1 /* Declarations for math functions. 2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006 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 __LDBL_COMPAT) 102 # ifdef __LDBL_COMPAT 103 104 # ifdef __USE_ISOC99 105 extern float __nldbl_nexttowardf (float __x, long double __y) 106 __THROW __attribute__ ((__const__)); 107 # ifdef __REDIRECT_NTH 108 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), 109 __nldbl_nexttowardf) 110 __attribute__ ((__const__)); 111 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), 112 nextafter) __attribute__ ((__const__)); 113 extern long double __REDIRECT_NTH (nexttowardl, 114 (long double __x, long double __y), 115 nextafter) __attribute__ ((__const__)); 116 # endif 117 # endif 118 119 /* Include the file of declarations again, this time using `long double' 120 instead of `double' and appending l to each function name. */ 121 122 # undef __MATHDECL_1 123 # define __MATHDECL_2(type, function,suffix, args, alias) \ 124 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ 125 args, alias) 126 # define __MATHDECL_1(type, function,suffix, args) \ 127 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) 128 # endif 129 130 # ifndef _Mlong_double_ 131 # define _Mlong_double_ long double 132 # endif 133 # define _Mdouble_ _Mlong_double_ 134 # ifdef __STDC__ 135 # define __MATH_PRECNAME(name,r) name##l##r 136 # else 137 # define __MATH_PRECNAME(name,r) name/**/l/**/r 138 # endif 139 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 140 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 141 # include <bits/mathcalls.h> 142 # undef _Mdouble_ 143 # undef _Mdouble_BEGIN_NAMESPACE 144 # undef _Mdouble_END_NAMESPACE 145 # undef __MATH_PRECNAME 146 147 # endif /* __STDC__ || __GNUC__ */ 148 149 #endif /* Use misc or ISO C99. */ 150 #undef __MATHDECL_1 151 #undef __MATHDECL 152 #undef __MATHCALL 153 154 155 #if defined __USE_MISC || defined __USE_XOPEN 156 /* This variable is used by `gamma' and `lgamma'. */ 157 extern int signgam; 158 #endif 159 160 161 /* ISO C99 defines some generic macros which work on any data type. */ 162 #ifdef __USE_ISOC99 163 164 /* Get the architecture specific values describing the floating-point 165 evaluation. The following symbols will get defined: 166 167 float_t floating-point type at least as wide as `float' used 168 to evaluate `float' expressions 169 double_t floating-point type at least as wide as `double' used 170 to evaluate `double' expressions 171 172 FLT_EVAL_METHOD 173 Defined to 174 0 if `float_t' is `float' and `double_t' is `double' 175 1 if `float_t' and `double_t' are `double' 176 2 if `float_t' and `double_t' are `long double' 177 else `float_t' and `double_t' are unspecified 178 179 INFINITY representation of the infinity value of type `float' 180 181 FP_FAST_FMA 182 FP_FAST_FMAF 183 FP_FAST_FMAL 184 If defined it indicates that the `fma' function 185 generally executes about as fast as a multiply and an add. 186 This macro is defined only iff the `fma' function is 187 implemented directly with a hardware multiply-add instructions. 188 189 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 190 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 191 192 DECIMAL_DIG Number of decimal digits supported by conversion between 193 decimal and all internal floating-point formats. 194 195 */ 196 197 /* All floating-point numbers can be put in one of these categories. */ 198 enum 199 { 200 FP_NAN, 201 # define FP_NAN FP_NAN 202 FP_INFINITE, 203 # define FP_INFINITE FP_INFINITE 204 FP_ZERO, 205 # define FP_ZERO FP_ZERO 206 FP_SUBNORMAL, 207 # define FP_SUBNORMAL FP_SUBNORMAL 208 FP_NORMAL 209 # define FP_NORMAL 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 is 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 #endif /* Use ISO C99. */ 281 282 #ifdef __USE_MISC 283 /* Support for various different standard error handling behaviors. */ 284 typedef enum 285 { 286 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 287 _SVID_, /* According to System V, release 4. */ 288 _XOPEN_, /* Nowadays also Unix98. */ 289 _POSIX_, 290 _ISOC_ /* Actually this is ISO C99. */ 291 } _LIB_VERSION_TYPE; 292 293 /* This variable can be changed at run-time to any of the values above to 294 affect floating point error handling behavior (it may also be necessary 295 to change the hardware FPU exception settings). */ 296 extern _LIB_VERSION_TYPE _LIB_VERSION; 297 #endif 298 299 300 #ifdef __USE_SVID 301 /* In SVID error handling, `matherr' is called with this description 302 of the exceptional condition. 303 304 We have a problem when using C++ since `exception' is a reserved 305 name in C++. */ 306 # ifdef __cplusplus 307 struct __exception 308 # else 309 struct exception 310 # endif 311 { 312 int type; 313 char *name; 314 double arg1; 315 double arg2; 316 double retval; 317 }; 318 319 # ifdef __cplusplus 320 extern int matherr (struct __exception *__exc) throw (); 321 # else 322 extern int matherr (struct exception *__exc); 323 # endif 324 325 # define X_TLOSS 1.41484755040568800000e+16 326 327 /* Types of exceptions in the `type' field. */ 328 # define DOMAIN 1 329 # define SING 2 330 # define OVERFLOW 3 331 # define UNDERFLOW 4 332 # define TLOSS 5 333 # define PLOSS 6 334 335 /* SVID mode specifies returning this large value instead of infinity. */ 336 # define HUGE 3.40282347e+38F 337 338 #else /* !SVID */ 339 340 # ifdef __USE_XOPEN 341 /* X/Open wants another strange constant. */ 342 # define MAXFLOAT 3.40282347e+38F 343 # endif 344 345 #endif /* SVID */ 346 347 348 /* Some useful constants. */ 349 #if defined __USE_BSD || defined __USE_XOPEN 350 # define M_E 2.7182818284590452354 /* e */ 351 # define M_LOG2E 1.4426950408889634074 /* log_2 e */ 352 # define M_LOG10E 0.43429448190325182765 /* log_10 e */ 353 # define M_LN2 0.69314718055994530942 /* log_e 2 */ 354 # define M_LN10 2.30258509299404568402 /* log_e 10 */ 355 # define M_PI 3.14159265358979323846 /* pi */ 356 # define M_PI_2 1.57079632679489661923 /* pi/2 */ 357 # define M_PI_4 0.78539816339744830962 /* pi/4 */ 358 # define M_1_PI 0.31830988618379067154 /* 1/pi */ 359 # define M_2_PI 0.63661977236758134308 /* 2/pi */ 360 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 361 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 362 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 363 #endif 364 365 /* The above constants are not adequate for computation using `long double's. 366 Therefore we provide as an extension constants with similar names as a 367 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 368 #ifdef __USE_GNU 369 # define M_El 2.7182818284590452353602874713526625L /* e */ 370 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ 371 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ 372 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ 373 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ 374 # define M_PIl 3.1415926535897932384626433832795029L /* pi */ 375 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ 376 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ 377 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ 378 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ 379 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ 380 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ 381 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ 382 #endif 383 384 385 /* When compiling in strict ISO C compatible mode we must not use the 386 inline functions since they, among other things, do not set the 387 `errno' variable correctly. */ 388 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 389 # define __NO_MATH_INLINES 1 390 #endif 391 392 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) 393 /* ISO C99 defines some macros to compare number while taking care for 394 unordered numbers. Many FPUs provide special instructions to support 395 these operations. Generic support in GCC for these as builtins went 396 in before 3.0.0, but not all cpus added their patterns. We define 397 versions that use the builtins here, and <bits/mathinline.h> will 398 undef/redefine as appropriate for the specific GCC version in use. */ 399 # define isgreater(x, y) __builtin_isgreater(x, y) 400 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) 401 # define isless(x, y) __builtin_isless(x, y) 402 # define islessequal(x, y) __builtin_islessequal(x, y) 403 # define islessgreater(x, y) __builtin_islessgreater(x, y) 404 # define isunordered(u, v) __builtin_isunordered(u, v) 405 #endif 406 407 /* Get machine-dependent inline versions (if there are any). */ 408 #ifdef __USE_EXTERN_INLINES 409 # include <bits/mathinline.h> 410 #endif 411 412 #ifdef __USE_ISOC99 413 /* If we've still got undefined comparison macros, provide defaults. */ 414 415 /* Return nonzero value if X is greater than Y. */ 416 # ifndef isgreater 417 # define isgreater(x, y) \ 418 (__extension__ \ 419 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 420 !isunordered (__x, __y) && __x > __y; })) 421 # endif 422 423 /* Return nonzero value if X is greater than or equal to Y. */ 424 # ifndef isgreaterequal 425 # define isgreaterequal(x, y) \ 426 (__extension__ \ 427 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 428 !isunordered (__x, __y) && __x >= __y; })) 429 # endif 430 431 /* Return nonzero value if X is less than Y. */ 432 # ifndef isless 433 # define isless(x, y) \ 434 (__extension__ \ 435 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 436 !isunordered (__x, __y) && __x < __y; })) 437 # endif 438 439 /* Return nonzero value if X is less than or equal to Y. */ 440 # ifndef islessequal 441 # define islessequal(x, y) \ 442 (__extension__ \ 443 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 444 !isunordered (__x, __y) && __x <= __y; })) 445 # endif 446 447 /* Return nonzero value if either X is less than Y or Y is less than X. */ 448 # ifndef islessgreater 449 # define islessgreater(x, y) \ 450 (__extension__ \ 451 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 452 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 453 # endif 454 455 /* Return nonzero value if arguments are unordered. */ 456 # ifndef isunordered 457 # define isunordered(u, v) \ 458 (__extension__ \ 459 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 460 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 461 # endif 462 463 #endif 464 465 __END_DECLS 466 467 468 #endif /* math.h */ 469
