FXdiv
Header-only library for division via fixed-point multiplication by inverse
On modern CPUs and GPUs integer division is several times slower than multiplication. FXdiv implements an algorithm to replace an integer division with a multiplication and two shifts. This algorithm improves performance when an application performs repeated divisions by the same divisor.
Features
- Integer division for
uint32_t,uint64_t, andsize_t - Header-only library, no installation or build required
- Compatible with C99, C++, OpenCL, and CUDA
- Uses platform-specific compiler intrinsics for optimal performance
- Covered with unit tests and microbenchmarks
Example
#include <fxdiv.h>
/* Division of array by a constant: reference implementation */
void divide_array_c(size_t length, uint32_t array[], uint32_t divisor) {
for (size_t i = 0; i < length; i++) {
array[i] /= divisor;
}
}
/* Division of array by a constant: implementation with FXdiv */
void divide_array_fxdiv(size_t length, uint32_t array[], uint32_t divisor) {
const struct fxdiv_divisor_uint32_t precomputed_divisor =
fxdiv_init_uint32_t(divisor);
for (size_t i = 0; i < length; i++) {
array[i] = fxdiv_quotient_uint32_t(array[i], precomputed_divisor);
}
}Status
Currently working features:
| Platform | uint32_t | uint64_t | size_t |
|---|---|---|---|
| x86-64 gcc | Works | Works | Works |
| x86-64 clang | Works | Works | Works |
| x86-64 MSVC | Works | Works | Works |
| x86 gcc | Works | Works | Works |
| x86 clang | Works | Works | Works |
| x86 MSVC | Works | Works | Works |
| ARMv7 gcc | Works | Works | Works |
| ARMv7 clang | Works | Works | Works |
| ARMv7 MSVC* | Compiles | Compiles | Compiles |
| ARM64 gcc | Works | Works | Works |
| ARM64 clang | Works | Works | Works |
| ARM64 MSVC* | Compiles | Compiles | Compiles |
| PPC64 gcc | Works | Works | Works |
| WAsm clang | Works | Works | Works |
| Asm.js clang | Works | Works | Works |
| PNaCl clang | Works | Works | Works |
| CUDA | Untested | Untested | Untested |
| OpenCL | Untested | Untested | Untested |
*ARMv7 and ARM64 builds with MSVC are presumed to work, but were only verified to compile successfully
References
- Granlund, Torbjörn, and Peter L. Montgomery. "Division by invariant integers using multiplication." In ACM SIGPLAN Notices, vol. 29, no. 6, pp. 61-72. ACM, 1994. Available: gmplib.org/~tege/divcnst-pldi94.pdf