SLEEF Vectorized Math Librarylogo

Table of contents


SLEEF stands for SIMD Library for Evaluating Elementary Functions. It implements vectorized versions of all C99 real floating point math functions. It can utilize SIMD instructions that are available on modern processors. SLEEF is designed to effciently perform computation with SIMD instruction by reducing the use of conditional branches and scatter/gather memory access. Our benchmarks show that the performance of SLEEF is comparable to that of the best commercial library. Unlike vendor-tuned assembly-optimized libraries, SLEEF can be easily ported to other architectures by writing a helper file, which is a thin abstraction layer of SIMD intrinsics. SLEEF is also designed to work with various operating systems and compilers. Link time optimization can be used to reduce the overhead of calling functions.

The library contains implementations of all C99 real FP math functions in double precision and single precision. Different accuracy of the results can be chosen for a subset of the elementary functions; for this subset there are versions with up to 1 ULP error (which is the maximum error, not the average) and even faster versions with a few ULPs of error. For non-finite inputs and outputs, the functions return correct results as specified in the C99 standard. All the functions in the library are thoroughly tested and confirmed that the evaluation error is within the designed limit, by comparing the returned values against high-precision evaluation using the GNU MPFR Library. Especially, we carefully checked the error of the trigonometric functions with arguments close to an integral multiple of π/2.

SLEEF also includes subroutines for discrete Fourier transform(DFT). These subroutines are fully vectorized, heavily unrolled, and parallelized in such a way that modern SIMD instructions and multiple cores can be utilized for efficient computation. It has an API similar to that of FFTW for easy migration, and distributed under BSL, which is a permissive open source license. The subroutines can utilize long vectors up to 2048 bits. The helper files for abstracting SIMD intrinsics are shared with SLEEF libm, and thus it is easy to port the DFT subroutines to other architectures. Preliminary results of benchmark are now available.

Supported environments

This library currently supports several SIMD architectures :

In addition to the SIMD implementation, Pure C (scalar) version is provided. The library provides dispatchers that automatically choose the best subroutines for the computer on which the library is executed. The supported combinations of the architecture, operating system and compiler are shown in Table 1.1.

Table 1.1: Environment support matrix
GCC Clang Intel Compiler MSVC
x86_64, Linux Supported Supported Supported N/A
AArch64, Linux Supported Supported N/A N/A
AArch32, Linux Supported(*1) Supported(*1) N/A N/A
PowerPC, Linux Supported Supported N/A N/A
System/390, Linux Supported Supported N/A N/A
x86_64, FreeBSD Supported N/A N/A
x86_64, OS X Supported(*2) Supported(*2) N/A
x86 (32 bit), Linux Supported Supported N/A
x86_64, Windows Supported(Cygwin)(*3) Supported(*3) Supported

The supported compiler versions are as follows.

*1 NEON has only single precision support. The computation results are not in full accuracy because NEON is not IEEE 754-compliant.

*2 LTO is not supported.

*3 AVX functions are not supported for Cygwin, because AVX is not supported by Cygwin ABI.

All functions in the library are thread safe unless otherwise noted.


Partner institutes and corporations

NAIST logo

Division of Information Science of Nara Institute of Science and Technology participates through Naoki Shibata.

ARM logo

As the leading IP company in semiconductors design, ARM participates through Francesco Petrogalli.

Unity Technologies logo

As the leading company in developing a video game engine, Unity Technologies participates through Alexandre Mutel.



SLEEF is distributed under Boost Software License Version 1.0.

open source logo   Boost Software License is OSI-certified. See this page for more information about Boost Software License.


3.6.0 (Not released yet)

3.5.1 (Released on Sep 15, 2020)

3.5 (Released on Sep 1, 2020)

3.4.1 (Released on Oct 1, 2019)

3.4 (Released on Apr 28, 2019)

3.3.1 (Released on Aug 21, 2018)

3.3 (Released on July 6, 2018)

3.2 (Released on Feb 26, 2018)

See Changelog for older changes.