math/math_private.h

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /*
  13  * from: @(#)fdlibm.h 5.1 93/09/24
  14  */
  15
  16 #ifndef _MATH_PRIVATE_H_
  17 #define _MATH_PRIVATE_H_
  18
  19 #include <endian.h>
  20 #include <stdint.h>
  21 #include <sys/types.h>
  22
  23 /* The original fdlibm code used statements like:
  24         n0 = ((*(int*)&one)>>29)^1;             * index of high word *
  25         ix0 = *(n0+(int*)&x);                   * high word of x *
  26         ix1 = *((1-n0)+(int*)&x);               * low word of x *
  27    to dig two 32 bit words out of the 64 bit IEEE floating point
  28    value.  That is non-ANSI, and, moreover, the gcc instruction
  29    scheduler gets it wrong.  We instead use the following macros.
  30    Unlike the original code, we determine the endianness at compile
  31    time, not at run time; I don't see much benefit to selecting
  32    endianness at run time.  */
  33
  34 /* A union which permits us to convert between a double and two 32 bit
  35    ints.  */
  36
  37 #if __FLOAT_WORD_ORDER == BIG_ENDIAN
  38
  39 typedef union
  40 {
  41   double value;
  42   struct
  43   {
  44     u_int32_t msw;
  45     u_int32_t lsw;
  46   } parts;
  47   uint64_t word;
  48 } ieee_double_shape_type;
  49
  50 #endif
  51
  52 #if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
  53
  54 typedef union
  55 {
  56   double value;
  57   struct
  58   {
  59     u_int32_t lsw;
  60     u_int32_t msw;
  61   } parts;
  62   uint64_t word;
  63 } ieee_double_shape_type;
  64
  65 #endif
  66
  67 /* Get two 32 bit ints from a double.  */
  68
  69 #define EXTRACT_WORDS(ix0,ix1,d)                                \
  70 do {                                                            \
  71   ieee_double_shape_type ew_u;                                  \
  72   ew_u.value = (d);                                             \
  73   (ix0) = ew_u.parts.msw;                                       \
  74   (ix1) = ew_u.parts.lsw;                                       \
  75 } while (0)
  76
  77 /* Get the more significant 32 bit int from a double.  */
  78
  79 #define GET_HIGH_WORD(i,d)                                      \
  80 do {                                                            \
  81   ieee_double_shape_type gh_u;                                  \
  82   gh_u.value = (d);                                             \
  83   (i) = gh_u.parts.msw;                                         \
  84 } while (0)
  85
  86 /* Get the less significant 32 bit int from a double.  */
  87
  88 #define GET_LOW_WORD(i,d)                                       \
  89 do {                                                            \
  90   ieee_double_shape_type gl_u;                                  \
  91   gl_u.value = (d);                                             \
  92   (i) = gl_u.parts.lsw;                                         \
  93 } while (0)
  94
  95 /* Get all in one, efficient on 64-bit machines.  */
  96 #define EXTRACT_WORDS64(i,d)                                    \
  97 do {                                                            \
  98   ieee_double_shape_type gh_u;                                  \
  99   gh_u.value = (d);                                             \
 100   (i) = gh_u.word;                                              \
 101 } while (0)
 102
 103 /* Set a double from two 32 bit ints.  */
 104
 105 #define INSERT_WORDS(d,ix0,ix1)                                 \
 106 do {                                                            \
 107   ieee_double_shape_type iw_u;                                  \
 108   iw_u.parts.msw = (ix0);                                       \
 109   iw_u.parts.lsw = (ix1);                                       \
 110   (d) = iw_u.value;                                             \
 111 } while (0)
 112
 113 /* Get all in one, efficient on 64-bit machines.  */
 114 #define INSERT_WORDS64(d,i)                                     \
 115 do {                                                            \
 116   ieee_double_shape_type iw_u;                                  \
 117   iw_u.word = (i);                                              \
 118   (d) = iw_u.value;                                             \
 119 } while (0)
 120
 121 /* Set the more significant 32 bits of a double from an int.  */
 122
 123 #define SET_HIGH_WORD(d,v)                                      \
 124 do {                                                            \
 125   ieee_double_shape_type sh_u;                                  \
 126   sh_u.value = (d);                                             \
 127   sh_u.parts.msw = (v);                                         \
 128   (d) = sh_u.value;                                             \
 129 } while (0)
 130
 131 /* Set the less significant 32 bits of a double from an int.  */
 132
 133 #define SET_LOW_WORD(d,v)                                       \
 134 do {                                                            \
 135   ieee_double_shape_type sl_u;                                  \
 136   sl_u.value = (d);                                             \
 137   sl_u.parts.lsw = (v);                                         \
 138   (d) = sl_u.value;                                             \
 139 } while (0)
 140
 141 /* A union which permits us to convert between a float and a 32 bit
 142    int.  */
 143
 144 typedef union
 145 {
 146   float value;
 147   u_int32_t word;
 148 } ieee_float_shape_type;
 149
 150 /* Get a 32 bit int from a float.  */
 151
 152 #define GET_FLOAT_WORD(i,d)                                     \
 153 do {                                                            \
 154   ieee_float_shape_type gf_u;                                   \
 155   gf_u.value = (d);                                             \
 156   (i) = gf_u.word;                                              \
 157 } while (0)
 158
 159 /* Set a float from a 32 bit int.  */
 160
 161 #define SET_FLOAT_WORD(d,i)                                     \
 162 do {                                                            \
 163   ieee_float_shape_type sf_u;                                   \
 164   sf_u.word = (i);                                              \
 165   (d) = sf_u.value;                                             \
 166 } while (0)
 167
 168 /* Get long double macros from a separate header.  */
 169 #include <math_ldbl.h>
 170
 171 /* ieee style elementary functions */
 172 extern double __ieee754_sqrt (double);
 173 extern double __ieee754_acos (double);
 174 extern double __ieee754_acosh (double);
 175 extern double __ieee754_log (double);
 176 extern double __ieee754_atanh (double);
 177 extern double __ieee754_asin (double);
 178 extern double __ieee754_atan2 (double,double);
 179 extern double __ieee754_exp (double);
 180 extern double __ieee754_exp2 (double);
 181 extern double __ieee754_exp10 (double);
 182 extern double __ieee754_cosh (double);
 183 extern double __ieee754_fmod (double,double);
 184 extern double __ieee754_pow (double,double);
 185 extern double __ieee754_lgamma_r (double,int *);
 186 extern double __ieee754_gamma_r (double,int *);
 187 extern double __ieee754_lgamma (double);
 188 extern double __ieee754_gamma (double);
 189 extern double __ieee754_log10 (double);
 190 extern double __ieee754_log2 (double);
 191 extern double __ieee754_sinh (double);
 192 extern double __ieee754_hypot (double,double);
 193 extern double __ieee754_j0 (double);
 194 extern double __ieee754_j1 (double);
 195 extern double __ieee754_y0 (double);
 196 extern double __ieee754_y1 (double);
 197 extern double __ieee754_jn (int,double);
 198 extern double __ieee754_yn (int,double);
 199 extern double __ieee754_remainder (double,double);
 200 extern int32_t __ieee754_rem_pio2 (double,double*);
 201 extern double __ieee754_scalb (double,double);
 202
 203 /* fdlibm kernel function */
 204 extern double __kernel_standard (double,double,int);
 205 extern float __kernel_standard_f (float,float,int);
 206 extern double __kernel_sin (double,double,int);
 207 extern double __kernel_cos (double,double);
 208 extern double __kernel_tan (double,double,int);
 209 extern int    __kernel_rem_pio2 (double*,double*,int,int,int, const int32_t*);
 210
 211 /* internal functions.  */
 212 extern double __copysign (double x, double __y);
 213
 214 #if __GNUC_PREREQ (4, 0)
 215 extern inline double __copysign (double x, double y)
 216 { return __builtin_copysign (x, y); }
 217 #endif
 218
 219 /* ieee style elementary float functions */
 220 extern float __ieee754_sqrtf (float);
 221 extern float __ieee754_acosf (float);
 222 extern float __ieee754_acoshf (float);
 223 extern float __ieee754_logf (float);
 224 extern float __ieee754_atanhf (float);
 225 extern float __ieee754_asinf (float);
 226 extern float __ieee754_atan2f (float,float);
 227 extern float __ieee754_expf (float);
 228 extern float __ieee754_exp2f (float);
 229 extern float __ieee754_exp10f (float);
 230 extern float __ieee754_coshf (float);
 231 extern float __ieee754_fmodf (float,float);
 232 extern float __ieee754_powf (float,float);
 233 extern float __ieee754_lgammaf_r (float,int *);
 234 extern float __ieee754_gammaf_r (float,int *);
 235 extern float __ieee754_lgammaf (float);
 236 extern float __ieee754_gammaf (float);
 237 extern float __ieee754_log10f (float);
 238 extern float __ieee754_log2f (float);
 239 extern float __ieee754_sinhf (float);
 240 extern float __ieee754_hypotf (float,float);
 241 extern float __ieee754_j0f (float);
 242 extern float __ieee754_j1f (float);
 243 extern float __ieee754_y0f (float);
 244 extern float __ieee754_y1f (float);
 245 extern float __ieee754_jnf (int,float);
 246 extern float __ieee754_ynf (int,float);
 247 extern float __ieee754_remainderf (float,float);
 248 extern int32_t __ieee754_rem_pio2f (float,float*);
 249 extern float __ieee754_scalbf (float,float);
 250
 251
 252 /* float versions of fdlibm kernel functions */
 253 extern float __kernel_sinf (float,float,int);
 254 extern float __kernel_cosf (float,float);
 255 extern float __kernel_tanf (float,float,int);
 256 extern int   __kernel_rem_pio2f (float*,float*,int,int,int, const int32_t*);
 257
 258 /* internal functions.  */
 259 extern float __copysignf (float x, float __y);
 260
 261 #if __GNUC_PREREQ (4, 0)
 262 extern inline float __copysignf (float x, float y)
 263 { return __builtin_copysignf (x, y); }
 264 #endif
 265
 266 /* ieee style elementary long double functions */
 267 extern long double __ieee754_sqrtl (long double);
 268 extern long double __ieee754_acosl (long double);
 269 extern long double __ieee754_acoshl (long double);
 270 extern long double __ieee754_logl (long double);
 271 extern long double __ieee754_atanhl (long double);
 272 extern long double __ieee754_asinl (long double);
 273 extern long double __ieee754_atan2l (long double,long double);
 274 extern long double __ieee754_expl (long double);
 275 extern long double __ieee754_exp2l (long double);
 276 extern long double __ieee754_exp10l (long double);
 277 extern long double __ieee754_coshl (long double);
 278 extern long double __ieee754_fmodl (long double,long double);
 279 extern long double __ieee754_powl (long double,long double);
 280 extern long double __ieee754_lgammal_r (long double,int *);
 281 extern long double __ieee754_gammal_r (long double,int *);
 282 extern long double __ieee754_lgammal (long double);
 283 extern long double __ieee754_gammal (long double);
 284 extern long double __ieee754_log10l (long double);
 285 extern long double __ieee754_log2l (long double);
 286 extern long double __ieee754_sinhl (long double);
 287 extern long double __ieee754_hypotl (long double,long double);
 288 extern long double __ieee754_j0l (long double);
 289 extern long double __ieee754_j1l (long double);
 290 extern long double __ieee754_y0l (long double);
 291 extern long double __ieee754_y1l (long double);
 292 extern long double __ieee754_jnl (int,long double);
 293 extern long double __ieee754_ynl (int,long double);
 294 extern long double __ieee754_remainderl (long double,long double);
 295 extern int   __ieee754_rem_pio2l (long double,long double*);
 296 extern long double __ieee754_scalbl (long double,long double);
 297
 298 /* long double versions of fdlibm kernel functions */
 299 extern long double __kernel_sinl (long double,long double,int);
 300 extern long double __kernel_cosl (long double,long double);
 301 extern long double __kernel_tanl (long double,long double,int);
 302 extern void __kernel_sincosl (long double,long double,
 303                               long double *,long double *, int);
 304 extern int   __kernel_rem_pio2l (long double*,long double*,int,int,
 305                                  int,const int*);
 306
 307 #ifndef NO_LONG_DOUBLE
 308 /* prototypes required to compile the ldbl-96 support without warnings */
 309 extern int __finitel (long double);
 310 extern int __ilogbl (long double);
 311 extern int __isinfl (long double);
 312 extern int __isnanl (long double);
 313 extern long double __atanl (long double);
 314 extern long double __copysignl (long double, long double);
 315 extern long double __expm1l (long double);
 316 extern long double __floorl (long double);
 317 extern long double __frexpl (long double, int *);
 318 extern long double __ldexpl (long double, int);
 319 extern long double __log1pl (long double);
 320 extern long double __nanl (const char *);
 321 extern long double __rintl (long double);
 322 extern long double __scalbnl (long double, int);
 323 extern long double __sqrtl (long double x);
 324 extern long double fabsl (long double x);
 325 extern void __sincosl (long double, long double *, long double *);
 326 extern long double __logbl (long double x);
 327 extern long double __significandl (long double x);
 328
 329 #if __GNUC_PREREQ (4, 0)
 330 extern inline long double __copysignl (long double x, long double y)
 331 { return __builtin_copysignl (x, y); }
 332 #endif
 333
 334 #endif
 335
 336 /* Prototypes for functions of the IBM Accurate Mathematical Library.  */
 337 extern double __exp1 (double __x, double __xx, double __error);
 338 extern double __sin (double __x);
 339 extern double __cos (double __x);
 340 extern int __branred (double __x, double *__a, double *__aa);
 341 extern void __doasin (double __x, double __dx, double __v[]);
 342 extern void __dubsin (double __x, double __dx, double __v[]);
 343 extern void __dubcos (double __x, double __dx, double __v[]);
 344 extern double __halfulp (double __x, double __y);
 345 extern double __sin32 (double __x, double __res, double __res1);
 346 extern double __cos32 (double __x, double __res, double __res1);
 347 extern double __mpsin (double __x, double __dx);
 348 extern double __mpcos (double __x, double __dx);
 349 extern double __mpsin1 (double __x);
 350 extern double __mpcos1 (double __x);
 351 extern double __slowexp (double __x);
 352 extern double __slowpow (double __x, double __y, double __z);
 353 extern void __docos (double __x, double __dx, double __v[]);
 354
 355 #ifndef math_opt_barrier
 356 #define math_opt_barrier(x) \
 357 ({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; })
 358 #define math_force_eval(x) \
 359 ({ __typeof (x) __x = (x); __asm __volatile ("" : : "m" (__x)); })
 360 #endif
 361
 362
 363 /* The standards only specify one variant of the fenv.h interfaces.
 364    But at least for some architectures we can be more efficient if we
 365    know what operations are going to be performed.  Therefore we
 366    define additional interfaces.  By default they refer to the normal
 367    interfaces.  */
 368 #define libc_fegetround() fegetround ()
 369 #define libc_fegetroundf() fegetround ()
 370 #define libc_fegetroundl() fegetround ()
 371
 372 #define libc_fesetround(r) (void) fesetround (r)
 373 #define libc_fesetroundf(r) (void) fesetround (r)
 374 #define libc_fesetroundl(r) (void) fesetround (r)
 375
 376 #define libc_feholdexcept(e) (void) feholdexcept (e)
 377 #define libc_feholdexceptf(e) (void) feholdexcept (e)
 378 #define libc_feholdexceptl(e) (void) feholdexcept (e)
 379
 380 #define libc_feholdexcept_setround(e, r) \
 381   do { feholdexcept (e); fesetround (r); } while (0)
 382 #define libc_feholdexcept_setroundf(e, r) \
 383   do { feholdexcept (e); fesetround (r); } while (0)
 384 #define libc_feholdexcept_setroundl(e, r) \
 385   do { feholdexcept (e); fesetround (r); } while (0)
 386
 387 #define libc_fetestexcept(e) fetestexcept (e)
 388 #define libc_fetestexceptf(e) fetestexcept (e)
 389 #define libc_fetestexceptl(e) fetestexcept (e)
 390
 391 #define libc_fesetenv(e) (void) fesetenv (e)
 392 #define libc_fesetenvf(e) (void) fesetenv (e)
 393 #define libc_fesetenvl(e) (void) fesetenv (e)
 394
 395 #define libc_feupdateenv(e) (void) feupdateenv (e)
 396 #define libc_feupdateenvf(e) (void) feupdateenv (e)
 397 #define libc_feupdateenvl(e) (void) feupdateenv (e)
 398
 399 #define __nan(str) \
 400   (__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
 401 #define __nanf(str) \
 402   (__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
 403 #define __nanl(str) \
 404   (__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
 405
 406 #endif /* _MATH_PRIVATE_H_ */