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   1 /* Software floating-point emulation. Common operations.
   2    Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Richard Henderson (rth@cygnus.com),
   5                   Jakub Jelinek (jj@ultra.linux.cz),
   6                   David S. Miller (davem@redhat.com) and
   7                   Peter Maydell (pmaydell@chiark.greenend.org.uk).
   8
   9    The GNU C Library is free software; you can redistribute it and/or
  10    modify it under the terms of the GNU Library General Public License as
  11    published by the Free Software Foundation; either version 2 of the
  12    License, or (at your option) any later version.
  13
  14    The GNU C Library is distributed in the hope that it will be useful,
  15    but WITHOUT ANY WARRANTY; without even the implied warranty of
  16    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  17    Library General Public License for more details.
  18
  19    You should have received a copy of the GNU Library General Public
  20    License along with the GNU C Library; see the file COPYING.LIB.  If
  21    not, write to the Free Software Foundation, Inc.,
  22    59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
  23
  24 #ifndef __MATH_EMU_OP_COMMON_H__
  25 #define __MATH_EMU_OP_COMMON_H__
  26
  27 #define _FP_DECL(wc, X)                 \
  28   _FP_I_TYPE X##_c=0, X##_s=0, X##_e=0; \
  29   _FP_FRAC_DECL_##wc(X)
  30
  31 /*
  32  * Finish truely unpacking a native fp value by classifying the kind
  33  * of fp value and normalizing both the exponent and the fraction.
  34  */
  35
  36 #define _FP_UNPACK_CANONICAL(fs, wc, X)                                 \
  37 do {                                                                    \
  38   switch (X##_e)                                                        \
  39   {                                                                     \
  40   default:                                                              \
  41     _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs;                      \
  42     _FP_FRAC_SLL_##wc(X, _FP_WORKBITS);                                 \
  43     X##_e -= _FP_EXPBIAS_##fs;                                          \
  44     X##_c = FP_CLS_NORMAL;                                              \
  45     break;                                                              \
  46                                                                         \
  47   case 0:                                                               \
  48     if (_FP_FRAC_ZEROP_##wc(X))                                         \
  49       X##_c = FP_CLS_ZERO;                                              \
  50     else                                                                \
  51       {                                                                 \
  52         /* a denormalized number */                                     \
  53         _FP_I_TYPE _shift;                                              \
  54         _FP_FRAC_CLZ_##wc(_shift, X);                                   \
  55         _shift -= _FP_FRACXBITS_##fs;                                   \
  56         _FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS));                    \
  57         X##_e -= _FP_EXPBIAS_##fs - 1 + _shift;                         \
  58         X##_c = FP_CLS_NORMAL;                                          \
  59         FP_SET_EXCEPTION(FP_EX_DENORM);                                 \
  60         if (FP_DENORM_ZERO)                                             \
  61           {                                                             \
  62             FP_SET_EXCEPTION(FP_EX_INEXACT);                            \
  63             X##_c = FP_CLS_ZERO;                                        \
  64           }                                                             \
  65       }                                                                 \
  66     break;                                                              \
  67                                                                         \
  68   case _FP_EXPMAX_##fs:                                                 \
  69     if (_FP_FRAC_ZEROP_##wc(X))                                         \
  70       X##_c = FP_CLS_INF;                                               \
  71     else                                                                \
  72       {                                                                 \
  73         X##_c = FP_CLS_NAN;                                             \
  74         /* Check for signaling NaN */                                   \
  75         if (!(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))            \
  76           FP_SET_EXCEPTION(FP_EX_INVALID);                              \
  77       }                                                                 \
  78     break;                                                              \
  79   }                                                                     \
  80 } while (0)
  81
  82 /*
  83  * Before packing the bits back into the native fp result, take care
  84  * of such mundane things as rounding and overflow.  Also, for some
  85  * kinds of fp values, the original parts may not have been fully
  86  * extracted -- but that is ok, we can regenerate them now.
  87  */
  88
  89 #define _FP_PACK_CANONICAL(fs, wc, X)                           \
  90 do {                                                            \
  91   switch (X##_c)                                                \
  92   {                                                             \
  93   case FP_CLS_NORMAL:                                           \
  94     X##_e += _FP_EXPBIAS_##fs;                                  \
  95     if (X##_e > 0)                                              \
  96       {                                                         \
  97         _FP_ROUND(wc, X);                                       \
  98         if (_FP_FRAC_OVERP_##wc(fs, X))                         \
  99           {                                                     \
 100             _FP_FRAC_CLEAR_OVERP_##wc(fs, X);                   \
 101             X##_e++;                                            \
 102           }                                                     \
 103         _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                     \
 104         if (X##_e >= _FP_EXPMAX_##fs)                           \
 105           {                                                     \
 106             /* overflow */                                      \
 107             switch (FP_ROUNDMODE)                               \
 108               {                                                 \
 109               case FP_RND_NEAREST:                              \
 110                 X##_c = FP_CLS_INF;                             \
 111                 break;                                          \
 112               case FP_RND_PINF:                                 \
 113                 if (!X##_s) X##_c = FP_CLS_INF;                 \
 114                 break;                                          \
 115               case FP_RND_MINF:                                 \
 116                 if (X##_s) X##_c = FP_CLS_INF;                  \
 117                 break;                                          \
 118               }                                                 \
 119             if (X##_c == FP_CLS_INF)                            \
 120               {                                                 \
 121                 /* Overflow to infinity */                      \
 122                 X##_e = _FP_EXPMAX_##fs;                        \
 123                 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);        \
 124               }                                                 \
 125             else                                                \
 126               {                                                 \
 127                 /* Overflow to maximum normal */                \
 128                 X##_e = _FP_EXPMAX_##fs - 1;                    \
 129                 _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc);         \
 130               }                                                 \
 131             FP_SET_EXCEPTION(FP_EX_OVERFLOW);                   \
 132             FP_SET_EXCEPTION(FP_EX_INEXACT);                    \
 133           }                                                     \
 134       }                                                         \
 135     else                                                        \
 136       {                                                         \
 137         /* we've got a denormalized number */                   \
 138         X##_e = -X##_e + 1;                                     \
 139         if (X##_e <= _FP_WFRACBITS_##fs)                        \
 140           {                                                     \
 141             _FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs);    \
 142             _FP_ROUND(wc, X);                                   \
 143             if (_FP_FRAC_HIGH_##fs(X)                           \
 144                 & (_FP_OVERFLOW_##fs >> 1))                     \
 145               {                                                 \
 146                 X##_e = 1;                                      \
 147                 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);        \
 148               }                                                 \
 149             else                                                \
 150               {                                                 \
 151                 X##_e = 0;                                      \
 152                 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);             \
 153                 FP_SET_EXCEPTION(FP_EX_UNDERFLOW);              \
 154               }                                                 \
 155           }                                                     \
 156         else                                                    \
 157           {                                                     \
 158             /* underflow to zero */                             \
 159             X##_e = 0;                                          \
 160             if (!_FP_FRAC_ZEROP_##wc(X))                        \
 161               {                                                 \
 162                 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);         \
 163                 _FP_ROUND(wc, X);                               \
 164                 _FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS);        \
 165               }                                                 \
 166             FP_SET_EXCEPTION(FP_EX_UNDERFLOW);                  \
 167           }                                                     \
 168       }                                                         \
 169     break;                                                      \
 170                                                                 \
 171   case FP_CLS_ZERO:                                             \
 172     X##_e = 0;                                                  \
 173     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 174     break;                                                      \
 175                                                                 \
 176   case FP_CLS_INF:                                              \
 177     X##_e = _FP_EXPMAX_##fs;                                    \
 178     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 179     break;                                                      \
 180                                                                 \
 181   case FP_CLS_NAN:                                              \
 182     X##_e = _FP_EXPMAX_##fs;                                    \
 183     if (!_FP_KEEPNANFRACP)                                      \
 184       {                                                         \
 185         _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs);                 \
 186         X##_s = _FP_NANSIGN_##fs;                               \
 187       }                                                         \
 188     else                                                        \
 189       _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs;            \
 190     break;                                                      \
 191   }                                                             \
 192 } while (0)
 193
 194 /* This one accepts raw argument and not cooked,  returns
 195  * 1 if X is a signaling NaN.
 196  */
 197 #define _FP_ISSIGNAN(fs, wc, X)                                 \
 198 ({                                                              \
 199   int __ret = 0;                                                \
 200   if (X##_e == _FP_EXPMAX_##fs)                                 \
 201     {                                                           \
 202       if (!_FP_FRAC_ZEROP_##wc(X)                               \
 203           && !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))   \
 204         __ret = 1;                                              \
 205     }                                                           \
 206   __ret;                                                        \
 207 })
 208
 209
 210
 211
 212
 213 /*
 214  * Main addition routine.  The input values should be cooked.
 215  */
 216
 217 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP)                                \
 218 do {                                                                         \
 219   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                                     \
 220   {                                                                          \
 221   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):                         \
 222     {                                                                        \
 223       /* shift the smaller number so that its exponent matches the larger */ \
 224       _FP_I_TYPE diff = X##_e - Y##_e;                                       \
 225                                                                              \
 226       if (diff < 0)                                                          \
 227         {                                                                    \
 228           diff = -diff;                                                      \
 229           if (diff <= _FP_WFRACBITS_##fs)                                    \
 230             _FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs);                  \
 231           else if (!_FP_FRAC_ZEROP_##wc(X))                                  \
 232             _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                          \
 233           R##_e = Y##_e;                                                     \
 234         }                                                                    \
 235       else                                                                   \
 236         {                                                                    \
 237           if (diff > 0)                                                      \
 238             {                                                                \
 239               if (diff <= _FP_WFRACBITS_##fs)                                \
 240                 _FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs);              \
 241               else if (!_FP_FRAC_ZEROP_##wc(Y))                              \
 242                 _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc);                      \
 243             }                                                                \
 244           R##_e = X##_e;                                                     \
 245         }                                                                    \
 246                                                                              \
 247       R##_c = FP_CLS_NORMAL;                                                 \
 248                                                                              \
 249       if (X##_s == Y##_s)                                                    \
 250         {                                                                    \
 251           R##_s = X##_s;                                                     \
 252           _FP_FRAC_ADD_##wc(R, X, Y);                                        \
 253           if (_FP_FRAC_OVERP_##wc(fs, R))                                    \
 254             {                                                                \
 255               _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);                   \
 256               R##_e++;                                                       \
 257             }                                                                \
 258         }                                                                    \
 259       else                                                                   \
 260         {                                                                    \
 261           R##_s = X##_s;                                                     \
 262           _FP_FRAC_SUB_##wc(R, X, Y);                                        \
 263           if (_FP_FRAC_ZEROP_##wc(R))                                        \
 264             {                                                                \
 265               /* return an exact zero */                                     \
 266               if (FP_ROUNDMODE == FP_RND_MINF)                               \
 267                 R##_s |= Y##_s;                                              \
 268               else                                                           \
 269                 R##_s &= Y##_s;                                              \
 270               R##_c = FP_CLS_ZERO;                                           \
 271             }                                                                \
 272           else                                                               \
 273             {                                                                \
 274               if (_FP_FRAC_NEGP_##wc(R))                                     \
 275                 {                                                            \
 276                   _FP_FRAC_SUB_##wc(R, Y, X);                                \
 277                   R##_s = Y##_s;                                             \
 278                 }                                                            \
 279                                                                              \
 280               /* renormalize after subtraction */                            \
 281               _FP_FRAC_CLZ_##wc(diff, R);                                    \
 282               diff -= _FP_WFRACXBITS_##fs;                                   \
 283               if (diff)                                                      \
 284                 {                                                            \
 285                   R##_e -= diff;                                             \
 286                   _FP_FRAC_SLL_##wc(R, diff);                                \
 287                 }                                                            \
 288             }                                                                \
 289         }                                                                    \
 290       break;                                                                 \
 291     }                                                                        \
 292                                                                              \
 293   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):                               \
 294     _FP_CHOOSENAN(fs, wc, R, X, Y, OP);                                      \
 295     break;                                                                   \
 296                                                                              \
 297   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):                           \
 298     R##_e = X##_e;                                                           \
 299   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):                            \
 300   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):                               \
 301   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):                              \
 302     _FP_FRAC_COPY_##wc(R, X);                                                \
 303     R##_s = X##_s;                                                           \
 304     R##_c = X##_c;                                                           \
 305     break;                                                                   \
 306                                                                              \
 307   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):                           \
 308     R##_e = Y##_e;                                                           \
 309   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):                            \
 310   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):                               \
 311   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):                              \
 312     _FP_FRAC_COPY_##wc(R, Y);                                                \
 313     R##_s = Y##_s;                                                           \
 314     R##_c = Y##_c;                                                           \
 315     break;                                                                   \
 316                                                                              \
 317   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):                               \
 318     if (X##_s != Y##_s)                                                      \
 319       {                                                                      \
 320         /* +INF + -INF => NAN */                                             \
 321         _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                              \
 322         R##_s = _FP_NANSIGN_##fs;                                            \
 323         R##_c = FP_CLS_NAN;                                                  \
 324         FP_SET_EXCEPTION(FP_EX_INVALID);                                     \
 325         break;                                                               \
 326       }                                                                      \
 327     /* FALLTHRU */                                                           \
 328                                                                              \
 329   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):                            \
 330   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):                              \
 331     R##_s = X##_s;                                                           \
 332     R##_c = FP_CLS_INF;                                                      \
 333     break;                                                                   \
 334                                                                              \
 335   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):                            \
 336   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):                              \
 337     R##_s = Y##_s;                                                           \
 338     R##_c = FP_CLS_INF;                                                      \
 339     break;                                                                   \
 340                                                                              \
 341   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):                             \
 342     /* make sure the sign is correct */                                      \
 343     if (FP_ROUNDMODE == FP_RND_MINF)                                         \
 344       R##_s = X##_s | Y##_s;                                                 \
 345     else                                                                     \
 346       R##_s = X##_s & Y##_s;                                                 \
 347     R##_c = FP_CLS_ZERO;                                                     \
 348     break;                                                                   \
 349                                                                              \
 350   default:                                                                   \
 351     abort();                                                                 \
 352   }                                                                          \
 353 } while (0)
 354
 355 #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
 356 #define _FP_SUB(fs, wc, R, X, Y)                                             \
 357   do {                                                                       \
 358     if (Y##_c != FP_CLS_NAN) Y##_s ^= 1;                                     \
 359     _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-');                                  \
 360   } while (0)
 361
 362
 363 /*
 364  * Main negation routine.  FIXME -- when we care about setting exception
 365  * bits reliably, this will not do.  We should examine all of the fp classes.
 366  */
 367
 368 #define _FP_NEG(fs, wc, R, X)           \
 369   do {                                  \
 370     _FP_FRAC_COPY_##wc(R, X);           \
 371     R##_c = X##_c;                      \
 372     R##_e = X##_e;                      \
 373     R##_s = 1 ^ X##_s;                  \
 374   } while (0)
 375
 376
 377 /*
 378  * Main multiplication routine.  The input values should be cooked.
 379  */
 380
 381 #define _FP_MUL(fs, wc, R, X, Y)                        \
 382 do {                                                    \
 383   R##_s = X##_s ^ Y##_s;                                \
 384   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 385   {                                                     \
 386   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 387     R##_c = FP_CLS_NORMAL;                              \
 388     R##_e = X##_e + Y##_e + 1;                          \
 389                                                         \
 390     _FP_MUL_MEAT_##fs(R,X,Y);                           \
 391                                                         \
 392     if (_FP_FRAC_OVERP_##wc(fs, R))                     \
 393       _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);      \
 394     else                                                \
 395       R##_e--;                                          \
 396     break;                                              \
 397                                                         \
 398   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 399     _FP_CHOOSENAN(fs, wc, R, X, Y, '*');                \
 400     break;                                              \
 401                                                         \
 402   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 403   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 404   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 405     R##_s = X##_s;                                      \
 406                                                         \
 407   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 408   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 409   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 410   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 411     _FP_FRAC_COPY_##wc(R, X);                           \
 412     R##_c = X##_c;                                      \
 413     break;                                              \
 414                                                         \
 415   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 416   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 417   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 418     R##_s = Y##_s;                                      \
 419                                                         \
 420   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 421   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 422     _FP_FRAC_COPY_##wc(R, Y);                           \
 423     R##_c = Y##_c;                                      \
 424     break;                                              \
 425                                                         \
 426   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 427   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 428     R##_s = _FP_NANSIGN_##fs;                           \
 429     R##_c = FP_CLS_NAN;                                 \
 430     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 431     FP_SET_EXCEPTION(FP_EX_INVALID);                    \
 432     break;                                              \
 433                                                         \
 434   default:                                              \
 435     abort();                                            \
 436   }                                                     \
 437 } while (0)
 438
 439
 440 /*
 441  * Main division routine.  The input values should be cooked.
 442  */
 443
 444 #define _FP_DIV(fs, wc, R, X, Y)                        \
 445 do {                                                    \
 446   R##_s = X##_s ^ Y##_s;                                \
 447   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 448   {                                                     \
 449   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 450     R##_c = FP_CLS_NORMAL;                              \
 451     R##_e = X##_e - Y##_e;                              \
 452                                                         \
 453     _FP_DIV_MEAT_##fs(R,X,Y);                           \
 454     break;                                              \
 455                                                         \
 456   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 457     _FP_CHOOSENAN(fs, wc, R, X, Y, '/');                \
 458     break;                                              \
 459                                                         \
 460   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 461   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 462   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 463     R##_s = X##_s;                                      \
 464     _FP_FRAC_COPY_##wc(R, X);                           \
 465     R##_c = X##_c;                                      \
 466     break;                                              \
 467                                                         \
 468   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 469   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 470   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 471     R##_s = Y##_s;                                      \
 472     _FP_FRAC_COPY_##wc(R, Y);                           \
 473     R##_c = Y##_c;                                      \
 474     break;                                              \
 475                                                         \
 476   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 477   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 478   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 479     R##_c = FP_CLS_ZERO;                                \
 480     break;                                              \
 481                                                         \
 482   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 483     FP_SET_EXCEPTION(FP_EX_DIVZERO);                    \
 484   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 485   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 486     R##_c = FP_CLS_INF;                                 \
 487     break;                                              \
 488                                                         \
 489   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 490   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 491     R##_s = _FP_NANSIGN_##fs;                           \
 492     R##_c = FP_CLS_NAN;                                 \
 493     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 494     FP_SET_EXCEPTION(FP_EX_INVALID);                    \
 495     break;                                              \
 496                                                         \
 497   default:                                              \
 498     abort();                                            \
 499   }                                                     \
 500 } while (0)
 501
 502
 503 /*
 504  * Main differential comparison routine.  The inputs should be raw not
 505  * cooked.  The return is -1,0,1 for normal values, 2 otherwise.
 506  */
 507
 508 #define _FP_CMP(fs, wc, ret, X, Y, un)                                  \
 509   do {                                                                  \
 510     /* NANs are unordered */                                            \
 511     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))           \
 512         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))       \
 513       {                                                                 \
 514         ret = un;                                                       \
 515       }                                                                 \
 516     else                                                                \
 517       {                                                                 \
 518         int __is_zero_x;                                                \
 519         int __is_zero_y;                                                \
 520                                                                         \
 521         __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0;       \
 522         __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0;       \
 523                                                                         \
 524         if (__is_zero_x && __is_zero_y)                                 \
 525                 ret = 0;                                                \
 526         else if (__is_zero_x)                                           \
 527                 ret = Y##_s ? 1 : -1;                                   \
 528         else if (__is_zero_y)                                           \
 529                 ret = X##_s ? -1 : 1;                                   \
 530         else if (X##_s != Y##_s)                                        \
 531           ret = X##_s ? -1 : 1;                                         \
 532         else if (X##_e > Y##_e)                                         \
 533           ret = X##_s ? -1 : 1;                                         \
 534         else if (X##_e < Y##_e)                                         \
 535           ret = X##_s ? 1 : -1;                                         \
 536         else if (_FP_FRAC_GT_##wc(X, Y))                                \
 537           ret = X##_s ? -1 : 1;                                         \
 538         else if (_FP_FRAC_GT_##wc(Y, X))                                \
 539           ret = X##_s ? 1 : -1;                                         \
 540         else                                                            \
 541           ret = 0;                                                      \
 542       }                                                                 \
 543   } while (0)
 544
 545
 546 /* Simplification for strict equality.  */
 547
 548 #define _FP_CMP_EQ(fs, wc, ret, X, Y)                                     \
 549   do {                                                                    \
 550     /* NANs are unordered */                                              \
 551     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))             \
 552         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))         \
 553       {                                                                   \
 554         ret = 1;                                                          \
 555       }                                                                   \
 556     else                                                                  \
 557       {                                                                   \
 558         ret = !(X##_e == Y##_e                                            \
 559                 && _FP_FRAC_EQ_##wc(X, Y)                                 \
 560                 && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
 561       }                                                                   \
 562   } while (0)
 563
 564 /*
 565  * Main square root routine.  The input value should be cooked.
 566  */
 567
 568 #define _FP_SQRT(fs, wc, R, X)                                          \
 569 do {                                                                    \
 570     _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S);                       \
 571     _FP_W_TYPE q;                                                       \
 572     switch (X##_c)                                                      \
 573     {                                                                   \
 574     case FP_CLS_NAN:                                                    \
 575         _FP_FRAC_COPY_##wc(R, X);                                       \
 576         R##_s = X##_s;                                                  \
 577         R##_c = FP_CLS_NAN;                                             \
 578         break;                                                          \
 579     case FP_CLS_INF:                                                    \
 580         if (X##_s)                                                      \
 581           {                                                             \
 582             R##_s = _FP_NANSIGN_##fs;                                   \
 583             R##_c = FP_CLS_NAN; /* NAN */                               \
 584             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 585             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 586           }                                                             \
 587         else                                                            \
 588           {                                                             \
 589             R##_s = 0;                                                  \
 590             R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */                 \
 591           }                                                             \
 592         break;                                                          \
 593     case FP_CLS_ZERO:                                                   \
 594         R##_s = X##_s;                                                  \
 595         R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */                      \
 596         break;                                                          \
 597     case FP_CLS_NORMAL:                                                 \
 598         R##_s = 0;                                                      \
 599         if (X##_s)                                                      \
 600           {                                                             \
 601             R##_c = FP_CLS_NAN; /* sNAN */                              \
 602             R##_s = _FP_NANSIGN_##fs;                                   \
 603             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 604             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 605             break;                                                      \
 606           }                                                             \
 607         R##_c = FP_CLS_NORMAL;                                          \
 608         if (X##_e & 1)                                                  \
 609           _FP_FRAC_SLL_##wc(X, 1);                                      \
 610         R##_e = X##_e >> 1;                                             \
 611         _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc);                        \
 612         _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc);                        \
 613         q = _FP_OVERFLOW_##fs >> 1;                                     \
 614         _FP_SQRT_MEAT_##wc(R, S, T, X, q);                              \
 615     }                                                                   \
 616   } while (0)
 617
 618 /*
 619  * Convert from FP to integer
 620  */
 621
 622 /* RSIGNED can have following values:
 623  * 0:  the number is required to be 0..(2^rsize)-1, if not, NV is set plus
 624  *     the result is either 0 or (2^rsize)-1 depending on the sign in such case.
 625  * 1:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 626  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 627  *     on the sign in such case.
 628  * 2:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 629  *     set plus the result is truncated to fit into destination.
 630  * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
 631  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 632  *     on the sign in such case.
 633  */
 634 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned)                                \
 635   do {                                                                          \
 636     switch (X##_c)                                                              \
 637       {                                                                         \
 638       case FP_CLS_NORMAL:                                                       \
 639         if (X##_e < 0)                                                          \
 640           {                                                                     \
 641             FP_SET_EXCEPTION(FP_EX_INEXACT);                                    \
 642           case FP_CLS_ZERO:                                                     \
 643             r = 0;                                                              \
 644           }                                                                     \
 645         else if (X##_e >= rsize - (rsigned > 0 || X##_s)                        \
 646                  || (!rsigned && X##_s))                                        \
 647           {     /* overflow */                                                  \
 648           case FP_CLS_NAN:                                                      \
 649           case FP_CLS_INF:                                                      \
 650             if (rsigned == 2)                                                   \
 651               {                                                                 \
 652                 if (X##_c != FP_CLS_NORMAL                                      \
 653                     || X##_e >= rsize - 1 + _FP_WFRACBITS_##fs)                 \
 654                   r = 0;                                                        \
 655                 else                                                            \
 656                   {                                                             \
 657                     _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));     \
 658                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 659                   }                                                             \
 660               }                                                                 \
 661             else if (rsigned)                                                   \
 662               {                                                                 \
 663                 r = 1;                                                          \
 664                 r <<= rsize - 1;                                                \
 665                 r -= 1 - X##_s;                                                 \
 666               }                                                                 \
 667             else                                                                \
 668               {                                                                 \
 669                 r = 0;                                                          \
 670                 if (X##_s)                                                      \
 671                   r = ~r;                                                       \
 672               }                                                                 \
 673             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 674           }                                                                     \
 675         else                                                                    \
 676           {                                                                     \
 677             if (_FP_W_TYPE_SIZE*wc < rsize)                                     \
 678               {                                                                 \
 679                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 680                 r <<= X##_e - _FP_WFRACBITS_##fs;                               \
 681               }                                                                 \
 682             else                                                                \
 683               {                                                                 \
 684                 if (X##_e >= _FP_WFRACBITS_##fs)                                \
 685                   _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));       \
 686                 else if (X##_e < _FP_WFRACBITS_##fs - 1)                        \
 687                   {                                                             \
 688                     _FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2),      \
 689                                       _FP_WFRACBITS_##fs);                      \
 690                     if (_FP_FRAC_LOW_##wc(X) & 1)                               \
 691                       FP_SET_EXCEPTION(FP_EX_INEXACT);                          \
 692                     _FP_FRAC_SRL_##wc(X, 1);                                    \
 693                   }                                                             \
 694                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 695               }                                                                 \
 696             if (rsigned && X##_s)                                               \
 697               r = -r;                                                           \
 698           }                                                                     \
 699         break;                                                                  \
 700       }                                                                         \
 701   } while (0)
 702
 703 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned)                          \
 704   do {                                                                          \
 705     r = 0;                                                                      \
 706     switch (X##_c)                                                              \
 707       {                                                                         \
 708       case FP_CLS_NORMAL:                                                       \
 709         if (X##_e >= _FP_FRACBITS_##fs - 1)                                     \
 710           {                                                                     \
 711             if (X##_e < rsize - 1 + _FP_WFRACBITS_##fs)                         \
 712               {                                                                 \
 713                 if (X##_e >= _FP_WFRACBITS_##fs - 1)                            \
 714                   {                                                             \
 715                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 716                     r <<= X##_e - _FP_WFRACBITS_##fs + 1;                       \
 717                   }                                                             \
 718                 else                                                            \
 719                   {                                                             \
 720                     _FP_FRAC_SRL_##wc(X, _FP_WORKBITS - X##_e                   \
 721                                       + _FP_FRACBITS_##fs - 1);                 \
 722                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 723                   }                                                             \
 724               }                                                                 \
 725           }                                                                     \
 726         else                                                                    \
 727           {                                                                     \
 728             if (X##_e <= -_FP_WORKBITS - 1)                                     \
 729               _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                           \
 730             else                                                                \
 731               _FP_FRAC_SRS_##wc(X, _FP_FRACBITS_##fs - 1 - X##_e,               \
 732                                 _FP_WFRACBITS_##fs);                            \
 733             _FP_ROUND(wc, X);                                                   \
 734             _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                                 \
 735             _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                                \
 736           }                                                                     \
 737         if (rsigned && X##_s)                                                   \
 738           r = -r;                                                               \
 739         if (X##_e >= rsize - (rsigned > 0 || X##_s)                             \
 740             || (!rsigned && X##_s))                                             \
 741           {     /* overflow */                                                  \
 742           case FP_CLS_NAN:                                                      \
 743           case FP_CLS_INF:                                                      \
 744             if (!rsigned)                                                       \
 745               {                                                                 \
 746                 r = 0;                                                          \
 747                 if (X##_s)                                                      \
 748                   r = ~r;                                                       \
 749               }                                                                 \
 750             else if (rsigned != 2)                                              \
 751               {                                                                 \
 752                 r = 1;                                                          \
 753                 r <<= rsize - 1;                                                \
 754                 r -= 1 - X##_s;                                                 \
 755               }                                                                 \
 756             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 757           }                                                                     \
 758         break;                                                                  \
 759       case FP_CLS_ZERO:                                                         \
 760         break;                                                                  \
 761       }                                                                         \
 762   } while (0)
 763
 764 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype)                        \
 765   do {                                                                  \
 766     if (r)                                                              \
 767       {                                                                 \
 768         unsigned rtype ur_;                                             \
 769         X##_c = FP_CLS_NORMAL;                                          \
 770                                                                         \
 771         if ((X##_s = (r < 0)))                                          \
 772           ur_ = (unsigned rtype) -r;                                    \
 773         else                                                            \
 774           ur_ = (unsigned rtype) r;                                     \
 775         if (rsize <= _FP_W_TYPE_SIZE)                                   \
 776           __FP_CLZ(X##_e, ur_);                                         \
 777         else                                                            \
 778           __FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE),       \
 779                      (_FP_W_TYPE)ur_);                                  \
 780         if (rsize < _FP_W_TYPE_SIZE)                                    \
 781                 X##_e -= (_FP_W_TYPE_SIZE - rsize);                     \
 782         X##_e = rsize - X##_e - 1;                                      \
 783                                                                         \
 784         if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e)    \
 785           __FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\
 786         _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize);                       \
 787         if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0)                       \
 788           _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));       \
 789       }                                                                 \
 790     else                                                                \
 791       {                                                                 \
 792         X##_c = FP_CLS_ZERO, X##_s = 0;                                 \
 793       }                                                                 \
 794   } while (0)
 795
 796
 797 #define FP_CONV(dfs,sfs,dwc,swc,D,S)                    \
 798   do {                                                  \
 799     _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S);        \
 800     D##_e = S##_e;                                      \
 801     D##_c = S##_c;                                      \
 802     D##_s = S##_s;                                      \
 803   } while (0)
 804
 805 /*
 806  * Helper primitives.
 807  */
 808
 809 /* Count leading zeros in a word.  */
 810
 811 #ifndef __FP_CLZ
 812 #if _FP_W_TYPE_SIZE < 64
 813 /* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
 814 #define __FP_CLZ(r, x)                          \
 815   do {                                          \
 816     _FP_W_TYPE _t = (x);                        \
 817     r = _FP_W_TYPE_SIZE - 1;                    \
 818     if (_t > 0xffff) r -= 16;                   \
 819     if (_t > 0xffff) _t >>= 16;                 \
 820     if (_t > 0xff) r -= 8;                      \
 821     if (_t > 0xff) _t >>= 8;                    \
 822     if (_t & 0xf0) r -= 4;                      \
 823     if (_t & 0xf0) _t >>= 4;                    \
 824     if (_t & 0xc) r -= 2;                       \
 825     if (_t & 0xc) _t >>= 2;                     \
 826     if (_t & 0x2) r -= 1;                       \
 827   } while (0)
 828 #else /* not _FP_W_TYPE_SIZE < 64 */
 829 #define __FP_CLZ(r, x)                          \
 830   do {                                          \
 831     _FP_W_TYPE _t = (x);                        \
 832     r = _FP_W_TYPE_SIZE - 1;                    \
 833     if (_t > 0xffffffff) r -= 32;               \
 834     if (_t > 0xffffffff) _t >>= 32;             \
 835     if (_t > 0xffff) r -= 16;                   \
 836     if (_t > 0xffff) _t >>= 16;                 \
 837     if (_t > 0xff) r -= 8;                      \
 838     if (_t > 0xff) _t >>= 8;                    \
 839     if (_t & 0xf0) r -= 4;                      \
 840     if (_t & 0xf0) _t >>= 4;                    \
 841     if (_t & 0xc) r -= 2;                       \
 842     if (_t & 0xc) _t >>= 2;                     \
 843     if (_t & 0x2) r -= 1;                       \
 844   } while (0)
 845 #endif /* not _FP_W_TYPE_SIZE < 64 */
 846 #endif /* ndef __FP_CLZ */
 847
 848 #define _FP_DIV_HELP_imm(q, r, n, d)            \
 849   do {                                          \
 850     q = n / d, r = n % d;                       \
 851   } while (0)
 852
 853 #endif /* __MATH_EMU_OP_COMMON_H__ */