1 /* Declarations for math functions.
2 Copyright (C) 1991-2016 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
20 * ISO C99 Standard: 7.12 Mathematics <math.h>
26 #define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
27 #include <bits/libc-header-start.h>
31 /* Get machine-dependent vector math functions declarations. */
32 #include <bits/math-vector.h>
34 /* Get machine-dependent HUGE_VAL value (returned on overflow).
35 On all IEEE754 machines, this is +Infinity. */
36 #include <bits/huge_val.h>
38 # include <bits/huge_valf.h>
39 # include <bits/huge_vall.h>
41 /* Get machine-dependent INFINITY value. */
42 # include <bits/inf.h>
44 /* Get machine-dependent NAN value (returned for some domain errors). */
45 # include <bits/nan.h>
46 #endif /* __USE_ISOC99 */
48 #if __GLIBC_USE (IEC_60559_BFP_EXT)
49 /* Signaling NaN macros, if supported. */
50 # if __GNUC_PREREQ (3, 3)
51 # define SNANF (__builtin_nansf (""))
52 # define SNAN (__builtin_nans (""))
53 # define SNANL (__builtin_nansl (""))
57 /* Get the architecture specific values describing the floating-point
58 evaluation. The following symbols will get defined:
60 float_t floating-point type at least as wide as `float' used
61 to evaluate `float' expressions
62 double_t floating-point type at least as wide as `double' used
63 to evaluate `double' expressions
68 If defined it indicates that the `fma' function
69 generally executes about as fast as a multiply and an add.
70 This macro is defined only iff the `fma' function is
71 implemented directly with a hardware multiply-add instructions.
73 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
74 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
78 #include <bits/mathdef.h>
80 /* The file <bits/mathcalls.h> contains the prototypes for all the
81 actual math functions. These macros are used for those prototypes,
82 so we can easily declare each function as both `name' and `__name',
83 and can declare the float versions `namef' and `__namef'. */
85 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
87 #define __MATHCALL_VEC(function, suffix, args) \
88 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
89 __MATHCALL (function, suffix, args)
91 #define __MATHDECL_VEC(type, function,suffix, args) \
92 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
93 __MATHDECL(type, function,suffix, args)
95 #define __MATHCALL(function,suffix, args) \
96 __MATHDECL (_Mdouble_,function,suffix, args)
97 #define __MATHDECL(type, function,suffix, args) \
98 __MATHDECL_1(type, function,suffix, args); \
99 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
100 #define __MATHCALLX(function,suffix, args, attrib) \
101 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
102 #define __MATHDECLX(type, function,suffix, args, attrib) \
103 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
104 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
105 #define __MATHDECL_1(type, function,suffix, args) \
106 extern type __MATH_PRECNAME(function,suffix) args __THROW
108 #define _Mdouble_ double
109 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
110 #define __MATH_DECLARING_DOUBLE 1
111 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
112 #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
113 #include <bits/mathcalls.h>
115 #undef _Mdouble_BEGIN_NAMESPACE
116 #undef _Mdouble_END_NAMESPACE
117 #undef __MATH_PRECNAME
118 #undef __MATH_DECLARING_DOUBLE
123 /* Include the file of declarations again, this time using `float'
124 instead of `double' and appending f to each function name. */
127 # define _Mfloat_ float
129 # define _Mdouble_ _Mfloat_
130 # define __MATH_PRECNAME(name,r) name##f##r
131 # define __MATH_DECLARING_DOUBLE 0
132 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
133 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
134 # include <bits/mathcalls.h>
136 # undef _Mdouble_BEGIN_NAMESPACE
137 # undef _Mdouble_END_NAMESPACE
138 # undef __MATH_PRECNAME
139 # undef __MATH_DECLARING_DOUBLE
141 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
142 || defined __LDBL_COMPAT \
143 || defined _LIBC_TEST
144 # ifdef __LDBL_COMPAT
147 extern float __nldbl_nexttowardf (float __x
, long double __y
)
148 __THROW
__attribute__ ((__const__
));
149 # ifdef __REDIRECT_NTH
150 extern float __REDIRECT_NTH (nexttowardf
, (float __x
, long double __y
),
152 __attribute__ ((__const__
));
153 extern double __REDIRECT_NTH (nexttoward
, (double __x
, long double __y
),
154 nextafter
) __attribute__ ((__const__
));
155 extern long double __REDIRECT_NTH (nexttowardl
,
156 (long double __x
, long double __y
),
157 nextafter
) __attribute__ ((__const__
));
162 # define __MATHDECL_2(type, function,suffix, args, alias) \
163 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
165 # define __MATHDECL_1(type, function,suffix, args) \
166 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
169 /* Include the file of declarations again, this time using `long double'
170 instead of `double' and appending l to each function name. */
172 # ifndef _Mlong_double_
173 # define _Mlong_double_ long double
175 # define _Mdouble_ _Mlong_double_
176 # define __MATH_PRECNAME(name,r) name##l##r
177 # define __MATH_DECLARING_DOUBLE 0
178 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
179 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
180 # define __MATH_DECLARE_LDOUBLE 1
181 # include <bits/mathcalls.h>
183 # undef _Mdouble_BEGIN_NAMESPACE
184 # undef _Mdouble_END_NAMESPACE
185 # undef __MATH_PRECNAME
186 # undef __MATH_DECLARING_DOUBLE
188 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
190 #endif /* Use ISO C99. */
196 #if defined __USE_MISC || defined __USE_XOPEN
197 /* This variable is used by `gamma' and `lgamma'. */
202 /* ISO C99 defines some generic macros which work on any data type. */
205 /* All floating-point numbers can be put in one of these categories. */
212 # define FP_INFINITE 1
218 # define FP_SUBNORMAL 3
225 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
226 so disable builtins if this is enabled. When fixed in a newer GCC,
227 the __SUPPORT_SNAN__ check may be skipped for those versions. */
229 /* Return number of classification appropriate for X. */
230 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
231 && !defined __OPTIMIZE_SIZE__
232 # define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
233 FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
234 # elif defined __NO_LONG_DOUBLE_MATH
235 # define fpclassify(x) \
236 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
238 # define fpclassify(x) \
239 (sizeof (x) == sizeof (float) \
240 ? __fpclassifyf (x) \
241 : sizeof (x) == sizeof (double) \
242 ? __fpclassify (x) : __fpclassifyl (x))
245 /* Return nonzero value if sign of X is negative. */
246 # if __GNUC_PREREQ (4,0)
247 # define signbit(x) \
248 (sizeof (x) == sizeof (float) \
249 ? __builtin_signbitf (x) \
250 : sizeof (x) == sizeof (double) \
251 ? __builtin_signbit (x) : __builtin_signbitl (x))
253 # ifdef __NO_LONG_DOUBLE_MATH
254 # define signbit(x) \
255 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
257 # define signbit(x) \
258 (sizeof (x) == sizeof (float) \
260 : sizeof (x) == sizeof (double) \
261 ? __signbit (x) : __signbitl (x))
265 /* Return nonzero value if X is not +-Inf or NaN. */
266 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
267 # define isfinite(x) __builtin_isfinite (x)
268 # elif defined __NO_LONG_DOUBLE_MATH
269 # define isfinite(x) \
270 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
272 # define isfinite(x) \
273 (sizeof (x) == sizeof (float) \
275 : sizeof (x) == sizeof (double) \
276 ? __finite (x) : __finitel (x))
279 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
280 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
281 # define isnormal(x) __builtin_isnormal (x)
283 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
286 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
287 we already have this functions `__isnan' and it is faster. */
288 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
289 # define isnan(x) __builtin_isnan (x)
290 # elif defined __NO_LONG_DOUBLE_MATH
292 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
295 (sizeof (x) == sizeof (float) \
297 : sizeof (x) == sizeof (double) \
298 ? __isnan (x) : __isnanl (x))
301 /* Return nonzero value if X is positive or negative infinity. */
302 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
303 # define isinf(x) __builtin_isinf_sign (x)
304 # elif defined __NO_LONG_DOUBLE_MATH
306 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
309 (sizeof (x) == sizeof (float) \
311 : sizeof (x) == sizeof (double) \
312 ? __isinf (x) : __isinfl (x))
315 /* Bitmasks for the math_errhandling macro. */
316 # define MATH_ERRNO 1 /* errno set by math functions. */
317 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
319 /* By default all functions support both errno and exception handling.
320 In gcc's fast math mode and if inline functions are defined this
321 might not be true. */
322 # ifndef __FAST_MATH__
323 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
326 #endif /* Use ISO C99. */
328 #if __GLIBC_USE (IEC_60559_BFP_EXT)
329 # include <bits/iscanonical.h>
331 /* Return nonzero value if X is a signaling NaN. */
332 # ifdef __NO_LONG_DOUBLE_MATH
333 # define issignaling(x) \
334 (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
336 # define issignaling(x) \
337 (sizeof (x) == sizeof (float) \
338 ? __issignalingf (x) \
339 : sizeof (x) == sizeof (double) \
340 ? __issignaling (x) : __issignalingl (x))
343 /* Return nonzero value if X is subnormal. */
344 # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
346 /* Return nonzero value if X is zero. */
348 # ifdef __SUPPORT_SNAN__
349 # define iszero(x) (fpclassify (x) == FP_ZERO)
351 # define iszero(x) (((__typeof (x)) (x)) == 0)
353 # else /* __cplusplus */
355 template <class __T
> inline bool
358 # ifdef __SUPPORT_SNAN__
359 return fpclassify (__val
) == FP_ZERO
;
365 # endif /* __cplusplus */
366 #endif /* Use IEC_60559_BFP_EXT. */
369 /* Support for various different standard error handling behaviors. */
372 _IEEE_
= -1, /* According to IEEE 754/IEEE 854. */
373 _SVID_
, /* According to System V, release 4. */
374 _XOPEN_
, /* Nowadays also Unix98. */
376 _ISOC_
/* Actually this is ISO C99. */
379 /* This variable can be changed at run-time to any of the values above to
380 affect floating point error handling behavior (it may also be necessary
381 to change the hardware FPU exception settings). */
382 extern _LIB_VERSION_TYPE _LIB_VERSION
;
387 /* In SVID error handling, `matherr' is called with this description
388 of the exceptional condition.
390 We have a problem when using C++ since `exception' is a reserved
406 extern int matherr (struct __exception
*__exc
) throw ();
408 extern int matherr (struct exception
*__exc
);
411 # define X_TLOSS 1.41484755040568800000e+16
413 /* Types of exceptions in the `type' field. */
421 /* SVID mode specifies returning this large value instead of infinity. */
422 # define HUGE 3.40282347e+38F
427 /* X/Open wants another strange constant. */
428 # define MAXFLOAT 3.40282347e+38F
434 /* Some useful constants. */
435 #if defined __USE_MISC || defined __USE_XOPEN
436 # define M_E 2.7182818284590452354 /* e */
437 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
438 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
439 # define M_LN2 0.69314718055994530942 /* log_e 2 */
440 # define M_LN10 2.30258509299404568402 /* log_e 10 */
441 # define M_PI 3.14159265358979323846 /* pi */
442 # define M_PI_2 1.57079632679489661923 /* pi/2 */
443 # define M_PI_4 0.78539816339744830962 /* pi/4 */
444 # define M_1_PI 0.31830988618379067154 /* 1/pi */
445 # define M_2_PI 0.63661977236758134308 /* 2/pi */
446 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
447 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
448 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
451 /* The above constants are not adequate for computation using `long double's.
452 Therefore we provide as an extension constants with similar names as a
453 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
455 # define M_El 2.718281828459045235360287471352662498L /* e */
456 # define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
457 # define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
458 # define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
459 # define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
460 # define M_PIl 3.141592653589793238462643383279502884L /* pi */
461 # define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
462 # define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
463 # define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
464 # define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
465 # define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
466 # define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
467 # define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
471 /* When compiling in strict ISO C compatible mode we must not use the
472 inline functions since they, among other things, do not set the
473 `errno' variable correctly. */
474 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
475 # define __NO_MATH_INLINES 1
478 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
479 /* ISO C99 defines some macros to compare number while taking care for
480 unordered numbers. Many FPUs provide special instructions to support
481 these operations. Generic support in GCC for these as builtins went
482 in before 3.0.0, but not all cpus added their patterns. We define
483 versions that use the builtins here, and <bits/mathinline.h> will
484 undef/redefine as appropriate for the specific GCC version in use. */
485 # define isgreater(x, y) __builtin_isgreater(x, y)
486 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
487 # define isless(x, y) __builtin_isless(x, y)
488 # define islessequal(x, y) __builtin_islessequal(x, y)
489 # define islessgreater(x, y) __builtin_islessgreater(x, y)
490 # define isunordered(u, v) __builtin_isunordered(u, v)
493 /* Get machine-dependent inline versions (if there are any). */
494 #ifdef __USE_EXTERN_INLINES
495 # include <bits/mathinline.h>
498 /* Define special entry points to use when the compiler got told to
499 only expect finite results. */
500 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
501 # include <bits/math-finite.h>
505 /* If we've still got undefined comparison macros, provide defaults. */
507 /* Return nonzero value if X is greater than Y. */
509 # define isgreater(x, y) \
511 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
512 !isunordered (__x, __y) && __x > __y; }))
515 /* Return nonzero value if X is greater than or equal to Y. */
516 # ifndef isgreaterequal
517 # define isgreaterequal(x, y) \
519 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
520 !isunordered (__x, __y) && __x >= __y; }))
523 /* Return nonzero value if X is less than Y. */
525 # define isless(x, y) \
527 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
528 !isunordered (__x, __y) && __x < __y; }))
531 /* Return nonzero value if X is less than or equal to Y. */
533 # define islessequal(x, y) \
535 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
536 !isunordered (__x, __y) && __x <= __y; }))
539 /* Return nonzero value if either X is less than Y or Y is less than X. */
540 # ifndef islessgreater
541 # define islessgreater(x, y) \
543 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
544 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
547 /* Return nonzero value if arguments are unordered. */
549 # define isunordered(u, v) \
551 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
552 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
557 #if __GLIBC_USE (IEC_60559_BFP_EXT)
558 /* Return X == Y but raising "invalid" and setting errno if X or Y is
560 # ifdef __NO_LONG_DOUBLE_MATH
561 # if (__FLT_EVAL_METHOD__ == 1 \
562 || __FLT_EVAL_METHOD__ == 2 \
563 || __FLT_EVAL_METHOD__ > 32)
564 # define iseqsig(x, y) __iseqsig ((x), (y))
566 # define iseqsig(x, y) \
567 (sizeof ((x) + (y)) == sizeof (float) \
568 ? __iseqsigf ((x), (y)) \
569 : __iseqsig ((x), (y)))
572 # if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
573 # define iseqsig(x, y) __iseqsigl ((x), (y))
574 # elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
575 # define iseqsig(x, y) \
576 (sizeof ((x) + (y)) <= sizeof (double) \
577 ? __iseqsig ((x), (y)) \
578 : __iseqsigl ((x), (y)))
580 # define iseqsig(x, y) \
581 (sizeof ((x) + (y)) == sizeof (float) \
582 ? __iseqsigf ((x), (y)) \
583 : sizeof ((x) + (y)) == sizeof (double) \
584 ? __iseqsig ((x), (y)) \
585 : __iseqsigl ((x), (y)))