1 /*
2 * Configuration for math routines.
3 *
4 * Copyright (c) 2017-2020, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8 #ifndef _MATH_CONFIG_H
9 #define _MATH_CONFIG_H
10
11 #include <math.h>
12 #include <stdint.h>
13
14 #ifndef WANT_ROUNDING
15 /* If defined to 1, return correct results for special cases in non-nearest
16 rounding modes (logf (1.0f) returns 0.0f with FE_DOWNWARD rather than -0.0f).
17 This may be set to 0 if there is no fenv support or if math functions only
18 get called in round to nearest mode. */
19 # define WANT_ROUNDING 1
20 #endif
21 #ifndef WANT_ERRNO
22 /* If defined to 1, set errno in math functions according to ISO C. Many math
23 libraries do not set errno, so this is 0 by default. It may need to be
24 set to 1 if math.h has (math_errhandling & MATH_ERRNO) != 0. */
25 # define WANT_ERRNO 0
26 #endif
27 #ifndef WANT_ERRNO_UFLOW
28 /* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
29 # define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
30 #endif
31
32 /* Compiler can inline round as a single instruction. */
33 #ifndef HAVE_FAST_ROUND
34 # if __aarch64__
35 # define HAVE_FAST_ROUND 1
36 # else
37 # define HAVE_FAST_ROUND 0
38 # endif
39 #endif
40
41 /* Compiler can inline lround, but not (long)round(x). */
42 #ifndef HAVE_FAST_LROUND
43 # if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__
44 # define HAVE_FAST_LROUND 1
45 # else
46 # define HAVE_FAST_LROUND 0
47 # endif
48 #endif
49
50 /* Compiler can inline fma as a single instruction. */
51 #ifndef HAVE_FAST_FMA
52 # if defined FP_FAST_FMA || __aarch64__
53 # define HAVE_FAST_FMA 1
54 # else
55 # define HAVE_FAST_FMA 0
56 # endif
57 #endif
58
59 /* Provide *_finite symbols and some of the glibc hidden symbols
60 so libmathlib can be used with binaries compiled against glibc
61 to interpose math functions with both static and dynamic linking. */
62 #ifndef USE_GLIBC_ABI
63 # if __GNUC__
64 # define USE_GLIBC_ABI 1
65 # else
66 # define USE_GLIBC_ABI 0
67 # endif
68 #endif
69
70 /* Optionally used extensions. */
71 #ifdef __GNUC__
72 # define HIDDEN __attribute__ ((__visibility__ ("hidden")))
73 # define NOINLINE __attribute__ ((noinline))
74 # define UNUSED __attribute__ ((unused))
75 # define likely(x) __builtin_expect (!!(x), 1)
76 # define unlikely(x) __builtin_expect (x, 0)
77 # if __GNUC__ >= 9
78 # define attribute_copy(f) __attribute__ ((copy (f)))
79 # else
80 # define attribute_copy(f)
81 # endif
82 # define strong_alias(f, a) \
83 extern __typeof (f) a __attribute__ ((alias (#f))) attribute_copy (f);
84 # define hidden_alias(f, a) \
85 extern __typeof (f) a __attribute__ ((alias (#f), visibility ("hidden"))) \
86 attribute_copy (f);
87 #else
88 # define HIDDEN
89 # define NOINLINE
90 # define UNUSED
91 # define likely(x) (x)
92 # define unlikely(x) (x)
93 #endif
94
95 #if HAVE_FAST_ROUND
96 /* When set, the roundtoint and converttoint functions are provided with
97 the semantics documented below. */
98 # define TOINT_INTRINSICS 1
99
100 /* Round x to nearest int in all rounding modes, ties have to be rounded
101 consistently with converttoint so the results match. If the result
102 would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
103 static inline double_t
roundtoint(double_t x)104 roundtoint (double_t x)
105 {
106 return round (x);
107 }
108
109 /* Convert x to nearest int in all rounding modes, ties have to be rounded
110 consistently with roundtoint. If the result is not representible in an
111 int32_t then the semantics is unspecified. */
112 static inline int32_t
converttoint(double_t x)113 converttoint (double_t x)
114 {
115 # if HAVE_FAST_LROUND
116 return lround (x);
117 # else
118 return (long) round (x);
119 # endif
120 }
121 #endif
122
123 static inline uint32_t
asuint(float f)124 asuint (float f)
125 {
126 union
127 {
128 float f;
129 uint32_t i;
130 } u = {f};
131 return u.i;
132 }
133
134 static inline float
asfloat(uint32_t i)135 asfloat (uint32_t i)
136 {
137 union
138 {
139 uint32_t i;
140 float f;
141 } u = {i};
142 return u.f;
143 }
144
145 static inline uint64_t
asuint64(double f)146 asuint64 (double f)
147 {
148 union
149 {
150 double f;
151 uint64_t i;
152 } u = {f};
153 return u.i;
154 }
155
156 static inline double
asdouble(uint64_t i)157 asdouble (uint64_t i)
158 {
159 union
160 {
161 uint64_t i;
162 double f;
163 } u = {i};
164 return u.f;
165 }
166
167 #ifndef IEEE_754_2008_SNAN
168 # define IEEE_754_2008_SNAN 1
169 #endif
170 static inline int
issignalingf_inline(float x)171 issignalingf_inline (float x)
172 {
173 uint32_t ix = asuint (x);
174 if (!IEEE_754_2008_SNAN)
175 return (ix & 0x7fc00000) == 0x7fc00000;
176 return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
177 }
178
179 static inline int
issignaling_inline(double x)180 issignaling_inline (double x)
181 {
182 uint64_t ix = asuint64 (x);
183 if (!IEEE_754_2008_SNAN)
184 return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
185 return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
186 }
187
188 #if __aarch64__ && __GNUC__
189 /* Prevent the optimization of a floating-point expression. */
190 static inline float
opt_barrier_float(float x)191 opt_barrier_float (float x)
192 {
193 __asm__ __volatile__ ("" : "+w" (x));
194 return x;
195 }
196 static inline double
opt_barrier_double(double x)197 opt_barrier_double (double x)
198 {
199 __asm__ __volatile__ ("" : "+w" (x));
200 return x;
201 }
202 /* Force the evaluation of a floating-point expression for its side-effect. */
203 static inline void
force_eval_float(float x)204 force_eval_float (float x)
205 {
206 __asm__ __volatile__ ("" : "+w" (x));
207 }
208 static inline void
force_eval_double(double x)209 force_eval_double (double x)
210 {
211 __asm__ __volatile__ ("" : "+w" (x));
212 }
213 #else
214 static inline float
opt_barrier_float(float x)215 opt_barrier_float (float x)
216 {
217 volatile float y = x;
218 return y;
219 }
220 static inline double
opt_barrier_double(double x)221 opt_barrier_double (double x)
222 {
223 volatile double y = x;
224 return y;
225 }
226 static inline void
force_eval_float(float x)227 force_eval_float (float x)
228 {
229 volatile float y UNUSED = x;
230 }
231 static inline void
force_eval_double(double x)232 force_eval_double (double x)
233 {
234 volatile double y UNUSED = x;
235 }
236 #endif
237
238 /* Evaluate an expression as the specified type, normally a type
239 cast should be enough, but compilers implement non-standard
240 excess-precision handling, so when FLT_EVAL_METHOD != 0 then
241 these functions may need to be customized. */
242 static inline float
eval_as_float(float x)243 eval_as_float (float x)
244 {
245 return x;
246 }
247 static inline double
eval_as_double(double x)248 eval_as_double (double x)
249 {
250 return x;
251 }
252
253 /* Error handling tail calls for special cases, with a sign argument.
254 The sign of the return value is set if the argument is non-zero. */
255
256 /* The result overflows. */
257 HIDDEN float __math_oflowf (uint32_t);
258 /* The result underflows to 0 in nearest rounding mode. */
259 HIDDEN float __math_uflowf (uint32_t);
260 /* The result underflows to 0 in some directed rounding mode only. */
261 HIDDEN float __math_may_uflowf (uint32_t);
262 /* Division by zero. */
263 HIDDEN float __math_divzerof (uint32_t);
264 /* The result overflows. */
265 HIDDEN double __math_oflow (uint32_t);
266 /* The result underflows to 0 in nearest rounding mode. */
267 HIDDEN double __math_uflow (uint32_t);
268 /* The result underflows to 0 in some directed rounding mode only. */
269 HIDDEN double __math_may_uflow (uint32_t);
270 /* Division by zero. */
271 HIDDEN double __math_divzero (uint32_t);
272
273 /* Error handling using input checking. */
274
275 /* Invalid input unless it is a quiet NaN. */
276 HIDDEN float __math_invalidf (float);
277 /* Invalid input unless it is a quiet NaN. */
278 HIDDEN double __math_invalid (double);
279
280 /* Error handling using output checking, only for errno setting. */
281
282 /* Check if the result overflowed to infinity. */
283 HIDDEN double __math_check_oflow (double);
284 /* Check if the result underflowed to 0. */
285 HIDDEN double __math_check_uflow (double);
286
287 /* Check if the result overflowed to infinity. */
288 static inline double
check_oflow(double x)289 check_oflow (double x)
290 {
291 return WANT_ERRNO ? __math_check_oflow (x) : x;
292 }
293
294 /* Check if the result underflowed to 0. */
295 static inline double
check_uflow(double x)296 check_uflow (double x)
297 {
298 return WANT_ERRNO ? __math_check_uflow (x) : x;
299 }
300
301 /* Check if the result overflowed to infinity. */
302 HIDDEN float __math_check_oflowf (float);
303 /* Check if the result underflowed to 0. */
304 HIDDEN float __math_check_uflowf (float);
305
306 /* Check if the result overflowed to infinity. */
307 static inline float
check_oflowf(float x)308 check_oflowf (float x)
309 {
310 return WANT_ERRNO ? __math_check_oflowf (x) : x;
311 }
312
313 /* Check if the result underflowed to 0. */
314 static inline float
check_uflowf(float x)315 check_uflowf (float x)
316 {
317 return WANT_ERRNO ? __math_check_uflowf (x) : x;
318 }
319
320 /* Shared between expf, exp2f and powf. */
321 #define EXP2F_TABLE_BITS 5
322 #define EXP2F_POLY_ORDER 3
323 extern const struct exp2f_data
324 {
325 uint64_t tab[1 << EXP2F_TABLE_BITS];
326 double shift_scaled;
327 double poly[EXP2F_POLY_ORDER];
328 double shift;
329 double invln2_scaled;
330 double poly_scaled[EXP2F_POLY_ORDER];
331 } __exp2f_data HIDDEN;
332
333 #define LOGF_TABLE_BITS 4
334 #define LOGF_POLY_ORDER 4
335 extern const struct logf_data
336 {
337 struct
338 {
339 double invc, logc;
340 } tab[1 << LOGF_TABLE_BITS];
341 double ln2;
342 double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
343 } __logf_data HIDDEN;
344
345 #define LOG2F_TABLE_BITS 4
346 #define LOG2F_POLY_ORDER 4
347 extern const struct log2f_data
348 {
349 struct
350 {
351 double invc, logc;
352 } tab[1 << LOG2F_TABLE_BITS];
353 double poly[LOG2F_POLY_ORDER];
354 } __log2f_data HIDDEN;
355
356 #define POWF_LOG2_TABLE_BITS 4
357 #define POWF_LOG2_POLY_ORDER 5
358 #if TOINT_INTRINSICS
359 # define POWF_SCALE_BITS EXP2F_TABLE_BITS
360 #else
361 # define POWF_SCALE_BITS 0
362 #endif
363 #define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
364 extern const struct powf_log2_data
365 {
366 struct
367 {
368 double invc, logc;
369 } tab[1 << POWF_LOG2_TABLE_BITS];
370 double poly[POWF_LOG2_POLY_ORDER];
371 } __powf_log2_data HIDDEN;
372
373
374 #define EXP_TABLE_BITS 7
375 #define EXP_POLY_ORDER 5
376 /* Use polynomial that is optimized for a wider input range. This may be
377 needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */
378 #define EXP_POLY_WIDE 0
379 /* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be
380 needed for good precision in non-nearest rouning and !EXP_POLY_WIDE. */
381 #define EXP_USE_TOINT_NARROW 0
382 #define EXP2_POLY_ORDER 5
383 #define EXP2_POLY_WIDE 0
384 extern const struct exp_data
385 {
386 double invln2N;
387 double shift;
388 double negln2hiN;
389 double negln2loN;
390 double poly[4]; /* Last four coefficients. */
391 double exp2_shift;
392 double exp2_poly[EXP2_POLY_ORDER];
393 uint64_t tab[2*(1 << EXP_TABLE_BITS)];
394 } __exp_data HIDDEN;
395
396 #define LOG_TABLE_BITS 7
397 #define LOG_POLY_ORDER 6
398 #define LOG_POLY1_ORDER 12
399 extern const struct log_data
400 {
401 double ln2hi;
402 double ln2lo;
403 double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
404 double poly1[LOG_POLY1_ORDER - 1];
405 struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
406 #if !HAVE_FAST_FMA
407 struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
408 #endif
409 } __log_data HIDDEN;
410
411 #define LOG2_TABLE_BITS 6
412 #define LOG2_POLY_ORDER 7
413 #define LOG2_POLY1_ORDER 11
414 extern const struct log2_data
415 {
416 double invln2hi;
417 double invln2lo;
418 double poly[LOG2_POLY_ORDER - 1];
419 double poly1[LOG2_POLY1_ORDER - 1];
420 struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
421 #if !HAVE_FAST_FMA
422 struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
423 #endif
424 } __log2_data HIDDEN;
425
426 #define POW_LOG_TABLE_BITS 7
427 #define POW_LOG_POLY_ORDER 8
428 extern const struct pow_log_data
429 {
430 double ln2hi;
431 double ln2lo;
432 double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
433 /* Note: the pad field is unused, but allows slightly faster indexing. */
434 struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
435 } __pow_log_data HIDDEN;
436
437 extern const struct erff_data
438 {
439 float erff_poly_A[6];
440 float erff_poly_B[7];
441 } __erff_data HIDDEN;
442
443 #define ERF_POLY_A_ORDER 19
444 #define ERF_POLY_A_NCOEFFS 10
445 #define ERFC_POLY_C_NCOEFFS 16
446 #define ERFC_POLY_D_NCOEFFS 18
447 #define ERFC_POLY_E_NCOEFFS 14
448 #define ERFC_POLY_F_NCOEFFS 17
449 extern const struct erf_data
450 {
451 double erf_poly_A[ERF_POLY_A_NCOEFFS];
452 double erf_ratio_N_A[5];
453 double erf_ratio_D_A[5];
454 double erf_ratio_N_B[7];
455 double erf_ratio_D_B[6];
456 double erfc_poly_C[ERFC_POLY_C_NCOEFFS];
457 double erfc_poly_D[ERFC_POLY_D_NCOEFFS];
458 double erfc_poly_E[ERFC_POLY_E_NCOEFFS];
459 double erfc_poly_F[ERFC_POLY_F_NCOEFFS];
460 } __erf_data HIDDEN;
461
462 #endif
463