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. 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, see 18 <http://www.gnu.org/licenses/>. */ 19 20 /* 21 * ISO C99 Standard: 7.12 Mathematics <math.h> 22 */ 23 24 #ifndef _MATH_H 25 #define _MATH_H 1 26 27 #include <features.h> 28 29 __BEGIN_DECLS 30 31 /* Get machine-dependent HUGE_VAL value (returned on overflow). 32 On all IEEE754 machines, this is +Infinity. */ 33 #include <bits/huge_val.h> 34 #ifdef __USE_ISOC99 35 # include <bits/huge_valf.h> 36 # include <bits/huge_vall.h> 37 38 /* Get machine-dependent INFINITY value. */ 39 # include <bits/inf.h> 40 41 /* Get machine-dependent NAN value (returned for some domain errors). */ 42 # include <bits/nan.h> 43 #endif /* __USE_ISOC99 */ 44 45 /* Get general and ISO C99 specific information. */ 46 #include <bits/mathdef.h> 47 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'. */ 52 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 65 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> 71 #undef _Mdouble_ 72 #undef _Mdouble_BEGIN_NAMESPACE 73 #undef _Mdouble_END_NAMESPACE 74 #undef __MATH_PRECNAME 75 76 #if defined __USE_MISC || defined __USE_ISOC99 77 78 79 /* Include the file of declarations again, this time using `float' 80 instead of `double' and appending f to each function name. */ 81 82 # ifndef _Mfloat_ 83 # define _Mfloat_ float 84 # endif 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> 90 # undef _Mdouble_ 91 # undef _Mdouble_BEGIN_NAMESPACE 92 # undef _Mdouble_END_NAMESPACE 93 # undef __MATH_PRECNAME 94 95 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \ 96 || defined __LDBL_COMPAT 97 # ifdef __LDBL_COMPAT 98 99 # ifdef __USE_ISOC99 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), 104 __nldbl_nexttowardf) 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__)); 111 # endif 112 # endif 113 # endif 114 115 # if defined __LDBL_COMPAT || defined __NO_LONG_DOUBLE_MATH 116 117 # undef __MATHDECL_1 118 # define __MATHDECL_2(type, function,suffix, args, alias) \ 119 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ 120 args, alias) 121 # define __MATHDECL_1(type, function,suffix, args) \ 122 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) 123 # endif 124 125 /* Include the file of declarations again, this time using `long double' 126 instead of `double' and appending l to each function name. */ 127 128 # ifndef _Mlong_double_ 129 # define _Mlong_double_ long double 130 # endif 131 # define _Mdouble_ _Mlong_double_ 132 # define __MATH_PRECNAME(name,r) name##l##r 133 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 134 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 135 # define __MATH_DECLARE_LDOUBLE 1 136 # include <bits/mathcalls.h> 137 # undef _Mdouble_ 138 # undef _Mdouble_BEGIN_NAMESPACE 139 # undef _Mdouble_END_NAMESPACE 140 # undef __MATH_PRECNAME 141 142 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */ 143 144 #endif /* Use misc or ISO C99. */ 145 #undef __MATHDECL_1 146 #undef __MATHDECL 147 #undef __MATHCALL 148 149 150 #if defined __USE_MISC || defined __USE_XOPEN 151 /* This variable is used by `gamma' and `lgamma'. */ 152 extern int signgam; 153 #endif 154 155 156 /* ISO C99 defines some generic macros which work on any data type. */ 157 #ifdef __USE_ISOC99 158 159 /* Get the architecture specific values describing the floating-point 160 evaluation. The following symbols will get defined: 161 162 float_t floating-point type at least as wide as `float' used 163 to evaluate `float' expressions 164 double_t floating-point type at least as wide as `double' used 165 to evaluate `double' expressions 166 167 FLT_EVAL_METHOD 168 Defined to 169 0 if `float_t' is `float' and `double_t' is `double' 170 1 if `float_t' and `double_t' are `double' 171 2 if `float_t' and `double_t' are `long double' 172 else `float_t' and `double_t' are unspecified 173 174 INFINITY representation of the infinity value of type `float' 175 176 FP_FAST_FMA 177 FP_FAST_FMAF 178 FP_FAST_FMAL 179 If defined it indicates that the `fma' function 180 generally executes about as fast as a multiply and an add. 181 This macro is defined only iff the `fma' function is 182 implemented directly with a hardware multiply-add instructions. 183 184 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 185 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 186 187 DECIMAL_DIG Number of decimal digits supported by conversion between 188 decimal and all internal floating-point formats. 189 190 */ 191 192 /* All floating-point numbers can be put in one of these categories. */ 193 enum 194 { 195 FP_NAN = 196 # define FP_NAN 0 197 FP_NAN, 198 FP_INFINITE = 199 # define FP_INFINITE 1 200 FP_INFINITE, 201 FP_ZERO = 202 # define FP_ZERO 2 203 FP_ZERO, 204 FP_SUBNORMAL = 205 # define FP_SUBNORMAL 3 206 FP_SUBNORMAL, 207 FP_NORMAL = 208 # define FP_NORMAL 4 209 FP_NORMAL 210 }; 211 212 /* Return number of classification appropriate for X. */ 213 # ifdef __NO_LONG_DOUBLE_MATH 214 # define fpclassify(x) \ 215 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) 216 # else 217 # define fpclassify(x) \ 218 (sizeof (x) == sizeof (float) \ 219 ? __fpclassifyf (x) \ 220 : sizeof (x) == sizeof (double) \ 221 ? __fpclassify (x) : __fpclassifyl (x)) 222 # endif 223 224 /* Return nonzero value if sign of X is negative. */ 225 # ifdef __NO_LONG_DOUBLE_MATH 226 # define signbit(x) \ 227 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) 228 # else 229 # define signbit(x) \ 230 (sizeof (x) == sizeof (float) \ 231 ? __signbitf (x) \ 232 : sizeof (x) == sizeof (double) \ 233 ? __signbit (x) : __signbitl (x)) 234 # endif 235 236 /* Return nonzero value if X is not +-Inf or NaN. */ 237 # ifdef __NO_LONG_DOUBLE_MATH 238 # define isfinite(x) \ 239 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) 240 # else 241 # define isfinite(x) \ 242 (sizeof (x) == sizeof (float) \ 243 ? __finitef (x) \ 244 : sizeof (x) == sizeof (double) \ 245 ? __finite (x) : __finitel (x)) 246 # endif 247 248 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ 249 # define isnormal(x) (fpclassify (x) == FP_NORMAL) 250 251 /* Return nonzero value if X is a NaN. We could use `fpclassify' but 252 we already have this functions `__isnan' and it is faster. */ 253 # ifdef __NO_LONG_DOUBLE_MATH 254 # define isnan(x) \ 255 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) 256 # else 257 # define isnan(x) \ 258 (sizeof (x) == sizeof (float) \ 259 ? __isnanf (x) \ 260 : sizeof (x) == sizeof (double) \ 261 ? __isnan (x) : __isnanl (x)) 262 # endif 263 264 /* Return nonzero value if X is positive or negative infinity. */ 265 # ifdef __NO_LONG_DOUBLE_MATH 266 # define isinf(x) \ 267 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) 268 # else 269 # define isinf(x) \ 270 (sizeof (x) == sizeof (float) \ 271 ? __isinff (x) \ 272 : sizeof (x) == sizeof (double) \ 273 ? __isinf (x) : __isinfl (x)) 274 # endif 275 276 /* Bitmasks for the math_errhandling macro. */ 277 # define MATH_ERRNO 1 /* errno set by math functions. */ 278 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ 279 280 /* By default all functions support both errno and exception handling. 281 In gcc's fast math mode and if inline functions are defined this 282 might not be true. */ 283 # ifndef __FAST_MATH__ 284 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT) 285 # endif 286 287 #endif /* Use ISO C99. */ 288 289 #ifdef __USE_MISC 290 /* Support for various different standard error handling behaviors. */ 291 typedef enum 292 { 293 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 294 _SVID_, /* According to System V, release 4. */ 295 _XOPEN_, /* Nowadays also Unix98. */ 296 _POSIX_, 297 _ISOC_ /* Actually this is ISO C99. */ 298 } _LIB_VERSION_TYPE; 299 300 /* This variable can be changed at run-time to any of the values above to 301 affect floating point error handling behavior (it may also be necessary 302 to change the hardware FPU exception settings). */ 303 extern _LIB_VERSION_TYPE _LIB_VERSION; 304 #endif 305 306 307 #ifdef __USE_SVID 308 /* In SVID error handling, `matherr' is called with this description 309 of the exceptional condition. 310 311 We have a problem when using C++ since `exception' is a reserved 312 name in C++. */ 313 # ifdef __cplusplus 314 struct __exception 315 # else 316 struct exception 317 # endif 318 { 319 int type; 320 char *name; 321 double arg1; 322 double arg2; 323 double retval; 324 }; 325 326 # ifdef __cplusplus 327 extern int matherr (struct __exception *__exc) throw (); 328 # else 329 extern int matherr (struct exception *__exc); 330 # endif 331 332 # define X_TLOSS 1.41484755040568800000e+16 333 334 /* Types of exceptions in the `type' field. */ 335 # define DOMAIN 1 336 # define SING 2 337 # define OVERFLOW 3 338 # define UNDERFLOW 4 339 # define TLOSS 5 340 # define PLOSS 6 341 342 /* SVID mode specifies returning this large value instead of infinity. */ 343 # define HUGE 3.40282347e+38F 344 345 #else /* !SVID */ 346 347 # ifdef __USE_XOPEN 348 /* X/Open wants another strange constant. */ 349 # define MAXFLOAT 3.40282347e+38F 350 # endif 351 352 #endif /* SVID */ 353 354 355 /* Some useful constants. */ 356 #if defined __USE_BSD || defined __USE_XOPEN 357 # define M_E 2.7182818284590452354 /* e */ 358 # define M_LOG2E 1.4426950408889634074 /* log_2 e */ 359 # define M_LOG10E 0.43429448190325182765 /* log_10 e */ 360 # define M_LN2 0.69314718055994530942 /* log_e 2 */ 361 # define M_LN10 2.30258509299404568402 /* log_e 10 */ 362 # define M_PI 3.14159265358979323846 /* pi */ 363 # define M_PI_2 1.57079632679489661923 /* pi/2 */ 364 # define M_PI_4 0.78539816339744830962 /* pi/4 */ 365 # define M_1_PI 0.31830988618379067154 /* 1/pi */ 366 # define M_2_PI 0.63661977236758134308 /* 2/pi */ 367 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 368 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 369 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 370 #endif 371 372 /* The above constants are not adequate for computation using `long double's. 373 Therefore we provide as an extension constants with similar names as a 374 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 375 #ifdef __USE_GNU 376 # define M_El 2.718281828459045235360287471352662498L /* e */ 377 # define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */ 378 # define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */ 379 # define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */ 380 # define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */ 381 # define M_PIl 3.141592653589793238462643383279502884L /* pi */ 382 # define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */ 383 # define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */ 384 # define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */ 385 # define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */ 386 # define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */ 387 # define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */ 388 # define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */ 389 #endif 390 391 392 /* When compiling in strict ISO C compatible mode we must not use the 393 inline functions since they, among other things, do not set the 394 `errno' variable correctly. */ 395 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 396 # define __NO_MATH_INLINES 1 397 #endif 398 399 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) 400 /* ISO C99 defines some macros to compare number while taking care for 401 unordered numbers. Many FPUs provide special instructions to support 402 these operations. Generic support in GCC for these as builtins went 403 in before 3.0.0, but not all cpus added their patterns. We define 404 versions that use the builtins here, and <bits/mathinline.h> will 405 undef/redefine as appropriate for the specific GCC version in use. */ 406 # define isgreater(x, y) __builtin_isgreater(x, y) 407 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) 408 # define isless(x, y) __builtin_isless(x, y) 409 # define islessequal(x, y) __builtin_islessequal(x, y) 410 # define islessgreater(x, y) __builtin_islessgreater(x, y) 411 # define isunordered(u, v) __builtin_isunordered(u, v) 412 #endif 413 414 /* Get machine-dependent inline versions (if there are any). */ 415 #ifdef __USE_EXTERN_INLINES 416 # include <bits/mathinline.h> 417 #endif 418 419 /* Define special entry points to use when the compiler got told to 420 only expect finite results. */ 421 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0 422 # include <bits/math-finite.h> 423 #endif 424 425 #ifdef __USE_ISOC99 426 /* If we've still got undefined comparison macros, provide defaults. */ 427 428 /* Return nonzero value if X is greater than Y. */ 429 # ifndef isgreater 430 # define isgreater(x, y) \ 431 (__extension__ \ 432 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 433 !isunordered (__x, __y) && __x > __y; })) 434 # endif 435 436 /* Return nonzero value if X is greater than or equal to Y. */ 437 # ifndef isgreaterequal 438 # define isgreaterequal(x, y) \ 439 (__extension__ \ 440 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 441 !isunordered (__x, __y) && __x >= __y; })) 442 # endif 443 444 /* Return nonzero value if X is less than Y. */ 445 # ifndef isless 446 # define isless(x, y) \ 447 (__extension__ \ 448 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 449 !isunordered (__x, __y) && __x < __y; })) 450 # endif 451 452 /* Return nonzero value if X is less than or equal to Y. */ 453 # ifndef islessequal 454 # define islessequal(x, y) \ 455 (__extension__ \ 456 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 457 !isunordered (__x, __y) && __x <= __y; })) 458 # endif 459 460 /* Return nonzero value if either X is less than Y or Y is less than X. */ 461 # ifndef islessgreater 462 # define islessgreater(x, y) \ 463 (__extension__ \ 464 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 465 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 466 # endif 467 468 /* Return nonzero value if arguments are unordered. */ 469 # ifndef isunordered 470 # define isunordered(u, v) \ 471 (__extension__ \ 472 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 473 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 474 # endif 475 476 #endif 477 478 __END_DECLS 479 480 481 #endif /* math.h */ 482