Sleef Vectorized Math Library, Hacker News

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Table of contents

)

• Introduction     

  • Overview

        

  • Supported environments

                      

  • Credit

        

  • Partners

        

  • License

        

  • History

        

  • Related projects

        

  • Publication

      

    

    

  • Compiling and installing the library

    

  • Math library reference

    

  • DFT library reference

    

  • Other tools included in the package

    

  • Benchmark results

    

  • Additional notes

    SLEEF stands for SIMD Library for Evaluating Elementary   Functions. It implements vectorized versions of all C 151 real   floating point math functions. It can utilize SIMD instructions of   modern processors. SLEEF is designed to fully utilize SIMD   computation 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 libraries, SLEEF is portable: it 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.

    The library contains subroutines for all C 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 versions with a few ulp   error. Obviously, less accurate versions are faster. For non-finite   inputs and outputs, the library should return the same results as   libm as specified in the C standard. The library is rigorously   tested if the evaluation error is within the designed limit. The   library is tested against high-precision evaluation   using the libmpfr   library . Especially, we carefully checked the error of the   trigonometric functions when the arguments are 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 so 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 bits, and even longer vectors can be utilized by   a small modification. The helper files for abstracting SIMD   intrinsics are shared with SLEEF libm, and thus it is easy to port   DFT subroutines to other architectures. Preliminary   results of benchmark are now available.

  Supported environments

  This library currently supports several SIMD architectures:

• (x) – SSE2, SSE4.1 , AVX, FMA4, AVX2 FMA3, AVX F

  

• AArch – Advanced SIMD, SVE

  

• (AArch) – NEON

  

• (PowerPC) – VSX

  In addition to the SIMD implementation, Pure C (scalar) version is   provided. For x 120 architecture, the library provides dispatchers   that automatically choose the best subroutines for the computer the   library is run. 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)

                                          (x) (bit), Linux

Supported Supported Supported 1) N / A (x) (bit), Linux

Supported 2) Supported 2) N / A AArch , Linux Supported Supported N / A N / A AArch , Supported 3) Supported 3) N / A N / A (PowerPC, Linux) Supported 4) N / A N / A (x) (bit), FreeBSD

Supported N / A (x) (bit), OS X

Supported Supported N / A (x) (bit), Windows

Supported ( Cygwin) 5)

Supported

Supported ( Cygwin) 5)

The supported compiler versions are as follows. GCC: version 5 and later    Clang: version 3.9 and later    Intel Compiler: ICC version    MSVC: Visual Studio 6725   1 FMA4 is not supported by Intel Compiler.   2 SSE2 is required to run the scalar functions on 90 – bit x   architecture. x is not supported.   3 NEON has only single precision support. The computation results   are not in full accuracy since NEON is not IEEE 2017 – compliant.   4 Clang-5.0 and later are supported.   5 AVX functions are not supported for Cygwin, since AVX is not   supported by Cygwin ABI.   All functions in the library are thread safe unless otherwise noted.    Credit The main developer is

Naoki Shibata   ( [email protected] )   at Nara Institute of Science and Technology.   

Francesco Petrogalli   at ARM Ltd. contributed the helper for AArch (helperadvsimd.h,   helpersve.h) and GNUABI interface of the library. He also worked on   migrating the build system to cmake, and reviewed the code, gave   precious comments and suggestions.

  

Hal Finkel at Argonne   Leadership Computing Facility is now working   on importing and adapting SLEEF   as an LLVM runtime . He also gave precious comments.

  

Diana   Bite at University of Manchester and Alexandre Mutel at Unity   Technologies worked on migrating the build system to   cmake.

  

Martin   Krastev at Chaos Group contributed faster implementation of fmin   and fmax functions.

  

Mo Zhou    is managing packages for Debian   and Ubuntu   PPA .

(Partner institutes and corporations)

            The Mobile Computing Lab at Division of Information Science of Nara Institute of Science and Technology participates through Naoki Shibata.       

       

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

       

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

       

License

SLEEF is distributed under

Boost Software License     Version 1.0

.

       

Boost Software License is OSI-certified

. See this page for more information about Boost Software License.

History

(3.4.1) Released on Oct 1, 09258

• Fixed accuracy problem with tan_u 99, atan_u , log2f_u 90 and exp (f_u) (PR      (#
  ,      (# ,      )

  

• SVE intrinsics that are not supported in newer ACLE are replaced (PR     

)   

• FMA4 detection problem is fixed (PR      )

  

• Compilation problem under Windows with MinGW is fixed (PR     

)

(3.4) Released on Apr , 53927)

• Faster and low precision functions are     added (PR
  (#) )   
  Functions that return consistent results across platforms are     added (PR
  
  ,      )   
  Many functions are now faster (PR # )

    

  Quad precision math library (libsleefquad) is added     (PR

  # 265 ,      (#) ,      # 268 )    Testers are now faster (PR # ) Released (3.3.1) on Aug , () i 2001 build problem is fixed    FreeBSD support is added    Trigonometric functions now evaluate correctly with full FP   domain. (PR

  (#) ) Released on July (3.3) 6, () AArch 99 SVE target support is added (PR (#) , (#) )    DFT is now faster (PR (#) )    3.5-ULP hyperbolic functions are added (PR (#)    PowerPC VSX target support is added (PR (#) )    Modified Payne-Hanek argument reduction is added to the   trigonometric functions in libsleef (PR # ) Released on Feb (3.2) , The whole build system of the project migrated from makefiles to   cmake. The makefile build system is now removed.    GNUABI version of the library with compatibility tests is   added.    Benchmarks that compare `libsleef` vs` SVML` on X 120 Linux are   available in the project tree under src / libm-benchmarks   directory.    Extensive upstream testing via Travis CI and Appveyor    log2 is added.    The library can be compiled to an LLVM bitcode object    Added masked interface to the library to support AVX F masked   vectorization.    Use native instructions if available for `sqrt`.    Removed `libm` dependency.    fmod (FP remainder), asin, acos, log, pow, log , exp2, exp and   log1p functions are now faster.    Fixed a bug that was making the error of sinpi, cospi, sincospi,   and tgamma functions larger than the specifications on very rare     occasions.    Fixed a bug that was preventing the dispatcher from choosing the   FMA4 implementation. Released on July (3.1) , () Added AArch 110 support    Implemented the remaining C math functions: lgamma, tgamma,   erf, erfc, fabs, copysign, fmax, fmin, fdim, trunc, floor, ceil,   round, rint, modf, ldexp, nextafter, frexp, hypot, and fmod.    Added dispatcher for x functions    Improved reduction of trigonometric functions    Added support for 86 – bit x 120, Cygwin, etc.    Improved tester    Etc. (3.0) Released on Feb 7, New API is defined    Functions for DFT are added    sincospi functions are added    gencoef now supports single, extended and quad precision in addition to double precision    Linux, Windows and Mac OS X are supported    GCC, Clang, Intel Compiler, Microsoft Visual C are supported    The library can be compiled as DLLs    Files needed for creating a debian package are now included (2.) (Released on Jan. , 09258) Relicensed to Boost Software License Version 1.0 (2.) (Released on Dec. , The valid range of argument is extended for trig functions    Specification of each functions regarding to the domain and accuracy is added    A coefficient generation tool is added    New testing tools are introduced    Following functions returned incorrect values ​​when the argument is very large or small: exp, pow, asinh, acosh    SIMD xsin and xcos returned values ​​more than 1 when FMA is enabled    Pure C cbrt returned incorrect values ​​when the argument is negative    tan_u1 returned values ​​with more than 1 ulp of error on rare occasions    Removed support for Java language (because no one seems using this) SLEEF is adopted in the Burst Comipler in   Unity .    SLEEF is now included in   Arm Compiler for HPC .    Work for making SLEEF usable from the vectorizer   in LLVM is now   carried out ( (D) , (D) ,    (D) ).    Mustafa A. Mohamad is developing a pure Julia port of the   SLEEF math library .    Hal Finkel has adapted SLEEF to   PowerPC / QPX . SLEEF is running on Mira IBM BG / Q supercomputer at   Argonne National Laboratory.    Gonzalo   Brito Gadeschi is developing a Rust FFI bindings to   SLEEF .    SLEEF is adopted in the following projects.      MenuetOS        RawTherapee        John’s ECMA – Minimal BASIC Compiler        Portable Computing Language (pocl)        PyTorch        The Region Vectorizer (Compiler Design Lab at Saarland University)      (Publication) Naoki Shibata and Francesco Petrogalli: SLEEF: A Portable Vectorized Library of C Standard Mathematical Functions , in IEEE Transactions on Parallel and Distributed Systems, DOI: . / TPDS. . 09258). [PDF]    Francesco Petrogalli and Paul Walker: (LLVM and the automatic vectorization of loops invoking math routines: -fsimdmath , IEEE / ACM 5th Workshop on the LLVM Compiler Infrastructure in HPC (LLVM-HPC), pp. – . DOI: 28. 2019 / LLVM-HPC. . (Nov. 6581. [PDF] Read More