soft-fp/extended.h

   1 /* Software floating-point emulation.
   2    Definitions for IEEE Extended Precision.
   3    Copyright (C) 1999,2006 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     if (!X##_e && (X##_f[1] || X##_f[0])                \
  98         && !(X##_f[1] & _FP_IMPLBIT_E))                 \
  99       {                                                 \
 100         X##_e++;                                        \
 101         FP_SET_EXCEPTION(FP_EX_DENORM);                 \
 102       }                                                 \
 103   } while (0)
 104
 105 #define FP_UNPACK_RAW_EP(X, val)                        \
 106   do {                                                  \
 107     union _FP_UNION_E *_flo =                           \
 108     (union _FP_UNION_E *)(val);                         \
 109                                                         \
 110     X##_f[2] = 0; X##_f[3] = 0;                         \
 111     X##_f[0] = _flo->bits.frac0;                        \
 112     X##_f[1] = _flo->bits.frac1;                        \
 113     X##_e  = _flo->bits.exp;                            \
 114     X##_s  = _flo->bits.sign;                           \
 115     if (!X##_e && (X##_f[1] || X##_f[0])                \
 116         && !(X##_f[1] & _FP_IMPLBIT_E))                 \
 117       {                                                 \
 118         X##_e++;                                        \
 119         FP_SET_EXCEPTION(FP_EX_DENORM);                 \
 120       }                                                 \
 121   } while (0)
 122
 123 #define FP_PACK_RAW_E(val, X)                           \
 124   do {                                                  \
 125     union _FP_UNION_E _flo;                             \
 126                                                         \
 127     if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;               \
 128     else X##_f[1] &= ~(_FP_IMPLBIT_E);                  \
 129     _flo.bits.frac0 = X##_f[0];                         \
 130     _flo.bits.frac1 = X##_f[1];                         \
 131     _flo.bits.exp   = X##_e;                            \
 132     _flo.bits.sign  = X##_s;                            \
 133                                                         \
 134     (val) = _flo.flt;                                   \
 135   } while (0)
 136
 137 #define FP_PACK_RAW_EP(val, X)                          \
 138   do {                                                  \
 139     if (!FP_INHIBIT_RESULTS)                            \
 140       {                                                 \
 141         union _FP_UNION_E *_flo =                       \
 142           (union _FP_UNION_E *)(val);                   \
 143                                                         \
 144         if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;           \
 145         else X##_f[1] &= ~(_FP_IMPLBIT_E);              \
 146         _flo->bits.frac0 = X##_f[0];                    \
 147         _flo->bits.frac1 = X##_f[1];                    \
 148         _flo->bits.exp   = X##_e;                       \
 149         _flo->bits.sign  = X##_s;                       \
 150       }                                                 \
 151   } while (0)
 152
 153 #define FP_UNPACK_E(X,val)              \
 154   do {                                  \
 155     FP_UNPACK_RAW_E(X,val);             \
 156     _FP_UNPACK_CANONICAL(E,4,X);        \
 157   } while (0)
 158
 159 #define FP_UNPACK_EP(X,val)             \
 160   do {                                  \
 161     FP_UNPACK_RAW_EP(X,val);            \
 162     _FP_UNPACK_CANONICAL(E,4,X);        \
 163   } while (0)
 164
 165 #define FP_UNPACK_SEMIRAW_E(X,val)      \
 166   do {                                  \
 167     _FP_UNPACK_RAW_E(X,val);            \
 168     _FP_UNPACK_SEMIRAW(E,4,X);          \
 169   } while (0)
 170
 171 #define FP_UNPACK_SEMIRAW_EP(X,val)     \
 172   do {                                  \
 173     _FP_UNPACK_RAW_EP(X,val);           \
 174     _FP_UNPACK_SEMIRAW(E,4,X);          \
 175   } while (0)
 176
 177 #define FP_PACK_E(val,X)                \
 178   do {                                  \
 179     _FP_PACK_CANONICAL(E,4,X);          \
 180     FP_PACK_RAW_E(val,X);               \
 181   } while (0)
 182
 183 #define FP_PACK_EP(val,X)               \
 184   do {                                  \
 185     _FP_PACK_CANONICAL(E,4,X);          \
 186     FP_PACK_RAW_EP(val,X);              \
 187   } while (0)
 188
 189 #define FP_PACK_SEMIRAW_E(val,X)        \
 190   do {                                  \
 191     _FP_PACK_SEMIRAW(E,4,X);            \
 192     _FP_PACK_RAW_E(val,X);              \
 193   } while (0)
 194
 195 #define FP_PACK_SEMIRAW_EP(val,X)       \
 196   do {                                  \
 197     _FP_PACK_SEMIRAW(E,4,X);            \
 198     _FP_PACK_RAW_EP(val,X);             \
 199   } while (0)
 200
 201 #define FP_ISSIGNAN_E(X)        _FP_ISSIGNAN(E,4,X)
 202 #define FP_NEG_E(R,X)           _FP_NEG(E,4,R,X)
 203 #define FP_ADD_E(R,X,Y)         _FP_ADD(E,4,R,X,Y)
 204 #define FP_SUB_E(R,X,Y)         _FP_SUB(E,4,R,X,Y)
 205 #define FP_MUL_E(R,X,Y)         _FP_MUL(E,4,R,X,Y)
 206 #define FP_DIV_E(R,X,Y)         _FP_DIV(E,4,R,X,Y)
 207 #define FP_SQRT_E(R,X)          _FP_SQRT(E,4,R,X)
 208
 209 /*
 210  * Square root algorithms:
 211  * We have just one right now, maybe Newton approximation
 212  * should be added for those machines where division is fast.
 213  * This has special _E version because standard _4 square
 214  * root would not work (it has to start normally with the
 215  * second word and not the first), but as we have to do it
 216  * anyway, we optimize it by doing most of the calculations
 217  * in two UWtype registers instead of four.
 218  */
 219
 220 #define _FP_SQRT_MEAT_E(R, S, T, X, q)                  \
 221   do {                                                  \
 222     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 223     _FP_FRAC_SRL_4(X, (_FP_WORKBITS));                  \
 224     while (q)                                           \
 225       {                                                 \
 226         T##_f[1] = S##_f[1] + q;                        \
 227         if (T##_f[1] <= X##_f[1])                       \
 228           {                                             \
 229             S##_f[1] = T##_f[1] + q;                    \
 230             X##_f[1] -= T##_f[1];                       \
 231             R##_f[1] += q;                              \
 232           }                                             \
 233         _FP_FRAC_SLL_2(X, 1);                           \
 234         q >>= 1;                                        \
 235       }                                                 \
 236     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 237     while (q)                                           \
 238       {                                                 \
 239         T##_f[0] = S##_f[0] + q;                        \
 240         T##_f[1] = S##_f[1];                            \
 241         if (T##_f[1] < X##_f[1] ||                      \
 242             (T##_f[1] == X##_f[1] &&                    \
 243              T##_f[0] <= X##_f[0]))                     \
 244           {                                             \
 245             S##_f[0] = T##_f[0] + q;                    \
 246             S##_f[1] += (T##_f[0] > S##_f[0]);          \
 247             _FP_FRAC_DEC_2(X, T);                       \
 248             R##_f[0] += q;                              \
 249           }                                             \
 250         _FP_FRAC_SLL_2(X, 1);                           \
 251         q >>= 1;                                        \
 252       }                                                 \
 253     _FP_FRAC_SLL_4(R, (_FP_WORKBITS));                  \
 254     if (X##_f[0] | X##_f[1])                            \
 255       {                                                 \
 256         if (S##_f[1] < X##_f[1] ||                      \
 257             (S##_f[1] == X##_f[1] &&                    \
 258              S##_f[0] < X##_f[0]))                      \
 259           R##_f[0] |= _FP_WORK_ROUND;                   \
 260         R##_f[0] |= _FP_WORK_STICKY;                    \
 261       }                                                 \
 262   } while (0)
 263
 264 #define FP_CMP_E(r,X,Y,un)      _FP_CMP(E,4,r,X,Y,un)
 265 #define FP_CMP_EQ_E(r,X,Y)      _FP_CMP_EQ(E,4,r,X,Y)
 266 #define FP_CMP_UNORD_E(r,X,Y)   _FP_CMP_UNORD(E,4,r,X,Y)
 267
 268 #define FP_TO_INT_E(r,X,rsz,rsg)        _FP_TO_INT(E,4,r,X,rsz,rsg)
 269 #define FP_FROM_INT_E(X,r,rs,rt)        _FP_FROM_INT(E,4,X,r,rs,rt)
 270
 271 #define _FP_FRAC_HIGH_E(X)      (X##_f[2])
 272 #define _FP_FRAC_HIGH_RAW_E(X)  (X##_f[1])
 273
 274 #else   /* not _FP_W_TYPE_SIZE < 64 */
 275 union _FP_UNION_E
 276 {
 277   XFtype flt;
 278   struct {
 279 #if __BYTE_ORDER == __BIG_ENDIAN
 280     unsigned long pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
 281     unsigned sign  : 1;
 282     unsigned exp   : _FP_EXPBITS_E;
 283     unsigned long frac : _FP_W_TYPE_SIZE;
 284 #else
 285     unsigned long frac : _FP_W_TYPE_SIZE;
 286     unsigned exp   : _FP_EXPBITS_E;
 287     unsigned sign  : 1;
 288 #endif
 289   } bits;
 290 };
 291
 292 #define FP_DECL_E(X)            _FP_DECL(2,X)
 293
 294 #define FP_UNPACK_RAW_E(X, val)                                 \
 295   do {                                                          \
 296     union _FP_UNION_E _flo; _flo.flt = (val);                   \
 297                                                                 \
 298     X##_f0 = _flo.bits.frac;                                    \
 299     X##_f1 = 0;                                                 \
 300     X##_e = _flo.bits.exp;                                      \
 301     X##_s = _flo.bits.sign;                                     \
 302     if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E))          \
 303       {                                                         \
 304         X##_e++;                                                \
 305         FP_SET_EXCEPTION(FP_EX_DENORM);                         \
 306       }                                                         \
 307   } while (0)
 308
 309 #define FP_UNPACK_RAW_EP(X, val)                                \
 310   do {                                                          \
 311     union _FP_UNION_E *_flo =                                   \
 312       (union _FP_UNION_E *)(val);                               \
 313                                                                 \
 314     X##_f0 = _flo->bits.frac;                                   \
 315     X##_f1 = 0;                                                 \
 316     X##_e = _flo->bits.exp;                                     \
 317     X##_s = _flo->bits.sign;                                    \
 318     if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E))          \
 319       {                                                         \
 320         X##_e++;                                                \
 321         FP_SET_EXCEPTION(FP_EX_DENORM);                         \
 322       }                                                         \
 323   } while (0)
 324
 325 #define FP_PACK_RAW_E(val, X)                                   \
 326   do {                                                          \
 327     union _FP_UNION_E _flo;                                     \
 328                                                                 \
 329     if (X##_e) X##_f0 |= _FP_IMPLBIT_E;                         \
 330     else X##_f0 &= ~(_FP_IMPLBIT_E);                            \
 331     _flo.bits.frac = X##_f0;                                    \
 332     _flo.bits.exp  = X##_e;                                     \
 333     _flo.bits.sign = X##_s;                                     \
 334                                                                 \
 335     (val) = _flo.flt;                                           \
 336   } while (0)
 337
 338 #define FP_PACK_RAW_EP(fs, val, X)                              \
 339   do {                                                          \
 340     if (!FP_INHIBIT_RESULTS)                                    \
 341       {                                                         \
 342         union _FP_UNION_E *_flo =                               \
 343           (union _FP_UNION_E *)(val);                           \
 344                                                                 \
 345         if (X##_e) X##_f0 |= _FP_IMPLBIT_E;                     \
 346         else X##_f0 &= ~(_FP_IMPLBIT_E);                        \
 347         _flo->bits.frac = X##_f0;                               \
 348         _flo->bits.exp  = X##_e;                                \
 349         _flo->bits.sign = X##_s;                                \
 350       }                                                         \
 351   } while (0)
 352
 353
 354 #define FP_UNPACK_E(X,val)              \
 355   do {                                  \
 356     FP_UNPACK_RAW_E(X,val);             \
 357     _FP_UNPACK_CANONICAL(E,2,X);        \
 358   } while (0)
 359
 360 #define FP_UNPACK_EP(X,val)             \
 361   do {                                  \
 362     FP_UNPACK_RAW_EP(X,val);            \
 363     _FP_UNPACK_CANONICAL(E,2,X);        \
 364   } while (0)
 365
 366 #define FP_UNPACK_SEMIRAW_E(X,val)      \
 367   do {                                  \
 368     _FP_UNPACK_RAW_E(X,val);            \
 369     _FP_UNPACK_SEMIRAW(E,2,X);          \
 370   } while (0)
 371
 372 #define FP_UNPACK_SEMIRAW_EP(X,val)     \
 373   do {                                  \
 374     _FP_UNPACK_RAW_EP(X,val);           \
 375     _FP_UNPACK_SEMIRAW(E,2,X);          \
 376   } while (0)
 377
 378 #define FP_PACK_E(val,X)                \
 379   do {                                  \
 380     _FP_PACK_CANONICAL(E,2,X);          \
 381     FP_PACK_RAW_E(val,X);               \
 382   } while (0)
 383
 384 #define FP_PACK_EP(val,X)               \
 385   do {                                  \
 386     _FP_PACK_CANONICAL(E,2,X);          \
 387     FP_PACK_RAW_EP(val,X);              \
 388   } while (0)
 389
 390 #define FP_PACK_SEMIRAW_E(val,X)        \
 391   do {                                  \
 392     _FP_PACK_SEMIRAW(E,2,X);            \
 393     _FP_PACK_RAW_E(val,X);              \
 394   } while (0)
 395
 396 #define FP_PACK_SEMIRAW_EP(val,X)       \
 397   do {                                  \
 398     _FP_PACK_SEMIRAW(E,2,X);            \
 399     _FP_PACK_RAW_EP(val,X);             \
 400   } while (0)
 401
 402 #define FP_ISSIGNAN_E(X)        _FP_ISSIGNAN(E,2,X)
 403 #define FP_NEG_E(R,X)           _FP_NEG(E,2,R,X)
 404 #define FP_ADD_E(R,X,Y)         _FP_ADD(E,2,R,X,Y)
 405 #define FP_SUB_E(R,X,Y)         _FP_SUB(E,2,R,X,Y)
 406 #define FP_MUL_E(R,X,Y)         _FP_MUL(E,2,R,X,Y)
 407 #define FP_DIV_E(R,X,Y)         _FP_DIV(E,2,R,X,Y)
 408 #define FP_SQRT_E(R,X)          _FP_SQRT(E,2,R,X)
 409
 410 /*
 411  * Square root algorithms:
 412  * We have just one right now, maybe Newton approximation
 413  * should be added for those machines where division is fast.
 414  * We optimize it by doing most of the calculations
 415  * in one UWtype registers instead of two, although we don't
 416  * have to.
 417  */
 418 #define _FP_SQRT_MEAT_E(R, S, T, X, q)                  \
 419   do {                                                  \
 420     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);         \
 421     _FP_FRAC_SRL_2(X, (_FP_WORKBITS));                  \
 422     while (q)                                           \
 423       {                                                 \
 424         T##_f0 = S##_f0 + q;                            \
 425         if (T##_f0 <= X##_f0)                           \
 426           {                                             \
 427             S##_f0 = T##_f0 + q;                        \
 428             X##_f0 -= T##_f0;                           \
 429             R##_f0 += q;                                \
 430           }                                             \
 431         _FP_FRAC_SLL_1(X, 1);                           \
 432         q >>= 1;                                        \
 433       }                                                 \
 434     _FP_FRAC_SLL_2(R, (_FP_WORKBITS));                  \
 435     if (X##_f0)                                         \
 436       {                                                 \
 437         if (S##_f0 < X##_f0)                            \
 438           R##_f0 |= _FP_WORK_ROUND;                     \
 439         R##_f0 |= _FP_WORK_STICKY;                      \
 440       }                                                 \
 441   } while (0)
 442
 443 #define FP_CMP_E(r,X,Y,un)      _FP_CMP(E,2,r,X,Y,un)
 444 #define FP_CMP_EQ_E(r,X,Y)      _FP_CMP_EQ(E,2,r,X,Y)
 445 #define FP_CMP_UNORD_E(r,X,Y)   _FP_CMP_UNORD(E,2,r,X,Y)
 446
 447 #define FP_TO_INT_E(r,X,rsz,rsg)        _FP_TO_INT(E,2,r,X,rsz,rsg)
 448 #define FP_FROM_INT_E(X,r,rs,rt)        _FP_FROM_INT(E,2,X,r,rs,rt)
 449
 450 #define _FP_FRAC_HIGH_E(X)      (X##_f1)
 451 #define _FP_FRAC_HIGH_RAW_E(X)  (X##_f0)
 452
 453 #endif /* not _FP_W_TYPE_SIZE < 64 */