include/math-emu/op-common.h

   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 | FP_EX_INVALID_SNAN);         \
  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                 FP_SET_EXCEPTION(FP_EX_INEXACT);                \
 149               }                                                 \
 150             else                                                \
 151               {                                                 \
 152                 X##_e = 0;                                      \
 153                 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);             \
 154               }                                                 \
 155             if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) ||          \
 156                 (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW))     \
 157                 FP_SET_EXCEPTION(FP_EX_UNDERFLOW);              \
 158           }                                                     \
 159         else                                                    \
 160           {                                                     \
 161             /* underflow to zero */                             \
 162             X##_e = 0;                                          \
 163             if (!_FP_FRAC_ZEROP_##wc(X))                        \
 164               {                                                 \
 165                 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);         \
 166                 _FP_ROUND(wc, X);                               \
 167                 _FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS);        \
 168               }                                                 \
 169             FP_SET_EXCEPTION(FP_EX_UNDERFLOW);                  \
 170           }                                                     \
 171       }                                                         \
 172     break;                                                      \
 173                                                                 \
 174   case FP_CLS_ZERO:                                             \
 175     X##_e = 0;                                                  \
 176     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 177     break;                                                      \
 178                                                                 \
 179   case FP_CLS_INF:                                              \
 180     X##_e = _FP_EXPMAX_##fs;                                    \
 181     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 182     break;                                                      \
 183                                                                 \
 184   case FP_CLS_NAN:                                              \
 185     X##_e = _FP_EXPMAX_##fs;                                    \
 186     if (!_FP_KEEPNANFRACP)                                      \
 187       {                                                         \
 188         _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs);                 \
 189         X##_s = _FP_NANSIGN_##fs;                               \
 190       }                                                         \
 191     else                                                        \
 192       _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs;            \
 193     break;                                                      \
 194   }                                                             \
 195 } while (0)
 196
 197 /* This one accepts raw argument and not cooked,  returns
 198  * 1 if X is a signaling NaN.
 199  */
 200 #define _FP_ISSIGNAN(fs, wc, X)                                 \
 201 ({                                                              \
 202   int __ret = 0;                                                \
 203   if (X##_e == _FP_EXPMAX_##fs)                                 \
 204     {                                                           \
 205       if (!_FP_FRAC_ZEROP_##wc(X)                               \
 206           && !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))   \
 207         __ret = 1;                                              \
 208     }                                                           \
 209   __ret;                                                        \
 210 })
 211
 212
 213
 214
 215
 216 /*
 217  * Main addition routine.  The input values should be cooked.
 218  */
 219
 220 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP)                                \
 221 do {                                                                         \
 222   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                                     \
 223   {                                                                          \
 224   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):                         \
 225     {                                                                        \
 226       /* shift the smaller number so that its exponent matches the larger */ \
 227       _FP_I_TYPE diff = X##_e - Y##_e;                                       \
 228                                                                              \
 229       if (diff < 0)                                                          \
 230         {                                                                    \
 231           diff = -diff;                                                      \
 232           if (diff <= _FP_WFRACBITS_##fs)                                    \
 233             _FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs);                  \
 234           else if (!_FP_FRAC_ZEROP_##wc(X))                                  \
 235             _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                          \
 236           R##_e = Y##_e;                                                     \
 237         }                                                                    \
 238       else                                                                   \
 239         {                                                                    \
 240           if (diff > 0)                                                      \
 241             {                                                                \
 242               if (diff <= _FP_WFRACBITS_##fs)                                \
 243                 _FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs);              \
 244               else if (!_FP_FRAC_ZEROP_##wc(Y))                              \
 245                 _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc);                      \
 246             }                                                                \
 247           R##_e = X##_e;                                                     \
 248         }                                                                    \
 249                                                                              \
 250       R##_c = FP_CLS_NORMAL;                                                 \
 251                                                                              \
 252       if (X##_s == Y##_s)                                                    \
 253         {                                                                    \
 254           R##_s = X##_s;                                                     \
 255           _FP_FRAC_ADD_##wc(R, X, Y);                                        \
 256           if (_FP_FRAC_OVERP_##wc(fs, R))                                    \
 257             {                                                                \
 258               _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);                   \
 259               R##_e++;                                                       \
 260             }                                                                \
 261         }                                                                    \
 262       else                                                                   \
 263         {                                                                    \
 264           R##_s = X##_s;                                                     \
 265           _FP_FRAC_SUB_##wc(R, X, Y);                                        \
 266           if (_FP_FRAC_ZEROP_##wc(R))                                        \
 267             {                                                                \
 268               /* return an exact zero */                                     \
 269               if (FP_ROUNDMODE == FP_RND_MINF)                               \
 270                 R##_s |= Y##_s;                                              \
 271               else                                                           \
 272                 R##_s &= Y##_s;                                              \
 273               R##_c = FP_CLS_ZERO;                                           \
 274             }                                                                \
 275           else                                                               \
 276             {                                                                \
 277               if (_FP_FRAC_NEGP_##wc(R))                                     \
 278                 {                                                            \
 279                   _FP_FRAC_SUB_##wc(R, Y, X);                                \
 280                   R##_s = Y##_s;                                             \
 281                 }                                                            \
 282                                                                              \
 283               /* renormalize after subtraction */                            \
 284               _FP_FRAC_CLZ_##wc(diff, R);                                    \
 285               diff -= _FP_WFRACXBITS_##fs;                                   \
 286               if (diff)                                                      \
 287                 {                                                            \
 288                   R##_e -= diff;                                             \
 289                   _FP_FRAC_SLL_##wc(R, diff);                                \
 290                 }                                                            \
 291             }                                                                \
 292         }                                                                    \
 293       break;                                                                 \
 294     }                                                                        \
 295                                                                              \
 296   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):                               \
 297     _FP_CHOOSENAN(fs, wc, R, X, Y, OP);                                      \
 298     break;                                                                   \
 299                                                                              \
 300   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):                           \
 301     R##_e = X##_e;                                                           \
 302   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):                            \
 303   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):                               \
 304   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):                              \
 305     _FP_FRAC_COPY_##wc(R, X);                                                \
 306     R##_s = X##_s;                                                           \
 307     R##_c = X##_c;                                                           \
 308     break;                                                                   \
 309                                                                              \
 310   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):                           \
 311     R##_e = Y##_e;                                                           \
 312   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):                            \
 313   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):                               \
 314   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):                              \
 315     _FP_FRAC_COPY_##wc(R, Y);                                                \
 316     R##_s = Y##_s;                                                           \
 317     R##_c = Y##_c;                                                           \
 318     break;                                                                   \
 319                                                                              \
 320   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):                               \
 321     if (X##_s != Y##_s)                                                      \
 322       {                                                                      \
 323         /* +INF + -INF => NAN */                                             \
 324         _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                              \
 325         R##_s = _FP_NANSIGN_##fs;                                            \
 326         R##_c = FP_CLS_NAN;                                                  \
 327         FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_ISI);                 \
 328         break;                                                               \
 329       }                                                                      \
 330     /* FALLTHRU */                                                           \
 331                                                                              \
 332   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):                            \
 333   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):                              \
 334     R##_s = X##_s;                                                           \
 335     R##_c = FP_CLS_INF;                                                      \
 336     break;                                                                   \
 337                                                                              \
 338   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):                            \
 339   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):                              \
 340     R##_s = Y##_s;                                                           \
 341     R##_c = FP_CLS_INF;                                                      \
 342     break;                                                                   \
 343                                                                              \
 344   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):                             \
 345     /* make sure the sign is correct */                                      \
 346     if (FP_ROUNDMODE == FP_RND_MINF)                                         \
 347       R##_s = X##_s | Y##_s;                                                 \
 348     else                                                                     \
 349       R##_s = X##_s & Y##_s;                                                 \
 350     R##_c = FP_CLS_ZERO;                                                     \
 351     break;                                                                   \
 352                                                                              \
 353   default:                                                                   \
 354     abort();                                                                 \
 355   }                                                                          \
 356 } while (0)
 357
 358 #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
 359 #define _FP_SUB(fs, wc, R, X, Y)                                             \
 360   do {                                                                       \
 361     if (Y##_c != FP_CLS_NAN) Y##_s ^= 1;                                     \
 362     _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-');                                  \
 363   } while (0)
 364
 365
 366 /*
 367  * Main negation routine.  FIXME -- when we care about setting exception
 368  * bits reliably, this will not do.  We should examine all of the fp classes.
 369  */
 370
 371 #define _FP_NEG(fs, wc, R, X)           \
 372   do {                                  \
 373     _FP_FRAC_COPY_##wc(R, X);           \
 374     R##_c = X##_c;                      \
 375     R##_e = X##_e;                      \
 376     R##_s = 1 ^ X##_s;                  \
 377   } while (0)
 378
 379
 380 /*
 381  * Main multiplication routine.  The input values should be cooked.
 382  */
 383
 384 #define _FP_MUL(fs, wc, R, X, Y)                        \
 385 do {                                                    \
 386   R##_s = X##_s ^ Y##_s;                                \
 387   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 388   {                                                     \
 389   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 390     R##_c = FP_CLS_NORMAL;                              \
 391     R##_e = X##_e + Y##_e + 1;                          \
 392                                                         \
 393     _FP_MUL_MEAT_##fs(R,X,Y);                           \
 394                                                         \
 395     if (_FP_FRAC_OVERP_##wc(fs, R))                     \
 396       _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);      \
 397     else                                                \
 398       R##_e--;                                          \
 399     break;                                              \
 400                                                         \
 401   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 402     _FP_CHOOSENAN(fs, wc, R, X, Y, '*');                \
 403     break;                                              \
 404                                                         \
 405   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 406   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 407   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 408     R##_s = X##_s;                                      \
 409                                                         \
 410   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 411   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 412   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 413   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 414     _FP_FRAC_COPY_##wc(R, X);                           \
 415     R##_c = X##_c;                                      \
 416     break;                                              \
 417                                                         \
 418   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 419   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 420   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 421     R##_s = Y##_s;                                      \
 422                                                         \
 423   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 424   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 425     _FP_FRAC_COPY_##wc(R, Y);                           \
 426     R##_c = Y##_c;                                      \
 427     break;                                              \
 428                                                         \
 429   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 430   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 431     R##_s = _FP_NANSIGN_##fs;                           \
 432     R##_c = FP_CLS_NAN;                                 \
 433     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 434     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_IMZ);\
 435     break;                                              \
 436                                                         \
 437   default:                                              \
 438     abort();                                            \
 439   }                                                     \
 440 } while (0)
 441
 442
 443 /*
 444  * Main division routine.  The input values should be cooked.
 445  */
 446
 447 #define _FP_DIV(fs, wc, R, X, Y)                        \
 448 do {                                                    \
 449   R##_s = X##_s ^ Y##_s;                                \
 450   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 451   {                                                     \
 452   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 453     R##_c = FP_CLS_NORMAL;                              \
 454     R##_e = X##_e - Y##_e;                              \
 455                                                         \
 456     _FP_DIV_MEAT_##fs(R,X,Y);                           \
 457     break;                                              \
 458                                                         \
 459   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 460     _FP_CHOOSENAN(fs, wc, R, X, Y, '/');                \
 461     break;                                              \
 462                                                         \
 463   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 464   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 465   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 466     R##_s = X##_s;                                      \
 467     _FP_FRAC_COPY_##wc(R, X);                           \
 468     R##_c = X##_c;                                      \
 469     break;                                              \
 470                                                         \
 471   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 472   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 473   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 474     R##_s = Y##_s;                                      \
 475     _FP_FRAC_COPY_##wc(R, Y);                           \
 476     R##_c = Y##_c;                                      \
 477     break;                                              \
 478                                                         \
 479   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 480   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 481   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 482     R##_c = FP_CLS_ZERO;                                \
 483     break;                                              \
 484                                                         \
 485   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 486     FP_SET_EXCEPTION(FP_EX_DIVZERO);                    \
 487   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 488   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 489     R##_c = FP_CLS_INF;                                 \
 490     break;                                              \
 491                                                         \
 492   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 493     R##_s = _FP_NANSIGN_##fs;                           \
 494     R##_c = FP_CLS_NAN;                                 \
 495     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 496     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_IDI);\
 497   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 498     R##_s = _FP_NANSIGN_##fs;                           \
 499     R##_c = FP_CLS_NAN;                                 \
 500     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 501     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_ZDZ);\
 502     break;                                              \
 503                                                         \
 504   default:                                              \
 505     abort();                                            \
 506   }                                                     \
 507 } while (0)
 508
 509
 510 /*
 511  * Main differential comparison routine.  The inputs should be raw not
 512  * cooked.  The return is -1,0,1 for normal values, 2 otherwise.
 513  */
 514
 515 #define _FP_CMP(fs, wc, ret, X, Y, un)                                  \
 516   do {                                                                  \
 517     /* NANs are unordered */                                            \
 518     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))           \
 519         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))       \
 520       {                                                                 \
 521         ret = un;                                                       \
 522       }                                                                 \
 523     else                                                                \
 524       {                                                                 \
 525         int __is_zero_x;                                                \
 526         int __is_zero_y;                                                \
 527                                                                         \
 528         __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0;       \
 529         __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0;       \
 530                                                                         \
 531         if (__is_zero_x && __is_zero_y)                                 \
 532                 ret = 0;                                                \
 533         else if (__is_zero_x)                                           \
 534                 ret = Y##_s ? 1 : -1;                                   \
 535         else if (__is_zero_y)                                           \
 536                 ret = X##_s ? -1 : 1;                                   \
 537         else if (X##_s != Y##_s)                                        \
 538           ret = X##_s ? -1 : 1;                                         \
 539         else if (X##_e > Y##_e)                                         \
 540           ret = X##_s ? -1 : 1;                                         \
 541         else if (X##_e < Y##_e)                                         \
 542           ret = X##_s ? 1 : -1;                                         \
 543         else if (_FP_FRAC_GT_##wc(X, Y))                                \
 544           ret = X##_s ? -1 : 1;                                         \
 545         else if (_FP_FRAC_GT_##wc(Y, X))                                \
 546           ret = X##_s ? 1 : -1;                                         \
 547         else                                                            \
 548           ret = 0;                                                      \
 549       }                                                                 \
 550   } while (0)
 551
 552
 553 /* Simplification for strict equality.  */
 554
 555 #define _FP_CMP_EQ(fs, wc, ret, X, Y)                                     \
 556   do {                                                                    \
 557     /* NANs are unordered */                                              \
 558     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))             \
 559         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))         \
 560       {                                                                   \
 561         ret = 1;                                                          \
 562       }                                                                   \
 563     else                                                                  \
 564       {                                                                   \
 565         ret = !(X##_e == Y##_e                                            \
 566                 && _FP_FRAC_EQ_##wc(X, Y)                                 \
 567                 && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
 568       }                                                                   \
 569   } while (0)
 570
 571 /*
 572  * Main square root routine.  The input value should be cooked.
 573  */
 574
 575 #define _FP_SQRT(fs, wc, R, X)                                          \
 576 do {                                                                    \
 577     _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S);                       \
 578     _FP_W_TYPE q;                                                       \
 579     switch (X##_c)                                                      \
 580     {                                                                   \
 581     case FP_CLS_NAN:                                                    \
 582         _FP_FRAC_COPY_##wc(R, X);                                       \
 583         R##_s = X##_s;                                                  \
 584         R##_c = FP_CLS_NAN;                                             \
 585         break;                                                          \
 586     case FP_CLS_INF:                                                    \
 587         if (X##_s)                                                      \
 588           {                                                             \
 589             R##_s = _FP_NANSIGN_##fs;                                   \
 590             R##_c = FP_CLS_NAN; /* NAN */                               \
 591             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 592             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 593           }                                                             \
 594         else                                                            \
 595           {                                                             \
 596             R##_s = 0;                                                  \
 597             R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */                 \
 598           }                                                             \
 599         break;                                                          \
 600     case FP_CLS_ZERO:                                                   \
 601         R##_s = X##_s;                                                  \
 602         R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */                      \
 603         break;                                                          \
 604     case FP_CLS_NORMAL:                                                 \
 605         R##_s = 0;                                                      \
 606         if (X##_s)                                                      \
 607           {                                                             \
 608             R##_c = FP_CLS_NAN; /* sNAN */                              \
 609             R##_s = _FP_NANSIGN_##fs;                                   \
 610             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 611             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 612             break;                                                      \
 613           }                                                             \
 614         R##_c = FP_CLS_NORMAL;                                          \
 615         if (X##_e & 1)                                                  \
 616           _FP_FRAC_SLL_##wc(X, 1);                                      \
 617         R##_e = X##_e >> 1;                                             \
 618         _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc);                        \
 619         _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc);                        \
 620         q = _FP_OVERFLOW_##fs >> 1;                                     \
 621         _FP_SQRT_MEAT_##wc(R, S, T, X, q);                              \
 622     }                                                                   \
 623   } while (0)
 624
 625 /*
 626  * Convert from FP to integer
 627  */
 628
 629 /* RSIGNED can have following values:
 630  * 0:  the number is required to be 0..(2^rsize)-1, if not, NV is set plus
 631  *     the result is either 0 or (2^rsize)-1 depending on the sign in such case.
 632  * 1:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 633  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 634  *     on the sign in such case.
 635  * 2:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 636  *     set plus the result is truncated to fit into destination.
 637  * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
 638  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 639  *     on the sign in such case.
 640  */
 641 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned)                                \
 642   do {                                                                          \
 643     switch (X##_c)                                                              \
 644       {                                                                         \
 645       case FP_CLS_NORMAL:                                                       \
 646         if (X##_e < 0)                                                          \
 647           {                                                                     \
 648             FP_SET_EXCEPTION(FP_EX_INEXACT);                                    \
 649           case FP_CLS_ZERO:                                                     \
 650             r = 0;                                                              \
 651           }                                                                     \
 652         else if (X##_e >= rsize - (rsigned > 0 || X##_s)                        \
 653                  || (!rsigned && X##_s))                                        \
 654           {     /* overflow */                                                  \
 655           case FP_CLS_NAN:                                                      \
 656           case FP_CLS_INF:                                                      \
 657             if (rsigned == 2)                                                   \
 658               {                                                                 \
 659                 if (X##_c != FP_CLS_NORMAL                                      \
 660                     || X##_e >= rsize - 1 + _FP_WFRACBITS_##fs)                 \
 661                   r = 0;                                                        \
 662                 else                                                            \
 663                   {                                                             \
 664                     _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));     \
 665                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 666                   }                                                             \
 667               }                                                                 \
 668             else if (rsigned)                                                   \
 669               {                                                                 \
 670                 r = 1;                                                          \
 671                 r <<= rsize - 1;                                                \
 672                 r -= 1 - X##_s;                                                 \
 673               }                                                                 \
 674             else                                                                \
 675               {                                                                 \
 676                 r = 0;                                                          \
 677                 if (X##_s)                                                      \
 678                   r = ~r;                                                       \
 679               }                                                                 \
 680             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 681           }                                                                     \
 682         else                                                                    \
 683           {                                                                     \
 684             if (_FP_W_TYPE_SIZE*wc < rsize)                                     \
 685               {                                                                 \
 686                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 687                 r <<= X##_e - _FP_WFRACBITS_##fs;                               \
 688               }                                                                 \
 689             else                                                                \
 690               {                                                                 \
 691                 if (X##_e >= _FP_WFRACBITS_##fs)                                \
 692                   _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));       \
 693                 else if (X##_e < _FP_WFRACBITS_##fs - 1)                        \
 694                   {                                                             \
 695                     _FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2),      \
 696                                       _FP_WFRACBITS_##fs);                      \
 697                     if (_FP_FRAC_LOW_##wc(X) & 1)                               \
 698                       FP_SET_EXCEPTION(FP_EX_INEXACT);                          \
 699                     _FP_FRAC_SRL_##wc(X, 1);                                    \
 700                   }                                                             \
 701                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 702               }                                                                 \
 703             if (rsigned && X##_s)                                               \
 704               r = -r;                                                           \
 705           }                                                                     \
 706         break;                                                                  \
 707       }                                                                         \
 708   } while (0)
 709
 710 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned)                          \
 711   do {                                                                          \
 712     r = 0;                                                                      \
 713     switch (X##_c)                                                              \
 714       {                                                                         \
 715       case FP_CLS_NORMAL:                                                       \
 716         if (X##_e >= _FP_FRACBITS_##fs - 1)                                     \
 717           {                                                                     \
 718             if (X##_e < rsize - 1 + _FP_WFRACBITS_##fs)                         \
 719               {                                                                 \
 720                 if (X##_e >= _FP_WFRACBITS_##fs - 1)                            \
 721                   {                                                             \
 722                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 723                     r <<= X##_e - _FP_WFRACBITS_##fs + 1;                       \
 724                   }                                                             \
 725                 else                                                            \
 726                   {                                                             \
 727                     _FP_FRAC_SRL_##wc(X, _FP_WORKBITS - X##_e                   \
 728                                       + _FP_FRACBITS_##fs - 1);                 \
 729                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 730                   }                                                             \
 731               }                                                                 \
 732           }                                                                     \
 733         else                                                                    \
 734           {                                                                     \
 735             if (X##_e <= -_FP_WORKBITS - 1)                                     \
 736               _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                           \
 737             else                                                                \
 738               _FP_FRAC_SRS_##wc(X, _FP_FRACBITS_##fs - 1 - X##_e,               \
 739                                 _FP_WFRACBITS_##fs);                            \
 740             _FP_ROUND(wc, X);                                                   \
 741             _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                                 \
 742             _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                                \
 743           }                                                                     \
 744         if (rsigned && X##_s)                                                   \
 745           r = -r;                                                               \
 746         if (X##_e >= rsize - (rsigned > 0 || X##_s)                             \
 747             || (!rsigned && X##_s))                                             \
 748           {     /* overflow */                                                  \
 749           case FP_CLS_NAN:                                                      \
 750           case FP_CLS_INF:                                                      \
 751             if (!rsigned)                                                       \
 752               {                                                                 \
 753                 r = 0;                                                          \
 754                 if (X##_s)                                                      \
 755                   r = ~r;                                                       \
 756               }                                                                 \
 757             else if (rsigned != 2)                                              \
 758               {                                                                 \
 759                 r = 1;                                                          \
 760                 r <<= rsize - 1;                                                \
 761                 r -= 1 - X##_s;                                                 \
 762               }                                                                 \
 763             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 764           }                                                                     \
 765         break;                                                                  \
 766       case FP_CLS_ZERO:                                                         \
 767         break;                                                                  \
 768       }                                                                         \
 769   } while (0)
 770
 771 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype)                        \
 772   do {                                                                  \
 773     if (r)                                                              \
 774       {                                                                 \
 775         unsigned rtype ur_;                                             \
 776         X##_c = FP_CLS_NORMAL;                                          \
 777                                                                         \
 778         if ((X##_s = (r < 0)))                                          \
 779           ur_ = (unsigned rtype) -r;                                    \
 780         else                                                            \
 781           ur_ = (unsigned rtype) r;                                     \
 782         if (rsize <= _FP_W_TYPE_SIZE)                                   \
 783           __FP_CLZ(X##_e, ur_);                                         \
 784         else                                                            \
 785           __FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE),       \
 786                      (_FP_W_TYPE)ur_);                                  \
 787         if (rsize < _FP_W_TYPE_SIZE)                                    \
 788                 X##_e -= (_FP_W_TYPE_SIZE - rsize);                     \
 789         X##_e = rsize - X##_e - 1;                                      \
 790                                                                         \
 791         if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e)    \
 792           __FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\
 793         _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize);                       \
 794         if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0)                       \
 795           _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));       \
 796       }                                                                 \
 797     else                                                                \
 798       {                                                                 \
 799         X##_c = FP_CLS_ZERO, X##_s = 0;                                 \
 800       }                                                                 \
 801   } while (0)
 802
 803
 804 #define FP_CONV(dfs,sfs,dwc,swc,D,S)                    \
 805   do {                                                  \
 806     _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S);        \
 807     D##_e = S##_e;                                      \
 808     D##_c = S##_c;                                      \
 809     D##_s = S##_s;                                      \
 810   } while (0)
 811
 812 /*
 813  * Helper primitives.
 814  */
 815
 816 /* Count leading zeros in a word.  */
 817
 818 #ifndef __FP_CLZ
 819 #if _FP_W_TYPE_SIZE < 64
 820 /* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
 821 #define __FP_CLZ(r, x)                          \
 822   do {                                          \
 823     _FP_W_TYPE _t = (x);                        \
 824     r = _FP_W_TYPE_SIZE - 1;                    \
 825     if (_t > 0xffff) r -= 16;                   \
 826     if (_t > 0xffff) _t >>= 16;                 \
 827     if (_t > 0xff) r -= 8;                      \
 828     if (_t > 0xff) _t >>= 8;                    \
 829     if (_t & 0xf0) r -= 4;                      \
 830     if (_t & 0xf0) _t >>= 4;                    \
 831     if (_t & 0xc) r -= 2;                       \
 832     if (_t & 0xc) _t >>= 2;                     \
 833     if (_t & 0x2) r -= 1;                       \
 834   } while (0)
 835 #else /* not _FP_W_TYPE_SIZE < 64 */
 836 #define __FP_CLZ(r, x)                          \
 837   do {                                          \
 838     _FP_W_TYPE _t = (x);                        \
 839     r = _FP_W_TYPE_SIZE - 1;                    \
 840     if (_t > 0xffffffff) r -= 32;               \
 841     if (_t > 0xffffffff) _t >>= 32;             \
 842     if (_t > 0xffff) r -= 16;                   \
 843     if (_t > 0xffff) _t >>= 16;                 \
 844     if (_t > 0xff) r -= 8;                      \
 845     if (_t > 0xff) _t >>= 8;                    \
 846     if (_t & 0xf0) r -= 4;                      \
 847     if (_t & 0xf0) _t >>= 4;                    \
 848     if (_t & 0xc) r -= 2;                       \
 849     if (_t & 0xc) _t >>= 2;                     \
 850     if (_t & 0x2) r -= 1;                       \
 851   } while (0)
 852 #endif /* not _FP_W_TYPE_SIZE < 64 */
 853 #endif /* ndef __FP_CLZ */
 854
 855 #define _FP_DIV_HELP_imm(q, r, n, d)            \
 856   do {                                          \
 857     q = n / d, r = n % d;                       \
 858   } while (0)
 859
 860 #endif /* __MATH_EMU_OP_COMMON_H__ */