1 /* Declarations for math functions. 2 Copyright (C) 1991-1993,1995-1999,2001,2002 Free Software Foundation, Inc. 3 This file is part of the GNU C Library. 4 5 The GNU C Library is free software; you can redistribute it and/or 6 modify it under the terms of the GNU Lesser General Public 7 License as published by the Free Software Foundation; either 8 version 2.1 of the License, or (at your option) any later version. 9 10 The GNU C Library is distributed in the hope that it will be useful, 11 but WITHOUT ANY WARRANTY; without even the implied warranty of 12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 13 Lesser General Public License for more details. 14 15 You should have received a copy of the GNU Lesser General Public 16 License along with the GNU C Library; if not, write to the Free 17 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 18 02111-1307 USA. */ 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 35 /* Get machine-dependent NAN value (returned for some domain errors). */ 36 #ifdef __USE_ISOC99 37 # include <bits/nan.h> 38 #endif 39 /* Get general and ISO C99 specific information. */ 40 #include <bits/mathdef.h> 41 42 43 /* The file <bits/mathcalls.h> contains the prototypes for all the 44 actual math functions. These macros are used for those prototypes, 45 so we can easily declare each function as both `name' and `__name', 46 and can declare the float versions `namef' and `__namef'. */ 47 48 #define __MATHCALL(function,suffix, args) \ 49 __MATHDECL (_Mdouble_,function,suffix, args) 50 #define __MATHDECL(type, function,suffix, args) \ 51 __MATHDECL_1(type, function,suffix, args); \ 52 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) 53 #define __MATHCALLX(function,suffix, args, attrib) \ 54 __MATHDECLX (_Mdouble_,function,suffix, args, attrib) 55 #define __MATHDECLX(type, function,suffix, args, attrib) \ 56 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ 57 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) 58 #define __MATHDECL_1(type, function,suffix, args) \ 59 extern type __MATH_PRECNAME(function,suffix) args __THROW 60 61 #define _Mdouble_ double 62 #define __MATH_PRECNAME(name,r) __CONCAT(name,r) 63 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD 64 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD 65 #include <bits/mathcalls.h> 66 #undef _Mdouble_ 67 #undef _Mdouble_BEGIN_NAMESPACE 68 #undef _Mdouble_END_NAMESPACE 69 #undef __MATH_PRECNAME 70 71 #if defined __USE_MISC || defined __USE_ISOC99 72 73 74 /* Include the file of declarations again, this time using `float' 75 instead of `double' and appending f to each function name. */ 76 77 # ifndef _Mfloat_ 78 # define _Mfloat_ float 79 # endif 80 # define _Mdouble_ _Mfloat_ 81 # ifdef __STDC__ 82 # define __MATH_PRECNAME(name,r) name##f##r 83 # else 84 # define __MATH_PRECNAME(name,r) name/**/f/**/r 85 # endif 86 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 87 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 88 # include <bits/mathcalls.h> 89 # undef _Mdouble_ 90 # undef _Mdouble_BEGIN_NAMESPACE 91 # undef _Mdouble_END_NAMESPACE 92 # undef __MATH_PRECNAME 93 94 # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH 95 /* Include the file of declarations again, this time using `long double' 96 instead of `double' and appending l to each function name. */ 97 98 # ifndef _Mlong_double_ 99 # define _Mlong_double_ long double 100 # endif 101 # define _Mdouble_ _Mlong_double_ 102 # ifdef __STDC__ 103 # define __MATH_PRECNAME(name,r) name##l##r 104 # else 105 # define __MATH_PRECNAME(name,r) name/**/l/**/r 106 # endif 107 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 108 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 109 # include <bits/mathcalls.h> 110 # undef _Mdouble_ 111 # undef _Mdouble_BEGIN_NAMESPACE 112 # undef _Mdouble_END_NAMESPACE 113 # undef __MATH_PRECNAME 114 115 # endif /* __STDC__ || __GNUC__ */ 116 117 #endif /* Use misc or ISO C99. */ 118 #undef __MATHDECL_1 119 #undef __MATHDECL 120 #undef __MATHCALL 121 122 123 #if defined __USE_MISC || defined __USE_XOPEN 124 /* This variable is used by `gamma' and `lgamma'. */ 125 extern int signgam; 126 #endif 127 128 129 /* ISO C99 defines some generic macros which work on any data type. */ 130 #if __USE_ISOC99 131 132 /* Get the architecture specific values describing the floating-point 133 evaluation. The following symbols will get defined: 134 135 float_t floating-point type at least as wide as `float' used 136 to evaluate `float' expressions 137 double_t floating-point type at least as wide as `double' used 138 to evaluate `double' expressions 139 140 FLT_EVAL_METHOD 141 Defined to 142 0 if `float_t' is `float' and `double_t' is `double' 143 1 if `float_t' and `double_t' are `double' 144 2 if `float_t' and `double_t' are `long double' 145 else `float_t' and `double_t' are unspecified 146 147 INFINITY representation of the infinity value of type `float' 148 149 FP_FAST_FMA 150 FP_FAST_FMAF 151 FP_FAST_FMAL 152 If defined it indicates that the `fma' function 153 generally executes about as fast as a multiply and an add. 154 This macro is defined only iff the `fma' function is 155 implemented directly with a hardware multiply-add instructions. 156 157 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. 158 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. 159 160 DECIMAL_DIG Number of decimal digits supported by conversion between 161 decimal and all internal floating-point formats. 162 163 */ 164 165 /* All floating-point numbers can be put in one of these categories. */ 166 enum 167 { 168 FP_NAN, 169 # define FP_NAN FP_NAN 170 FP_INFINITE, 171 # define FP_INFINITE FP_INFINITE 172 FP_ZERO, 173 # define FP_ZERO FP_ZERO 174 FP_SUBNORMAL, 175 # define FP_SUBNORMAL FP_SUBNORMAL 176 FP_NORMAL 177 # define FP_NORMAL FP_NORMAL 178 }; 179 180 /* Return number of classification appropriate for X. */ 181 # ifdef __NO_LONG_DOUBLE_MATH 182 # define fpclassify(x) \ 183 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) 184 # else 185 # define fpclassify(x) \ 186 (sizeof (x) == sizeof (float) \ 187 ? __fpclassifyf (x) \ 188 : sizeof (x) == sizeof (double) \ 189 ? __fpclassify (x) : __fpclassifyl (x)) 190 # endif 191 192 /* Return nonzero value if sign of X is negative. */ 193 # ifdef __NO_LONG_DOUBLE_MATH 194 # define signbit(x) \ 195 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) 196 # else 197 # define signbit(x) \ 198 (sizeof (x) == sizeof (float) \ 199 ? __signbitf (x) \ 200 : sizeof (x) == sizeof (double) \ 201 ? __signbit (x) : __signbitl (x)) 202 # endif 203 204 /* Return nonzero value if X is not +-Inf or NaN. */ 205 # ifdef __NO_LONG_DOUBLE_MATH 206 # define isfinite(x) \ 207 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) 208 # else 209 # define isfinite(x) \ 210 (sizeof (x) == sizeof (float) \ 211 ? __finitef (x) \ 212 : sizeof (x) == sizeof (double) \ 213 ? __finite (x) : __finitel (x)) 214 # endif 215 216 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ 217 # define isnormal(x) (fpclassify (x) == FP_NORMAL) 218 219 /* Return nonzero value if X is a NaN. We could use `fpclassify' but 220 we already have this functions `__isnan' and it is faster. */ 221 # ifdef __NO_LONG_DOUBLE_MATH 222 # define isnan(x) \ 223 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) 224 # else 225 # define isnan(x) \ 226 (sizeof (x) == sizeof (float) \ 227 ? __isnanf (x) \ 228 : sizeof (x) == sizeof (double) \ 229 ? __isnan (x) : __isnanl (x)) 230 # endif 231 232 /* Return nonzero value is X is positive or negative infinity. */ 233 # ifdef __NO_LONG_DOUBLE_MATH 234 # define isinf(x) \ 235 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) 236 # else 237 # define isinf(x) \ 238 (sizeof (x) == sizeof (float) \ 239 ? __isinff (x) \ 240 : sizeof (x) == sizeof (double) \ 241 ? __isinf (x) : __isinfl (x)) 242 # endif 243 244 /* Bitmasks for the math_errhandling macro. */ 245 # define MATH_ERRNO 1 /* errno set by math functions. */ 246 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ 247 248 #endif /* Use ISO C99. */ 249 250 #ifdef __USE_MISC 251 /* Support for various different standard error handling behaviors. */ 252 typedef enum 253 { 254 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ 255 _SVID_, /* According to System V, release 4. */ 256 _XOPEN_, /* Nowadays also Unix98. */ 257 _POSIX_, 258 _ISOC_ /* Actually this is ISO C99. */ 259 } _LIB_VERSION_TYPE; 260 261 /* This variable can be changed at run-time to any of the values above to 262 affect floating point error handling behavior (it may also be necessary 263 to change the hardware FPU exception settings). */ 264 extern _LIB_VERSION_TYPE _LIB_VERSION; 265 #endif 266 267 268 #ifdef __USE_SVID 269 /* In SVID error handling, `matherr' is called with this description 270 of the exceptional condition. 271 272 We have a problem when using C++ since `exception' is a reserved 273 name in C++. */ 274 # ifdef __cplusplus 275 struct __exception 276 # else 277 struct exception 278 # endif 279 { 280 int type; 281 char *name; 282 double arg1; 283 double arg2; 284 double retval; 285 }; 286 287 # ifdef __cplusplus 288 extern int matherr (struct __exception *__exc) throw (); 289 # else 290 extern int matherr (struct exception *__exc); 291 # endif 292 293 # define X_TLOSS 1.41484755040568800000e+16 294 295 /* Types of exceptions in the `type' field. */ 296 # define DOMAIN 1 297 # define SING 2 298 # define OVERFLOW 3 299 # define UNDERFLOW 4 300 # define TLOSS 5 301 # define PLOSS 6 302 303 /* SVID mode specifies returning this large value instead of infinity. */ 304 # define HUGE 3.40282347e+38F 305 306 #else /* !SVID */ 307 308 # ifdef __USE_XOPEN 309 /* X/Open wants another strange constant. */ 310 # define MAXFLOAT 3.40282347e+38F 311 # endif 312 313 #endif /* SVID */ 314 315 316 /* Some useful constants. */ 317 #if defined __USE_BSD || defined __USE_XOPEN 318 # define M_E 2.7182818284590452354 /* e */ 319 # define M_LOG2E 1.4426950408889634074 /* log_2 e */ 320 # define M_LOG10E 0.43429448190325182765 /* log_10 e */ 321 # define M_LN2 0.69314718055994530942 /* log_e 2 */ 322 # define M_LN10 2.30258509299404568402 /* log_e 10 */ 323 # define M_PI 3.14159265358979323846 /* pi */ 324 # define M_PI_2 1.57079632679489661923 /* pi/2 */ 325 # define M_PI_4 0.78539816339744830962 /* pi/4 */ 326 # define M_1_PI 0.31830988618379067154 /* 1/pi */ 327 # define M_2_PI 0.63661977236758134308 /* 2/pi */ 328 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 329 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 330 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 331 #endif 332 333 /* The above constants are not adequate for computation using `long double's. 334 Therefore we provide as an extension constants with similar names as a 335 GNU extension. Provide enough digits for the 128-bit IEEE quad. */ 336 #ifdef __USE_GNU 337 # define M_El 2.7182818284590452353602874713526625L /* e */ 338 # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ 339 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ 340 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ 341 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ 342 # define M_PIl 3.1415926535897932384626433832795029L /* pi */ 343 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ 344 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ 345 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ 346 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ 347 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ 348 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ 349 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ 350 #endif 351 352 353 /* When compiling in strict ISO C compatible mode we must not use the 354 inline functions since they, among other things, do not set the 355 `errno' variable correctly. */ 356 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES 357 # define __NO_MATH_INLINES 1 358 #endif 359 360 /* Get machine-dependent inline versions (if there are any). */ 361 #ifdef __USE_EXTERN_INLINES 362 # include <bits/mathinline.h> 363 #endif 364 365 366 #if __USE_ISOC99 367 /* ISO C99 defines some macros to compare number while taking care 368 for unordered numbers. Since many FPUs provide special 369 instructions to support these operations and these tests are 370 defined in <bits/mathinline.h>, we define the generic macros at 371 this late point and only if they are not defined yet. */ 372 373 /* Return nonzero value if X is greater than Y. */ 374 # ifndef isgreater 375 # define isgreater(x, y) \ 376 (__extension__ \ 377 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 378 !isunordered (__x, __y) && __x > __y; })) 379 # endif 380 381 /* Return nonzero value if X is greater than or equal to Y. */ 382 # ifndef isgreaterequal 383 # define isgreaterequal(x, y) \ 384 (__extension__ \ 385 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 386 !isunordered (__x, __y) && __x >= __y; })) 387 # endif 388 389 /* Return nonzero value if X is less than Y. */ 390 # ifndef isless 391 # define isless(x, y) \ 392 (__extension__ \ 393 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 394 !isunordered (__x, __y) && __x < __y; })) 395 # endif 396 397 /* Return nonzero value if X is less than or equal to Y. */ 398 # ifndef islessequal 399 # define islessequal(x, y) \ 400 (__extension__ \ 401 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 402 !isunordered (__x, __y) && __x <= __y; })) 403 # endif 404 405 /* Return nonzero value if either X is less than Y or Y is less than X. */ 406 # ifndef islessgreater 407 # define islessgreater(x, y) \ 408 (__extension__ \ 409 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ 410 !isunordered (__x, __y) && (__x < __y || __y < __x); })) 411 # endif 412 413 /* Return nonzero value if arguments are unordered. */ 414 # ifndef isunordered 415 # define isunordered(u, v) \ 416 (__extension__ \ 417 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ 418 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) 419 # endif 420 421 #endif 422 423 __END_DECLS 424 425 426 #endif /* math.h */ 427