1 /* Declarations for math functions. 2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009, 2011 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 && defined _LIBC) \ 102 || defined __LDBL_COMPAT) 103 # ifdef __LDBL_COMPAT 104 105 # ifdef __USE_ISOC99 106 extern float __nldbl_nexttowardf (float __x, long double __y) 107 __THROW __attribute__ ((__const__)); 108 # ifdef __REDIRECT_NTH 109 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), 110 __nldbl_nexttowardf) 111 __attribute__ ((__const__)); 112 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), 113 nextafter) __attribute__ ((__const__)); 114 extern long double __REDIRECT_NTH (nexttowardl, 115 (long double __x, long double __y), 116 nextafter) __attribute__ ((__const__)); 117 # endif 118 # endif 119 # endif 120 121 # if defined __LDBL_COMPAT || defined __NO_LONG_DOUBLE_MATH 122 123 # undef __MATHDECL_1 124 # define __MATHDECL_2(type, function,suffix, args, alias) \ 125 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ 126 args, alias) 127 # define __MATHDECL_1(type, function,suffix, args) \ 128 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) 129 # endif 130 131 /* Include the file of declarations again, this time using `long double' 132 instead of `double' and appending l to each function name. */ 133 134 # 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 # define __MATH_DECLARE_LDOUBLE 1 146 # include <bits/mathcalls.h> 147 # undef _Mdouble_ 148 # undef _Mdouble_BEGIN_NAMESPACE 149 # undef _Mdouble_END_NAMESPACE 150 # undef __MATH_PRECNAME 151 152 # endif /* __STDC__ || __GNUC__ */ 153 154 #endif /* Use misc or ISO C99. */ 155 #undef __MATHDECL_1 156 #undef __MATHDECL 157 #undef __MATHCALL 158 159 160 #if defined __USE_MISC || defined __USE_XOPEN 161 /* This variable is used by `gamma' and `lgamma'. */ 162 extern int signgam; 163 #endif 164 165 166 /* ISO C99 defines some generic macros which work on any data type. */ 167 #ifdef __USE_ISOC99 168 169 /* Get the architecture specific values describing the floating-point 170 evaluation. The following symbols will get defined: 171 172 float_t floating-point type at least as wide as `float' used 173 to evaluate `float' expressions 174 double_t floating-point type at least as wide as `double' used 175 to evaluate `double' expressions 176 177 FLT_EVAL_METHOD 178 Defined to 179 0 if `float_t' is `float' and `double_t' is `double' 180 1 if `float_t' and `double_t' are `double' 181 2 if `float_t' and `double_t' are `long double' 182 else `float_t' and `double_t' are unspecified 183 184 INFINITY representation of the infinity value of type `float' 185 186 FP_FAST_FMA 187 FP_FAST_FMAF 188 FP_FAST_FMAL 189 If defined it indicates that the `fma' function 190 generally executes about as fast as a multiply and an add. 191 This macro is defined only iff the `fma' function is 192 implemented directly with a hardware multiply-add instructions. 193 194 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 195 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 196 197 DECIMAL_DIG Number of decimal digits supported by conversion between 198 decimal and all internal floating-point formats. 199 200 */ 201 202 /* All floating-point numbers can be put in one of these categories. */ 203 enum 204 { 205 FP_NAN, 206 # define FP_NAN FP_NAN 207 FP_INFINITE, 208 # define FP_INFINITE FP_INFINITE 209 FP_ZERO, 210 # define FP_ZERO FP_ZERO 211 FP_SUBNORMAL, 212 # define FP_SUBNORMAL FP_SUBNORMAL 213 FP_NORMAL 214 # define FP_NORMAL FP_NORMAL 215 }; 216 217 /* Return number of classification appropriate for X. */ 218 # ifdef __NO_LONG_DOUBLE_MATH 219 # define fpclassify(x) \ 220 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) 221 # else 222 # define fpclassify(x) \ 223 (sizeof (x) == sizeof (float) \ 224 ? __fpclassifyf (x) \ 225 : sizeof (x) == sizeof (double) \ 226 ? __fpclassify (x) : __fpclassifyl (x)) 227 # endif 228 229 /* Return nonzero value if sign of X is negative. */ 230 # ifdef __NO_LONG_DOUBLE_MATH 231 # define signbit(x) \ 232 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) 233 # else 234 # define signbit(x) \ 235 (sizeof (x) == sizeof (float) \ 236 ? __signbitf (x) \ 237 : sizeof (x) == sizeof (double) \ 238 ? __signbit (x) : __signbitl (x)) 239 # endif 240 241 /* Return nonzero value if X is not +-Inf or NaN. */ 242 # ifdef __NO_LONG_DOUBLE_MATH 243 # define isfinite(x) \ 244 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) 245 # else 246 # define isfinite(x) \ 247 (sizeof (x) == sizeof (float) \ 248 ? __finitef (x) \ 249 : sizeof (x) == sizeof (double) \ 250 ? __finite (x) : __finitel (x)) 251 # endif 252 253 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ 254 # define isnormal(x) (fpclassify (x) == FP_NORMAL) 255 256 /* Return nonzero value if X is a NaN. We could use `fpclassify' but 257 we already have this functions `__isnan' and it is faster. */ 258 # ifdef __NO_LONG_DOUBLE_MATH 259 # define isnan(x) \ 260 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) 261 # else 262 # define isnan(x) \ 263 (sizeof (x) == sizeof (float) \ 264 ? __isnanf (x) \ 265 : sizeof (x) == sizeof (double) \ 266 ? __isnan (x) : __isnanl (x)) 267 # endif 268 269 /* Return nonzero value if X is positive or negative infinity. */ 270 # ifdef __NO_LONG_DOUBLE_MATH 271 # define isinf(x) \ 272 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) 273 # else 274 # define isinf(x) \ 275 (sizeof (x) == sizeof (float) \ 276 ? __isinff (x) \ 277 : sizeof (x) == sizeof (double) \ 278 ? __isinf (x) : __isinfl (x)) 279 # endif 280 281 /* Bitmasks for the math_errhandling macro. */ 282 # define MATH_ERRNO 1 /* errno set by math functions. */ 283 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ 284 285 /* By default all functions support both errno and exception handling. 286 In gcc's fast math mode and if inline functions are defined this 287 might not be true. */ 288 # ifndef __FAST_MATH__ 289 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT) 290 # endif 291 292 #endif /* Use ISO C99. */ 293 294 #ifdef __USE_MISC 295 /* Support for various different standard error handling behaviors. */ 296 typedef enum 297 { 298 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 299 _SVID_, /* According to System V, release 4. */ 300 _XOPEN_, /* Nowadays also Unix98. */ 301 _POSIX_, 302 _ISOC_ /* Actually this is ISO C99. */ 303 } _LIB_VERSION_TYPE; 304 305 /* This variable can be changed at run-time to any of the values above to 306 affect floating point error handling behavior (it may also be necessary 307 to change the hardware FPU exception settings). */ 308 extern _LIB_VERSION_TYPE _LIB_VERSION; 309 #endif 310 311 312 #ifdef __USE_SVID 313 /* In SVID error handling, `matherr' is called with this description 314 of the exceptional condition. 315 316 We have a problem when using C++ since `exception' is a reserved 317 name in C++. */ 318 # ifdef __cplusplus 319 struct __exception 320 # else 321 struct exception 322 # endif 323 { 324 int type; 325 char *name; 326 double arg1; 327 double arg2; 328 double retval; 329 }; 330 331 # ifdef __cplusplus 332 extern int matherr (struct __exception *__exc) throw (); 333 # else 334 extern int matherr (struct exception *__exc); 335 # endif 336 337 # define X_TLOSS 1.41484755040568800000e+16 338 339 /* Types of exceptions in the `type' field. */ 340 # define DOMAIN 1 341 # define SING 2 342 # define OVERFLOW 3 343 # define UNDERFLOW 4 344 # define TLOSS 5 345 # define PLOSS 6 346 347 /* SVID mode specifies returning this large value instead of infinity. */ 348 # define HUGE 3.40282347e+38F 349 350 #else /* !SVID */ 351 352 # ifdef __USE_XOPEN 353 /* X/Open wants another strange constant. */ 354 # define MAXFLOAT 3.40282347e+38F 355 # endif 356 357 #endif /* SVID */ 358 359 360 /* Some useful constants. */ 361 #if defined __USE_BSD || defined __USE_XOPEN 362 # define M_E 2.7182818284590452354 /* e */ 363 # define M_LOG2E 1.4426950408889634074 /* log_2 e */ 364 # define M_LOG10E 0.43429448190325182765 /* log_10 e */ 365 # define M_LN2 0.69314718055994530942 /* log_e 2 */ 366 # define M_LN10 2.30258509299404568402 /* log_e 10 */ 367 # define M_PI 3.14159265358979323846 /* pi */ 368 # define M_PI_2 1.57079632679489661923 /* pi/2 */ 369 # define M_PI_4 0.78539816339744830962 /* pi/4 */ 370 # define M_1_PI 0.31830988618379067154 /* 1/pi */ 371 # define M_2_PI 0.63661977236758134308 /* 2/pi */ 372 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 373 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 374 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 375 #endif 376 377 /* The above constants are not adequate for computation using `long double's. 378 Therefore we provide as an extension constants with similar names as a 379 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 380 #ifdef __USE_GNU 381 # define M_El 2.7182818284590452353602874713526625L /* e */ 382 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ 383 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ 384 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ 385 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ 386 # define M_PIl 3.1415926535897932384626433832795029L /* pi */ 387 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ 388 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ 389 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ 390 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ 391 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ 392 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ 393 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ 394 #endif 395 396 397 /* When compiling in strict ISO C compatible mode we must not use the 398 inline functions since they, among other things, do not set the 399 `errno' variable correctly. */ 400 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 401 # define __NO_MATH_INLINES 1 402 #endif 403 404 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) 405 /* ISO C99 defines some macros to compare number while taking care for 406 unordered numbers. Many FPUs provide special instructions to support 407 these operations. Generic support in GCC for these as builtins went 408 in before 3.0.0, but not all cpus added their patterns. We define 409 versions that use the builtins here, and <bits/mathinline.h> will 410 undef/redefine as appropriate for the specific GCC version in use. */ 411 # define isgreater(x, y) __builtin_isgreater(x, y) 412 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) 413 # define isless(x, y) __builtin_isless(x, y) 414 # define islessequal(x, y) __builtin_islessequal(x, y) 415 # define islessgreater(x, y) __builtin_islessgreater(x, y) 416 # define isunordered(u, v) __builtin_isunordered(u, v) 417 #endif 418 419 /* Get machine-dependent inline versions (if there are any). */ 420 #ifdef __USE_EXTERN_INLINES 421 # include <bits/mathinline.h> 422 #endif 423 424 /* Define special entry points to use when the compiler got told to 425 only expect finite results. */ 426 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0 427 # include <bits/math-finite.h> 428 #endif 429 430 #ifdef __USE_ISOC99 431 /* If we've still got undefined comparison macros, provide defaults. */ 432 433 /* Return nonzero value if X is greater than Y. */ 434 # ifndef isgreater 435 # define isgreater(x, y) \ 436 (__extension__ \ 437 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 438 !isunordered (__x, __y) && __x > __y; })) 439 # endif 440 441 /* Return nonzero value if X is greater than or equal to Y. */ 442 # ifndef isgreaterequal 443 # define isgreaterequal(x, y) \ 444 (__extension__ \ 445 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 446 !isunordered (__x, __y) && __x >= __y; })) 447 # endif 448 449 /* Return nonzero value if X is less than Y. */ 450 # ifndef isless 451 # define isless(x, y) \ 452 (__extension__ \ 453 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 454 !isunordered (__x, __y) && __x < __y; })) 455 # endif 456 457 /* Return nonzero value if X is less than or equal to Y. */ 458 # ifndef islessequal 459 # define islessequal(x, y) \ 460 (__extension__ \ 461 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 462 !isunordered (__x, __y) && __x <= __y; })) 463 # endif 464 465 /* Return nonzero value if either X is less than Y or Y is less than X. */ 466 # ifndef islessgreater 467 # define islessgreater(x, y) \ 468 (__extension__ \ 469 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 470 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 471 # endif 472 473 /* Return nonzero value if arguments are unordered. */ 474 # ifndef isunordered 475 # define isunordered(u, v) \ 476 (__extension__ \ 477 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 478 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 479 # endif 480 481 #endif 482 483 __END_DECLS 484 485 486 #endif /* math.h */ 487
