1 /* Declarations for math functions.
2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009, 2011, 2012
3 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
21 * ISO C99 Standard: 7.12 Mathematics <math.h>
31 /* Get machine-dependent HUGE_VAL value (returned on overflow).
32 On all IEEE754 machines, this is +Infinity. */
33 #include <bits/huge_val.h>
35 # include <bits/huge_valf.h>
36 # include <bits/huge_vall.h>
38 /* Get machine-dependent INFINITY value. */
39 # include <bits/inf.h>
41 /* Get machine-dependent NAN value (returned for some domain errors). */
42 # include <bits/nan.h>
43 #endif /* __USE_ISOC99 */
45 /* Get general and ISO C99 specific information. */
46 #include <bits/mathdef.h>
48 /* The file <bits/mathcalls.h> contains the prototypes for all the
49 actual math functions. These macros are used for those prototypes,
50 so we can easily declare each function as both `name' and `__name',
51 and can declare the float versions `namef' and `__namef'. */
53 #define __MATHCALL(function,suffix, args) \
54 __MATHDECL (_Mdouble_,function,suffix, args)
55 #define __MATHDECL(type, function,suffix, args) \
56 __MATHDECL_1(type, function,suffix, args); \
57 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
58 #define __MATHCALLX(function,suffix, args, attrib) \
59 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
60 #define __MATHDECLX(type, function,suffix, args, attrib) \
61 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
62 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
63 #define __MATHDECL_1(type, function,suffix, args) \
64 extern type __MATH_PRECNAME(function,suffix) args __THROW
66 #define _Mdouble_ double
67 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
68 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
69 #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
70 #include <bits/mathcalls.h>
72 #undef _Mdouble_BEGIN_NAMESPACE
73 #undef _Mdouble_END_NAMESPACE
74 #undef __MATH_PRECNAME
76 #if defined __USE_MISC || defined __USE_ISOC99
79 /* Include the file of declarations again, this time using `float'
80 instead of `double' and appending f to each function name. */
83 # define _Mfloat_ float
85 # define _Mdouble_ _Mfloat_
86 # define __MATH_PRECNAME(name,r) name##f##r
87 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
88 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
89 # include <bits/mathcalls.h>
91 # undef _Mdouble_BEGIN_NAMESPACE
92 # undef _Mdouble_END_NAMESPACE
93 # undef __MATH_PRECNAME
95 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
96 || defined __LDBL_COMPAT
100 extern float __nldbl_nexttowardf (float __x, long double __y)
101 __THROW __attribute__ ((__const__));
102 # ifdef __REDIRECT_NTH
103 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
105 __attribute__ ((__const__));
106 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
107 nextafter) __attribute__ ((__const__));
108 extern long double __REDIRECT_NTH (nexttowardl,
109 (long double __x, long double __y),
110 nextafter) __attribute__ ((__const__));
115 # define __MATHDECL_2(type, function,suffix, args, alias) \
116 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
118 # define __MATHDECL_1(type, function,suffix, args) \
119 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
122 /* Include the file of declarations again, this time using `long double'
123 instead of `double' and appending l to each function name. */
125 # ifndef _Mlong_double_
126 # define _Mlong_double_ long double
128 # define _Mdouble_ _Mlong_double_
129 # define __MATH_PRECNAME(name,r) name##l##r
130 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
131 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
132 # define __MATH_DECLARE_LDOUBLE 1
133 # include <bits/mathcalls.h>
135 # undef _Mdouble_BEGIN_NAMESPACE
136 # undef _Mdouble_END_NAMESPACE
137 # undef __MATH_PRECNAME
139 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
141 #endif /* Use misc or ISO C99. */
147 #if defined __USE_MISC || defined __USE_XOPEN
148 /* This variable is used by `gamma' and `lgamma'. */
153 /* ISO C99 defines some generic macros which work on any data type. */
156 /* Get the architecture specific values describing the floating-point
157 evaluation. The following symbols will get defined:
159 float_t floating-point type at least as wide as `float' used
160 to evaluate `float' expressions
161 double_t floating-point type at least as wide as `double' used
162 to evaluate `double' expressions
166 0 if `float_t' is `float' and `double_t' is `double'
167 1 if `float_t' and `double_t' are `double'
168 2 if `float_t' and `double_t' are `long double'
169 else `float_t' and `double_t' are unspecified
171 INFINITY representation of the infinity value of type `float'
176 If defined it indicates that the `fma' function
177 generally executes about as fast as a multiply and an add.
178 This macro is defined only iff the `fma' function is
179 implemented directly with a hardware multiply-add instructions.
181 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
182 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
184 DECIMAL_DIG Number of decimal digits supported by conversion between
185 decimal and all internal floating-point formats.
189 /* All floating-point numbers can be put in one of these categories. */
193 # define FP_NAN FP_NAN
195 # define FP_INFINITE FP_INFINITE
197 # define FP_ZERO FP_ZERO
199 # define FP_SUBNORMAL FP_SUBNORMAL
201 # define FP_NORMAL FP_NORMAL
204 /* Return number of classification appropriate for X. */
205 # ifdef __NO_LONG_DOUBLE_MATH
206 # define fpclassify(x) \
207 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
209 # define fpclassify(x) \
210 (sizeof (x) == sizeof (float) \
211 ? __fpclassifyf (x) \
212 : sizeof (x) == sizeof (double) \
213 ? __fpclassify (x) : __fpclassifyl (x))
216 /* Return nonzero value if sign of X is negative. */
217 # ifdef __NO_LONG_DOUBLE_MATH
218 # define signbit(x) \
219 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
221 # define signbit(x) \
222 (sizeof (x) == sizeof (float) \
224 : sizeof (x) == sizeof (double) \
225 ? __signbit (x) : __signbitl (x))
228 /* Return nonzero value if X is not +-Inf or NaN. */
229 # ifdef __NO_LONG_DOUBLE_MATH
230 # define isfinite(x) \
231 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
233 # define isfinite(x) \
234 (sizeof (x) == sizeof (float) \
236 : sizeof (x) == sizeof (double) \
237 ? __finite (x) : __finitel (x))
240 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
241 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
243 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
244 we already have this functions `__isnan' and it is faster. */
245 # ifdef __NO_LONG_DOUBLE_MATH
247 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
250 (sizeof (x) == sizeof (float) \
252 : sizeof (x) == sizeof (double) \
253 ? __isnan (x) : __isnanl (x))
256 /* Return nonzero value if X is positive or negative infinity. */
257 # ifdef __NO_LONG_DOUBLE_MATH
259 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
262 (sizeof (x) == sizeof (float) \
264 : sizeof (x) == sizeof (double) \
265 ? __isinf (x) : __isinfl (x))
268 /* Bitmasks for the math_errhandling macro. */
269 # define MATH_ERRNO 1 /* errno set by math functions. */
270 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
272 /* By default all functions support both errno and exception handling.
273 In gcc's fast math mode and if inline functions are defined this
274 might not be true. */
275 # ifndef __FAST_MATH__
276 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
279 #endif /* Use ISO C99. */
282 /* Support for various different standard error handling behaviors. */
285 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
286 _SVID_, /* According to System V, release 4. */
287 _XOPEN_, /* Nowadays also Unix98. */
289 _ISOC_ /* Actually this is ISO C99. */
292 /* This variable can be changed at run-time to any of the values above to
293 affect floating point error handling behavior (it may also be necessary
294 to change the hardware FPU exception settings). */
295 extern _LIB_VERSION_TYPE _LIB_VERSION;
300 /* In SVID error handling, `matherr' is called with this description
301 of the exceptional condition.
303 We have a problem when using C++ since `exception' is a reserved
319 extern int matherr (struct __exception *__exc) throw ();
321 extern int matherr (struct exception *__exc);
324 # define X_TLOSS 1.41484755040568800000e+16
326 /* Types of exceptions in the `type' field. */
334 /* SVID mode specifies returning this large value instead of infinity. */
335 # define HUGE 3.40282347e+38F
340 /* X/Open wants another strange constant. */
341 # define MAXFLOAT 3.40282347e+38F
347 /* Some useful constants. */
348 #if defined __USE_BSD || defined __USE_XOPEN
349 # define M_E 2.7182818284590452354 /* e */
350 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
351 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
352 # define M_LN2 0.69314718055994530942 /* log_e 2 */
353 # define M_LN10 2.30258509299404568402 /* log_e 10 */
354 # define M_PI 3.14159265358979323846 /* pi */
355 # define M_PI_2 1.57079632679489661923 /* pi/2 */
356 # define M_PI_4 0.78539816339744830962 /* pi/4 */
357 # define M_1_PI 0.31830988618379067154 /* 1/pi */
358 # define M_2_PI 0.63661977236758134308 /* 2/pi */
359 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
360 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
361 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
364 /* The above constants are not adequate for computation using `long double's.
365 Therefore we provide as an extension constants with similar names as a
366 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
368 # define M_El 2.7182818284590452353602874713526625L /* e */
369 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */
370 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
371 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
372 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
373 # define M_PIl 3.1415926535897932384626433832795029L /* pi */
374 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
375 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
376 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
377 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
378 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
379 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
380 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
384 /* When compiling in strict ISO C compatible mode we must not use the
385 inline functions since they, among other things, do not set the
386 `errno' variable correctly. */
387 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
388 # define __NO_MATH_INLINES 1
391 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
392 /* ISO C99 defines some macros to compare number while taking care for
393 unordered numbers. Many FPUs provide special instructions to support
394 these operations. Generic support in GCC for these as builtins went
395 in before 3.0.0, but not all cpus added their patterns. We define
396 versions that use the builtins here, and <bits/mathinline.h> will
397 undef/redefine as appropriate for the specific GCC version in use. */
398 # define isgreater(x, y) __builtin_isgreater(x, y)
399 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
400 # define isless(x, y) __builtin_isless(x, y)
401 # define islessequal(x, y) __builtin_islessequal(x, y)
402 # define islessgreater(x, y) __builtin_islessgreater(x, y)
403 # define isunordered(u, v) __builtin_isunordered(u, v)
406 /* Get machine-dependent inline versions (if there are any). */
407 #ifdef __USE_EXTERN_INLINES
408 # include <bits/mathinline.h>
411 /* Define special entry points to use when the compiler got told to
412 only expect finite results. */
413 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
414 # include <bits/math-finite.h>
418 /* If we've still got undefined comparison macros, provide defaults. */
420 /* Return nonzero value if X is greater than Y. */
422 # define isgreater(x, y) \
424 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
425 !isunordered (__x, __y) && __x > __y; }))
428 /* Return nonzero value if X is greater than or equal to Y. */
429 # ifndef isgreaterequal
430 # define isgreaterequal(x, y) \
432 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
433 !isunordered (__x, __y) && __x >= __y; }))
436 /* Return nonzero value if X is less than Y. */
438 # define isless(x, y) \
440 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
441 !isunordered (__x, __y) && __x < __y; }))
444 /* Return nonzero value if X is less than or equal to Y. */
446 # define islessequal(x, y) \
448 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
449 !isunordered (__x, __y) && __x <= __y; }))
452 /* Return nonzero value if either X is less than Y or Y is less than X. */
453 # ifndef islessgreater
454 # define islessgreater(x, y) \
456 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
457 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
460 /* Return nonzero value if arguments are unordered. */
462 # define isunordered(u, v) \
464 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
465 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))