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, 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 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 __MATHDECL_1(type,function,suffix,args) \ 55 extern type __MATH_PRECNAME(function,suffix) args __THROW 56 57 #define __MATHDECL(type,function,suffix,args) \ 58 __MATHDECL_1(type,function,suffix,args); 59 60 #define __MATHCALL(function,suffix,args) \ 61 __MATHDECL(_Mdouble_,function,suffix,args) 62 63 #define __MATHDECLX(type,function,suffix,args,attrib) \ 64 __MATHDECL_1(type,function,suffix,args) __attribute__ (attrib); \ 65 __MATH_maybe_libm_hidden_proto(function) 66 67 #define __MATHCALLX(function,suffix,args,attrib) \ 68 __MATHDECLX(_Mdouble_,function,suffix,args,attrib) 69 70 /* Decls which are also used internally in libm. 71 Only the main variant is used internally, no need to try to avoid relocs 72 for the {l,f} variants. */ 73 #define __MATHDECLI(type,function,suffix,args) \ 74 __MATHDECL_1(type,function,suffix,args); \ 75 __MATH_maybe_libm_hidden_proto(function) 76 77 #define __MATHCALLI(function,suffix,args) \ 78 __MATHDECLI(_Mdouble_,function,suffix,args) 79 80 /* Private helpers for purely macro impls below. 81 Only make __foo{,f,l} visible but not (the macro-only) foo. */ 82 #if defined _LIBC 83 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \ 84 __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); \ 85 libm_hidden_proto(__MATH_PRECNAME(__##function,suffix)) 86 #else 87 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \ 88 __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); 89 #endif 90 91 92 /* Include the file of declarations, declaring double versions */ 93 94 #if defined _LIBC 95 # define __MATH_maybe_libm_hidden_proto(x) libm_hidden_proto(x) 96 #else 97 # define __MATH_maybe_libm_hidden_proto(x) 98 #endif 99 #define _Mdouble_ double 100 #define __MATH_PRECNAME(name,r) __CONCAT(name,r) 101 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD 102 #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD 103 #include <bits/mathcalls.h> 104 #undef _Mdouble_ 105 #undef _Mdouble_BEGIN_NAMESPACE 106 #undef _Mdouble_END_NAMESPACE 107 #undef __MATH_PRECNAME 108 #undef __MATH_maybe_libm_hidden_proto 109 110 111 #if defined __USE_MISC || defined __USE_ISOC99 112 113 /* Include the file of declarations again, this time using `float' 114 instead of `double' and appending f to each function name. */ 115 116 # define __MATH_maybe_libm_hidden_proto(x) 117 # ifndef _Mfloat_ 118 # define _Mfloat_ float 119 # endif 120 # define _Mdouble_ _Mfloat_ 121 # ifdef __STDC__ 122 # define __MATH_PRECNAME(name,r) name##f##r 123 # else 124 # define __MATH_PRECNAME(name,r) name/**/f/**/r 125 # endif 126 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 127 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 128 # include <bits/mathcalls.h> 129 # undef _Mdouble_ 130 # undef _Mdouble_BEGIN_NAMESPACE 131 # undef _Mdouble_END_NAMESPACE 132 # undef __MATH_PRECNAME 133 # undef __MATH_maybe_libm_hidden_proto 134 135 136 # if (defined __STDC__ || defined __GNUC__) \ 137 && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT) 138 # ifdef __LDBL_COMPAT 139 140 # ifdef __USE_ISOC99 141 extern float __nldbl_nexttowardf (float __x, long double __y) __THROW 142 __attribute__ ((__const__)); 143 # ifdef __REDIRECT_NTH 144 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), __nldbl_nexttowardf) 145 __attribute__ ((__const__)); 146 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), nextafter) 147 __attribute__ ((__const__)); 148 extern long double __REDIRECT_NTH (nexttowardl, (long double __x, long double __y), nextafter) 149 __attribute__ ((__const__)); 150 # endif 151 # endif 152 153 /* Include the file of declarations again, this time using `long double' 154 instead of `double' and appending l to each function name. */ 155 156 # undef __MATHDECL_1 157 # define __MATHDECL_2(type,function,suffix,args,alias) \ 158 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix),args,alias) 159 # define __MATHDECL_1(type,function,suffix,args) \ 160 __MATHDECL_2(type,function,suffix,args,__CONCAT(function,suffix)) 161 # endif 162 163 # define __MATH_maybe_libm_hidden_proto(x) 164 # ifndef _Mlong_double_ 165 # define _Mlong_double_ long double 166 # endif 167 # define _Mdouble_ _Mlong_double_ 168 # ifdef __STDC__ 169 # define __MATH_PRECNAME(name,r) name##l##r 170 # else 171 # define __MATH_PRECNAME(name,r) name/**/l/**/r 172 # endif 173 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 174 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 175 # include <bits/mathcalls.h> 176 # undef _Mdouble_ 177 # undef _Mdouble_BEGIN_NAMESPACE 178 # undef _Mdouble_END_NAMESPACE 179 # undef __MATH_PRECNAME 180 # undef __MATH_maybe_libm_hidden_proto 181 182 # endif /* __STDC__ || __GNUC__ */ 183 184 #endif /* Use misc or ISO C99. */ 185 #undef __MATHDECL_1 186 #undef __MATHDECL 187 #undef __MATHCALL 188 189 190 #if defined __USE_MISC || defined __USE_XOPEN 191 /* This variable is used by `gamma' and `lgamma'. */ 192 extern int signgam; 193 #endif 194 195 196 /* ISO C99 defines some generic macros which work on any data type. */ 197 #ifdef __USE_ISOC99 198 199 /* Get the architecture specific values describing the floating-point 200 evaluation. The following symbols will get defined: 201 202 float_t floating-point type at least as wide as `float' used 203 to evaluate `float' expressions 204 double_t floating-point type at least as wide as `double' used 205 to evaluate `double' expressions 206 207 FLT_EVAL_METHOD 208 Defined to 209 0 if `float_t' is `float' and `double_t' is `double' 210 1 if `float_t' and `double_t' are `double' 211 2 if `float_t' and `double_t' are `long double' 212 else `float_t' and `double_t' are unspecified 213 214 INFINITY representation of the infinity value of type `float' 215 216 FP_FAST_FMA 217 FP_FAST_FMAF 218 FP_FAST_FMAL 219 If defined it indicates that the `fma' function 220 generally executes about as fast as a multiply and an add. 221 This macro is defined only iff the `fma' function is 222 implemented directly with a hardware multiply-add instructions. 223 224 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 225 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 226 227 DECIMAL_DIG Number of decimal digits supported by conversion between 228 decimal and all internal floating-point formats. 229 230 */ 231 232 /* All floating-point numbers can be put in one of these categories. */ 233 enum 234 { 235 FP_NAN, 236 # define FP_NAN FP_NAN 237 FP_INFINITE, 238 # define FP_INFINITE FP_INFINITE 239 FP_ZERO, 240 # define FP_ZERO FP_ZERO 241 FP_SUBNORMAL, 242 # define FP_SUBNORMAL FP_SUBNORMAL 243 FP_NORMAL 244 # define FP_NORMAL FP_NORMAL 245 }; 246 247 /* Return number of classification appropriate for X. */ 248 # ifdef __NO_LONG_DOUBLE_MATH 249 # define fpclassify(x) \ 250 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) 251 # else 252 # define fpclassify(x) \ 253 (sizeof (x) == sizeof (float) \ 254 ? __fpclassifyf (x) \ 255 : sizeof (x) == sizeof (double) \ 256 ? __fpclassify (x) : __fpclassifyl (x)) 257 # endif 258 259 /* Return nonzero value if sign of X is negative. */ 260 # ifdef __NO_LONG_DOUBLE_MATH 261 # define signbit(x) \ 262 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) 263 # else 264 # define signbit(x) \ 265 (sizeof (x) == sizeof (float) \ 266 ? __signbitf (x) \ 267 : sizeof (x) == sizeof (double) \ 268 ? __signbit (x) : __signbitl (x)) 269 # endif 270 271 /* Return nonzero value if X is not +-Inf or NaN. */ 272 # ifdef __NO_LONG_DOUBLE_MATH 273 # define isfinite(x) \ 274 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) 275 # else 276 # define isfinite(x) \ 277 (sizeof (x) == sizeof (float) \ 278 ? __finitef (x) \ 279 : sizeof (x) == sizeof (double) \ 280 ? __finite (x) : __finitel (x)) 281 # endif 282 283 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ 284 # define isnormal(x) (fpclassify (x) == FP_NORMAL) 285 286 /* Return nonzero value if X is a NaN. We could use `fpclassify' but 287 we already have this functions `__isnan' and it is faster. */ 288 # ifdef __NO_LONG_DOUBLE_MATH 289 # define isnan(x) \ 290 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) 291 # else 292 # define isnan(x) \ 293 (sizeof (x) == sizeof (float) \ 294 ? __isnanf (x) \ 295 : sizeof (x) == sizeof (double) \ 296 ? __isnan (x) : __isnanl (x)) 297 # endif 298 299 /* Return nonzero value is X is positive or negative infinity. */ 300 # ifdef __NO_LONG_DOUBLE_MATH 301 # define isinf(x) \ 302 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) 303 # else 304 # define isinf(x) \ 305 (sizeof (x) == sizeof (float) \ 306 ? __isinff (x) \ 307 : sizeof (x) == sizeof (double) \ 308 ? __isinf (x) : __isinfl (x)) 309 # endif 310 311 /* Bitmasks for the math_errhandling macro. */ 312 # define MATH_ERRNO 1 /* errno set by math functions. */ 313 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ 314 315 #endif /* Use ISO C99. */ 316 317 #ifdef __USE_MISC 318 /* Support for various different standard error handling behaviors. */ 319 typedef enum 320 { 321 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 322 _SVID_, /* According to System V, release 4. */ 323 _XOPEN_, /* Nowadays also Unix98. */ 324 _POSIX_, 325 _ISOC_ /* Actually this is ISO C99. */ 326 } _LIB_VERSION_TYPE; 327 328 /* This variable can be changed at run-time to any of the values above to 329 affect floating point error handling behavior (it may also be necessary 330 to change the hardware FPU exception settings). */ 331 extern _LIB_VERSION_TYPE _LIB_VERSION; 332 #endif 333 334 335 #ifdef __USE_SVID 336 /* In SVID error handling, `matherr' is called with this description 337 of the exceptional condition. 338 339 We have a problem when using C++ since `exception' is a reserved 340 name in C++. */ 341 # ifdef __cplusplus 342 struct __exception 343 # else 344 struct exception 345 # endif 346 { 347 int type; 348 char *name; 349 double arg1; 350 double arg2; 351 double retval; 352 }; 353 354 # ifdef __cplusplus 355 extern int matherr (struct __exception *__exc) throw (); 356 # else 357 extern int matherr (struct exception *__exc); 358 # endif 359 360 # define X_TLOSS 1.41484755040568800000e+16 361 362 /* Types of exceptions in the `type' field. */ 363 # define DOMAIN 1 364 # define SING 2 365 # define OVERFLOW 3 366 # define UNDERFLOW 4 367 # define TLOSS 5 368 # define PLOSS 6 369 370 /* SVID mode specifies returning this large value instead of infinity. */ 371 # define HUGE 3.40282347e+38F 372 373 #else /* !SVID */ 374 375 # ifdef __USE_XOPEN 376 # ifdef __UCLIBC_SUSV4_LEGACY__ 377 /* X/Open wants another strange constant. */ 378 # define MAXFLOAT 3.40282347e+38F 379 # endif 380 # endif 381 382 #endif /* SVID */ 383 384 385 /* Some useful constants. */ 386 #if defined __USE_BSD || defined __USE_XOPEN 387 # define M_E 2.7182818284590452354 /* e */ 388 # define M_LOG2E 1.4426950408889634074 /* log_2 e */ 389 # define M_LOG10E 0.43429448190325182765 /* log_10 e */ 390 # define M_LN2 0.69314718055994530942 /* log_e 2 */ 391 # define M_LN10 2.30258509299404568402 /* log_e 10 */ 392 # define M_PI 3.14159265358979323846 /* pi */ 393 # define M_PI_2 1.57079632679489661923 /* pi/2 */ 394 # define M_PI_4 0.78539816339744830962 /* pi/4 */ 395 # define M_1_PI 0.31830988618379067154 /* 1/pi */ 396 # define M_2_PI 0.63661977236758134308 /* 2/pi */ 397 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 398 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 399 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 400 #endif 401 402 /* The above constants are not adequate for computation using `long double's. 403 Therefore we provide as an extension constants with similar names as a 404 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 405 #ifdef __USE_GNU 406 # define M_El 2.7182818284590452353602874713526625L /* e */ 407 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ 408 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ 409 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ 410 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ 411 # define M_PIl 3.1415926535897932384626433832795029L /* pi */ 412 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ 413 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ 414 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ 415 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ 416 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ 417 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ 418 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ 419 #endif 420 421 422 /* When compiling in strict ISO C compatible mode we must not use the 423 inline functions since they, among other things, do not set the 424 `errno' variable correctly. */ 425 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 426 # define __NO_MATH_INLINES 1 427 #endif 428 429 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) 430 /* ISO C99 defines some macros to compare number while taking care for 431 unordered numbers. Many FPUs provide special instructions to support 432 these operations. Generic support in GCC for these as builtins went 433 in before 3.0.0, but not all cpus added their patterns. We define 434 versions that use the builtins here, and <bits/mathinline.h> will 435 undef/redefine as appropriate for the specific GCC version in use. */ 436 # define isgreater(x, y) __builtin_isgreater(x, y) 437 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) 438 # define isless(x, y) __builtin_isless(x, y) 439 # define islessequal(x, y) __builtin_islessequal(x, y) 440 # define islessgreater(x, y) __builtin_islessgreater(x, y) 441 # define isunordered(u, v) __builtin_isunordered(u, v) 442 #endif 443 444 /* Get machine-dependent inline versions (if there are any). */ 445 #ifdef __USE_EXTERN_INLINES 446 # include <bits/mathinline.h> 447 #endif 448 449 #ifdef __USE_ISOC99 450 /* If we've still got undefined comparison macros, provide defaults. */ 451 452 /* Return nonzero value if X is greater than Y. */ 453 # ifndef isgreater 454 # define isgreater(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 X is greater than or equal to Y. */ 461 # ifndef isgreaterequal 462 # define isgreaterequal(x, y) \ 463 (__extension__ \ 464 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 465 !isunordered (__x, __y) && __x >= __y; })) 466 # endif 467 468 /* Return nonzero value if X is less than Y. */ 469 # ifndef isless 470 # define isless(x, y) \ 471 (__extension__ \ 472 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 473 !isunordered (__x, __y) && __x < __y; })) 474 # endif 475 476 /* Return nonzero value if X is less than or equal to Y. */ 477 # ifndef islessequal 478 # define islessequal(x, y) \ 479 (__extension__ \ 480 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 481 !isunordered (__x, __y) && __x <= __y; })) 482 # endif 483 484 /* Return nonzero value if either X is less than Y or Y is less than X. */ 485 # ifndef islessgreater 486 # define islessgreater(x, y) \ 487 (__extension__ \ 488 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 489 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 490 # endif 491 492 /* Return nonzero value if arguments are unordered. */ 493 # ifndef isunordered 494 # define isunordered(u, v) \ 495 (__extension__ \ 496 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 497 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 498 # endif 499 500 #endif 501 502 __END_DECLS 503 504 505 #endif /* math.h */ 506