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
|
.. _math:
==============
Math Functions
==============
.. include:: ../check.rst
.. raw:: html
<style> .green {color:green} </style>
.. role:: green
.. toctree::
:hidden:
log.rst
stdfix.rst
.. contents:: Table of Contents
:depth: 4
:local:
Source Locations
================
- The main source is located at: `libc/src/math <https://github.com/llvm/llvm-project/tree/main/libc/src/math>`_.
- The tests are located at: `libc/test/src/math <https://github.com/llvm/llvm-project/tree/main/libc/test/src/math>`_.
- The floating point utilities are located at: `libc/src/__support/FPUtil <https://github.com/llvm/llvm-project/tree/main/libc/src/__support/FPUtil>`_.
Implementation Requirements / Goals
===================================
* The highest priority is to be as accurate as possible, according to the C and
IEEE 754 standards. By default, we will aim to be correctly rounded for `all rounding modes <https://en.cppreference.com/w/c/numeric/fenv/FE_round>`_.
The current rounding mode of the floating point environment is used to perform
computations and produce the final results.
- To test for correctness, we compare the outputs with other correctly rounded
multiple-precision math libraries such as the `GNU MPFR library <https://www.mpfr.org/>`_
or the `CORE-MATH library <https://core-math.gitlabpages.inria.fr/>`_.
* Our next requirement is that the outputs are consistent across all platforms.
Notice that the consistency requirement will be satisfied automatically if the
implementation is correctly rounded.
* Our last requirement for the implementations is to have good and predicable
performance:
- The average performance should be comparable to other ``libc``
implementations.
- The worst case performance should be within 10X-20X of the average.
- Platform-specific implementations or instructions could be added whenever it
makes sense and provides significant performance boost.
* For other use cases that have strict requirements on the code size, memory
footprint, or latency, such as embedded systems, we will aim to be as accurate
as possible within the memory or latency budgets, and consistent across all
platforms.
Add a new math function to LLVM libc
====================================
* To add a new math function, follow the steps at: `libc/src/math/docs/add_math_function.md <https://github.com/llvm/llvm-project/tree/main/libc/src/math/docs/add_math_function.md>`_.
Implementation Status
=====================
* To check math functions enabled for Linux:
- `linux-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/x86_64/entrypoints.txt>`_
- `linux-aarch64 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/aarch64/entrypoints.txt>`_
- `linux-aarch32 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/arm/entrypoints.txt>`_
- `linux-riscv64 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/riscv64/entrypoints.txt>`_
* To check math functions enabled for Windows:
- `windows-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/windows/entrypoints.txt>`_
- windows-aarch64 - to be added
* To check math functions enabled for macOS:
- `darwin-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/darwin/x86_64/entrypoints.txt>`_
- `darwin-aarch64 <https://github.com/llvm/llvm-project/tree/main/libc/config/darwin/arm/entrypoints.txt>`_
* To check math functions enabled for GPU:
- `gpu-entrypoints <https://github.com/llvm/llvm-project/tree/main/libc/config/gpu/entrypoints.txt>`_
* To check math functions enabled for embedded system:
- `baremetal-aarch32 <https://github.com/llvm/llvm-project/tree/main/libc/config/baremetal/arm/entrypoints.txt>`_
- baremetal-riscv32 - to be added
Basic Operations
================
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
+==================+==================+=================+========================+======================+========================+========================+============================+
| ceil | |check| | |check| | |check| | |check| | |check| | 7.12.9.1 | F.10.6.1 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| canonicalize | |check| | |check| | |check| | |check| | |check| | 7.12.11.7 | F.10.8.7 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| copysign | |check| | |check| | |check| | |check| | |check| | 7.12.11.1 | F.10.8.1 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| dadd | N/A | N/A | | N/A | | 7.12.14.1 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ddiv | N/A | N/A | | N/A | | 7.12.14.4 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| dfma | N/A | N/A | | N/A | | 7.12.14.5 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| dmul | N/A | N/A | | N/A | | 7.12.14.3 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| dsub | N/A | N/A | | N/A | | 7.12.14.2 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| f16fma | |check| | | | N/A | | 7.12.14.5 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fabs | |check| | |check| | |check| | |check| | |check| | 7.12.7.3 | F.10.4.3 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fadd | N/A | | | N/A | | 7.12.14.1 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fdim | |check| | |check| | |check| | |check| | |check| | 7.12.12.1 | F.10.9.1 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fdiv | N/A | | | N/A | | 7.12.14.4 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ffma | N/A | | | N/A | | 7.12.14.5 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| floor | |check| | |check| | |check| | |check| | |check| | 7.12.9.2 | F.10.6.2 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmax | |check| | |check| | |check| | |check| | |check| | 7.12.12.2 | F.10.9.2 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmaximum | |check| | |check| | |check| | |check| | |check| | 7.12.12.4 | F.10.9.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmaximum_mag | |check| | |check| | |check| | |check| | |check| | 7.12.12.6 | F.10.9.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmaximum_mag_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.10 | F.10.9.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmaximum_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.8 | F.10.9.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmin | |check| | |check| | |check| | |check| | |check| | 7.12.12.3 | F.10.9.3 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fminimum | |check| | |check| | |check| | |check| | |check| | 7.12.12.5 | F.10.9.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fminimum_mag | |check| | |check| | |check| | |check| | |check| | 7.12.12.7 | F.10.9.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fminimum_mag_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.11 | F.10.9.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fminimum_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.9 | F.10.9.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmod | |check| | |check| | |check| | |check| | |check| | 7.12.10.1 | F.10.7.1 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fmul | N/A | |check| | | N/A | | 7.12.14.3 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| frexp | |check| | |check| | |check| | |check| | |check| | 7.12.6.7 | F.10.3.7 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fromfp | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fromfpx | |check| | |check| | |check| | |check| | |check| | 7.12.9.11 | F.10.6.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fsub | N/A | | | N/A | | 7.12.14.2 | F.10.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| getpayload | | | | |check| | | F.10.13.1 | N/A |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ilogb | |check| | |check| | |check| | |check| | |check| | 7.12.6.8 | F.10.3.8 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ldexp | |check| | |check| | |check| | |check| | |check| | 7.12.6.9 | F.10.3.9 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| llogb | |check| | |check| | |check| | |check| | |check| | 7.12.6.10 | F.10.3.10 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| llrint | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| llround | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| logb | |check| | |check| | |check| | |check| | |check| | 7.12.6.17 | F.10.3.17 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| lrint | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| lround | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| modf | |check| | |check| | |check| | |check| | |check| | 7.12.6.18 | F.10.3.18 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nan | |check| | |check| | |check| | |check| | |check| | 7.12.11.2 | F.10.8.2 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nearbyint | |check| | |check| | |check| | |check| | |check| | 7.12.9.3 | F.10.6.3 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nextafter | |check| | |check| | |check| | |check| | |check| | 7.12.11.3 | F.10.8.3 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nextdown | |check| | |check| | |check| | |check| | |check| | 7.12.11.6 | F.10.8.6 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nexttoward | |check| | |check| | |check| | |check| | N/A | 7.12.11.4 | F.10.8.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| nextup | |check| | |check| | |check| | |check| | |check| | 7.12.11.5 | F.10.8.5 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| remainder | |check| | |check| | |check| | |check| | | 7.12.10.2 | F.10.7.2 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| remquo | |check| | |check| | |check| | |check| | |check| | 7.12.10.3 | F.10.7.3 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| rint | |check| | |check| | |check| | |check| | |check| | 7.12.9.4 | F.10.6.4 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| round | |check| | |check| | |check| | |check| | |check| | 7.12.9.6 | F.10.6.6 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| roundeven | |check| | |check| | |check| | |check| | |check| | 7.12.9.8 | F.10.6.8 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| scalbln | | | | |check| | | 7.12.6.19 | F.10.3.19 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| scalbn | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| setpayload | | | | |check| | | F.10.13.2 | N/A |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| setpayloadsig | | | | |check| | | F.10.13.3 | N/A |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| totalorder | | | | |check| | | F.10.12.1 | N/A |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| totalordermag | | | | |check| | | F.10.12.2 | N/A |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| trunc | |check| | |check| | |check| | |check| | |check| | 7.12.9.9 | F.10.6.9 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ufromfp | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| ufromfpx | |check| | |check| | |check| | |check| | |check| | 7.12.9.11 | F.10.6.11 |
+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
Higher Math Functions
=====================
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
+===========+==================+=================+========================+======================+========================+========================+============================+
| acos | |check| | | | | | 7.12.4.1 | F.10.1.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| acosh | |check| | | | | | 7.12.5.1 | F.10.2.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| acospi | | | | | | 7.12.4.8 | F.10.1.8 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| asin | |check| | | | | | 7.12.4.2 | F.10.1.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| asinh | |check| | | | | | 7.12.5.2 | F.10.2.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| asinpi | | | | | | 7.12.4.9 | F.10.1.9 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan | |check| | | | | | 7.12.4.3 | F.10.1.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan2 | |check| | | | | | 7.12.4.4 | F.10.1.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan2pi | | | | | | 7.12.4.11 | F.10.1.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atanh | |check| | | | | | 7.12.5.3 | F.10.2.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atanpi | | | | | | 7.12.4.10 | F.10.1.10 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cbrt | | | | | | 7.12.7.1 | F.10.4.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| compoundn | | | | | | 7.12.7.2 | F.10.4.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cos | |check| | large | | | | 7.12.4.5 | F.10.1.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cosh | |check| | | | | | 7.12.5.4 | F.10.2.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cospi | | | | | | 7.12.4.12 | F.10.1.12 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| dsqrt | N/A | N/A | | N/A | | 7.12.14.6 | F.10.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| erf | |check| | | | | | 7.12.8.1 | F.10.5.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| erfc | | | | | | 7.12.8.2 | F.10.5.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp | |check| | |check| | | | | 7.12.6.1 | F.10.3.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp10 | |check| | |check| | | | | 7.12.6.2 | F.10.3.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp10m1 | | | | | | 7.12.6.3 | F.10.3.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp2 | |check| | |check| | | | | 7.12.6.4 | F.10.3.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp2m1 | |check| | | | | | 7.12.6.5 | F.10.3.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| expm1 | |check| | |check| | | | | 7.12.6.6 | F.10.3.6 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fma | |check| | |check| | | | | 7.12.13.1 | F.10.10.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| f16sqrt | |check| | | | N/A | | 7.12.14.6 | F.10.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| fsqrt | N/A | | | N/A | | 7.12.14.6 | F.10.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| hypot | |check| | |check| | | | | 7.12.7.4 | F.10.4.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| lgamma | | | | | | 7.12.8.3 | F.10.5.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log | |check| | |check| | | | | 7.12.6.11 | F.10.3.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log10 | |check| | |check| | | | | 7.12.6.12 | F.10.3.12 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log10p1 | | | | | | 7.12.6.13 | F.10.3.13 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log1p | |check| | |check| | | | | 7.12.6.14 | F.10.3.14 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log2 | |check| | |check| | | | | 7.12.6.15 | F.10.3.15 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| log2p1 | | | | | | 7.12.6.16 | F.10.3.16 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| logp1 | | | | | | 7.12.6.14 | F.10.3.14 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| pow | |check| | | | | | 7.12.7.5 | F.10.4.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| pown | | | | | | 7.12.7.6 | F.10.4.6 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| powr | | | | | | 7.12.7.7 | F.10.4.7 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| rootn | | | | | | 7.12.7.8 | F.10.4.8 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| rsqrt | | | | | | 7.12.7.9 | F.10.4.9 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sin | |check| | large | | | | 7.12.4.6 | F.10.1.6 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sincos | |check| | large | | | | | |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sinh | |check| | | | | | 7.12.5.5 | F.10.2.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sinpi | | | | | | 7.12.4.13 | F.10.1.13 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sqrt | |check| | |check| | |check| | | |check| | 7.12.7.10 | F.10.4.10 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tan | |check| | | | | | 7.12.4.7 | F.10.1.7 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tanh | |check| | | | | | 7.12.5.6 | F.10.2.6 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tanpi | | | | | | 7.12.4.14 | F.10.1.14 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tgamma | | | | | | 7.12.8.4 | F.10.5.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
Legends:
* |check| : correctly rounded for all 4 rounding modes.
* CR: correctly rounded for the default rounding mode (round-to-the-nearest,
tie-to-even).
* x ULPs: largest errors recorded.
* N/A: Not defined in the standard or will not be added.
..
TODO(lntue): Add a new page to discuss about the algorithms used in the
implementations and include the link here.
Performance
===========
* Simple performance testings are located at: `libc/test/src/math/performance_testing <https://github.com/llvm/llvm-project/tree/main/libc/test/src/math/performance_testing>`_.
* We also use the *perf* tool from the `CORE-MATH <https://core-math.gitlabpages.inria.fr/>`_
project: `link <https://gitlab.inria.fr/core-math/core-math/-/tree/master>`_.
The performance results from the CORE-MATH's perf tool are reported in the
table below, using the system library as reference (such as the `GNU C library <https://www.gnu.org/software/libc/>`_
on Linux). Fmod performance results obtained with "performance_testing".
+--------------+-------------------------------+-------------------------------+-------------------------------------+----------------------------------------------------------------------+
| <Func> | Reciprocal throughput (clk) | Latency (clk) | Testing ranges | Testing configuration |
| +-----------+-------------------+-----------+-------------------+ +-------------+-------------------------+--------------+---------------+
| | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) | | CPU | OS | Compiler | Special flags |
+==============+===========+===================+===========+===================+=====================================+=============+=========================+==============+===============+
| acosf | 24 | 29 | 62 | 77 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| acoshf | 18 | 26 | 73 | 74 | :math:`[1, 21]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| asinf | 23 | 27 | 62 | 62 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| asinhf | 21 | 39 | 77 | 91 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| atanf | 27 | 29 | 79 | 68 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| atanhf | 18 | 66 | 68 | 133 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| cosf | 13 | 32 | 53 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| coshf | 14 | 20 | 50 | 48 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| expf | 9 | 7 | 44 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| exp10f | 10 | 8 | 40 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| exp2f | 9 | 6 | 35 | 31 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| expm1f | 9 | 44 | 42 | 121 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| fmodf | 73 | 263 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| | 9 | 11 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| fmod | 595 | 3297 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| | 14 | 13 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| hypotf | 25 | 15 | 64 | 49 | :math:`[-10, 10] \times [-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| logf | 12 | 10 | 56 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| log10f | 9 | 17 | 35 | 48 | :math:`[e^{-1}, e]` | Ryzen 5900X | Ubuntu 22.04 LTS x86_64 | Clang 15.0.6 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| log1pf | 16 | 33 | 61 | 97 | :math:`[e^{-0.5} - 1, e^{0.5} - 1]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| log2f | 13 | 10 | 57 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| sinf | 12 | 25 | 51 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| sincosf | 19 | 30 | 57 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| sinhf | 13 | 63 | 48 | 137 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| tanf | 16 | 50 | 61 | 107 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
| tanhf | 13 | 55 | 57 | 123 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
Algorithms + Implementation Details
===================================
* :doc:`log`
Fixed-point Arithmetics
=======================
* :doc:`stdfix`
References
==========
* `CRLIBM <https://hal-ens-lyon.archives-ouvertes.fr/ensl-01529804/file/crlibm.pdf>`_.
* `RLIBM <https://people.cs.rutgers.edu/~sn349/rlibm/>`_.
* `Sollya <https://www.sollya.org/>`_.
* `The CORE-MATH Project <https://core-math.gitlabpages.inria.fr/>`_.
* `The GNU C Library (glibc) <https://www.gnu.org/software/libc/>`_.
* `The GNU MPFR Library <https://www.mpfr.org/>`_.
|