1/* Declarations for math functions. 2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009 3 Free Software Foundation, Inc. 4 This file is part of the GNU C Library. 5 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. 10 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. 15 16 You should have received a copy of the GNU Lesser General Public 17 License along with the GNU C Library; if not, write to the Free 18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 19 02111-1307 USA. */ 20 21/* 22 * ISO C99 Standard: 7.12 Mathematics <math.h> 23 */ 24 25#ifndef _MATH_H 26#define _MATH_H 1 27 28#include <features.h> 29 30__BEGIN_DECLS 31 32/* Get machine-dependent HUGE_VAL value (returned on overflow). 33 On all IEEE754 machines, this is +Infinity. */ 34#include <bits/huge_val.h> 35#ifdef __USE_ISOC99 36# include <bits/huge_valf.h> 37# include <bits/huge_vall.h> 38 39/* Get machine-dependent INFINITY value. */ 40# include <bits/inf.h> 41 42/* Get machine-dependent NAN value (returned for some domain errors). */ 43# include <bits/nan.h> 44#endif /* __USE_ISOC99 */ 45 46/* Get general and ISO C99 specific information. */ 47#include <bits/mathdef.h> 48 49/* The file <bits/mathcalls.h> contains the prototypes for all the 50 actual math functions. These macros are used for those prototypes, 51 so we can easily declare each function as both `name' and `__name', 52 and can declare the float versions `namef' and `__namef'. */ 53 54#define __MATHCALL(function,suffix, args) \ 55 __MATHDECL (_Mdouble_,function,suffix, args) 56#define __MATHDECL(type, function,suffix, args) \ 57 __MATHDECL_1(type, function,suffix, args); \ 58 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) 59#define __MATHCALLX(function,suffix, args, attrib) \ 60 __MATHDECLX (_Mdouble_,function,suffix, args, attrib) 61#define __MATHDECLX(type, function,suffix, args, attrib) \ 62 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ 63 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) 64#define __MATHDECL_1(type, function,suffix, args) \ 65 extern type __MATH_PRECNAME(function,suffix) args __THROW 66 67#define _Mdouble_ double 68#define __MATH_PRECNAME(name,r) __CONCAT(name,r) 69# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD 70# define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD 71#include <bits/mathcalls.h> 72#undef _Mdouble_ 73#undef _Mdouble_BEGIN_NAMESPACE 74#undef _Mdouble_END_NAMESPACE 75#undef __MATH_PRECNAME 76 77#if defined __USE_MISC || defined __USE_ISOC99 78 79 80/* Include the file of declarations again, this time using `float' 81 instead of `double' and appending f to each function name. */ 82 83# ifndef _Mfloat_ 84# define _Mfloat_ float 85# endif 86# define _Mdouble_ _Mfloat_ 87# ifdef __STDC__ 88# define __MATH_PRECNAME(name,r) name##f##r 89# else 90# define __MATH_PRECNAME(name,r) name/**/f/**/r 91# endif 92# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 93# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 94# include <bits/mathcalls.h> 95# undef _Mdouble_ 96# undef _Mdouble_BEGIN_NAMESPACE 97# undef _Mdouble_END_NAMESPACE 98# undef __MATH_PRECNAME 99 100# if (__STDC__ - 0 || __GNUC__ - 0) \ 101 && (!defined __NO_LONG_DOUBLE_MATH \ 102 || defined __LDBL_COMPAT \ 103 || !defined _LIBC) 104# ifdef __LDBL_COMPAT 105 106# ifdef __USE_ISOC99 107extern float __nldbl_nexttowardf (float __x, long double __y) 108 __THROW __attribute__ ((__const__)); 109# ifdef __REDIRECT_NTH 110extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), 111 __nldbl_nexttowardf) 112 __attribute__ ((__const__)); 113extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), 114 nextafter) __attribute__ ((__const__)); 115extern long double __REDIRECT_NTH (nexttowardl, 116 (long double __x, long double __y), 117 nextafter) __attribute__ ((__const__)); 118# endif 119# endif 120# endif 121 122# if defined __LDBL_COMPAT || defined __NO_LONG_DOUBLE_MATH 123 124# undef __MATHDECL_1 125# define __MATHDECL_2(type, function,suffix, args, alias) \ 126 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ 127 args, alias) 128# define __MATHDECL_1(type, function,suffix, args) \ 129 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) 130# endif 131 132/* Include the file of declarations again, this time using `long double' 133 instead of `double' and appending l to each function name. */ 134# ifndef _Mlong_double_ 135# define _Mlong_double_ long double 136# endif 137# define _Mdouble_ _Mlong_double_ 138# ifdef __STDC__ 139# define __MATH_PRECNAME(name,r) name##l##r 140# else 141# define __MATH_PRECNAME(name,r) name/**/l/**/r 142# endif 143# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 144# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 145# include <bits/mathcalls.h> 146# undef _Mdouble_ 147# undef _Mdouble_BEGIN_NAMESPACE 148# undef _Mdouble_END_NAMESPACE 149# undef __MATH_PRECNAME 150 151# endif /* __STDC__ || __GNUC__ */ 152 153#endif /* Use misc or ISO C99. */ 154#undef __MATHDECL_1 155#undef __MATHDECL 156#undef __MATHCALL 157 158 159#if defined __USE_MISC || defined __USE_XOPEN 160/* This variable is used by `gamma' and `lgamma'. */ 161extern int signgam; 162#endif 163 164 165/* ISO C99 defines some generic macros which work on any data type. */ 166#ifdef __USE_ISOC99 167 168/* Get the architecture specific values describing the floating-point 169 evaluation. The following symbols will get defined: 170 171 float_t floating-point type at least as wide as `float' used 172 to evaluate `float' expressions 173 double_t floating-point type at least as wide as `double' used 174 to evaluate `double' expressions 175 176 FLT_EVAL_METHOD 177 Defined to 178 0 if `float_t' is `float' and `double_t' is `double' 179 1 if `float_t' and `double_t' are `double' 180 2 if `float_t' and `double_t' are `long double' 181 else `float_t' and `double_t' are unspecified 182 183 INFINITY representation of the infinity value of type `float' 184 185 FP_FAST_FMA 186 FP_FAST_FMAF 187 FP_FAST_FMAL 188 If defined it indicates that the `fma' function 189 generally executes about as fast as a multiply and an add. 190 This macro is defined only iff the `fma' function is 191 implemented directly with a hardware multiply-add instructions. 192 193 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 194 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 195 196 DECIMAL_DIG Number of decimal digits supported by conversion between 197 decimal and all internal floating-point formats. 198 199*/ 200 201/* All floating-point numbers can be put in one of these categories. */ 202enum 203 { 204 FP_NAN, 205# define FP_NAN FP_NAN 206 FP_INFINITE, 207# define FP_INFINITE FP_INFINITE 208 FP_ZERO, 209# define FP_ZERO FP_ZERO 210 FP_SUBNORMAL, 211# define FP_SUBNORMAL FP_SUBNORMAL 212 FP_NORMAL 213# define FP_NORMAL FP_NORMAL 214 }; 215 216/* Return number of classification appropriate for X. */ 217# ifdef __NO_LONG_DOUBLE_MATH 218# define fpclassify(x) \ 219 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) 220# else 221# define fpclassify(x) \ 222 (sizeof (x) == sizeof (float) \ 223 ? __fpclassifyf (x) \ 224 : sizeof (x) == sizeof (double) \ 225 ? __fpclassify (x) : __fpclassifyl (x)) 226# endif 227 228/* Return nonzero value if sign of X is negative. */ 229# ifdef __NO_LONG_DOUBLE_MATH 230# define signbit(x) \ 231 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) 232# else 233# define signbit(x) \ 234 (sizeof (x) == sizeof (float) \ 235 ? __signbitf (x) \ 236 : sizeof (x) == sizeof (double) \ 237 ? __signbit (x) : __signbitl (x)) 238# endif 239 240/* Return nonzero value if X is not +-Inf or NaN. */ 241# ifdef __NO_LONG_DOUBLE_MATH 242# define isfinite(x) \ 243 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) 244# else 245# define isfinite(x) \ 246 (sizeof (x) == sizeof (float) \ 247 ? __finitef (x) \ 248 : sizeof (x) == sizeof (double) \ 249 ? __finite (x) : __finitel (x)) 250# endif 251 252/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ 253# define isnormal(x) (fpclassify (x) == FP_NORMAL) 254 255/* Return nonzero value if X is a NaN. We could use `fpclassify' but 256 we already have this functions `__isnan' and it is faster. */ 257# ifdef __NO_LONG_DOUBLE_MATH 258# define isnan(x) \ 259 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) 260# else 261# define isnan(x) \ 262 (sizeof (x) == sizeof (float) \ 263 ? __isnanf (x) \ 264 : sizeof (x) == sizeof (double) \ 265 ? __isnan (x) : __isnanl (x)) 266# endif 267 268/* Return nonzero value is X is positive or negative infinity. */ 269# ifdef __NO_LONG_DOUBLE_MATH 270# define isinf(x) \ 271 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) 272# else 273# define isinf(x) \ 274 (sizeof (x) == sizeof (float) \ 275 ? __isinff (x) \ 276 : sizeof (x) == sizeof (double) \ 277 ? __isinf (x) : __isinfl (x)) 278# endif 279 280/* Bitmasks for the math_errhandling macro. */ 281# define MATH_ERRNO 1 /* errno set by math functions. */ 282# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ 283 284/* By default all functions support both errno and exception handling. 285 In gcc's fast math mode and if inline functions are defined this 286 might not be true. */ 287# ifndef __FAST_MATH__ 288# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT) 289# endif 290 291#endif /* Use ISO C99. */ 292 293#ifdef __USE_MISC 294/* Support for various different standard error handling behaviors. */ 295typedef enum 296{ 297 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 298 _SVID_, /* According to System V, release 4. */ 299 _XOPEN_, /* Nowadays also Unix98. */ 300 _POSIX_, 301 _ISOC_ /* Actually this is ISO C99. */ 302} _LIB_VERSION_TYPE; 303 304/* This variable can be changed at run-time to any of the values above to 305 affect floating point error handling behavior (it may also be necessary 306 to change the hardware FPU exception settings). */ 307extern _LIB_VERSION_TYPE _LIB_VERSION; 308#endif 309 310 311#ifdef __USE_SVID 312/* In SVID error handling, `matherr' is called with this description 313 of the exceptional condition. 314 315 We have a problem when using C++ since `exception' is a reserved 316 name in C++. */ 317# ifdef __cplusplus 318struct __exception 319# else 320struct exception 321# endif 322 { 323 int type; 324 char *name; 325 double arg1; 326 double arg2; 327 double retval; 328 }; 329 330# ifdef __cplusplus 331extern int matherr (struct __exception *__exc) throw (); 332# else 333extern int matherr (struct exception *__exc); 334# endif 335 336# define X_TLOSS 1.41484755040568800000e+16 337 338/* Types of exceptions in the `type' field. */ 339# define DOMAIN 1 340# define SING 2 341# define OVERFLOW 3 342# define UNDERFLOW 4 343# define TLOSS 5 344# define PLOSS 6 345 346/* SVID mode specifies returning this large value instead of infinity. */ 347# define HUGE 3.40282347e+38F 348 349#else /* !SVID */ 350 351# ifdef __USE_XOPEN 352/* X/Open wants another strange constant. */ 353# define MAXFLOAT 3.40282347e+38F 354# endif 355 356#endif /* SVID */ 357 358 359/* Some useful constants. */ 360#if defined __USE_BSD || defined __USE_XOPEN 361# define M_E 2.7182818284590452354 /* e */ 362# define M_LOG2E 1.4426950408889634074 /* log_2 e */ 363# define M_LOG10E 0.43429448190325182765 /* log_10 e */ 364# define M_LN2 0.69314718055994530942 /* log_e 2 */ 365# define M_LN10 2.30258509299404568402 /* log_e 10 */ 366# define M_PI 3.14159265358979323846 /* pi */ 367# define M_PI_2 1.57079632679489661923 /* pi/2 */ 368# define M_PI_4 0.78539816339744830962 /* pi/4 */ 369# define M_1_PI 0.31830988618379067154 /* 1/pi */ 370# define M_2_PI 0.63661977236758134308 /* 2/pi */ 371# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 372# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 373# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 374#endif 375 376/* The above constants are not adequate for computation using `long double's. 377 Therefore we provide as an extension constants with similar names as a 378 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 379#ifdef __USE_GNU 380# define M_El 2.7182818284590452353602874713526625L /* e */ 381# define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ 382# define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ 383# define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ 384# define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ 385# define M_PIl 3.1415926535897932384626433832795029L /* pi */ 386# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ 387# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ 388# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ 389# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ 390# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ 391# define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ 392# define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ 393#endif 394 395 396/* When compiling in strict ISO C compatible mode we must not use the 397 inline functions since they, among other things, do not set the 398 `errno' variable correctly. */ 399#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 400# define __NO_MATH_INLINES 1 401#endif 402 403#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) 404/* ISO C99 defines some macros to compare number while taking care for 405 unordered numbers. Many FPUs provide special instructions to support 406 these operations. Generic support in GCC for these as builtins went 407 in before 3.0.0, but not all cpus added their patterns. We define 408 versions that use the builtins here, and <bits/mathinline.h> will 409 undef/redefine as appropriate for the specific GCC version in use. */ 410# define isgreater(x, y) __builtin_isgreater(x, y) 411# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) 412# define isless(x, y) __builtin_isless(x, y) 413# define islessequal(x, y) __builtin_islessequal(x, y) 414# define islessgreater(x, y) __builtin_islessgreater(x, y) 415# define isunordered(u, v) __builtin_isunordered(u, v) 416#endif 417 418/* Get machine-dependent inline versions (if there are any). */ 419#ifdef __USE_EXTERN_INLINES 420# include <bits/mathinline.h> 421#endif 422 423#ifdef __USE_ISOC99 424/* If we've still got undefined comparison macros, provide defaults. */ 425 426/* Return nonzero value if X is greater than Y. */ 427# ifndef isgreater 428# define isgreater(x, y) \ 429 (__extension__ \ 430 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 431 !isunordered (__x, __y) && __x > __y; })) 432# endif 433 434/* Return nonzero value if X is greater than or equal to Y. */ 435# ifndef isgreaterequal 436# define isgreaterequal(x, y) \ 437 (__extension__ \ 438 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 439 !isunordered (__x, __y) && __x >= __y; })) 440# endif 441 442/* Return nonzero value if X is less than Y. */ 443# ifndef isless 444# define isless(x, y) \ 445 (__extension__ \ 446 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 447 !isunordered (__x, __y) && __x < __y; })) 448# endif 449 450/* Return nonzero value if X is less than or equal to Y. */ 451# ifndef islessequal 452# define islessequal(x, y) \ 453 (__extension__ \ 454 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 455 !isunordered (__x, __y) && __x <= __y; })) 456# endif 457 458/* Return nonzero value if either X is less than Y or Y is less than X. */ 459# ifndef islessgreater 460# define islessgreater(x, y) \ 461 (__extension__ \ 462 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 463 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 464# endif 465 466/* Return nonzero value if arguments are unordered. */ 467# ifndef isunordered 468# define isunordered(u, v) \ 469 (__extension__ \ 470 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 471 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 472# endif 473 474#endif 475 476__END_DECLS 477 478 479#endif /* math.h */ 480