1 /* Copyright (C) 1997, 1998, 1999, 2000, 2001, 2003, 2004, 2005, 2007 2 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: 7.22 Type-generic math <tgmath.h> 22 */ 23 24 #ifndef _TGMATH_H 25 #define _TGMATH_H 1 26 27 /* Include the needed headers. */ 28 #include <math.h> 29 #include <complex.h> 30 31 32 /* Since `complex' is currently not really implemented in most C compilers 33 and if it is implemented, the implementations differ. This makes it 34 quite difficult to write a generic implementation of this header. We 35 do not try this for now and instead concentrate only on GNU CC. Once 36 we have more information support for other compilers might follow. */ 37 38 #if __GNUC_PREREQ (2, 7) 39 40 # ifdef __NO_LONG_DOUBLE_MATH 41 # define __tgml(fct) fct 42 # else 43 # define __tgml(fct) fct ## l 44 # endif 45 46 /* This is ugly but unless gcc gets appropriate builtins we have to do 47 something like this. Don't ask how it works. */ 48 49 /* 1 if 'type' is a floating type, 0 if 'type' is an integer type. 50 Allows for _Bool. Expands to an integer constant expression. */ 51 # define __floating_type(type) (((type) 0.25) && ((type) 0.25 - 1)) 52 53 /* The tgmath real type for T, where E is 0 if T is an integer type and 54 1 for a floating type. */ 55 # define __tgmath_real_type_sub(T, E) \ 56 __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0 \ 57 : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0)) 58 59 /* The tgmath real type of EXPR. */ 60 # define __tgmath_real_type(expr) \ 61 __tgmath_real_type_sub (__typeof__ ((__typeof__ (expr)) 0), \ 62 __floating_type (__typeof__ (expr))) 63 64 65 /* We have two kinds of generic macros: to support functions which are 66 only defined on real valued parameters and those which are defined 67 for complex functions as well. */ 68 # define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \ 69 (__extension__ ((sizeof (Val) == sizeof (double) \ 70 || __builtin_classify_type (Val) != 8) \ 71 ? (__tgmath_real_type (Val)) Fct (Val) \ 72 : (sizeof (Val) == sizeof (float)) \ 73 ? (__tgmath_real_type (Val)) Fct##f (Val) \ 74 : (__tgmath_real_type (Val)) __tgml(Fct) (Val))) 75 76 # define __TGMATH_UNARY_REAL_RET_ONLY(Val, RetType, Fct) \ 77 (__extension__ ((sizeof (Val) == sizeof (double) \ 78 || __builtin_classify_type (Val) != 8) \ 79 ? (RetType) Fct (Val) \ 80 : (sizeof (Val) == sizeof (float)) \ 81 ? (RetType) Fct##f (Val) \ 82 : (RetType) __tgml(Fct) (Val))) 83 84 # define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \ 85 (__extension__ ((sizeof (Val1) == sizeof (double) \ 86 || __builtin_classify_type (Val1) != 8) \ 87 ? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \ 88 : (sizeof (Val1) == sizeof (float)) \ 89 ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \ 90 : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2))) 91 92 # define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \ 93 (__extension__ (((sizeof (Val1) > sizeof (double) \ 94 || sizeof (Val2) > sizeof (double)) \ 95 && __builtin_classify_type ((Val1) + (Val2)) == 8) \ 96 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 97 + (__tgmath_real_type (Val2)) 0)) \ 98 __tgml(Fct) (Val1, Val2) \ 99 : (sizeof (Val1) == sizeof (double) \ 100 || sizeof (Val2) == sizeof (double) \ 101 || __builtin_classify_type (Val1) != 8 \ 102 || __builtin_classify_type (Val2) != 8) \ 103 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 104 + (__tgmath_real_type (Val2)) 0)) \ 105 Fct (Val1, Val2) \ 106 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 107 + (__tgmath_real_type (Val2)) 0)) \ 108 Fct##f (Val1, Val2))) 109 110 # define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \ 111 (__extension__ (((sizeof (Val1) > sizeof (double) \ 112 || sizeof (Val2) > sizeof (double)) \ 113 && __builtin_classify_type ((Val1) + (Val2)) == 8) \ 114 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 115 + (__tgmath_real_type (Val2)) 0)) \ 116 __tgml(Fct) (Val1, Val2, Val3) \ 117 : (sizeof (Val1) == sizeof (double) \ 118 || sizeof (Val2) == sizeof (double) \ 119 || __builtin_classify_type (Val1) != 8 \ 120 || __builtin_classify_type (Val2) != 8) \ 121 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 122 + (__tgmath_real_type (Val2)) 0)) \ 123 Fct (Val1, Val2, Val3) \ 124 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 125 + (__tgmath_real_type (Val2)) 0)) \ 126 Fct##f (Val1, Val2, Val3))) 127 128 # define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \ 129 (__extension__ (((sizeof (Val1) > sizeof (double) \ 130 || sizeof (Val2) > sizeof (double) \ 131 || sizeof (Val3) > sizeof (double)) \ 132 && __builtin_classify_type ((Val1) + (Val2) + (Val3)) \ 133 == 8) \ 134 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 135 + (__tgmath_real_type (Val2)) 0 \ 136 + (__tgmath_real_type (Val3)) 0)) \ 137 __tgml(Fct) (Val1, Val2, Val3) \ 138 : (sizeof (Val1) == sizeof (double) \ 139 || sizeof (Val2) == sizeof (double) \ 140 || sizeof (Val3) == sizeof (double) \ 141 || __builtin_classify_type (Val1) != 8 \ 142 || __builtin_classify_type (Val2) != 8 \ 143 || __builtin_classify_type (Val3) != 8) \ 144 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 145 + (__tgmath_real_type (Val2)) 0 \ 146 + (__tgmath_real_type (Val3)) 0)) \ 147 Fct (Val1, Val2, Val3) \ 148 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 149 + (__tgmath_real_type (Val2)) 0 \ 150 + (__tgmath_real_type (Val3)) 0)) \ 151 Fct##f (Val1, Val2, Val3))) 152 153 /* XXX This definition has to be changed as soon as the compiler understands 154 the imaginary keyword. */ 155 # define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \ 156 (__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \ 157 || __builtin_classify_type (__real__ (Val)) != 8) \ 158 ? ((sizeof (__real__ (Val)) == sizeof (Val)) \ 159 ? (__tgmath_real_type (Val)) Fct (Val) \ 160 : (__tgmath_real_type (Val)) Cfct (Val)) \ 161 : (sizeof (__real__ (Val)) == sizeof (float)) \ 162 ? ((sizeof (__real__ (Val)) == sizeof (Val)) \ 163 ? (__tgmath_real_type (Val)) Fct##f (Val) \ 164 : (__tgmath_real_type (Val)) Cfct##f (Val)) \ 165 : ((sizeof (__real__ (Val)) == sizeof (Val)) \ 166 ? (__tgmath_real_type (Val)) __tgml(Fct) (Val) \ 167 : (__tgmath_real_type (Val)) __tgml(Cfct) (Val)))) 168 169 # define __TGMATH_UNARY_IMAG(Val, Cfct) \ 170 (__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \ 171 || __builtin_classify_type (__real__ (Val)) != 8) \ 172 ? (__typeof__ ((__tgmath_real_type (Val)) 0 \ 173 + _Complex_I)) Cfct (Val) \ 174 : (sizeof (__real__ (Val)) == sizeof (float)) \ 175 ? (__typeof__ ((__tgmath_real_type (Val)) 0 \ 176 + _Complex_I)) Cfct##f (Val) \ 177 : (__typeof__ ((__tgmath_real_type (Val)) 0 \ 178 + _Complex_I)) __tgml(Cfct) (Val))) 179 180 /* XXX This definition has to be changed as soon as the compiler understands 181 the imaginary keyword. */ 182 # define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \ 183 (__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \ 184 || __builtin_classify_type (__real__ (Val)) != 8) \ 185 ? ((sizeof (__real__ (Val)) == sizeof (Val)) \ 186 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 187 Fct (Val) \ 188 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 189 Cfct (Val)) \ 190 : (sizeof (__real__ (Val)) == sizeof (float)) \ 191 ? ((sizeof (__real__ (Val)) == sizeof (Val)) \ 192 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 193 Fct##f (Val) \ 194 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 195 Cfct##f (Val)) \ 196 : ((sizeof (__real__ (Val)) == sizeof (Val)) \ 197 ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 198 __tgml(Fct) (Val) \ 199 : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\ 200 __tgml(Cfct) (Val)))) 201 202 /* XXX This definition has to be changed as soon as the compiler understands 203 the imaginary keyword. */ 204 # define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \ 205 (__extension__ (((sizeof (__real__ (Val1)) > sizeof (double) \ 206 || sizeof (__real__ (Val2)) > sizeof (double)) \ 207 && __builtin_classify_type (__real__ (Val1) \ 208 + __real__ (Val2)) == 8) \ 209 ? ((sizeof (__real__ (Val1)) == sizeof (Val1) \ 210 && sizeof (__real__ (Val2)) == sizeof (Val2)) \ 211 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 212 + (__tgmath_real_type (Val2)) 0)) \ 213 __tgml(Fct) (Val1, Val2) \ 214 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 215 + (__tgmath_real_type (Val2)) 0)) \ 216 __tgml(Cfct) (Val1, Val2)) \ 217 : (sizeof (__real__ (Val1)) == sizeof (double) \ 218 || sizeof (__real__ (Val2)) == sizeof (double) \ 219 || __builtin_classify_type (__real__ (Val1)) != 8 \ 220 || __builtin_classify_type (__real__ (Val2)) != 8) \ 221 ? ((sizeof (__real__ (Val1)) == sizeof (Val1) \ 222 && sizeof (__real__ (Val2)) == sizeof (Val2)) \ 223 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 224 + (__tgmath_real_type (Val2)) 0)) \ 225 Fct (Val1, Val2) \ 226 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 227 + (__tgmath_real_type (Val2)) 0)) \ 228 Cfct (Val1, Val2)) \ 229 : ((sizeof (__real__ (Val1)) == sizeof (Val1) \ 230 && sizeof (__real__ (Val2)) == sizeof (Val2)) \ 231 ? (__typeof ((__tgmath_real_type (Val1)) 0 \ 232 + (__tgmath_real_type (Val2)) 0)) \ 233 Fct##f (Val1, Val2) \ 234 : (__typeof ((__tgmath_real_type (Val1)) 0 \ 235 + (__tgmath_real_type (Val2)) 0)) \ 236 Cfct##f (Val1, Val2)))) 237 #else 238 # error "Unsupported compiler; you cannot use <tgmath.h>" 239 #endif 240 241 242 /* Unary functions defined for real and complex values. */ 243 244 245 /* Trigonometric functions. */ 246 247 /* Arc cosine of X. */ 248 #define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos) 249 /* Arc sine of X. */ 250 #define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin) 251 /* Arc tangent of X. */ 252 #define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan) 253 /* Arc tangent of Y/X. */ 254 #define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2) 255 256 /* Cosine of X. */ 257 #define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos) 258 /* Sine of X. */ 259 #define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin) 260 /* Tangent of X. */ 261 #define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan) 262 263 264 /* Hyperbolic functions. */ 265 266 /* Hyperbolic arc cosine of X. */ 267 #define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh) 268 /* Hyperbolic arc sine of X. */ 269 #define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh) 270 /* Hyperbolic arc tangent of X. */ 271 #define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh) 272 273 /* Hyperbolic cosine of X. */ 274 #define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh) 275 /* Hyperbolic sine of X. */ 276 #define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh) 277 /* Hyperbolic tangent of X. */ 278 #define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh) 279 280 281 /* Exponential and logarithmic functions. */ 282 283 /* Exponential function of X. */ 284 #define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp) 285 286 /* Break VALUE into a normalized fraction and an integral power of 2. */ 287 #define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp) 288 289 /* X times (two to the EXP power). */ 290 #define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp) 291 292 /* Natural logarithm of X. */ 293 #define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog) 294 295 /* Base-ten logarithm of X. */ 296 #ifdef __USE_GNU 297 # define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, __clog10) 298 #else 299 # define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10) 300 #endif 301 302 /* Return exp(X) - 1. */ 303 #define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1) 304 305 /* Return log(1 + X). */ 306 #define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p) 307 308 /* Return the base 2 signed integral exponent of X. */ 309 #define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb) 310 311 /* Compute base-2 exponential of X. */ 312 #define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2) 313 314 /* Compute base-2 logarithm of X. */ 315 #define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2) 316 317 318 /* Power functions. */ 319 320 /* Return X to the Y power. */ 321 #define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow) 322 323 /* Return the square root of X. */ 324 #define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt) 325 326 /* Return `sqrt(X*X + Y*Y)'. */ 327 #define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot) 328 329 /* Return the cube root of X. */ 330 #define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt) 331 332 333 /* Nearest integer, absolute value, and remainder functions. */ 334 335 /* Smallest integral value not less than X. */ 336 #define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil) 337 338 /* Absolute value of X. */ 339 #define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs) 340 341 /* Largest integer not greater than X. */ 342 #define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor) 343 344 /* Floating-point modulo remainder of X/Y. */ 345 #define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod) 346 347 /* Round X to integral valuein floating-point format using current 348 rounding direction, but do not raise inexact exception. */ 349 #define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint) 350 351 /* Round X to nearest integral value, rounding halfway cases away from 352 zero. */ 353 #define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round) 354 355 /* Round X to the integral value in floating-point format nearest but 356 not larger in magnitude. */ 357 #define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc) 358 359 /* Compute remainder of X and Y and put in *QUO a value with sign of x/y 360 and magnitude congruent `mod 2^n' to the magnitude of the integral 361 quotient x/y, with n >= 3. */ 362 #define remquo(Val1, Val2, Val3) \ 363 __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo) 364 365 /* Round X to nearest integral value according to current rounding 366 direction. */ 367 #define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lrint) 368 #define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llrint) 369 370 /* Round X to nearest integral value, rounding halfway cases away from 371 zero. */ 372 #define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lround) 373 #define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llround) 374 375 376 /* Return X with its signed changed to Y's. */ 377 #define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign) 378 379 /* Error and gamma functions. */ 380 #define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf) 381 #define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc) 382 #define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma) 383 #define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma) 384 385 386 /* Return the integer nearest X in the direction of the 387 prevailing rounding mode. */ 388 #define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint) 389 390 /* Return X + epsilon if X < Y, X - epsilon if X > Y. */ 391 #define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter) 392 #define nexttoward(Val1, Val2) \ 393 __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, nexttoward) 394 395 /* Return the remainder of integer divison X / Y with infinite precision. */ 396 #define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder) 397 398 /* Return X times (2 to the Nth power). */ 399 #if defined __USE_MISC || defined __USE_XOPEN_EXTENDED 400 # define scalb(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, scalb) 401 #endif 402 403 /* Return X times (2 to the Nth power). */ 404 #define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn) 405 406 /* Return X times (2 to the Nth power). */ 407 #define scalbln(Val1, Val2) \ 408 __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln) 409 410 /* Return the binary exponent of X, which must be nonzero. */ 411 #define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, int, ilogb) 412 413 414 /* Return positive difference between X and Y. */ 415 #define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim) 416 417 /* Return maximum numeric value from X and Y. */ 418 #define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax) 419 420 /* Return minimum numeric value from X and Y. */ 421 #define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin) 422 423 424 /* Multiply-add function computed as a ternary operation. */ 425 #define fma(Val1, Val2, Val3) \ 426 __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma) 427 428 429 /* Absolute value, conjugates, and projection. */ 430 431 /* Argument value of Z. */ 432 #define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, carg, carg) 433 434 /* Complex conjugate of Z. */ 435 #define conj(Val) __TGMATH_UNARY_IMAG (Val, conj) 436 437 /* Projection of Z onto the Riemann sphere. */ 438 #define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj) 439 440 441 /* Decomposing complex values. */ 442 443 /* Imaginary part of Z. */ 444 #define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, cimag, cimag) 445 446 /* Real part of Z. */ 447 #define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, creal, creal) 448 449 #endif /* tgmath.h */ 450
