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  1. 63058ef Export LICENSE file in Bazel build by Marat Dukhan · 3 years ago upstream/master
  2. b408327 Disable _udiv64 and _udiv128 intrinsics on clang-cl and icpc by Marat Dukhan · 3 years, 8 months ago
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MIT License Build Status

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.


  • Integer division for uint32_t, uint64_t, and size_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


#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 =
  for (size_t i = 0; i < length; i++) {
    array[i] = fxdiv_quotient_uint32_t(array[i], precomputed_divisor);


Currently working features:

x86-64 gccWorksWorksWorks
x86-64 clangWorksWorksWorks
x86-64 MSVCWorksWorksWorks
x86 gccWorksWorksWorks
x86 clangWorksWorksWorks
x86 MSVCWorksWorksWorks
ARMv7 gccWorksWorksWorks
ARMv7 clangWorksWorksWorks
ARMv7 MSVC*CompilesCompilesCompiles
ARM64 gccWorksWorksWorks
ARM64 clangWorksWorksWorks
ARM64 MSVC*CompilesCompilesCompiles
PPC64 gccWorksWorksWorks
WAsm clangWorksWorksWorks
Asm.js clangWorksWorksWorks
PNaCl clangWorksWorksWorks

*ARMv7 and ARM64 builds with MSVC are presumed to work, but were only verified to compile successfully


  • 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: