[llvm-dev] RFC: SIMD math-function library

Wed Jul 13 09:45:52 PDT 2016

Hi Naoki,

SLEEF looks very promising!

Are SLEEF routines validated against libm, in addition to libmpfr? Are
performance tracking tests in place to detect execution time or code size
regressions? If these are missing, IMO it would be good to add them to the
roadmap.

best,
vedant

> On Jul 13, 2016, at 4:45 AM, Naoki Shibata via llvm-dev <llvm-dev at lists.llvm.org> wrote:
> 
> 
> Dear LLVM contributors,
> 
> I am Naoki Shibata, an associate professor at Nara Institute of Science and Technology.
> 
> I and Hal Finkel would like to jointly propose to add my vectorized math library to LLVM.
> 
> The library has been available as public domain software for years, I am going to double-license the library if necessary.
> 
> ********
> 
> Below is a proposal to add my vectorized math library, SLEEF [1], for
> evaluating elementary functions (trigonometry, log, exp, etc.) to LLVM. The library can be used directly, or can be targeted by an autovectorization infrastructure. Patches to tie SLEEF into LLVM's autovectorizer have been developed by Hal Finkel as part of the bgclang project (which provides LLVM/Clang ported to the IBM BG/Q supercomputer architecture). Hal has also developed a user-facing header for the library, in the style of Clang's intrinsics headers, which we can use as part of this project. SLEEF has been used as part of bgclang in this way for several years.
> 
> The library currently supports several architectures:
> * x86 - SSE2, FMA4, AVX, AVX2+FMA3
> * ARM - NEON (single-precision only)
> * A pure C (scalar) version
> * Hal's version supports PowerPC/QPX.
> 
> It is faily easy to port to other architectures. The library provides similar functionality to Intel's Short Vector Math Library (available with Intel's Compiler).
> 
> Roadmap:
> --------
> 1) Get agreement on incorporating the library.
> 2) Renaming the public interface to use only the
>   implementation-reserved namespace (i.e. names starting with
>   underscores), as is appropriate for a compiler runtime library.
> 3) Convert the functions to use LLVM's naming conventions (including, if
>   desired, converting the source files to C++ allowing the use of function
>   overloading).
> 4) Create and document a public interface to the library.
> 5) Add support for targeting the library to LLVM's autovectorizer.
> 6) Work with the community to port the library to other architectures.
> 
> Motivation:
> 
> Recent CPUs and GPUs have vectorized FP multipliers and adders for improving throughput of FP computation. In order to extract the maximum computation power from processors with vectorized ALUs, the software has to be vectorized to use SIMD data structures. It is also preferred that conditional branches and scatter/gather memory access are eliminated as much as possible. However, rewriting existing software in this fashion is a very hard and time consuming task that involves converting data structures. Thus, realization of efficient libraries and automatic vectorization is desired.
> 
> In this proposal, we are going to incorporate a vectorized math library,
> currently named SLEEF, into LLVM runtime library. By doing this, elementary functions can be directly evaluated using SIMD data types. We can also expect extra performance improvements by allowing LLVM to automatically target the functions (and inline them with LTO).
> 
> Functionality of the library:
> 
> For each elementary function, the library contains subroutines for evaluation in single precision and double 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 and versions with a few ulp error. Obviously, less accurate versions are faster. Please note that we have 0.5 ulp maximum error when we convert a real number into a floating point number. In Hal's bgclang port, the less accurate versions are used with -ffast-math, and the more-accurate ones otherwise.
> 
> For non-finite inputs and outputs, the library should return the same results as libm. The library is tested if the evaluation error is within the designed limit. The library is tested against high-precision evaluation using the libmpfr library. Especially, we rigorously checked the error of the trigonometric functions when the arguments are close to an integral multiple of PI/2.
> 
> The size of the functions is very small.
> 
> Implementation of the library:
> 
> Basically, each function consists of reduction and kernel. For the kernel, a polynomial approximation is used. The coefficients are carefully set to minimize the number of multiplications and additions while reducing the error. The reduction is devised so that the same kernel can be used for all range of the input arguments. In order to improve the accuracy in the functions with 1-ulp error, double-double calculations are used. Use of fused multiply-add operations, which is quite common recently, can further improve performance of these functions. Some of the implementation techniques used in the library are
> explained in [3].
> 
> [1] https://github.com/shibatch/sleef
> [2] https://github.com/hfinkel/sleef-bgq/blob/master/simd/qpxmath.h
> [3] http://ito-lab.naist.jp/~n-sibata/pdfs/isc10simd.pdf
> 
> 
> ********
> 
> Regards,
> 
> Naoki Shibata
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