1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
|
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
<meta name="viewport" content="width=device-width, initial-scale=0.4"/>
<meta name="description" content="SLEEF implements vectorized C99 math functions. It utilizes vector extensions including SSE2, AVX, AVX2, AVX512F for x86, and Advanced SIMD for ARM processors." />
<meta name="google" content="notranslate" />
<link rel="canonical" href="https://sleef.org/" />
<link rel="icon" href="favicon.png" />
<link rel="stylesheet" type="text/css" href="texlike.css"/>
<link rel="stylesheet" type="text/css" href="sleef.css"/>
<title>SLEEF Vectorized Math Library</title>
</head>
<body translate="no" class="notranslate">
<h1>SLEEF Vectorized Math Library<img src="sleeflogo3.png" alt="logo" width="25%" height="25%" style="float: right" /></h1>
<ul class="none" style="font-family: arial, sansserif; margin-top: 1.0cm;">
<li><a class="underlined" style="color:#a00000;" href="https://github.com/shibatch/sleef/releases">Download the latest version</a></li>
<li><a class="underlined" href="https://sleef.org/">Latest documentation on the web</a></li>
<li><a class="underlined" href="https://github.com/shibatch/sleef">GitHub repository</a></li>
<li><a class="underlined" href="https://sourceforge.net/p/sleef/mailman/">Mailing list</a></li>
<li><a class="underlined" href="https://sourceforge.net/p/sleef/discussion/general/">Discussion forum</a></li>
</ul>
<h2>Table of contents</h2>
<ul class="none" style="font-family: arial, sansserif; padding-left: 0.5cm;">
<li><a class="underlined" href="index.xhtml">Introduction</a>
<ul class="disc">
<li><a href="index.xhtml#overview">Overview</a></li>
<li><a href="index.xhtml#environment">Supported environments</a></li>
<!--<li><a href="index.xhtml#compatibility">Compatibility with other libraries</a></li>-->
<!--<li><a href="index.xhtml#porting">Porting</a></li>-->
<li><a href="index.xhtml#credit">Credit</a></li>
<li><a href="index.xhtml#partners">Partners</a></li>
<li><a href="index.xhtml#license">License</a></li>
<li><a href="index.xhtml#history">History of this software</a></li>
<li><a href="index.xhtml#related">Related projects</a></li>
</ul>
</li>
<li> </li>
<li><a class="underlined" href="compile.xhtml">Compiling and installing the library</a></li>
<li><a class="underlined" href="purec.xhtml">Math library reference</a></li>
<li><a class="underlined" href="dft.xhtml">DFT library reference</a></li>
<li><a class="underlined" href="misc.xhtml">Other tools included in the package</a></li>
<li><a class="underlined" href="benchmark.xhtml">Benchmark results</a></li>
<li><a class="underlined" href="additional.xhtml">Additional notes</a></li>
</ul>
<h2 id="overview">Overview</h2>
<p class="noindent">
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 of
modern processors. SLEEF is designed to fully utilize SIMD
computation by reducing the use of conditional branches and
scatter/gather memory access. Our <a class="underlined"
href="benchmark.xhtml">benchmarks</a> 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.
</p>
<p>
The library contains subroutines for 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 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 C99 standard. The library is rigorously
tested if the evaluation error is within the designed limit. The
library is tested against high-precision evaluation
using <a class="underlined" href="http://www.mpfr.org/">the libmpfr
library</a>. Especially, we carefully checked the error of the
trigonometric functions when the arguments are close to an integral
multiple of <i class="math">π</i>/2.
</p>
<p>
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
<a class="underlined"
href="http://www.boost.org/users/license.html">BSL</a>, which is a
permissive open source license. The subroutines can utilize long
vectors up to 2048 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. <a class="underlined"
href="https://github.com/shibatch/sleef/wiki/DFT-Performance">Preliminary
results of benchmark</a> are now available.
</p>
<h2 id="environment">Supported environments</h2>
<p class="noindent">
This library currently supports several SIMD architectures :
</p>
<div><br/></div>
<ul class="disc">
<li><a href="x86.xhtml">x86 - SSE2, SSE4.1, AVX, FMA4, AVX2+FMA3, AVX512F</a></li>
<li><a href="aarch64.xhtml">AArch64 - Advanced SIMD, SVE</a></li>
<li><a href="aarch32.xhtml">AArch32 - NEON</a></li>
<li><a href="ppc64.xhtml">PowerPC64 - VSX</a></li>
</ul>
<div><br/></div>
<p>
In addition to the SIMD implementation, Pure C (scalar) version is
provided. For x86 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.
</p>
<div style="margin-top: 1.0cm;"></div>
<table style="text-align:center;" align="center">
<tr align="center">
<td class="caption">Table 1.1: Environment support matrix</td>
</tr>
<tr align="center">
<td>
<table class="lt">
<tr>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
</tr>
<tr>
<td class="lt-br"></td>
<td class="lt-hl"></td>
<td class="lt-blr" align="center">GCC</td>
<td class="lt-br" align="center">Clang</td>
<td class="lt-br" align="center">Intel Compiler</td>
<td class="lt-b" align="center">MSVC</td>
</tr>
<tr>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
<td class="lt-hl"></td>
</tr>
<tr>
<td class="lt-r" align="left">x86 (64bit), Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Supported</td>
<td class="lt-r" align="center">Supported(*1)</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">x86 (32bit), Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported(*2)</td>
<td class="lt-r" align="center">Supported(*2)</td>
<td class="lt-r" align="center"></td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">AArch64, Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Supported</td>
<td class="lt-r" align="center">N/A</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">AArch32, Linux</td>
<td></td>
<td class="lt-lr" align="center">Supported(*3)</td>
<td class="lt-r" align="center">Supported(*3)</td>
<td class="lt-r" align="center">N/A</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">PowerPC, Linux</td>
<td></td>
<td class="lt-lr" align="center"></td>
<td class="lt-r" align="center">Supported(*4)</td>
<td class="lt-r" align="center">N/A</td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-r" align="left">x86 (64bit), OS X</td>
<td></td>
<td class="lt-lr" align="center">Supported</td>
<td class="lt-r" align="center">Supported</td>
<td class="lt-r" align="center"></td>
<td class="lt-" align="center">N/A</td>
</tr>
<tr>
<td class="lt-br" align="left">x86 (64bit), Windows</td>
<td class="lt-hl"></td>
<td class="lt-blr" align="center">Supported(Cygwin)(*5)</td>
<td class="lt-br" align="center">Supported(Cygwin)(*5)</td>
<td class="lt-br" align="center"></td>
<td class="lt-b" align="center">Supported</td>
</tr>
</table>
</td>
</tr>
</table>
<div style="margin-top: 2.0cm;"></div>
<p>
The supported compiler versions are as follows.
</p>
<div><br/></div>
<ul class="disc">
<li>GCC : version 5 and later</li>
<li>Clang : version 3.9 and later</li>
<li>Intel Compiler : ICC version 17</li>
<li>MSVC : Visual Studio 2017</li>
</ul>
<div><br/></div>
<p>
*1 FMA4 is not supported by Intel Compiler.
</p>
<p>
*2 SSE2 is required to run the scalar functions on 32-bit x86
architecture. x87 is not supported.
</p>
<p>
*3 NEON has only single precision support. The computation results
are not in full accuracy since NEON is not IEEE 754-compliant.
</p>
<p>
*4 Clang-5.0 and later are supported.
</p>
<p>
*5 AVX functions are not supported for Cygwin, since AVX is not
supported by Cygwin ABI.
</p>
<div style="margin-top: 1.0cm;"></div>
<p>
All functions in the library are thread safe unless otherwise noted.
</p>
<h2 id="credit">Credit</h2>
<ul class="disc">
<li>The main developer is <a class="underlined"
href="https://github.com/shibatch">Naoki Shibata</a>
( <a href="mailto:shibatch@users.sourceforge.net">shibatch@users.sourceforge.net</a> )
at Nara Institute of Science and Technology.</li>
<li><a class="underlined"
href="https://github.com/fpetrogalli-arm">Francesco Petrogalli</a>
at ARM Ltd. contributed the helper for AArch64 (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.</li>
<li><a class="underlined" href="https://github.com/hfinkel">Hal Finkel</a> at Argonne
Leadership Computing Facility is now working
on <a class="underlined"
href="https://reviews.llvm.org/D24951">importing and adapting SLEEF
as an LLVM runtime</a>. He also gave precious comments.</li>
<li><a class="underlined" href="https://github.com/diaena">Diana
Bite</a> at University of Manchester and <a class="underlined"
href="https://github.com/xoofx">Alexandre Mutel</a> at Unity
Technologies worked on migrating the build system to
cmake.</li>
<li><a class="underlined" href="https://github.com/blu">Martin
Krastev</a> at Chaos Group contributed faster implementation of fmin
and fmax functions.</li>
</ul>
<h2 id="partners">Partner institutes and corporations</h2>
<table style="margin-top:1cm;">
<tr><td> </td></tr>
<tr>
<td style="text-align:center;"><a href="https://www.naist.jp/en/"><img src="naistlogo.svg"
height="135px" alt="NAIST logo"/></a></td>
<td style="vertical-align: top;">
<p class="noindent" style="margin-left:2em;">
The <a class="underlined" href="http://ito-lab.naist.jp/">Mobile
Computing Lab</a> at Division of Information Science of Nara Institute
of Science and Technology participates through Naoki Shibata.
</p>
</td>
</tr>
<tr><td> </td></tr>
<tr><td> </td></tr>
<tr><td> </td></tr>
<tr>
<td style="text-align:center;"><a href="https://www.arm.com/"><img src="https://sleef.org/Arm-logo-blue-pms313.svg" alt="ARM logo"
height="60px" /></a></td>
<td style="vertical-align: top;">
<p class="noindent" style="margin-left:2em;">
As the leading IP company in semiconductors
design, <a class="underlined" href="https://www.arm.com/">ARM</a>
participates through Francesco Petrogalli.
</p>
</td>
</tr>
<tr><td> </td></tr>
<tr><td> </td></tr>
<tr><td> </td></tr>
<tr>
<td style="text-align:center;"><a href="https://unity3d.com/"><img src="https://sleef.org/Unity_Technologies_logo.svg" alt="Unity Technologies logo"
height="92px" /></a></td>
<td style="vertical-align: top;">
<p class="noindent" style="margin-left:2em;">As the leading
company in developing a video game engine, <a class="underlined"
href="https://unity3d.com/">Unity Technologies</a> participates
through Alexandre Mutel.
</p>
</td>
</tr>
<tr><td> </td></tr>
</table>
<h2 id="license">License</h2>
<p class="noindent">
SLEEF is distributed under <a class="underlined"
href="http://www.boost.org/LICENSE_1_0.txt">Boost Software License
Version 1.0</a>.
</p>
<p class="noindent" style="margin-top: 0.8cm;">
<a class="nothing" href="https://opensource.org/">
<img src="osi_logo.png" width="90" height="103" alt="open source logo" style="position:relative; top:3px;"/>
</a>
Boost Software License is <a class="underlined"
href="https://opensource.org/licenses/BSL-1.0">OSI-certified</a>.
See <a class="underlined"
href="http://www.boost.org/users/license.html">this page</a> for more
information about Boost Software License.
</p>
<h2 id="history">History</h2>
<h4>3.3.1 (Released on Aug 21, 2018)</h4>
<ul class="disc">
<li>i386 build problem is fixed</li>
<li>FreeBSD support is added</li>
<li>Trigonometric functions now evaluate correctly with full FP
domain. (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/197">#210</a>)</li>
</ul>
<h4>3.3 (Released on July 6, 2018)</h4>
<ul class="disc">
<li>AArch64 SVE target support is added (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/180">#180</a>, <a class="underlined"
href="https://github.com/shibatch/sleef/pull/182">#182</a>)</li>
<li>DFT is now faster (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/186">#186</a>)</li>
<li>3.5-ULP hyperbolic functions are added (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/192">#192</a>)</li>
<li>PowerPC VSX target support is added (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/195">#195</a>)</li>
<li>Modified Payne-Hanek argument reduction is added to the
trigonometric functions in libsleef (PR <a class="underlined"
href="https://github.com/shibatch/sleef/pull/197">#197</a>)</li>
</ul>
<h4>3.2 (Released on Feb 26, 2018)</h4>
<ul class="disc">
<li>The whole build system of the project migrated from makefiles to
cmake. The makefile build system is now removed.</li>
<li>GNUABI version of the library with compatibility tests is
added.</li>
<li>Benchmarks that compare `libsleef` vs `SVML` on X86 Linux are
available in the project tree under src/libm-benchmarks
directory.</li>
<li>Extensive upstream testing via Travis CI and Appveyor</li>
<li>log2 is added.</li>
<li>The library can be compiled to an LLVM bitcode object</li>
<li>Added masked interface to the library to support AVX512F masked
vectorization.</li>
<li>Use native instructions if available for `sqrt`.</li>
<li>Removed `libm` dependency.</li>
<li>fmod(FP remainder), asin, acos, log, pow, log10, exp2, exp10 and
log1p functions are now faster.</li>
<li>Fixed a bug that was making the error of sinpi, cospi, sincospi,
and tgamma functions larger than the specifications on very rare
occasions.</li>
<li>Fixed a bug that was preventing the dispatcher from choosing the
FMA4 implementation.</li>
</ul>
<h4>3.1 (Released on July 19, 2017)</h4>
<ul class="disc">
<li>Added AArch64 support</li>
<li>Implemented the remaining C99 math functions : lgamma, tgamma,
erf, erfc, fabs, copysign, fmax, fmin, fdim, trunc, floor, ceil,
round, rint, modf, ldexp, nextafter, frexp, hypot, and fmod.</li>
<li>Added dispatcher for x86 functions</li>
<li>Improved reduction of trigonometric functions</li>
<li>Added support for 32-bit x86, Cygwin, etc.</li>
<li>Improved tester</li>
<li>Etc.</li>
</ul>
<h4>3.0 (Released on Feb. 7, 2017)</h4>
<ul class="disc">
<li>New API is defined</li>
<li>Functions for DFT are added</li>
<li>sincospi functions are added</li>
<li>gencoef now supports single, extended and quad precision in addition to double precision</li>
<li>Linux, Windows and Mac OS X are supported</li>
<li>GCC, Clang, Intel Compiler, Microsoft Visual C++ are supported</li>
<li>The library can be compiled as DLLs</li>
<li>Files needed for creating a debian package are now included</li>
</ul>
<h4>2.120 (Released on Jan. 30, 2017)</h4>
<ul class="disc">
<li>Relicensed to Boost Software License Version 1.0</li>
</ul>
<h4>2.110 (Released on Dec. 11, 2016)</h4>
<ul class="disc">
<li>The valid range of argument is extended for trig functions</li>
<li>Specification of each functions regarding to the domain and accuracy is added</li>
<li>A coefficient generation tool is added</li>
<li>New testing tools are introduced</li>
<li>Following functions returned incorrect values when the argument is very large or small : exp, pow, asinh, acosh</li>
<li>SIMD xsin and xcos returned values more than 1 when FMA is enabled</li>
<li>Pure C cbrt returned incorrect values when the argument is negative</li>
<li>tan_u1 returned values with more than 1 ulp of error on rare occasions</li>
<li>Removed support for Java language(because no one seems using this)</li>
</ul>
<h2 id="related">Related projects and links</h2>
<ul class="disc">
<li>SLEEF is now included in <a class="underlined"
href="https://developer.arm.com/products/software-development-tools/hpc/documentation/vector-math-routines">
Arm Compiler for HPC</a>.</li>
<li>Mustafa A. Mohamad is developing <a class="underlined"
href="https://github.com/musm/SLEEF.jl">a pure Julia port of the
SLEEF math library</a>.</li>
<li>Hal Finkel has <a class="underlined"
href="https://github.com/hfinkel/sleef-bgq">adapted SLEEF to
PowerPC/QPX</a>. SLEEF is running on Mira IBM BG/Q supercomputer at
Argonne National Laboratory.</li>
<li>SLEEF is adopted in the following projects.
<ul class="circle">
<li><a href="http://www.menuetos.net/sc151.html">MenuetOS</a></li>
<li><a href="https://github.com/Beep6581/RawTherapee/tree/dev/rtengine">RawTherapee</a></li>
<li><a href="http://buraphakit.sourceforge.net/BASIC.shtml">John's ECMA-55 Minimal BASIC Compiler</a></li>
<li><a href="https://github.com/pocl/pocl/tree/master/lib/kernel/sleef">Portable Computing Language(pocl)</a></li>
<li><a href="https://github.com/pytorch/pytorch/pull/6725">PyTorch</a></li>
</ul>
</li>
<li style="margin-top: 1em;"><a class="underlined"
href="https://software.intel.com/en-us/node/524289">Intel Short
Vector Math Library (SVML)</a> is a commercial library of vectorized
math functions, which provides similar functionality to
SLEEF. Recently, some of the codes are published as free software,
and it is now <a class="underlined"
href="https://sourceware.org/git/?p=glibc.git;a=tree;f=sysdeps/x86_64/fpu/multiarch">
a part of glibc</a>.</li>
</ul>
<p class="footer">
Copyright © 2018 SLEEF Project.<br/>
SLEEF is open-source software and is distributed under the Boost Software License, Version 1.0.
</p>
<!--TEST-->
</body>
</html>
|