
• vsub2, vsub4
• vavrg2, vavrg4
• vabsdiff2, vabsdiff4
• vmin2, vmin4
• vmax2, vmax4
• vset2, vset4
PTX instructions, such as the SIMD video instructions, can be included in CUDA programs by way of the assembler, asm(), statement.

The basic syntax of an asm() statement is:

`asm("template-string" : "constraint"(output) : "constraint"(input)"));`

An example of using the vabsdiff4 PTX instruction is:

`asm("vabsdiff4.u32.u32.u32.add" " %0, %1, %2, %3;": "=r" (result):"r" (A), "r" (B), "r" (C));`

This uses the vabsdiff4 instruction to compute an integer quad byte SIMD sum of absolute differences. The absolute difference value is computed for each byte of the unsigned integers A and B in SIMD fashion. The optional accumulate operation (.add) is specified to sum these differences.

Refer to the document "Using Inline PTX Assembly in CUDA" for details on using the assembly statement in your code. Refer to the PTX ISA documentation ("Parallel Thread Execution ISA Version 3.0" for example) for details on the PTX instructions for the version of PTX that you are using.

## C. CUDA Dynamic Parallelism

### C.1.1. Overview

Dynamic Parallelism is an extension to the CUDA programming model enabling a CUDA kernel to create and synchronize with new work directly on the GPU. The creation of parallelism dynamically at whichever point in a program that it is needed offers exciting new capabilities.

The ability to create work directly from the GPU can reduce the need to transfer execution control and data between host and device, as launch configuration decisions can now be made at runtime by threads executing on the device. Additionally, data-dependent parallel work can be generated inline within a kernel at run-time, taking advantage of the GPU's hardware schedulers and load balancers dynamically and adapting in response to data-driven decisions or workloads. Algorithms and programming patterns that had previously required modifications to eliminate recursion, irregular loop structure, or other constructs that do not fit a flat, single-level of parallelism may more transparently be expressed.

This document describes the extended capabilities of CUDA which enable Dynamic Parallelism, including the modifications and additions to the CUDA programming model necessary to take advantage of these, as well as guidelines and best practices for exploiting this added capacity.

Dynamic Parallelism is only supported by devices of compute capability 3.5 and higher.

### C.1.2. Glossary

Definitions for terms used in this guide.

Grid
A Grid is a collection of Threads. Threads in a Grid execute a Kernel Function and are divided into Thread Blocks.
Kernel Function
A Kernel Function is an implicitly parallel subroutine that executes under the CUDA execution and memory model for every Thread in a Grid.
Host
The Host refers to the execution environment that initially invoked CUDA. Typically the thread running on a system's CPU processor.
Parent
A Parent Thread, Thread Block, or Grid is one that has launched new grid(s), the Child Grid(s). The Parent is not considered completed until all of its launched Child Grids have also completed.
Child
A Child thread, block, or grid is one that has been launched by a Parent grid. A Child grid must complete before the Parent Thread, Thread Block, or Grid are considered complete.
Objects with Thread Block Scope have the lifetime of a single Thread Block. They only have defined behavior when operated on by Threads in the Thread Block that created the object and are destroyed when the Thread Block that created them is complete.
Device Runtime
The Device Runtime refers to the runtime system and APIs available to enable Kernel Functions to use Dynamic Parallelism.

### C.2.1. Execution Environment

The CUDA execution model is based on primitives of threads, thread blocks, and grids, with kernel functions defining the program executed by individual threads within a thread block and grid. When a kernel function is invoked the grid's properties are described by an execution configuration, which has a special syntax in CUDA. Support for dynamic parallelism in CUDA extends the ability to configure, launch, and synchronize upon new grids to threads that are running on the device.

### C.2.1.1. Parent and Child Grids

A device thread that configures and launches a new grid belongs to the parent grid, and the grid created by the invocation is a child grid.

The invocation and completion of child grids is properly nested, meaning that the parent grid is not considered complete until all child grids created by its threads have completed. Even if the invoking threads do not explicitly synchronize on the child grids launched, the runtime guarantees an implicit synchronization between the parent and child.

Figure 12. Parent-Child Launch Nesting

### C.2.1.2. Scope of CUDA Primitives

On both host and device, the CUDA runtime offers an API for launching kernels, for waiting for launched work to complete, and for tracking dependencies between launches via streams and events. On the host system, the state of launches and the CUDA primitives referencing streams and events are shared by all threads within a process; however processes execute independently and may not share CUDA objects.

A similar hierarchy exists on the device: launched kernels and CUDA objects are visible to all threads in a thread block, but are independent between thread blocks. This means for example that a stream may be created by one thread and used by any other thread in the same thread block, but may not be shared with threads in any other thread block.

### C.2.1.3. Synchronization

CUDA runtime operations from any thread, including kernel launches, are visible across a thread block. This means that an invoking thread in the parent grid may perform synchronization on the grids launched by that thread, by other threads in the thread block, or on streams created within the same thread block. Execution of a thread block is not considered complete until all launches by all threads in the block have completed. If all threads in a block exit before all child launches have completed, a synchronization operation will automatically be triggered.

### C.2.1.4. Streams and Events

CUDA Streams and Events allow control over dependencies between grid launches: grids launched into the same stream execute in-order, and events may be used to create dependencies between streams. Streams and events created on the device serve this exact same purpose.

Streams and events created within a grid exist within thread block scope but have undefined behavior when used outside of the thread block where they were created. As described above, all work launched by a thread block is implicitly synchronized when the block exits; work launched into streams is included in this, with all dependencies resolved appropriately. The behavior of operations on a stream that has been modified outside of thread block scope is undefined.

Streams and events created on the host have undefined behavior when used within any kernel, just as streams and events created by a parent grid have undefined behavior if used within a child grid.

### C.2.1.5. Ordering and Concurrency

The ordering of kernel launches from the device runtime follows CUDA Stream ordering semantics. Within a thread block, all kernel launches into the same stream are executed in-order. With multiple threads in the same thread block launching into the same stream, the ordering within the stream is dependent on the thread scheduling within the block, which may be controlled with synchronization primitives such as __syncthreads().

Note that because streams are shared by all threads within a thread block, the implicit NULL stream is also shared. If multiple threads in a thread block launch into the implicit stream, then these launches will be executed in-order. If concurrency is desired, explicit named streams should be used.

Dynamic Parallelism enables concurrency to be expressed more easily within a program; however, the device runtime introduces no new concurrency guarantees within the CUDA execution model. There is no guarantee of concurrent execution between any number of different thread blocks on a device.

The lack of concurrency guarantee extends to parent thread blocks and their child grids. When a parent thread block launches a child grid, the child is not guaranteed to begin execution until the parent thread block reaches an explicit synchronization point (e.g. cudaDeviceSynchronize()).

While concurrency will often easily be achieved, it may vary as a function of deviceconfiguration, application workload, and runtime scheduling. It is therefore unsafe to depend upon any concurrency between different thread blocks.

### C.2.1.6. Device Management

There is no multi-GPU support from the device runtime; the device runtime is only capable of operating on the device upon which it is currently executing. It is permitted, however, to query properties for any CUDA capable device in the system.

### C.2.2. Memory Model

Parent and child grids share the same global and constant memory storage, but have distinct local and shared memory.

### C.2.2.1.1. Global Memory

Parent and child grids have coherent access to global memory, with weak consistency guarantees between child and parent. There are two points in the execution of a child grid when its view of memory is fully consistent with the parent thread: when the child grid is invoked by the parent, and when the child grid completes as signaled by a synchronization API invocation in the parent thread.

All global memory operations in the parent thread prior to the child grid's invocation are visible to the child grid. All memory operations of the child grid are visible to the parent after the parent has synchronized on the child grid's completion.

In the following example, the child grid executing child_launch is only guaranteed to see the modifications to data made before the child grid was launched. Since thread 0 of the parent is performing the launch, the child will be consistent with the memory seen by thread 0 of the parent. Due to the first __syncthreads() call, the child will see data[0]=0, data[1]=1, ..., data[255]=255 (without the __syncthreads() call, only data[0] would be guaranteed to be seen by the child). When the child grid returns, thread 0 is guaranteed to see modifications made by the threads in its child grid. Those modifications become available to the other threads of the parent grid only after the second __syncthreads() call:

```__global__ void child_launch(int *data) {
}

__global__ void parent_launch(int *data) {

child_launch<<< 1, 256 >>>(data);
}

}

void host_launch(int *data) {
parent_launch<<< 1, 256 >>>(data);
}```

### C.2.2.1.2. Zero Copy Memory

Zero-copy system memory has identical coherence and consistency guarantees to global memory, and follows the semantics detailed above. A kernel may not allocate or free zero-copy memory, but may use pointers to zero-copy passed in from the host program.

### C.2.2.1.3. Constant Memory

Constants are immutable and may not be modified from the device, even between parent and child launches. That is to say, the value of all __constant__ variables must be set from the host prior to launch. Constant memory is inherited automatically by all child kernels from their respective parents.

Taking the address of a constant memory object from within a kernel thread has the same semantics as for all CUDA programs, and passing that pointer from parent to child or from a child to parent is naturally supported.

### C.2.2.1.4. Shared and Local Memory

Shared and Local memory is private to a thread block or thread, respectively, and is not visible or coherent between parent and child. Behavior is undefined when an object in one of these locations is referenced outside of the scope within which it belongs, and may cause an error.

The NVIDIA compiler will attempt to warn if it can detect that a pointer to local or shared memory is being passed as an argument to a kernel launch. At runtime, the programmer may use the __isGlobal() intrinsic to determine whether a pointer references global memory and so may safely be passed to a child launch.

Note that calls to cudaMemcpy*Async() or cudaMemset*Async() may invoke new child kernels on the device in order to preserve stream semantics. As such, passing shared or local memory pointers to these APIs is illegal and will return an error.

### C.2.2.1.5. Local Memory

Local memory is private storage for an executing thread, and is not visible outside of that thread. It is illegal to pass a pointer to local memory as a launch argument when launching a child kernel. The result of dereferencing such a local memory pointer from a child will be undefined.

For example the following is illegal, with undefined behavior if x_array is accessed by child_launch:

```int x_array[10];       // Creates x_array in parent's local memory
child_launch<<< 1, 1 >>>(x_array);```

It is sometimes difficult for a programmer to be aware of when a variable is placed into local memory by the compiler. As a general rule, all storage passed to a child kernel should be allocated explicitly from the global-memory heap, either with cudaMalloc(), new() or by declaring __device__ storage at global scope. For example:

```// Correct - "value" is global storage
__device__ int value;
__device__ void x() {
value = 5;
child<<< 1, 1 >>>(&value);
}```
```// Invalid - "value" is local storage
__device__ void y() {
int value = 5;
child<<< 1, 1 >>>(&value);
}```

### Texture Memory

Writes to the global memory region over which a texture is mapped are incoherent with respect to texture accesses. Coherence for texture memory is enforced at the invocation of a child grid and when a child grid completes. This means that writes to memory prior to a child kernel launch are reflected in texture memory accesses of the child. Similarly, writes to memory by a child will be reflected in the texture memory accesses by a parent, but only after the parent synchronizes on the child's completion. Concurrent accesses by parent and child may result in inconsistent data.

### C.3.1. CUDA C/C++ Reference

This section describes changes and additions to the CUDA C/C++ language extensions for supporting Dynamic Parallelism.

The language interface and API available to CUDA kernels using CUDA C/C++ for Dynamic Parallelism, referred to as the Device Runtime, is substantially like that of the CUDA Runtime API available on the host. Where possible the syntax and semantics of the CUDA Runtime API have been retained in order to facilitate ease of code reuse for routines that may run in either the host or device environments.

As with all code in CUDA C/C++, the APIs and code outlined here is per-thread code. This enables each thread to make unique, dynamic decisions regarding what kernel or operation to execute next. There are no synchronization requirements between threads within a block to execute any of the provided device runtime APIs, which enables the device runtime API functions to be called in arbitrarily divergent kernel code without deadlock.

### C.3.1.1. Device-Side Kernel Launch

Kernels may be launched from the device using the standard CUDA <<< >>> syntax:

`kernel_name<<< Dg, Db, Ns, S >>>([kernel arguments]);`
• Dg is of type dim3 and specifies the dimensions and size of the grid
• Db is of type dim3 and specifies the dimensions and size of each thread block
• Ns is of type size_t and specifies the number of bytes of shared memory that is dynamically allocated per thread block for this call and addition to statically allocated memory. Ns is an optional argument that defaults to 0.
• S is of type cudaStream_t and specifies the stream associated with this call. The stream must have been allocated in the same thread block where the call is being made. S is an optional argument that defaults to 0.

### C.3.1.1.1. Launches are Asynchronous

Identical to host-side launches, all device-side kernel launches are asynchronous with respect to the launching thread. That is to say, the <<<>>> launch command will return immediately and the launching thread will continue to execute until it hits an explicit launch-synchronization point such as cudaDeviceSynchronize(). The grid launch is posted to the device and will execute independently of the parent thread. The child grid may begin execution at any time after launch, but is not guaranteed to begin execution until the launching thread reaches an explicit launch-synchronization point.

### C.3.1.1.2. Launch Environment Configuration

All global device configuration settings (e.g., shared memory and L1 cache size as returned from cudaDeviceGetCacheConfig(), and device limits returned from cudaDeviceGetLimit()) will be inherited from the parent. That is to say if, when the parent is launched, execution is configured globally for 16k of shared memory and 48k of L1 cache, then the child's execution state will be configured identically. Likewise, device limits such as stack size will remain as-configured.

For host-launched kernels, per-kernel configurations set from the host will take precedence over the global setting. These configurations will be used when the kernel is launched from the device as well. It is not possible to reconfigure a kernel's environment from the device.

### C.3.1.1.3. Launch from __host__ __device__ Functions

Although the device runtime enables kernel launches from either the host or device, kernel launches from __host__ __device__ functions are unsupported. The compiler will fail to compile if a __host__ device__ function is used to launch a kernel.

### Streams

Both named and unnamed (NULL) streams are available from the device runtime. Named streams may be used by any thread within a thread-block, but stream handles may not be passed to other blocks or child/parent kernels. In other words, a stream should be treated as private to the block in which it is created. Stream handles are not guaranteed to be unique between blocks, so using a stream handle within a block that did not allocate it will result in undefined behavior.

Similar to host-side launch, work launched into separate streams may run concurrently, but actual concurrency is not guaranteed. Programs that depend upon concurrency between child kernels are not supported by the CUDA programming model and will have undefined behavior.

The host-side NULL stream's cross-stream barrier semantic is not supported on the device (see below for details). In order to retain semantic compatibility with the host runtime, all device streams must be created using the cudaStreamCreateWithFlags() API, passing the cudaStreamNonBlocking flag. The cudaStreamCreate() call is a host-runtime- only API and will fail to compile for the device.

As cudaStreamSynchronize() and cudaStreamQuery() are unsupported by the device runtime, cudaDeviceSynchronize() should be used instead when the application needs to know that stream-launched child kernels have completed.

### C.3.1.2.1. The Implicit (NULL) Stream

Within a host program, the unnamed (NULL) stream has additional barrier synchronization semantics with other streams (see Default Stream for details). The device runtime offers a single implicit, unnamed stream shared between all threads in a block, but as all named streams must be created with the cudaStreamNonBlocking flag, work launched into the NULL stream will not insert an implicit dependency on pending work in any other streams.

### Events

Only the inter-stream synchronization capabilities of CUDA events are supported. This means that cudaStreamWaitEvent() is supported, but cudaEventSynchronize(), cudaEventElapsedTime(), and cudaEventQuery() are not. As cudaEventElapsedTime() is not supported, cudaEvents must be created via cudaEventCreateWithFlags(), passing the cudaEventDisableTiming flag.

As for all device runtime objects, event objects may be shared between all threads withinthe thread-block which created them but are local to that block and may not be passed to other kernels, or between blocks within the same kernel. Event handles are not guaranteed to be unique between blocks, so using an event handle within a block that did not create it will result in undefined behavior.

### C.3.1.4. Synchronization

The cudaDeviceSynchronize() function will synchronize on all work launched by any thread in the thread-block up to the point where cudaDeviceSynchronize() was called. Note that cudaDeviceSynchronize() may be called from within divergent code (see Block Wide Synchronization).

It is up to the program to perform sufficient additional inter-thread synchronization, for example via a call to __syncthreads(), if the calling thread is intended to synchronize with child grids invoked from other threads.

### C.3.1.4.1. Block Wide Synchronization

The cudaDeviceSynchronize() function does not imply intra-block synchronization. In particular, without explicit synchronization via a __syncthreads() directive the calling thread can make no assumptions about what work has been launched by any thread other than itself. For example if multiple threads within a block are each launching work and synchronization is desired for all this work at once (perhaps because of event-based dependencies), it is up to the program to guarantee that this work is submitted by all threads before calling cudaDeviceSynchronize().

Because the implementation is permitted to synchronize on launches from any thread in the block, it is quite possible that simultaneous calls to cudaDeviceSynchronize() by multiple threads will drain all work in the first call and then have no effect for the later calls.

### C.3.1.5. Device Management

Only the device on which a kernel is running will be controllable from that kernel. This means that device APIs such as cudaSetDevice() are not supported by the device runtime. The active device as seen from the GPU (returned from cudaGetDevice()) will have the same device number as seen from the host system. The cudaGetDeviceProperty() call may request information about another device as this API allows specification of a device ID as a parameter of the call. Note that the catch-all cudaGetDeviceProperties() API is not offered by the device runtime - properties must be queried individually.

### C.3.1.6.1. Device and Constant Memory

Memory declared at file scope with __device__ or __constant__ qualifiers behave identically when using the device runtime. All kernels may read or write device variables, whether the kernel was initially launched by the host or device runtime. Equivalently, all kernels will have the same view of __constant__s as declared at the module scope.

### C.3.1.6.2. Textures & Surfaces

CUDA supports dynamically created texture and surface objects1, where a texture reference may be created on the host, passed to a kernel, used by that kernel, and then destroyed from the host. The device runtime does not allow creation or destruction of texture or surface objects from within device code, but texture and surface objects created from the host may be used and passed around freely on the device. Regardless of where they are created, dynamically created texture objects are always valid and may be passed to child kernels from a parent.

Note: The device runtime does not support legacy module-scope (i.e., Fermi-style) textures and surfaces within a kernel launched from the device. Module-scope (legacy) textures may be created from the host and used in device code as for any kernel, but may only be used by a top-level kernel (i.e., the one which is launched from the host).

### C.3.1.6.3. Shared Memory Variable Declarations

In CUDA C/C++ shared memory can be declared either as a statically sized file-scope or function-scoped variable, or as an extern variable with the size determined at runtime by the kernel's caller via a launch configuration argument. Both types of declarations are valid under the device runtime.

```__global__ void permute(int n, int *data) {
extern __shared__ int smem[];
if (n <= 1)
return;

permute_data(smem, n);

// Write back to GMEM since we can't pass SMEM to children.

permute<<< 1, 256, n/2*sizeof(int) >>>(n/2, data);
permute<<< 1, 256, n/2*sizeof(int) >>>(n/2, data+n/2);
}
}

void host_launch(int *data) {
permute<<< 1, 256, 256*sizeof(int) >>>(256, data);
}```

Device-side symbols (i.e., those marked __device__) may be referenced from within a kernel simply via the & operator, as all global-scope device variables are in the kernel's visible address space. This also applies to __constant__ symbols, although in this case the pointer will reference read-only data.

Given that device-side symbols can be referenced directly, those CUDA runtime APIs which reference symbols (e.g., cudaMemcpyToSymbol() or cudaGetSymbolAddress()) are redundant and hence not supported by the device runtime. Note this implies that constant data cannot be altered from within a running kernel, even ahead of a child kernel launch, as references to __constant__ space are read-only.

### C.3.1.7. API Errors and Launch Failures

As usual for the CUDA runtime, any function may return an error code. The last error code returned is recorded and may be retrieved via the cudaGetLastError() call. Errors are recorded per-thread, so that each thread can identify the most recent error that it has generated. The error code is of type cudaError_t.

Similar to a host-side launch, device-side launches may fail for many reasons (invalid arguments, etc). The user must call cudaGetLastError() to determine if a launch generated an error, however lack of an error after launch does not imply the child kernel completed successfully.

For device-side exceptions, e.g., access to an invalid address, an error in a child grid will be returned to the host instead of being returned by the parent's call to cudaDeviceSynchronize().

### C.3.1.7.1. Launch Setup APIs

Kernel launch is a system-level mechanism exposed through the device runtime library, and as such is available directly from PTX via the underlying cudaGetParameterBuffer() and cudaLaunchDevice() APIs. It is permitted for a CUDA application to call these APIs itself, with the same requirements as for PTX. In both cases, the user is then responsible for correctly populating all necessary data structures in the correct format according to specification. Backwards compatibility is guaranteed in these data structures.

As with host-side launch, the device-side operator <<<>>> maps to underlying kernel launch APIs. This is so that users targeting PTX will be able to enact a launch, and so that the compiler front-end can translate <<<>>> into these calls.

Table 4. New Device-only Launch Implementation Functions
Runtime API Launch Functions Description of Difference From Host Runtime Behaviour (behaviour is identical if no description)
cudaGetParameterBuffer Generated automatically from <<<>>>. Note different API to host equivalent.
cudaLaunchDevice Generated automatically from <<<>>>. Note different API to host equivalent.

The APIs for these launch functions are different to those of the CUDA Runtime API, and are defined as follows:

```extern   device   cudaError_t cudaGetParameterBuffer(void **params);
extern __device__ cudaError_t cudaLaunchDevice(void *kernel,
void *params, dim3 gridDim,
dim3 blockDim,
unsigned int sharedMemSize = 0,
cudaStream_t stream = 0);```

### C.3.1.8. API Reference

The portions of the CUDA Runtime API supported in the device runtime are detailed here. Host and device runtime APIs have identical syntax; semantics are the same except where indicated. The table below provides an overview of the API relative to the version available from the host.

Table 5. Supported API Functions
Runtime API Functions Details
cudaGetLastError Last error is per-thread state, not per-block state
cudaPeekAtLastError
cudaGetErrorString
cudaGetDeviceCount
cudaGetDeviceProperty Will return properties for any device
cudaGetDevice Always returns current device ID as would be seen from host
cudaStreamCreateWithFlags Must pass cudaStreamNonBlocking flag
cudaStreamDestroy
cudaStreamWaitEvent
cudaEventCreateWithFlags Must pass cudaEventDisableTiming flag
cudaEventRecord
cudaEventDestroy
cudaFuncGetAttributes
cudaMemcpyAsync Notes about all memcpy/memset functions:
• Only async memcpy/set functions are supported
• Only device-to-device memcpy is permitted
• May not pass in local or shared memory pointers
cudaMemcpy2DAsync
cudaMemcpy3DAsync
cudaMemsetAsync
cudaMemset2DAsync
cudaMemset3DAsync
cudaRuntimeGetVersion
cudaMalloc May not call cudaFree on the device on a pointer created on the host, and vice-versa
cudaFree

### C.3.2. Device-side Launch from PTX

This section is for the programming language and compiler implementers who target Parallel Thread Execution (PTX) and plan to support Dynamic Parallelism in their language. It provides the low-level details related to supporting kernel launches at the PTX level.

### C.3.2.1. Kernel Launch APIs

Device-side kernel launches can be implemented using the following two APIs accessible from PTX: cudaLaunchDevice() and cudaGetParameterBuffer(). cudaLaunchDevice() launches the specified kernel with the parameter buffer that is obtained by calling cudaGetParameterBuffer() and filled with the parameters to the launched kernel. The parameter buffer can be NULL, i.e., no need to invoke cudaGetParameterBuffer(), if the launched kernel does not take any parameters.

### C.3.2.1.1. cudaLaunchDevice

At the PTX level, cudaLaunchDevice()needs to be declared in one of the two forms shown below before it is used.

```// PTX-level Declaration of cudaLaunchDevice() when .address_size is 64
.extern .func(.param .b32 func_retval0) cudaLaunchDevice
(
.param .b64 func,
.param .b64 parameterBuffer,
.param .align 4 .b8 gridDimension[12],
.param .align 4 .b8 blockDimension[12],
.param .b32 sharedMemSize,
.param .b64 stream
)
;```
```// PTX-level Declaration of cudaLaunchDevice() when .address_size is 32
.extern .func(.param .b32 func_retval0) cudaLaunchDevice
(
.param .b32 func,
.param .b32 parameterBuffer,
.param .align 4 .b8 gridDimension[12],
.param .align 4 .b8 blockDimension[12],
.param .b32 sharedMemSize,
.param .b32 stream
)
;```

The CUDA-level declaration below is mapped to one of the aforementioned PTX-level declarations and is found in the system header file cuda_device_runtime_api.h. The function is defined in the cudadevrt system library, which must be linked with a program in order to use device-side kernel launch functionality.

```// CUDA-level declaration of cudaLaunchDevice()
extern "C" __device__
cudaError_t cudaLaunchDevice(void *func, void *parameterBuffer,
dim3 gridDimension, dim3 blockDimension,
unsigned int sharedMemSize,
cudaStream_t stream);```

The first parameter is a pointer to the kernel to be is launched, and the second parameter is the parameter buffer that holds the actual parameters to the launched kernel. The layout of the parameter buffer is explained in Parameter Buffer Layout, below. Other parameters specify the launch configuration, i.e., as grid dimension, block dimension, shared memory size, and the stream associated with the launch (please refer to Execution Configuration for the detailed description of launch configuration.

### cudaGetParameterBuffer

cudaGetParameterBuffer() needs to be declared at the PTX level before it's used. The PTX-level declaration must be in one of the two forms given below, depending on address size:

```// PTX-level Declaration of cudaGetParameterBuffer() when .address_size is 64
.extern .func(.param .b64 func_retval0) cudaGetParameterBuffer
(
.param .b64 alignment,
.param .b64 size
)
;```
```// PTX-level Declaration of cudaGetParameterBuffer() when .address_size is 32
.extern .func(.param .b32 func_retval0) cudaGetParameterBuffer
(
.param .b32 alignment,
.param .b32 size
)
;```

The following CUDA-level declaration of cudaGetParameterBuffer() is mapped to the aforementioned PTX-level declaration:

```// CUDA-level Declaration of cudaGetParameterBuffer()
extern "C" __device__
void *cudaGetParameterBuffer(size_t alignment, size_t size);```

The first parameter specifies the alignment requirement of the parameter buffer and the second parameter the size requirement in bytes. In the current implementation, the parameter buffer returned by cudaGetParameterBuffer() is always guaranteed to be 64- byte aligned, and the alignment requirement parameter is ignored. However, it is recommended to pass the correct alignment requirement value - which is the largest alignment of any parameter to be placed in the parameter buffer - to cudaGetParameterBuffer() to ensure portability in the future.

### C.3.2.2. Parameter Buffer Layout

Parameter reordering in the parameter buffer is prohibited, and each individual parameter placed in the parameter buffer is required to be aligned. That is, each parameter must be placed at the nth byte in the parameter buffer, where n is the smallest multiple of the parameter size that is greater than the offset of the last byte taken by the preceding parameter. The maximum size of the parameter buffer is 4KB.

For a more detailed description of PTX code generated by the CUDA compiler, please refer to the PTX-3.5 specification.

### C.3.3.1. Including Device Runtime API in CUDA Code

Similar to the host-side runtime API, prototypes for the CUDA device runtime API are included automatically during program compilation. There is no need to include cuda_device_runtime_api.h explicitly.

CUDA programs are automatically linked with the host runtime library when compiled with nvcc, but the device runtime is shipped as a static library which must explicitly be linked with a program which wishes to use it.

The device runtime is offered as a static library (cudadevrt.lib on Windows, libcudadevrt.a under Linux and MacOS), against which a GPU application that uses the device runtime must be linked. Linking of device libraries can be accomplished through nvcc and/or nvlink. Two simple examples are shown below.

A device runtime program may be compiled and linked in a single step, if all required source files can be specified from the command line:

`\$ nvcc -arch=sm_35 -rdc=true hello_world.cu -o hello -lcudadevrt`

It is also possible to compile CUDA .cu source files first to object files, and then link these together in a two-stage process:

```\$ nvcc -arch=sm_35 -dc hello_world.cu -o hello_world.o
\$ nvcc -arch=sm_35 -rdc=true hello_world.o -o hello -lcudadevrt```

Please see the Using Separate Compilation section of The CUDA Driver Compiler NVCC guide for more details.

### C.4.1. Basics

The device runtime is a functional subset of the host runtime. API level device management, kernel launching, device memcpy, stream management, and event management are exposed from the device runtime.

Programming for the device runtime should be familiar to someone who already has experience with CUDA. Device runtime syntax and semantics are largely the same as that of the host API, with any exceptions detailed earlier in this document.

The following example shows a simple Hello World program incorporating dynamic parallelism:

```#include <stdio.h>

__global__ void childKernel()
{
printf("Hello ");
}

__global__ void parentKernel()
{
// launch child
childKernel<<<1,1>>>();
if (cudaSuccess != cudaGetLastError()) {
return;
}

// wait for child to complete
return;
}

printf("World!\n");
}

int main(int argc, char *argv[])
{
// launch parent
parentKernel<<<1,1>>>();
if (cudaSuccess != cudaGetLastError()) {
return 1;
}

// wait for parent to complete
return 2;
}

return 0;
}```

This program may be built in a single step from the command line as follows:

`\$ nvcc -arch=sm_35 -rdc=true hello_world.cu -o hello -lcudadevrt`

### C.4.2.1. Synchronization

Synchronization by one thread may impact the performance of other threads in the same Thread Block, even when those other threads do not call cudaDeviceSynchronize() themselves. This impact will depend upon the underlying implementation.

System software which is active when controlling dynamic launches may impose an overhead on any kernel which is running at the time, whether or not it invokes kernel launches of its own. This overhead arises from the device runtime's execution tracking and management software and may result in decreased performance for e.g., library calls when made from the device compared to from the host side. This overhead is, in general, incurred for applications that link against the device runtime library.

### C.4.3. Implementation Restrictions and Limitations

Dynamic Parallelism guarantees all semantics described in this document, however, certain hardware and software resources are implementation-dependent and limit the scale, performance and other properties of a program which uses the device runtime.

### C.4.3.1.1. Memory Footprint

The device runtime system software reserves memory for various management purposes, in particular one reservation which is used for saving parent-grid state during synchronization, and a second reservation for tracking pending grid launches. Configuration controls are available to reduce the size of these reservations in exchange for certain launch limitations. See Configuration Options, below, for details.

The majority of reserved memory is allocated as backing-store for parent kernel state, for use when synchronizing on a child launch. Conservatively, this memory must support storing of state for the maximum number of live threads possible on the device. This means that each parent generation at which cudaDeviceSynchronize() is callable may require up to 150MB of device memory, depending on the device configuration, which will be unavailable for program use even if it is not all consumed.

### C.4.3.1.2. Nesting and Synchronization Depth

Using the device runtime, one kernel may launch another kernel, and that kernel may launch another, and so on. Each subordinate launch is considered a new nesting level, and the total number of levels is the nesting depth of the program. The synchronization depth is defined as the deepest level at which the program will explicitly synchronize on a child launch. Typically this is one less than the nesting depth of the program, but if the program does not need to call cudaDeviceSynchronize() at all levels then the synchronization depth might be substantially different to the nesting depth.

The overall maximum nesting depth is limited to 24, but practically speaking the real limit will be the amount of memory required by the system for each new level (see Memory Footprint above). Any launch which would result in a kernel at a deeper level than the maximum will fail. Note that this may also apply to cudaMemcpyAsync(), which might itself generate a kernel launch. See Configuration Options for details.

By default, sufficient storage is reserved for two levels of synchronization. This maximum synchronization depth (and hence reserved storage) may be controlled by calling cudaDeviceSetLimit() and specifying cudaLimitDevRuntimeSyncDepth. The number of levels to be supported must be configured before the top-level kernel is launched from the host, in order to guarantee successful execution of a nested program. Calling cudaDeviceSynchronize() at a depth greater than the specified maximum synchronization depth will return an error.

An optimization is permitted where the system detects that it need not reserve space for the parent's state in cases where the parent kernel never calls cudaDeviceSynchronize(). In this case, because explicit parent/child synchronization never occurs, the memory footprint required for a program will be much less than the conservative maximum. Such a program could specify a shallower maximum synchronization depth to avoid over-allocation of backing store.

### C.4.3.1.3. Pending Kernel Launches

When a kernel is launched, all associated configuration and parameter data is tracked until the kernel completes. This data is stored within a system-managed launch pool. The size of the launch pool is configurable by calling cudaDeviceSetLimit() from the host and specifying cudaLimitDevRuntimePendingLaunchCount.

### C.4.3.1.4. Configuration Options

Resource allocation for the device runtime system software is controlled via the cudaDeviceSetLimit() API from the host program. Limits must be set before any kernel is launched, and may not be changed while the GPU is actively running programs.

The following named limits may be set:

Limit Behavior
cudaLimitDevRuntimeSyncDepth Sets the maximum depth at which cudaDeviceSynchronize() may be called. Launches may be performed deeper than this, but explicit synchronization deeper than this limit will return the cudaErrorLaunchMaxDepthExceeded. The default maximum sync depth is 2.
cudaLimitDevRuntimePendingLaunchCount Controls the amount of memory set aside for buffering kernel launches which have not yet begun to execute, due either to unresolved dependencies or lack of execution resources. When the buffer is full, launches will set the thread's last error to cudaErrorLaunchPendingCountExceeded. The default pending launch count is 2048 launches.

### C.4.3.1.5. Memory Allocation and Lifetime

cudaMalloc() and cudaFree() have distinct semantics between the host and device environments. When invoked from the host, cudaMalloc() allocates a new region from unused device memory. When invoked from the device runtime these functions map to device-side malloc() and free(). This implies that within the device environment the total allocatable memory is limited to the device malloc() heap size, which may be smaller than the available unused device memory. Also, it is an error to invoke cudaFree() from the host program on a pointer which was allocated by cudaMalloc() on the device or vice-versa.

cudaMalloc() on Host cudaMalloc() on Device
cudaFree() on Host Supported Not Supported
cudaFree() on Device Not Supported Supported
Allocation limit Free device memory cudaLimitMallocHeapSize

### C.4.3.1.6. SM Id and Warp Id

Note that in PTX %smid and %warpid are defined as volatile values. The device runtime may reschedule thread blocks onto different SMs in order to more efficiently manage resources. As such, it is unsafe to rely upon %smid or %warpid remaining unchanged across the lifetime of a thread or thread block.

### C.4.3.1.7. ECC Errors

No notification of ECC errors is available to code within a CUDA kernel. ECC errors are reported at the host side once the entire launch tree has completed. Any ECC errors which arise during execution of a nested program will either generate an exception or continue execution (depending upon error and configuration).

## D. Mathematical Functions

The reference manual lists, along with their description, all the functions of the C/C++ standard library mathematical functions that are supported in device code, as well as all intrinsic functions (that are only supported in device code).

This appendix provides accuracy information for some of these functions when applicable.

### D.1. Standard Functions

The functions from this section can be used in both host and device code.

This section specifies the error bounds of each function when executed on the device and also when executed on the host in the case where the host does not supply the function.

The error bounds are generated from extensive but not exhaustive tests, so they are not guaranteed bounds.

### Single-Precision Floating-Point Functions

Addition and multiplication are IEEE-compliant, so have a maximum error of 0.5 ulp. However, on the device, the compiler often combines them into a single multiply-add instruction (FMAD) and for devices of compute capability 1.x, FMAD truncates the intermediate result of the multiplication as mentioned in Floating-Point Standard.This combination can be avoided by using the __fadd_[rn,rz,ru,rd]() and __fmul_[rn,rz,ru,rd]() intrinsic functions (see Intrinsic Functions).

The recommended way to round a single-precision floating-point operand to an integer, with the result being a single-precision floating-point number is rintf(), not roundf(). The reason is that roundf() maps to an 8-instruction sequence on the device, whereas rintf() maps to a single instruction. truncf(), ceilf(), and floorf() each map to a single instruction as well.

Table 6. Single-Precision Mathematical Standard Library Functions with Maximum ULP Error. The maximum error is stated as the absolute value of the difference in ulps between a correctly rounded single-precision result and the result returned by the CUDA library function.
Function Maximum ulp error
x+y

0 (IEEE-754 round-to-nearest-even)

(except for devices of compute capability 1.x when addition is merged into an FMAD)

x*y

0 (IEEE-754 round-to-nearest-even)

(except for devices of compute capability 1.x when multiplication is merged into an FMAD)

x/y

0 for compute capability ≥ 2 when compiled with -prec-div=true

2 (full range), otherwise

1/x

0 for compute capability ≥ 2 when compiled with -prec-div=true

1 (full range), otherwise

rsqrtf(x)

1/sqrtf(x)

2 (full range)

Applies to 1/sqrtf(x) only when it is converted to rsqrtf(x) by the compiler.

sqrtf(x)

0 for compute capability ≥ 2 when compiled with -prec-sqrt=true

3 (full range), otherwise

cbrtf(x) 1 (full range)
rcbrtf(x) 2 (full range)
hypotf(x,y) 3 (full range)
expf(x) 2 (full range)
exp2f(x) 2 (full range)
exp10f(x) 2 (full range)
expm1f(x) 1 (full range)
logf(x) 1 (full range)
log2f(x) 3 (full range)
log10f(x) 3 (full range)
log1pf(x) 2 (full range)
sinf(x) 2 (full range)
cosf(x) 2 (full range)
tanf(x) 4 (full range)
sincosf(x,sptr,cptr) 2 (full range)
sinpif(x) 2 (full range)
cospif(x) 2 (full range)
sincospif(x,sptr,cptr) 2 (full range)
asinf(x) 4 (full range)
acosf(x) 3 (full range)
atanf(x) 2 (full range)
atan2f(y,x) 3 (full range)
sinhf(x) 3 (full range)
coshf(x) 2 (full range)
tanhf(x) 2 (full range)
asinhf(x) 3 (full range)
acoshf(x) 4 (full range)
atanhf(x) 3 (full range)
powf(x,y) 8 (full range)
erff(x) 2 (full range)
erfcf(x) 6 (full range)
erfinvf(x) 3 (full range)
erfcinvf(x) 4 (full range)
erfcxf(x) 6 (full range)
normcdff(x) 6 (full range)
normcdfinvf(x) 5 (full range)
lgammaf(x) 6 (outside interval -10.001 ... -2.264; larger inside)
tgammaf(x) 11 (full range)
fmaf(x,y,z) 0 (full range)
frexpf(x,exp) 0 (full range)
ldexpf(x,exp) 0 (full range)
scalbnf(x,n) 0 (full range)
scalblnf(x,l) 0 (full range)
logbf(x) 0 (full range)
ilogbf(x) 0 (full range)
j0f(x)

9 for |x| < 8

otherwise, the maximum absolute error is 2.2 x 10-6

j1f(x)

9 for |x| < 8

otherwise, the maximum absolute error is 2.2 x 10-6

jnf(x) For n = 128, the maximum absolute error is 2.2 x 10-6
y0f(x)

9 for |x| < 8

otherwise, the maximum absolute error is 2.2 x 10-6

y1f(x)

9 for |x| < 8

otherwise, the maximum absolute error is 2.2 x 10-6

ynf(x)

ceil(2 + 2.5n) for |x| < n

otherwise, the maximum absolute error is 2.2 x 10-6

fmodf(x,y) 0 (full range)
remainderf(x,y) 0 (full range)
remquof(x,y,iptr) 0 (full range)
modff(x,iptr) 0 (full range)
fdimf(x,y) 0 (full range)
truncf(x) 0 (full range)
roundf(x) 0 (full range)
rintf(x) 0 (full range)
nearbyintf(x) 0 (full range)
ceilf(x) 0 (full range)
floorf(x) 0 (full range)
lrintf(x) 0 (full range)
lroundf(x) 0 (full range)
llrintf(x) 0 (full range)
llroundf(x) 0 (full range)

### Double-Precision Floating-Point Functions

The errors listed below only apply when compiling for devices with native double-precision support. When compiling for devices without such support, such as devices of compute capability 1.2 and lower, the double type gets demoted to float by default and the double-precision math functions are mapped to their single-precision equivalents.

The recommended way to round a double-precision floating-point operand to an integer, with the result being a double-precision floating-point number is rint(), not round(). The reason is that round() maps to an 8-instruction sequence on the device, whereas rint() maps to a single instruction. trunc(), ceil(), and floor() each map to a single instruction as well.

Table 7. Double-Precision Mathematical Standard Library Functions with Maximum ULP Error. The maximum error is stated as the absolute value of the difference in ulps between a correctly rounded double-precision result and the result returned by the CUDA library function.
Function Maximum ulp error
x+y

0 (IEEE-754 round-to-nearest-even)

x*y

0 (IEEE-754 round-to-nearest-even)

x/y

0 (IEEE-754 round-to-nearest-even)

1/x

0 (IEEE-754 round-to-nearest-even)

sqrt(x) 0 (IEEE-754 round-to-nearest-even)
rsqrt(x)

1 (full range)

cbrt(x) 1 (full range)
rcbrt(x) 1 (full range)
hypot(x,y) 2 (full range)
exp(x) 1 (full range)
exp2(x) 1 (full range)
exp10(x) 1 (full range)
expm1(x) 1 (full range)
log(x) 1 (full range)
log2(x) 1 (full range)
log10(x) 1 (full range)
log1p(x) 1 (full range)
sin(x) 1 (full range)
cos(x) 1 (full range)
tan(x) 2 (full range)
sincos(x,sptr,cptr) 1 (full range)
sinpi(x) 1 (full range)
cospi(x) 1 (full range)
sincospi(x,sptr,cptr) 1 (full range)
asin(x) 2 (full range)
acos(x) 2 (full range)
atan(x) 2 (full range)
atan2(y,x) 2 (full range)
sinh(x) 1 (full range)
cosh(x) 1 (full range)
tanh(x) 1 (full range)
asinh(x) 2 (full range)
acosh(x) 2 (full range)
atanh(x) 2 (full range)
pow(x,y) 2 (full range)
erf(x) 2 (full range)
erfc(x) 4 (full range)
erfinv(x) 5 (full range)
erfcinv(x) 6 (full range)
erfcx(x) 3 (full range)
normcdf(x) 5 (full range)
normcdfinv(x) 7 (full range)
lgamma(x) 4 (outside interval -11.0001 ... -2.2637; larger inside)
tgamma(x) 8 (full range)
fma(x,y,z) 0 (IEEE-754 round-to-nearest-even)
frexp(x,exp) 0 (full range)
ldexp(x,exp) 0 (full range)
scalbn(x,n) 0 (full range)
scalbln(x,l) 0 (full range)
logb(x) 0 (full range)
ilogb(x) 0 (full range)
j0(x)

7 for |x| < 8

otherwise, the maximum absolute error is 5 x 10-12

j1(x)

7 for |x| < 8

otherwise, the maximum absolute error is 5 x 10-12

jn(x) For n = 128, the maximum absolute error is 5 x 10-12
y0(x)

7 for |x| < 8

otherwise, the maximum absolute error is 5 x 10-12

y1(x)

7 for |x| < 8

otherwise, the maximum absolute error is 5 x 10-12

yn(x)

For |x| > 1.5n, the maximum absolute error is 5 x 10-12

fmod(x,y) 0 (full range)
remainder(x,y) 0 (full range)
remquo(x,y,iptr) 0 (full range)
mod(x,iptr) 0 (full range)
fdim(x,y) 0 (full range)
trunc(x) 0 (full range)
round(x) 0 (full range)
rint(x) 0 (full range)
nearbyint(x) 0 (full range)
ceil(x) 0 (full range)
floor(x) 0 (full range)
lrint(x) 0 (full range)
lround(x) 0 (full range)
llrint(x) 0 (full range)
llround(x) 0 (full range)

### D.2. Intrinsic Functions

The functions from this section can only be used in device code.

Among these functions are the less accurate, but faster versions of some of the functions of Standard Functions .They have the same name prefixed with __ (such as __sinf(x)). They are faster as they map to fewer native instructions. The compiler has an option (-use_fast_math) that forces each function in Table 8 to compile to its intrinsic counterpart. In addition to reducing the accuracy of the affected functions, it may also cause some differences in special case handling. A more robust approach is to selectively replace mathematical function calls by calls to intrinsic functions only where it is merited by the performance gains and where changed properties such as reduced accuracy and different special case handling can be tolerated.

Table 8. Functions Affected by -use_fast_math
Operator/Function Device Function
x/y

__fdividef(x,y)

sinf(x)

__sinf(x)

cosf(x)

__cosf(x)

tanf(x) __tanf(x)
sincosf(x,sptr,cptr) __sincosf(x,sptr,cptr)
logf(x)

__logf(x)

log2f(x) __log2f(x)
log10f(x) __log10f(x)
expf(x) __expf(x)
exp10f(x) __exp10f(x)
powf(x,y) __powf(x,y)

Functions suffixed with _rn operate using the round to nearest even rounding mode.

Functions suffixed with _rz operate using the round towards zero rounding mode.

Functions suffixed with _ru operate using the round up (to positive infinity) rounding mode.

Functions suffixed with _rd operate using the round down (to negative infinity) rounding mode.

### Single-Precision Floating-Point Functions

__fadd_[rn,rz,ru,rd]() and __fmul_[rn,rz,ru,rd]() map to addition and multiplication operations that the compiler never merges into FMADs. By contrast, additions and multiplications generated from the '*' and '+' operators will frequently be combined into FMADs.

The accuracy of floating-point division varies depending on the compute capability of the device and whether the code is compiled with -prec-div=false or -prec-div=true. For devices of compute capability 2.x and higher when the code is compiled with -prec-div=false or for devices of compute capability 1.x, both the regular division / operator and __fdividef(x,y) have the same accuracy, but for 2126 < y < 2128, __fdividef(x,y) delivers a result of zero, whereas the / operator delivers the correct result to within the accuracy stated in Table 9. Also, for 2126 < y < 2128, if x is infinity, __fdividef(x,y) delivers a NaN (as a result of multiplying infinity by zero), while the / operator returns infinity. On the other hand, the / operator is IEEE-compliant on devices of compute capability 2.x and higher when the code is compiled with -prec-div=true or without any -prec-div option at all since its default value is true.

Table 9. Single-Precision Floating-Point Intrinsic Functions. (Supported by the CUDA Runtime Library with Respective Error Bounds)
Function Error bounds

IEEE-compliant.

__fsub_[rn,rz,ru,rd](x,y)

IEEE-compliant.

__fmul_[rn,rz,ru,rd](x,y)

IEEE-compliant.

__fmaf_[rn,rz,ru,rd](x,y,z)

IEEE-compliant.

__frcp_[rn,rz,ru,rd](x) IEEE-compliant.
__fsqrt_[rn,rz,ru,rd](x) IEEE-compliant.
__frsqrt_rn(x) IEEE-compliant.
__fdiv_[rn,rz,ru,rd](x,y)

IEEE-compliant.

__fdividef(x,y) For y in [2-126, 2126], the maximum ulp error is 2.
__expf(x) The maximum ulp error is 2 + floor(abs(1.16 * x)).
__exp10f(x) The maximum ulp error is 2+ floor(abs(2.95 * x)).
__logf(x) For x in [0.5, 2], the maximum absolute error is 2-21.41, otherwise, the maximum ulp error is 3.
__log2f(x) For x in [0.5, 2], the maximum absolute error is 2-22, otherwise, the maximum ulp error is 2.
__log10f(x) For x in [0.5, 2], the maximum absolute error is 2-24, otherwise, the maximum ulp error is 3.
__sinf(x) For x in [-π,π], the maximum absolute error is 2-21.41, and larger otherwise.
__cosf(x) For x in [-π,π], the maximum absolute error is 2-21.19, and larger otherwise.
__sincosf(x,sptr,cptr) Same as sinf(x) and cosf(x).
__tanf(x) Derived from its implementation as __sinf(x) * (1/__cosf(x)).
__powf(x, y) Derived from its implementation as exp2f(y * __log2f(x)).

### Double-Precision Floating-Point Functions

__dadd_rn() and __dmul_rn() map to addition and multiplication operations that the compiler never merges into FMADs. By contrast, additions and multiplications generated from the '*' and '+' operators will frequently be combined into FMADs.

Table 10. Double-Precision Floating-Point Intrinsic Functions. (Supported by the CUDA Runtime Library with Respective Error Bounds)
Function Error bounds

IEEE-compliant.

__dsub_[rn,rz,ru,rd](x,y)

IEEE-compliant.

__dmul_[rn,rz,ru,rd](x,y)

IEEE-compliant.

__fma_[rn,rz,ru,rd](x,y,z)

IEEE-compliant.

__ddiv_[rn,rz,ru,rd](x,y)(x,y)

IEEE-compliant.

Requires compute capability > 2.

__drcp_[rn,rz,ru,rd](x)

IEEE-compliant.

Requires compute capability > 2.

__dsqrt_[rn,rz,ru,rd](x)

IEEE-compliant.

Requires compute capability > 2.

## E. C/C++ Language Support

As described in Compilation with NVCC, source files compiled with nvcc can include a mix of host code and device code.

For the host code, nvcc supports whatever part of the C++ ISO/IEC 14882:2003 specification the host c++ compiler supports.

For the device code, nvcc supports the features illustrated in Code Samples with some restrictions described in Restrictions; it does not support run time type information (RTTI), exception handling, and the C++ Standard Library.

### E.1.1. Data Aggregation Class

```class PixelRGBA {
public:
__device__ PixelRGBA(): r_(0), g_(0), b_(0), a_(0) { }

__device__ PixelRGBA(unsigned char r, unsigned char g,
unsigned char b, unsigned char a = 255):
r_(r), g_(g), b_(b), a_(a) { }

private:
unsigned char r_, g_, b_, a_;

friend PixelRGBA operator+(const PixelRGBA const PixelRGBA&);
};

__device__
PixelRGBA operator+(const PixelRGBA& p1, const PixelRGBA& p2)
{
return PixelRGBA(p1.r_ + p2.r_, p1.g_ + p2.g_,
p1.b_ + p2.b_, p1.a_ + p2.a_);
}

__device__ void func(void)
{
PixelRGBA p1, p2;
// ...      // Initialization of p1 and p2 here
PixelRGBA p3 = p1 + p2;
}```

### E.1.2. Derived Class

```__device__ void* operator new(size_t bytes, MemoryPool& p);
__device__ void operator delete(void*, MemoryPool& p);
class Shape {
public:
__device__ Shape(void) { }
__device__ void putThis(PrintBuffer *p) const;
__device__ virtual void Draw(PrintBuffer *p) const {
p->put("Shapeless");
}
__device__ virtual ~Shape() {}
};
class Point : public Shape {
public:
__device__ Point() : x(0), y(0) {}
__device__ Point(int ix, int iy) : x(ix), y(iy) { }
__device__ void PutCoord(PrintBuffer *p) const;
__device__ void Draw(PrintBuffer *p) const;
__device__ ~Point() {}
private:
int x, y;
};
__device__ Shape* GetPointObj(MemoryPool& pool)
{
Shape* shape = new(pool) Point(rand(-20,10), rand(-100,-20));
return shape;
}```

### E.1.3. Class Template

```template <class T>
class myValues {
T values[MAX_VALUES];
public:
__device__ myValues(T clear) { ... }
__device__ void setValue(int Idx, T value) { ... }
__device__ void putToMemory(T* valueLocation) { ... }
};

template <class T>
void __global__ useValues(T* memoryBuffer) {
myValues<T> myLocation(0);
...
}

__device__ void* buffer;

int main()
{
...
...
}```

### E.1.4. Function Template

```template <typename T>
__device__ bool func(T x)
{
...
return (...);
}

template <>
__device__ bool func<int>(T x) // Specialization
{
return true;
}

// Explicit argument specification
bool result = func<double>(0.5);

// Implicit argument deduction
int x = 1;
bool result = func(x);```

### E.1.5. Functor Class

```class Add {
public:
__device__  float operator() (float a, float b) const
{
return a + b;
}
};

class Sub {
public:
__device__  float operator() (float a, float b) const
{
return a - b;
}
};

// Device code
template<class O> __global__
void VectorOperation(const float * A, const float * B, float * C,
unsigned int N, O op)
{
unsigned int iElement = blockDim.x * blockIdx.x + threadIdx.x;
if (iElement < N)
C[iElement] = op(A[iElement], B[iElement]);
}

// Host code
int main()
{
...
...
}```

### E.2.1. Preprocessor Symbols

If a __global__ function template is instantiated and launched from the host, the function template must be instantiated with the same types irrespective of whether __CUDA_ARCH__ is defined and regardless of the value of the __CUDA_ARCH__ macro.

In the following example, the instantiation kern<int> only occurs when __CUDA_ARCH__ is not defined. This is not supported.
```  __device__ int result;
template <typename T>
__global__ void kern(T in)
{
result = in;
}

__host__ __device__ void foo(void)
{
#if !defined(__CUDA_ARCH__)
kern<<<1,1>>>(1);      // instantiation "kern<int>"
#endif /* !defined(__CUDA_ARCH__) */
}

int main(void)
{
foo();
return 0;
}```

### E.2.2.1. Device Memory Qualifiers

The __device__, __shared__ and __constant__ qualifiers are not allowed on:

• class, struct, and union data members,
• formal parameters,
• local variables within a function that executes on the host.

__shared__ and __constant__ variables have implied static storage.

__device__ and __constant__ variable definitions are only allowed in namespace scope (including global namespace scope).

__device__, __constant__ and __shared__ variables defined in namespace scope, that are of class type, cannot have a non-empty constructor or a non-empty destructor. A constructor for a class type is considered empty at a point in the translation unit, if it is either a trivial constructor or it satisfies all of the following conditions:

• The constructor function has been defined.
• The constructor function has no parameters, the initializer list is empty and the function body is an empty compound statement.
• Its class has no virtual functions and no virtual base classes.
• The default constructors of all base classes of its class can be considered empty.
• For all the nonstatic data members of its class that are of class type (or array thereof), the default constructors can be considered empty.

A destructor for a class is considered empty at a point in the translation unit, if it is either a trivial destructor or it satisfies all of the following conditions:

• The destructor function has been defined.
• The destructor function body is an empty compound statement.
• Its class has no virtual functions and no virtual base classes.
• The destructors of all base classes of its class can be considered empty.
• For all the nonstatic data members of its class that are of class type (or array thereof), the destructor can be considered empty.

When compiling in the whole program compilation mode (see the nvcc user manual for a description of this mode), __device__, __shared__, and __constant__ variables cannot be defined as external using the extern keyword. The only exception is for dynamically allocated __shared__ variables as described in __shared__.

When compiling in the separate compilation mode (see the nvcc user manual for a description of this mode), __device__, __shared__, and __constant__ variables can be defined as external using the extern keyword. nvlink will generate an error when it cannot find a definition for an external variable (unless it is a dynamically allocated __shared__ variable).

### E.2.2.2. Volatile Qualifier

Only after the execution of a __threadfence_block(), __threadfence(), or __syncthreads() (Memory Fence Functions and Synchronization Functions) are prior writes to global or shared memory guaranteed to be visible by other threads. As long as this requirement is met, the compiler is free to optimize reads and writes to global or shared memory.

This behavior can be changed using the volatile keyword: If a variable located in global or shared memory is declared as volatile, the compiler assumes that its value can be changed or used at any time by another thread and therefore any reference to this variable compiles to an actual memory read or write instruction.

### E.2.3. Pointers

For devices of compute capability 1.x, pointers in code that is executed on the device are supported as long as the compiler is able to resolve whether they point to either the shared memory space, the global memory space, or the local memory space, otherwise they are restricted to only point to memory allocated or declared in the global memory space. For devices of compute capability 2.x and higher, pointers are supported without any restriction.

Dereferencing a pointer either to global or shared memory in code that is executed on the host, or to host memory in code that is executed on the device results in an undefined behavior, most often in a segmentation fault and application termination.

The address obtained by taking the address of a __device__, __shared__ or __constant__ variable can only be used in device code. The address of a __device__ or __constant__ variable obtained through cudaGetSymbolAddress() as described in Device Memory can only be used in host code.

As a consequence of the use of C++ syntax rules, void pointers (e.g., returned by malloc()) cannot be assigned to non-void pointers without a typecast.

### E.2.4.1. Assignment Operator

__constant__ variables can only be assigned from the host code through runtime functions (Device Memory); they cannot be assigned from the device code.

__shared__ variables cannot have an initialization as part of their declaration.

It is not allowed to assign values to any of the built-in variables defined in Built-in Variables.

It is not allowed to take the address of any of the built-in variables defined in Built-in Variables.

### E.2.5.1. Compiler generated functions

The execution space qualifiers (__host__, __device__) for a compiler generated function are the union of the execution space qualifiers of all the functions that invoke it (note that a __global__ caller will be treated as a __device__ caller for this analysis). For example:
```class Base {
int x;
public:
__host__ __device__ Base(void) : x(10) {}
};

class Derived : public Base {
int y;
};

class Other: public Base {
int z;
};

__device__ void foo(void)
{
Derived D1;
Other D2;
}

__host__ void bar(void)
{
Other D3;
}```
Here, the compiler generated constructor function "Derived::Derived" will be treated as a __device__ function, since it is invoked only from the __device__ function "foo". The compiler generated constructor function "Other::Other" will be treated as a __host__ __device__ function, since it is invoked both from a __device__ function "foo" and a __host__ function "bar".

### E.2.5.2. Function Parameters

__global__ function parameters are passed to the device:

• via shared memory and are limited to 256 bytes on devices of compute capability 1.x,
• via constant memory and are limited to 4 KB on devices of compute capability 2.x and higher.

__device__ and __global__ functions cannot have a variable number of arguments.

### E.2.5.3. Static Variables within Function

Within the body of a __device__ or __global__ function, only __shared__ variables may be declared with static storage class.

### E.2.5.4. Function Pointers

Function pointers to __global__ functions are supported in host code, but not in device code.

Function pointers to __device__ functions are only supported in device code compiled for devices of compute capability 2.x and higher.

It is not allowed to take the address of a __device__ function in host code.

### E.2.5.5. Function Recursion

__global__ functions do not support recursion.

__device__ functions only support recursion in device code compiled for devices of compute capability 2.x and higher.

### E.2.6.1. Data Members

Static data members are not supported.

The layout of bit-fields in device code may currently not match the layout in host code on Windows.

### E.2.6.2. Function Members

Static member functions cannot be __global__ functions.

### E.2.6.3. Virtual Functions

When a function in a derived class overrides a virtual function in a base class, the execution space qualifiers (i.e., __host__, __device__) on the overridden and overriding functions must match.

It is not allowed to pass as an argument to a __global__ function an object of a class with virtual functions.

The virtual function table is placed in global or constant memory by the compiler.

### E.2.6.4. Virtual Base Classes

It is not allowed to pass as an argument to a __global__ function an object of a class derived from virtual base classes.

Use of virtual base class members is unsupported on devices of compute capability 1.x. For example, nvcc gives an error when the code below is compiled with -arch compute_10.

```class Base {
public:
int x;
};

class Derived : public virtual Base {
public:
int y;
};

__global__ void k(Derived *d)
{
int v = d->x; // Unsupported on compute capability 1.x.
...
}```

Casting an object to its virtual base type is also unsupported on devices of compute capability 1.x. An example of such cases is shown below.

```class Base { };

class Derived : public virtual Base { };

__device__ Base *get(Derived *x)
{
return static_cast<Base *>(x); // Unsupported on compute capability 1.x
}```

### Anonymous Unions

Member variables of a namespace scope anonymous union cannot be referenced in a __global__ or __device__ function.

### E.2.6.6. Windows-Specific

On Windows, the CUDA compiler may produce a different memory layout, compared to the host Microsoft compiler, for a C++ object of class type T that satisfies any of the following conditions:

• T has virtual functions or derives from a direct or indirect base class that has virtual functions;
• T has a direct or indirect virtual base class;
• T has multiple inheritance with more than one direct or indirect empty base class.

The size for such an object may also be different in host and device code. As long as type T is used exclusively in host or device code, the program should work correctly. Do not pass objects of type T between host and device code (e.g., as arguments to __global__ functions or through cudaMemcpy*() calls).

### E.2.7. Templates

A __global__ function template cannot be instantiated with a type or typedef that is defined within a function or is private to a class or structure, as illustrated in the following code sample:

```template <typename T>
__global__ void myKernel1(void) { }

template <typename T>
__global__ void myKernel2(T par) { }

class myClass {
private:
struct inner_t { };
public:
static void launch(void)
{
// Both kernel launches below are disallowed
// as myKernel1 and myKernel2 are instantiated
// with private type inner_t

myKernel1<inner_t><<<1,1>>>();

inner_t var;
myKernel2<<<1,1>>>(var);
}
};```

## F. Texture Fetching

This appendix gives the formula used to compute the value returned by the texture functions of Texture Functions depending on the various attributes of the texture reference (see Texture and Surface Memory).

The texture bound to the texture reference is represented as an array T of

• N texels for a one-dimensional texture,
• N x M texels for a two-dimensional texture,
• N x M x L texels for a three-dimensional texture.

It is fetched using non-normalized texture coordinates x, y, and z, or the normalized texture coordinates x/N, y/M, and z/L as described in Texture Memory. In this appendix, the coordinates are assumed to be in the valid range. Texture Memory explained how out-of-range coordinates are remapped to the valid range based on the addressing mode.

### F.1. Nearest-Point Sampling

In this filtering mode, the value returned by the texture fetch is

• tex(x)=T[i] for a one-dimensional texture,
• tex(x,y)=T[i,j] for a two-dimensional texture,
• tex(x,y,z)=T[i,j,k] for a three-dimensional texture,

where i=floor(x), j=floor(y), and k=floor(z).

Figure 13 illustrates nearest-point sampling for a one-dimensional texture with N=4.

For integer textures, the value returned by the texture fetch can be optionally remapped to [0.0, 1.0] (see Texture Memory).

Figure 13. Nearest-Point Sampling Filtering Mode. Nearest-point sampling of a one-dimensional texture of four texels.

### F.2. Linear Filtering

In this filtering mode, which is only available for floating-point textures, the value returned by the texture fetch is

• tex(x)=(1−α)T[i]+αT[i+1] for a one-dimensional texture,
• tex(x,y)=(1−α)(1−β)T[i,j]+α(1−β)T[i+1,j]+(1−α)βT[i,j+1]+αβT[i+1,j+1] for a two-dimensional texture,
• tex(x,y,z) =

(1−α)(1−β)(1−γ)T[i,j,k]+α(1−β)(1−γ)T[i+1,j,k]+

(1−α)β(1−γ)T[i,j+1,k]+αβ(1−γ)T[i+1,j+1,k]+

(1−α)(1−β)γT[i,j,k+1]+α(1−β)γT[i+1,j,k+1]+

(1−α)βγT[i,j+1,k+1]+αβγT[i+1,j+1,k+1]

for a three-dimensional texture,

where:

• i=floor(xB), α=frac(xB), xB=x-0.5,
• j=floor(yB), β=frac(yB), yB=y-0.5,
• k=floor(zB), γ=frac(zB), zB= z-0.5,

α, β, and γ are stored in 9-bit fixed point format with 8 bits of fractional value (so 1.0 is exactly represented).

Figure 14 illustrates linear filtering of a one-dimensional texture with N=4.

Figure 14. Linear Filtering Mode. Linear filtering of a one-dimensional texture of four texels in clamp addressing mode.

### F.3. Table Lookup

A table lookup TL(x) where x spans the interval [0,R] can be implemented as TL(x)=tex((N-1)/R)x+0.5) in order to ensure that TL(0)=T[0] and TL(R)=T[N-1].

Figure 15 illustrates the use of texture filtering to implement a table lookup with R=4 or R=1 from a one-dimensional texture with N=4.

Figure 15. One-Dimensional Table Lookup Using Linear Filtering

## G. Compute Capabilities

The general specifications and features of a compute device depend on its compute capability (see Compute Capability).

Table 11 gives the features and technical specifications associated to each compute capability.

Floating-Point Standard reviews the compliance with the IEEE floating-point standard.

Section Compute Capability 1.x, Compute Capability 2.x, and Compute Capability 3.x give more details on the architecture of devices of compute capability 1.x, 2.x, and 3.x, respectively.

### G.1. Features and Technical Specifications

Table 11. Feature Support per Compute Capability
Feature Support Compute Capability
(Unlisted features are supported for all compute capabilities) 1.0 1.1 1.2 1.3 2.x, 3.0 3.5
Atomic functions operating on 32-bit integer values in global memory (Atomic Functions) No Yes
atomicExch() operating on 32-bit floating point values in global memory (atomicExch())
Atomic functions operating on 32-bit integer values in shared memory (Atomic Functions) No Yes
atomicExch() operating on 32-bit floating point values in shared memory (atomicExch())
Atomic functions operating on 64-bit integer values in global memory (Atomic Functions)
Warp vote functions (Warp Vote Functions)
Double-precision floating-point numbers No Yes
Atomic functions operating on 64-bit integer values in shared memory (Atomic Functions) No Yes
Atomic addition operating on 32-bit floating point values in global and shared memory (atomicAdd())
__ballot() (Warp Vote Functions)

Surface functions (Surface Functions)
Funnel shift (see reference manual) No Yes
Table 12. Technical Specifications per Compute Capability
Compute Capability
Technical Specifications 1.0 1.1 1.2 1.3 2.x 3.0 3.5
Maximum dimensionality of grid of thread blocks 2 3
Maximum x-dimension of a grid of thread blocks 65535 231-1
Maximum y- or z-dimension of a grid of thread blocks 65535
Maximum dimensionality of thread block 3
Maximum x- or y-dimension of a block 512 1024
Maximum z-dimension of a block 64
Maximum number of threads per block 512 1024
Warp size 32
Maximum number of resident blocks per multiprocessor 8 16
Maximum number of resident warps per multiprocessor 24 32 48 64
Maximum number of resident threads per multiprocessor 768 1024 1536 2048
Number of 32-bit registers per multiprocessor 8 K 16 K 32 K 64 K
Maximum number of 32-bit registers per thread 128 63 255
Maximum amount of shared memory per multiprocessor 16 KB 48 KB
Number of shared memory banks 16 32
Amount of local memory per thread 16 KB 512 KB
Constant memory size 64 KB
Cache working set per multiprocessor for constant memory 8 KB
Cache working set per multiprocessor for texture memory Device dependent, between 6 KB and 8 KB 12 KB Between 12 KB and 48 KB
Maximum width for a 1D texture reference bound to a CUDA array 8192 65536
Maximum width for a 1D texture reference bound to linear memory 227
Maximum width and number of layers for a 1D layered texture reference 8192 x 512 16384 x 2048
Maximum width and height for a 2D texture reference bound to a CUDA array 65536 x 32768 65536 x 65535
Maximum width and height for a 2D texture reference bound to linear memory 65000 x 65000 65000 x 65000
Maximum width and height for a 2D texture reference bound to a CUDA array supporting texture gather N/A 16384 x 16384
Maximum width, height, and number of layers for a 2D layered texture reference 8192 x 8192 x 512 16384 x 16384 x 2048
Maximum width, height, and depth for a 3D texture reference bound to a CUDA array 2048 x 2048 x 2048 4096 x 4096 x 4096
Maximum width (and height) for a cubemap texture reference N/A 16384
Maximum width (and height) and number of layers for a cubemap layered texture reference N/A 16384 x 2046
Maximum number of textures that can be bound to a kernel 128 256
Maximum width for a 1D surface reference bound to a CUDA array N/A 65536
Maximum width and number of layers for a 1D layered surface reference 65536 x 2048
Maximum width and height for a 2D surface reference bound to a CUDA array 65536 x 32768
Maximum width, height, and number of layers for a 2D layered surface reference 65536 x 32768 x 2048
Maximum width, height, and depth for a 3D surface reference bound to a CUDA array 65536 x 32768 x 2048
Maximum width (and height) for a cubemap surface reference bound to a CUDA array 32768
Maximum width (and height) and number of layers for a cubemap layered surface reference 32768 x 2046
Maximum number of surfaces that can be bound to a kernel 8 16
Maximum number of instructions per kernel 2 million 512 million

### G.2. Floating-Point Standard

All compute devices follow the IEEE 754-2008 standard for binary floating-point arithmetic with the following deviations:

• There is no dynamically configurable rounding mode; however, most of the operations support multiple IEEE rounding modes, exposed via device intrinsics;
• There is no mechanism for detecting that a floating-point exception has occurred and all operations behave as if the IEEE-754 exceptions are always masked, and deliver the masked response as defined by IEEE-754 if there is an exceptional event; for the same reason, while SNaN encodings are supported, they are not signaling and are handled as quiet;
• The result of a single-precision floating-point operation involving one or more input NaNs is the quiet NaN of bit pattern 0x7fffffff;
• Double-precision floating-point absolute value and negation are not compliant with IEEE-754 with respect to NaNs; these are passed through unchanged;
• For single-precision floating-point numbers on devices of compute capability 1.x:
• Denormalized numbers are not supported; floating-point arithmetic and comparison instructions convert denormalized operands to zero prior to the floating-point operation;
• Underflowed results are flushed to zero;
• Some instructions are not IEEE-compliant:
• Addition and multiplication are often combined into a single multiply-add instruction (FMAD), which truncates (i.e., without rounding) the intermediate mantissa of the multiplication;
• Division is implemented via the reciprocal in a non-standard-compliant way;
• Square root is implemented via the reciprocal square root in a non-standard-compliant way;
• For addition and multiplication, only round-to-nearest-even and round-towards-zero are supported via static rounding modes; directed rounding towards +/- infinity is not supported.

To mitigate the impact of these restrictions, IEEE-compliant software (and therefore slower) implementations are provided through the following intrinsics (c.f. Intrinsic Functions):

• __fmaf_r{n,z,u,d}(float, float, float): single-precision fused multiply-add with IEEE rounding modes,
• __frcp_r[n,z,u,d](float): single-precision reciprocal with IEEE rounding modes,
• __fdiv_r[n,z,u,d](float, float): single-precision division with IEEE rounding modes,
• __fsqrt_r[n,z,u,d](float): single-precision square root with IEEE rounding modes,
• __fsub_r[u,d](float, float): single-precision subtraction with IEEE directed rounding,
• __fmul_r[u,d](float, float): single-precision multiplication with IEEE directed rounding;
• For double-precision floating-point numbers on devices of compute capability 1.x:
• Round-to-nearest-even is the only supported IEEE rounding mode for reciprocal, division, and square root.

When compiling for devices without native double-precision floating-point support, i.e., devices of compute capability 1.2 and lower, each double variable is converted to single-precision floating-point format (but retains its size of 64 bits) and double-precision floating-point arithmetic gets demoted to single-precision floating-point arithmetic.

For devices of compute capability 2.x and higher, code must be compiled with -ftz=false, -prec-div=true, and -prec-sqrt=true to ensure IEEE compliance (this is the default setting; see the nvcc user manual for description of these compilation flags); code compiled with -ftz=true, -prec-div=false, and -prec-sqrt=false comes closest to the code generated for devices of compute capability 1.x.

• FMAD for single precision on devices of compute capability 1.x,
• FFMA for single precision on devices of compute capability 2.x and higher.

As mentioned above, FMAD truncates the mantissa prior to use it in the addition. FFMA, on the other hand, is an IEEE-754(2008) compliant fused multiply-add instruction, so the full-width product is being used in the addition and a single rounding occurs during generation of the final result. While FFMA in general has superior numerical properties compared to FMAD, the switch from FMAD to FFMA can cause slight changes in numeric results and can in rare circumstances lead to slightly larger error in final results.

In accordance to the IEEE-754R standard, if one of the input parameters to fminf(), fmin(), fmaxf(), or fmax() is NaN, but not the other, the result is the non-NaN parameter.

The conversion of a floating-point value to an integer value in the case where the floating-point value falls outside the range of the integer format is left undefined by IEEE-754. For compute devices, the behavior is to clamp to the end of the supported range. This is unlike the x86 architecture behavior.

The behavior of integer division by zero and integer overflow is left undefined by IEEE-754. For compute devices, there is no mechanism for detecting that such integer operation exceptions have occurred. Integer division by zero yields an unspecified, machine-specific value.

http://developer.nvidia.com/content/precision-performance-floating-point-and-ieee-754-compliance-nvidia-gpus includes more information on the floating point accuracy and compliance of NVIDIA GPUs.

### G.3.1. Architecture

For devices of compute capability 1.x, a multiprocessor consists of:

• 8 CUDA cores for arithmetic operations (see Arithmetic Instructions for throughputs of arithmetic operations),
• 1 double-precision floating-point unit for double-precision floating-point arithmetic operations (this is only for devices of compute capability 1.3 and above),
• 2 special function units for single-precision floating-point transcendental functions (these units can also handle single-precision floating-point multiplications),
• 1 warp scheduler.

To execute an instruction for all threads of a warp, the warp scheduler must therefore issue the instruction over:

• 4 clock cycles for an integer or single-precision floating-point arithmetic instruction,
• 32 clock cycles for a double-precision floating-point arithmetic instruction (this is only for devices of compute capability 1.3 and above),
• 16 clock cycles for a single-precision floating-point transcendental instruction.

A multiprocessor also has a read-only constant cache that is shared by all functional units and speeds up reads from the constant memory space, which resides in device memory.

Multiprocessors are grouped into Texture Processor Clusters (TPCs). The number of multiprocessors per TPC is:

• 2 for devices of compute capabilities 1.0 and 1.1,
• 3 for devices of compute capabilities 1.2 and 1.3.

Each TPC has a read-only texture cache that is shared by all multiprocessors and speeds up reads from the texture memory space, which resides in device memory. Each multiprocessor accesses the texture cache via a texture unit that implements the various addressing modes and data filtering mentioned in Texture and Surface Memory.

The local and global memory spaces reside in device memory and are not cached.

### G.3.2. Global Memory

A global memory request for a warp is split into two memory requests, one for each half-warp, that are issued independently. Devices of Compute Capability 1.0 and 1.1 and Devices of Compute Capability 1.2 and 1.3 describe how the memory accesses of threads within a half-warp are coalesced into one or more memory transactions depending on the compute capability of the device. Figure 16 shows some examples of global memory accesses and corresponding memory transactions based on compute capability.

The resulting memory transactions are serviced at the throughput of device memory.

#### Devices of Compute Capability 1.0 and 1.1

To coalesce, the memory request for a half-warp must satisfy the following conditions:

• The size of the words accessed by the threads must be 4, 8, or 16 bytes;
• If this size is:
• 4, all 16 words must lie in the same 64-byte segment,
• 8, all 16 words must lie in the same 128-byte segment,
• 16, the first 8 words must lie in the same 128-byte segment and the last 8 words in the following 128-byte segment;
• Threads must access the words in sequence: The kth thread in the half-warp must access the kth word.

If the half-warp meets these requirements, a 64-byte memory transaction, a 128-byte memory transaction, or two 128-byte memory transactions are issued if the size of the words accessed by the threads is 4, 8, or 16, respectively. Coalescing is achieved even if the warp is divergent, i.e., there are some inactive threads that do not actually access memory.

If the half-warp does not meet these requirements, 16 separate 32-