soft-fp/extended.h

   1 /* Software floating-point emulation.
   2    Definitions for IEEE Extended Precision.
   3    Copyright (C) 1999,2006,2007 Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5    Contributed by Jakub Jelinek (jj@ultra.linux.cz).
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    In addition to the permissions in the GNU Lesser General Public
  13    License, the Free Software Foundation gives you unlimited
  14    permission to link the compiled version of this file into
  15    combinations with other programs, and to distribute those
  16    combinations without any restriction coming from the use of this
  17    file.  (The Lesser General Public License restrictions do apply in
  18    other respects; for example, they cover modification of the file,
  19    and distribution when not linked into a combine executable.)
  20
  21    The GNU C Library is distributed in the hope that it will be useful,
  22    but WITHOUT ANY WARRANTY; without even the implied warranty of
  23    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  24    Lesser General Public License for more details.
  25
  26    You should have received a copy of the GNU Lesser General Public
  27    License along with the GNU C Library; if not, write to the Free
  28    Software Foundation, 51 Franklin Street, Fifth Floor, Boston,
  29    MA 02110-1301, USA.  */
  30
  31 #if _FP_W_TYPE_SIZE < 32
  32 #error "Here's a nickel, kid. Go buy yourself a real computer."
  33 #endif
  34
  35 #if _FP_W_TYPE_SIZE < 64
  36 #define _FP_FRACTBITS_E         (4*_FP_W_TYPE_SIZE)
  37 #else
  38 #define _FP_FRACTBITS_E         (2*_FP_W_TYPE_SIZE)
  39 #endif
  40
  41 #define _FP_FRACBITS_E          64
  42 #define _FP_FRACXBITS_E         (_FP_FRACTBITS_E - _FP_FRACBITS_E)
  43 #define _FP_WFRACBITS_E         (_FP_WORKBITS + _FP_FRACBITS_E)
  44 #define _FP_WFRACXBITS_E        (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
  45 #define _FP_EXPBITS_E           15
  46 #define _FP_EXPBIAS_E           16383
  47 #define _FP_EXPMAX_E            32767
  48
  49 #define _FP_QNANBIT_E           \
  50         ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
  51 #define _FP_QNANBIT_SH_E                \
  52         ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
  53 #define _FP_IMPLBIT_E           \
  54         ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
  55 #define _FP_IMPLBIT_SH_E                \
  56         ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
  57 #define _FP_OVERFLOW_E          \
  58         ((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
  59
  60 typedef float XFtype __attribute__((mode(XF)));
  61
  62 #if _FP_W_TYPE_SIZE < 64
  63
  64 union _FP_UNION_E
  65 {
  66    XFtype flt;
  67    struct
  68    {
  69 #if __BYTE_ORDER == __BIG_ENDIAN
  70       unsigned long pad1 : _FP_W_TYPE_SIZE;
  71       unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
  72       unsigned long sign : 1;
  73       unsigned long exp : _FP_EXPBITS_E;
  74       unsigned long frac1 : _FP_W_TYPE_SIZE;
  75       unsigned long frac0 : _FP_W_TYPE_SIZE;
  76 #else
  77       unsigned long frac0 : _FP_W_TYPE_SIZE;
  78       unsigned long frac1 : _FP_W_TYPE_SIZE;
  79       unsigned exp : _FP_EXPBITS_E;
  80       unsigned sign : 1;
  81 #endif /* not bigendian */
  82    } bits __attribute__((packed));
  83 };
  84
  85
  86 #define FP_DECL_E(X)            _FP_DECL(4,X)
  87
  88 #define FP_UNPACK_RAW_E(X, val)                         \
  89   do {                                                  \
  90     union _FP_UNION_E _flo; _flo.flt = (val);           \
  91                                                         \
  92     X##_f[2] = 0; X##_f[3] = 0;                         \
  93     X##_f[0] = _flo.bits.frac0;                         \
  94     X##_f[1] = _flo.bits.frac1;                         \
  95     X##_e  = _flo.bits.exp;                             \
  96     X##_s  = _flo.bits.sign;                            \
  97   } while (0)
  98
  99 #define FP_UNPACK_RAW_EP(X, val)                        \
 100   do {                                                  \
 101     union _FP_UNION_E *_flo =                           \
 102     (union _FP_UNION_E *)(val);                         \
 103                                                         \
 104     X##_f[2] = 0; X##_f[3] = 0;                         \
 105     X##_f[0] = _flo->bits.frac0;                        \
 106     X##_f[1] = _flo->bits.frac1;                        \
 107     X##_e  = _flo->bits.exp;                            \
 108     X##_s  = _flo->bits.sign;                           \
 109   } while (0)
 110
 111 #define FP_PACK_RAW_E(val, X)                           \
 112   do {                                                  \
 113     union _FP_UNION_E _flo;                             \
 114                                                         \
 115     if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;               \
 116     else X##_f[1] &= ~(_FP_IMPLBIT_E);                  \
 117     _flo.bits.frac0 = X##_f[0];                         \
 118     _flo.bits.frac1 = X##_f[1];                         \
 119     _flo.bits.exp   = X##_e;                            \
 120     _flo.bits.sign  = X##_s;                            \
 121                                                         \
 122     (val) = _flo.flt;                                   \
 123   } while (0)
 124
 125 #define FP_PACK_RAW_EP(val, X)                          \
 126   do {                                                  \
 127     if (!FP_INHIBIT_RESULTS)                            \
 128       {                                                 \
 129         union _FP_UNION_E *_flo =                       \
 130           (union _FP_UNION_E *)(val);                   \
 131                                                         \
 132         if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;           \
 133         else X##_f[1] &= ~(_FP_IMPLBIT_E);              \
 134         _flo->bits.frac0 = X##_f[0];                    \
 135         _flo->bits.frac1 = X##_f[1];                    \
 136         _flo->bits.exp   = X##_e;                       \
 137         _flo->bits.sign  = X##_s;                       \
 138       }                                                 \
 139   } while (0)
 140
 141 #define FP_UNPACK_E(X,val)              \
 142   do {                                  \
 143     FP_UNPACK_RAW_E(X,val);             \
 144     _FP_UNPACK_CANONICAL(E,4,X);        \
 145   } while (0)
 146
 147 #define FP_UNPACK_EP(X,val)             \
 148   do {                                  \
 149     FP_UNPACK_RAW_EP(X,val);            \
 150     _FP_UNPACK_CANONICAL(E,4,X);        \
 151   } while (0)
 152
 153 #define FP_UNPACK_SEMIRAW_E(X,val)      \
 154   do {                                  \
 155     FP_UNPACK_RAW_E(X,val);             \
 156     _FP_UNPACK_SEMIRAW(E,4,X);          \
 157   } while (0)
 158
 159 #define FP_UNPACK_SEMIRAW_EP(X,val)     \
 160   do {                                  \
 161     FP_UNPACK_RAW_EP(X,val);            \
 162     _FP_UNPACK_SEMIRAW(E,4,X);          \
 163   } while (0)
 164
 165 #define FP_PACK_E(val,X)                \
 166   do {                                  \
 167     _FP_PACK_CANONICAL(E,4,X);          \
 168     FP_PACK_RAW_E(val,X);               \
 169   } while (0)
 170
 171 #define FP_PACK_EP(val,X)               \
 172   do {                                  \
 173     _FP_PACK_CANONICAL(E,4,X);          \
 174     FP_PACK_RAW_EP(val,X);              \
 175   } while (0)
 176
 177 #define FP_PACK_SEMIRAW_E(val,X)        \
 178   do {                                  \
 179     _FP_PACK_SEMIRAW(E,4,X);            \
 180     FP_PACK_RAW_E(val,X);               \
 181   } while (0)
 182
 183 #define FP_PACK_SEMIRAW_EP(val,X)       \
 184   do {                                  \
 185     _FP_PACK_SEMIRAW(E,4,X);            \
 186     FP_PACK_RAW_EP(val,X);              \
 187   } while (0)
 188
 189 #define FP_ISSIGNAN_E(X)        _FP_ISSIGNAN(E,4,X)
 190 #define FP_NEG_E(R,X)           _FP_NEG(E,4,R,X)
 191 #define FP_ADD_E(R,X,Y)         _FP_ADD(E,4,R,X,Y)
 192 #define FP_SUB_E(R,X,Y)         _FP_SUB(E,4,R,X,Y)
 193 #define FP_MUL_E(R,X,Y)         _FP_MUL(E,4,R,X,Y)
 194 #define FP_DIV_E(R,X,Y)         _FP_DIV(E,4,R,X,Y)
 195 #define FP_SQRT_E(R,X)          _FP_SQRT(E,4,R,X)
 196
 197 /*
 198  * Square root algorithms:
 199  * We have just one right now, maybe Newton approximation
 200  * should be added for those machines where division is fast.
 201  * This has special _E version because standard _4 square
 202  * root would not work (it has to start normally with the
 203  * second word and not the first), but as we have to do it
 204  * anyway, we optimize it by doing most of the calculations
 205  * in two UWtype registers instead of four.
 206  */
 207
 208 #define _FP_SQRT_MEAT_E(R, S, T, X, q)                  \
 209   do {                                                  \
 210     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 211     _FP_FRAC_SRL_4(X, (_FP_WORKBITS));                  \
 212     while (q)                                           \
 213       {                                                 \
 214         T##_f[1] = S##_f[1] + q;                        \
 215         if (T##_f[1] <= X##_f[1])                       \
 216           {                                             \
 217             S##_f[1] = T##_f[1] + q;                    \
 218             X##_f[1] -= T##_f[1];                       \
 219             R##_f[1] += q;                              \
 220           }                                             \
 221         _FP_FRAC_SLL_2(X, 1);                           \
 222         q >>= 1;                                        \
 223       }                                                 \
 224     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 225     while (q)                                           \
 226       {                                                 \
 227         T##_f[0] = S##_f[0] + q;                        \
 228         T##_f[1] = S##_f[1];                            \
 229         if (T##_f[1] < X##_f[1] ||                      \
 230             (T##_f[1] == X##_f[1] &&                    \
 231              T##_f[0] <= X##_f[0]))                     \
 232           {                                             \
 233             S##_f[0] = T##_f[0] + q;                    \
 234             S##_f[1] += (T##_f[0] > S##_f[0]);          \
 235             _FP_FRAC_DEC_2(X, T);                       \
 236             R##_f[0] += q;                              \
 237           }                                             \
 238         _FP_FRAC_SLL_2(X, 1);                           \
 239         q >>= 1;                                        \
 240       }                                                 \
 241     _FP_FRAC_SLL_4(R, (_FP_WORKBITS));                  \
 242     if (X##_f[0] | X##_f[1])                            \
 243       {                                                 \
 244         if (S##_f[1] < X##_f[1] ||                      \
 245             (S##_f[1] == X##_f[1] &&                    \
 246              S##_f[0] < X##_f[0]))                      \
 247           R##_f[0] |= _FP_WORK_ROUND;                   \
 248         R##_f[0] |= _FP_WORK_STICKY;                    \
 249       }                                                 \
 250   } while (0)
 251
 252 #define FP_CMP_E(r,X,Y,un)      _FP_CMP(E,4,r,X,Y,un)
 253 #define FP_CMP_EQ_E(r,X,Y)      _FP_CMP_EQ(E,4,r,X,Y)
 254 #define FP_CMP_UNORD_E(r,X,Y)   _FP_CMP_UNORD(E,4,r,X,Y)
 255
 256 #define FP_TO_INT_E(r,X,rsz,rsg)        _FP_TO_INT(E,4,r,X,rsz,rsg)
 257 #define FP_FROM_INT_E(X,r,rs,rt)        _FP_FROM_INT(E,4,X,r,rs,rt)
 258
 259 #define _FP_FRAC_HIGH_E(X)      (X##_f[2])
 260 #define _FP_FRAC_HIGH_RAW_E(X)  (X##_f[1])
 261
 262 #else   /* not _FP_W_TYPE_SIZE < 64 */
 263 union _FP_UNION_E
 264 {
 265   XFtype flt;
 266   struct {
 267 #if __BYTE_ORDER == __BIG_ENDIAN
 268     _FP_W_TYPE pad  : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
 269     unsigned sign   : 1;
 270     unsigned exp    : _FP_EXPBITS_E;
 271     _FP_W_TYPE frac : _FP_W_TYPE_SIZE;
 272 #else
 273     _FP_W_TYPE frac : _FP_W_TYPE_SIZE;
 274     unsigned exp    : _FP_EXPBITS_E;
 275     unsigned sign   : 1;
 276 #endif
 277   } bits;
 278 };
 279
 280 #define FP_DECL_E(X)            _FP_DECL(2,X)
 281
 282 #define FP_UNPACK_RAW_E(X, val)                                 \
 283   do {                                                          \
 284     union _FP_UNION_E _flo; _flo.flt = (val);                   \
 285                                                                 \
 286     X##_f0 = _flo.bits.frac;                                    \
 287     X##_f1 = 0;                                                 \
 288     X##_e = _flo.bits.exp;                                      \
 289     X##_s = _flo.bits.sign;                                     \
 290   } while (0)
 291
 292 #define FP_UNPACK_RAW_EP(X, val)                                \
 293   do {                                                          \
 294     union _FP_UNION_E *_flo =                                   \
 295       (union _FP_UNION_E *)(val);                               \
 296                                                                 \
 297     X##_f0 = _flo->bits.frac;                                   \
 298     X##_f1 = 0;                                                 \
 299     X##_e = _flo->bits.exp;                                     \
 300     X##_s = _flo->bits.sign;                                    \
 301   } while (0)
 302
 303 #define FP_PACK_RAW_E(val, X)                                   \
 304   do {                                                          \
 305     union _FP_UNION_E _flo;                                     \
 306                                                                 \
 307     if (X##_e) X##_f0 |= _FP_IMPLBIT_E;                         \
 308     else X##_f0 &= ~(_FP_IMPLBIT_E);                            \
 309     _flo.bits.frac = X##_f0;                                    \
 310     _flo.bits.exp  = X##_e;                                     \
 311     _flo.bits.sign = X##_s;                                     \
 312                                                                 \
 313     (val) = _flo.flt;                                           \
 314   } while (0)
 315
 316 #define FP_PACK_RAW_EP(fs, val, X)                              \
 317   do {                                                          \
 318     if (!FP_INHIBIT_RESULTS)                                    \
 319       {                                                         \
 320         union _FP_UNION_E *_flo =                               \
 321           (union _FP_UNION_E *)(val);                           \
 322                                                                 \
 323         if (X##_e) X##_f0 |= _FP_IMPLBIT_E;                     \
 324         else X##_f0 &= ~(_FP_IMPLBIT_E);                        \
 325         _flo->bits.frac = X##_f0;                               \
 326         _flo->bits.exp  = X##_e;                                \
 327         _flo->bits.sign = X##_s;                                \
 328       }                                                         \
 329   } while (0)
 330
 331
 332 #define FP_UNPACK_E(X,val)              \
 333   do {                                  \
 334     FP_UNPACK_RAW_E(X,val);             \
 335     _FP_UNPACK_CANONICAL(E,2,X);        \
 336   } while (0)
 337
 338 #define FP_UNPACK_EP(X,val)             \
 339   do {                                  \
 340     FP_UNPACK_RAW_EP(X,val);            \
 341     _FP_UNPACK_CANONICAL(E,2,X);        \
 342   } while (0)
 343
 344 #define FP_UNPACK_SEMIRAW_E(X,val)      \
 345   do {                                  \
 346     FP_UNPACK_RAW_E(X,val);             \
 347     _FP_UNPACK_SEMIRAW(E,2,X);          \
 348   } while (0)
 349
 350 #define FP_UNPACK_SEMIRAW_EP(X,val)     \
 351   do {                                  \
 352     FP_UNPACK_RAW_EP(X,val);            \
 353     _FP_UNPACK_SEMIRAW(E,2,X);          \
 354   } while (0)
 355
 356 #define FP_PACK_E(val,X)                \
 357   do {                                  \
 358     _FP_PACK_CANONICAL(E,2,X);          \
 359     FP_PACK_RAW_E(val,X);               \
 360   } while (0)
 361
 362 #define FP_PACK_EP(val,X)               \
 363   do {                                  \
 364     _FP_PACK_CANONICAL(E,2,X);          \
 365     FP_PACK_RAW_EP(val,X);              \
 366   } while (0)
 367
 368 #define FP_PACK_SEMIRAW_E(val,X)        \
 369   do {                                  \
 370     _FP_PACK_SEMIRAW(E,2,X);            \
 371     FP_PACK_RAW_E(val,X);               \
 372   } while (0)
 373
 374 #define FP_PACK_SEMIRAW_EP(val,X)       \
 375   do {                                  \
 376     _FP_PACK_SEMIRAW(E,2,X);            \
 377     FP_PACK_RAW_EP(val,X);              \
 378   } while (0)
 379
 380 #define FP_ISSIGNAN_E(X)        _FP_ISSIGNAN(E,2,X)
 381 #define FP_NEG_E(R,X)           _FP_NEG(E,2,R,X)
 382 #define FP_ADD_E(R,X,Y)         _FP_ADD(E,2,R,X,Y)
 383 #define FP_SUB_E(R,X,Y)         _FP_SUB(E,2,R,X,Y)
 384 #define FP_MUL_E(R,X,Y)         _FP_MUL(E,2,R,X,Y)
 385 #define FP_DIV_E(R,X,Y)         _FP_DIV(E,2,R,X,Y)
 386 #define FP_SQRT_E(R,X)          _FP_SQRT(E,2,R,X)
 387
 388 /*
 389  * Square root algorithms:
 390  * We have just one right now, maybe Newton approximation
 391  * should be added for those machines where division is fast.
 392  * We optimize it by doing most of the calculations
 393  * in one UWtype registers instead of two, although we don't
 394  * have to.
 395  */
 396 #define _FP_SQRT_MEAT_E(R, S, T, X, q)                  \
 397   do {                                                  \
 398     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 399     _FP_FRAC_SRL_2(X, (_FP_WORKBITS));                  \
 400     while (q)                                           \
 401       {                                                 \
 402         T##_f0 = S##_f0 + q;                            \
 403         if (T##_f0 <= X##_f0)                           \
 404           {                                             \
 405             S##_f0 = T##_f0 + q;                        \
 406             X##_f0 -= T##_f0;                           \
 407             R##_f0 += q;                                \
 408           }                                             \
 409         _FP_FRAC_SLL_1(X, 1);                           \
 410         q >>= 1;                                        \
 411       }                                                 \
 412     _FP_FRAC_SLL_2(R, (_FP_WORKBITS));                  \
 413     if (X##_f0)                                         \
 414       {                                                 \
 415         if (S##_f0 < X##_f0)                            \
 416           R##_f0 |= _FP_WORK_ROUND;                     \
 417         R##_f0 |= _FP_WORK_STICKY;                      \
 418       }                                                 \
 419   } while (0)
 420
 421 #define FP_CMP_E(r,X,Y,un)      _FP_CMP(E,2,r,X,Y,un)
 422 #define FP_CMP_EQ_E(r,X,Y)      _FP_CMP_EQ(E,2,r,X,Y)
 423 #define FP_CMP_UNORD_E(r,X,Y)   _FP_CMP_UNORD(E,2,r,X,Y)
 424
 425 #define FP_TO_INT_E(r,X,rsz,rsg)        _FP_TO_INT(E,2,r,X,rsz,rsg)
 426 #define FP_FROM_INT_E(X,r,rs,rt)        _FP_FROM_INT(E,2,X,r,rs,rt)
 427
 428 #define _FP_FRAC_HIGH_E(X)      (X##_f1)
 429 #define _FP_FRAC_HIGH_RAW_E(X)  (X##_f0)
 430
 431 #endif /* not _FP_W_TYPE_SIZE < 64 */