1 | /* |
2 | * Configuration for math routines. |
3 | * |
4 | * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
5 | * See https://llvm.org/LICENSE.txt for license information. |
6 | * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
7 | */ |
8 | |
9 | #ifndef _MATH_CONFIG_H |
10 | #define _MATH_CONFIG_H |
11 | |
12 | #include <math.h> |
13 | #include <stdint.h> |
14 | |
15 | #ifndef WANT_ROUNDING |
16 | /* If defined to 1, return correct results for special cases in non-nearest |
17 | rounding modes (logf (1.0f) returns 0.0f with FE_DOWNWARD rather than -0.0f). |
18 | This may be set to 0 if there is no fenv support or if math functions only |
19 | get called in round to nearest mode. */ |
20 | # define WANT_ROUNDING 1 |
21 | #endif |
22 | #ifndef WANT_ERRNO |
23 | /* If defined to 1, set errno in math functions according to ISO C. Many math |
24 | libraries do not set errno, so this is 0 by default. It may need to be |
25 | set to 1 if math.h has (math_errhandling & MATH_ERRNO) != 0. */ |
26 | # define WANT_ERRNO 0 |
27 | #endif |
28 | #ifndef WANT_ERRNO_UFLOW |
29 | /* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */ |
30 | # define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO) |
31 | #endif |
32 | |
33 | /* Compiler can inline round as a single instruction. */ |
34 | #ifndef HAVE_FAST_ROUND |
35 | # if __aarch64__ |
36 | # define HAVE_FAST_ROUND 1 |
37 | # else |
38 | # define HAVE_FAST_ROUND 0 |
39 | # endif |
40 | #endif |
41 | |
42 | /* Compiler can inline lround, but not (long)round(x). */ |
43 | #ifndef HAVE_FAST_LROUND |
44 | # if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__ |
45 | # define HAVE_FAST_LROUND 1 |
46 | # else |
47 | # define HAVE_FAST_LROUND 0 |
48 | # endif |
49 | #endif |
50 | |
51 | /* Compiler can inline fma as a single instruction. */ |
52 | #ifndef HAVE_FAST_FMA |
53 | # if defined FP_FAST_FMA || __aarch64__ |
54 | # define HAVE_FAST_FMA 1 |
55 | # else |
56 | # define HAVE_FAST_FMA 0 |
57 | # endif |
58 | #endif |
59 | |
60 | /* Provide *_finite symbols and some of the glibc hidden symbols |
61 | so libmathlib can be used with binaries compiled against glibc |
62 | to interpose math functions with both static and dynamic linking. */ |
63 | #ifndef USE_GLIBC_ABI |
64 | # if __GNUC__ |
65 | # define USE_GLIBC_ABI 1 |
66 | # else |
67 | # define USE_GLIBC_ABI 0 |
68 | # endif |
69 | #endif |
70 | |
71 | /* Optionally used extensions. */ |
72 | #ifdef __GNUC__ |
73 | # define HIDDEN __attribute__ ((__visibility__ ("hidden"))) |
74 | # define NOINLINE __attribute__ ((noinline)) |
75 | # define UNUSED __attribute__ ((unused)) |
76 | # define likely(x) __builtin_expect (!!(x), 1) |
77 | # define unlikely(x) __builtin_expect (x, 0) |
78 | # if __GNUC__ >= 9 |
79 | # define attribute_copy(f) __attribute__ ((copy (f))) |
80 | # else |
81 | # define attribute_copy(f) |
82 | # endif |
83 | # define strong_alias(f, a) \ |
84 | extern __typeof (f) a __attribute__ ((alias (#f))) attribute_copy (f); |
85 | # define hidden_alias(f, a) \ |
86 | extern __typeof (f) a __attribute__ ((alias (#f), visibility ("hidden"))) \ |
87 | attribute_copy (f); |
88 | #else |
89 | # define HIDDEN |
90 | # define NOINLINE |
91 | # define UNUSED |
92 | # define likely(x) (x) |
93 | # define unlikely(x) (x) |
94 | #endif |
95 | |
96 | #if HAVE_FAST_ROUND |
97 | /* When set, the roundtoint and converttoint functions are provided with |
98 | the semantics documented below. */ |
99 | # define TOINT_INTRINSICS 1 |
100 | |
101 | /* Round x to nearest int in all rounding modes, ties have to be rounded |
102 | consistently with converttoint so the results match. If the result |
103 | would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */ |
104 | static inline double_t |
105 | roundtoint (double_t x) |
106 | { |
107 | return round (x); |
108 | } |
109 | |
110 | /* Convert x to nearest int in all rounding modes, ties have to be rounded |
111 | consistently with roundtoint. If the result is not representable in an |
112 | int32_t then the semantics is unspecified. */ |
113 | static inline int32_t |
114 | converttoint (double_t x) |
115 | { |
116 | # if HAVE_FAST_LROUND |
117 | return lround (x); |
118 | # else |
119 | return (long) round (x); |
120 | # endif |
121 | } |
122 | #endif |
123 | |
124 | static inline uint32_t |
125 | asuint (float f) |
126 | { |
127 | union |
128 | { |
129 | float f; |
130 | uint32_t i; |
131 | } u = {.f: f}; |
132 | return u.i; |
133 | } |
134 | |
135 | static inline float |
136 | asfloat (uint32_t i) |
137 | { |
138 | union |
139 | { |
140 | uint32_t i; |
141 | float f; |
142 | } u = {.i: i}; |
143 | return u.f; |
144 | } |
145 | |
146 | static inline uint64_t |
147 | asuint64 (double f) |
148 | { |
149 | union |
150 | { |
151 | double f; |
152 | uint64_t i; |
153 | } u = {.f: f}; |
154 | return u.i; |
155 | } |
156 | |
157 | static inline double |
158 | asdouble (uint64_t i) |
159 | { |
160 | union |
161 | { |
162 | uint64_t i; |
163 | double f; |
164 | } u = {.i: i}; |
165 | return u.f; |
166 | } |
167 | |
168 | #ifndef IEEE_754_2008_SNAN |
169 | # define IEEE_754_2008_SNAN 1 |
170 | #endif |
171 | static inline int |
172 | issignalingf_inline (float x) |
173 | { |
174 | uint32_t ix = asuint (f: x); |
175 | if (!IEEE_754_2008_SNAN) |
176 | return (ix & 0x7fc00000) == 0x7fc00000; |
177 | return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000; |
178 | } |
179 | |
180 | static inline int |
181 | issignaling_inline (double x) |
182 | { |
183 | uint64_t ix = asuint64 (f: x); |
184 | if (!IEEE_754_2008_SNAN) |
185 | return (ix & 0x7ff8000000000000) == 0x7ff8000000000000; |
186 | return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL; |
187 | } |
188 | |
189 | #if __aarch64__ && __GNUC__ |
190 | /* Prevent the optimization of a floating-point expression. */ |
191 | static inline float |
192 | opt_barrier_float (float x) |
193 | { |
194 | __asm__ __volatile__ ("" : "+w" (x)); |
195 | return x; |
196 | } |
197 | static inline double |
198 | opt_barrier_double (double x) |
199 | { |
200 | __asm__ __volatile__ ("" : "+w" (x)); |
201 | return x; |
202 | } |
203 | /* Force the evaluation of a floating-point expression for its side-effect. */ |
204 | static inline void |
205 | force_eval_float (float x) |
206 | { |
207 | __asm__ __volatile__ ("" : "+w" (x)); |
208 | } |
209 | static inline void |
210 | force_eval_double (double x) |
211 | { |
212 | __asm__ __volatile__ ("" : "+w" (x)); |
213 | } |
214 | #else |
215 | static inline float |
216 | opt_barrier_float (float x) |
217 | { |
218 | volatile float y = x; |
219 | return y; |
220 | } |
221 | static inline double |
222 | opt_barrier_double (double x) |
223 | { |
224 | volatile double y = x; |
225 | return y; |
226 | } |
227 | static inline void |
228 | force_eval_float (float x) |
229 | { |
230 | volatile float y UNUSED = x; |
231 | } |
232 | static inline void |
233 | force_eval_double (double x) |
234 | { |
235 | volatile double y UNUSED = x; |
236 | } |
237 | #endif |
238 | |
239 | /* Evaluate an expression as the specified type, normally a type |
240 | cast should be enough, but compilers implement non-standard |
241 | excess-precision handling, so when FLT_EVAL_METHOD != 0 then |
242 | these functions may need to be customized. */ |
243 | static inline float |
244 | eval_as_float (float x) |
245 | { |
246 | return x; |
247 | } |
248 | static inline double |
249 | eval_as_double (double x) |
250 | { |
251 | return x; |
252 | } |
253 | |
254 | /* Error handling tail calls for special cases, with a sign argument. |
255 | The sign of the return value is set if the argument is non-zero. */ |
256 | |
257 | /* The result overflows. */ |
258 | HIDDEN float __math_oflowf (uint32_t); |
259 | /* The result underflows to 0 in nearest rounding mode. */ |
260 | HIDDEN float __math_uflowf (uint32_t); |
261 | /* The result underflows to 0 in some directed rounding mode only. */ |
262 | HIDDEN float __math_may_uflowf (uint32_t); |
263 | /* Division by zero. */ |
264 | HIDDEN float __math_divzerof (uint32_t); |
265 | /* The result overflows. */ |
266 | HIDDEN double __math_oflow (uint32_t); |
267 | /* The result underflows to 0 in nearest rounding mode. */ |
268 | HIDDEN double __math_uflow (uint32_t); |
269 | /* The result underflows to 0 in some directed rounding mode only. */ |
270 | HIDDEN double __math_may_uflow (uint32_t); |
271 | /* Division by zero. */ |
272 | HIDDEN double __math_divzero (uint32_t); |
273 | |
274 | /* Error handling using input checking. */ |
275 | |
276 | /* Invalid input unless it is a quiet NaN. */ |
277 | HIDDEN float __math_invalidf (float); |
278 | /* Invalid input unless it is a quiet NaN. */ |
279 | HIDDEN double __math_invalid (double); |
280 | |
281 | /* Error handling using output checking, only for errno setting. */ |
282 | |
283 | /* Check if the result overflowed to infinity. */ |
284 | HIDDEN double __math_check_oflow (double); |
285 | /* Check if the result underflowed to 0. */ |
286 | HIDDEN double __math_check_uflow (double); |
287 | |
288 | /* Check if the result overflowed to infinity. */ |
289 | static inline double |
290 | check_oflow (double x) |
291 | { |
292 | return WANT_ERRNO ? __math_check_oflow (x) : x; |
293 | } |
294 | |
295 | /* Check if the result underflowed to 0. */ |
296 | static inline double |
297 | check_uflow (double x) |
298 | { |
299 | return WANT_ERRNO ? __math_check_uflow (x) : x; |
300 | } |
301 | |
302 | |
303 | /* Shared between expf, exp2f and powf. */ |
304 | #define EXP2F_TABLE_BITS 5 |
305 | #define EXP2F_POLY_ORDER 3 |
306 | extern const struct exp2f_data |
307 | { |
308 | uint64_t tab[1 << EXP2F_TABLE_BITS]; |
309 | double shift_scaled; |
310 | double poly[EXP2F_POLY_ORDER]; |
311 | double shift; |
312 | double invln2_scaled; |
313 | double poly_scaled[EXP2F_POLY_ORDER]; |
314 | } __exp2f_data HIDDEN; |
315 | |
316 | #define LOGF_TABLE_BITS 4 |
317 | #define LOGF_POLY_ORDER 4 |
318 | extern const struct logf_data |
319 | { |
320 | struct |
321 | { |
322 | double invc, logc; |
323 | } tab[1 << LOGF_TABLE_BITS]; |
324 | double ln2; |
325 | double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */ |
326 | } __logf_data HIDDEN; |
327 | |
328 | #define LOG2F_TABLE_BITS 4 |
329 | #define LOG2F_POLY_ORDER 4 |
330 | extern const struct log2f_data |
331 | { |
332 | struct |
333 | { |
334 | double invc, logc; |
335 | } tab[1 << LOG2F_TABLE_BITS]; |
336 | double poly[LOG2F_POLY_ORDER]; |
337 | } __log2f_data HIDDEN; |
338 | |
339 | #define POWF_LOG2_TABLE_BITS 4 |
340 | #define POWF_LOG2_POLY_ORDER 5 |
341 | #if TOINT_INTRINSICS |
342 | # define POWF_SCALE_BITS EXP2F_TABLE_BITS |
343 | #else |
344 | # define POWF_SCALE_BITS 0 |
345 | #endif |
346 | #define POWF_SCALE ((double) (1 << POWF_SCALE_BITS)) |
347 | extern const struct powf_log2_data |
348 | { |
349 | struct |
350 | { |
351 | double invc, logc; |
352 | } tab[1 << POWF_LOG2_TABLE_BITS]; |
353 | double poly[POWF_LOG2_POLY_ORDER]; |
354 | } __powf_log2_data HIDDEN; |
355 | |
356 | |
357 | #define EXP_TABLE_BITS 7 |
358 | #define EXP_POLY_ORDER 5 |
359 | /* Use polynomial that is optimized for a wider input range. This may be |
360 | needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */ |
361 | #define EXP_POLY_WIDE 0 |
362 | /* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be |
363 | needed for good precision in non-nearest rounding and !EXP_POLY_WIDE. */ |
364 | #define EXP_USE_TOINT_NARROW 0 |
365 | #define EXP2_POLY_ORDER 5 |
366 | #define EXP2_POLY_WIDE 0 |
367 | extern const struct exp_data |
368 | { |
369 | double invln2N; |
370 | double shift; |
371 | double negln2hiN; |
372 | double negln2loN; |
373 | double poly[4]; /* Last four coefficients. */ |
374 | double exp2_shift; |
375 | double exp2_poly[EXP2_POLY_ORDER]; |
376 | uint64_t tab[2*(1 << EXP_TABLE_BITS)]; |
377 | } __exp_data HIDDEN; |
378 | |
379 | #define LOG_TABLE_BITS 7 |
380 | #define LOG_POLY_ORDER 6 |
381 | #define LOG_POLY1_ORDER 12 |
382 | extern const struct log_data |
383 | { |
384 | double ln2hi; |
385 | double ln2lo; |
386 | double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ |
387 | double poly1[LOG_POLY1_ORDER - 1]; |
388 | struct {double invc, logc;} tab[1 << LOG_TABLE_BITS]; |
389 | #if !HAVE_FAST_FMA |
390 | struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS]; |
391 | #endif |
392 | } __log_data HIDDEN; |
393 | |
394 | #define LOG2_TABLE_BITS 6 |
395 | #define LOG2_POLY_ORDER 7 |
396 | #define LOG2_POLY1_ORDER 11 |
397 | extern const struct log2_data |
398 | { |
399 | double invln2hi; |
400 | double invln2lo; |
401 | double poly[LOG2_POLY_ORDER - 1]; |
402 | double poly1[LOG2_POLY1_ORDER - 1]; |
403 | struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS]; |
404 | #if !HAVE_FAST_FMA |
405 | struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS]; |
406 | #endif |
407 | } __log2_data HIDDEN; |
408 | |
409 | #define POW_LOG_TABLE_BITS 7 |
410 | #define POW_LOG_POLY_ORDER 8 |
411 | extern const struct pow_log_data |
412 | { |
413 | double ln2hi; |
414 | double ln2lo; |
415 | double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ |
416 | /* Note: the pad field is unused, but allows slightly faster indexing. */ |
417 | struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS]; |
418 | } __pow_log_data HIDDEN; |
419 | |
420 | #endif |
421 | |