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);                              \
  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);                                     \
 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);                    \
 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   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 494     R##_s = _FP_NANSIGN_##fs;                           \
 495     R##_c = FP_CLS_NAN;                                 \
 496     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 497     FP_SET_EXCEPTION(FP_EX_INVALID);                    \
 498     break;                                              \
 499                                                         \
 500   default:                                              \
 501     abort();                                            \
 502   }                                                     \
 503 } while (0)
 504
 505
 506 /*
 507  * Main differential comparison routine.  The inputs should be raw not
 508  * cooked.  The return is -1,0,1 for normal values, 2 otherwise.
 509  */
 510
 511 #define _FP_CMP(fs, wc, ret, X, Y, un)                                  \
 512   do {                                                                  \
 513     /* NANs are unordered */                                            \
 514     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))           \
 515         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))       \
 516       {                                                                 \
 517         ret = un;                                                       \
 518       }                                                                 \
 519     else                                                                \
 520       {                                                                 \
 521         int __is_zero_x;                                                \
 522         int __is_zero_y;                                                \
 523                                                                         \
 524         __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0;       \
 525         __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0;       \
 526                                                                         \
 527         if (__is_zero_x && __is_zero_y)                                 \
 528                 ret = 0;                                                \
 529         else if (__is_zero_x)                                           \
 530                 ret = Y##_s ? 1 : -1;                                   \
 531         else if (__is_zero_y)                                           \
 532                 ret = X##_s ? -1 : 1;                                   \
 533         else if (X##_s != Y##_s)                                        \
 534           ret = X##_s ? -1 : 1;                                         \
 535         else if (X##_e > Y##_e)                                         \
 536           ret = X##_s ? -1 : 1;                                         \
 537         else if (X##_e < Y##_e)                                         \
 538           ret = X##_s ? 1 : -1;                                         \
 539         else if (_FP_FRAC_GT_##wc(X, Y))                                \
 540           ret = X##_s ? -1 : 1;                                         \
 541         else if (_FP_FRAC_GT_##wc(Y, X))                                \
 542           ret = X##_s ? 1 : -1;                                         \
 543         else                                                            \
 544           ret = 0;                                                      \
 545       }                                                                 \
 546   } while (0)
 547
 548
 549 /* Simplification for strict equality.  */
 550
 551 #define _FP_CMP_EQ(fs, wc, ret, X, Y)                                     \
 552   do {                                                                    \
 553     /* NANs are unordered */                                              \
 554     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))             \
 555         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))         \
 556       {                                                                   \
 557         ret = 1;                                                          \
 558       }                                                                   \
 559     else                                                                  \
 560       {                                                                   \
 561         ret = !(X##_e == Y##_e                                            \
 562                 && _FP_FRAC_EQ_##wc(X, Y)                                 \
 563                 && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
 564       }                                                                   \
 565   } while (0)
 566
 567 /*
 568  * Main square root routine.  The input value should be cooked.
 569  */
 570
 571 #define _FP_SQRT(fs, wc, R, X)                                          \
 572 do {                                                                    \
 573     _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S);                       \
 574     _FP_W_TYPE q;                                                       \
 575     switch (X##_c)                                                      \
 576     {                                                                   \
 577     case FP_CLS_NAN:                                                    \
 578         _FP_FRAC_COPY_##wc(R, X);                                       \
 579         R##_s = X##_s;                                                  \
 580         R##_c = FP_CLS_NAN;                                             \
 581         break;                                                          \
 582     case FP_CLS_INF:                                                    \
 583         if (X##_s)                                                      \
 584           {                                                             \
 585             R##_s = _FP_NANSIGN_##fs;                                   \
 586             R##_c = FP_CLS_NAN; /* NAN */                               \
 587             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 588             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 589           }                                                             \
 590         else                                                            \
 591           {                                                             \
 592             R##_s = 0;                                                  \
 593             R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */                 \
 594           }                                                             \
 595         break;                                                          \
 596     case FP_CLS_ZERO:                                                   \
 597         R##_s = X##_s;                                                  \
 598         R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */                      \
 599         break;                                                          \
 600     case FP_CLS_NORMAL:                                                 \
 601         R##_s = 0;                                                      \
 602         if (X##_s)                                                      \
 603           {                                                             \
 604             R##_c = FP_CLS_NAN; /* sNAN */                              \
 605             R##_s = _FP_NANSIGN_##fs;                                   \
 606             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 607             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 608             break;                                                      \
 609           }                                                             \
 610         R##_c = FP_CLS_NORMAL;                                          \
 611         if (X##_e & 1)                                                  \
 612           _FP_FRAC_SLL_##wc(X, 1);                                      \
 613         R##_e = X##_e >> 1;                                             \
 614         _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc);                        \
 615         _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc);                        \
 616         q = _FP_OVERFLOW_##fs >> 1;                                     \
 617         _FP_SQRT_MEAT_##wc(R, S, T, X, q);                              \
 618     }                                                                   \
 619   } while (0)
 620
 621 /*
 622  * Convert from FP to integer
 623  */
 624
 625 /* RSIGNED can have following values:
 626  * 0:  the number is required to be 0..(2^rsize)-1, if not, NV is set plus
 627  *     the result is either 0 or (2^rsize)-1 depending on the sign in such case.
 628  * 1:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 629  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 630  *     on the sign in such case.
 631  * 2:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 632  *     set plus the result is truncated to fit into destination.
 633  * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
 634  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 635  *     on the sign in such case.
 636  */
 637 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned)                                \
 638   do {                                                                          \
 639     switch (X##_c)                                                              \
 640       {                                                                         \
 641       case FP_CLS_NORMAL:                                                       \
 642         if (X##_e < 0)                                                          \
 643           {                                                                     \
 644             FP_SET_EXCEPTION(FP_EX_INEXACT);                                    \
 645           case FP_CLS_ZERO:                                                     \
 646             r = 0;                                                              \
 647           }                                                                     \
 648         else if (X##_e >= rsize - (rsigned > 0 || X##_s)                        \
 649                  || (!rsigned && X##_s))                                        \
 650           {     /* overflow */                                                  \
 651           case FP_CLS_NAN:                                                      \
 652           case FP_CLS_INF:                                                      \
 653             if (rsigned == 2)                                                   \
 654               {                                                                 \
 655                 if (X##_c != FP_CLS_NORMAL                                      \
 656                     || X##_e >= rsize - 1 + _FP_WFRACBITS_##fs)                 \
 657                   r = 0;                                                        \
 658                 else                                                            \
 659                   {                                                             \
 660                     _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));     \
 661                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 662                   }                                                             \
 663               }                                                                 \
 664             else if (rsigned)                                                   \
 665               {                                                                 \
 666                 r = 1;                                                          \
 667                 r <<= rsize - 1;                                                \
 668                 r -= 1 - X##_s;                                                 \
 669               }                                                                 \
 670             else                                                                \
 671               {                                                                 \
 672                 r = 0;                                                          \
 673                 if (X##_s)                                                      \
 674                   r = ~r;                                                       \
 675               }                                                                 \
 676             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 677           }                                                                     \
 678         else                                                                    \
 679           {                                                                     \
 680             if (_FP_W_TYPE_SIZE*wc < rsize)                                     \
 681               {                                                                 \
 682                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 683                 r <<= X##_e - _FP_WFRACBITS_##fs;                               \
 684               }                                                                 \
 685             else                                                                \
 686               {                                                                 \
 687                 if (X##_e >= _FP_WFRACBITS_##fs)                                \
 688                   _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));       \
 689                 else if (X##_e < _FP_WFRACBITS_##fs - 1)                        \
 690                   {                                                             \
 691                     _FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2),      \
 692                                       _FP_WFRACBITS_##fs);                      \
 693                     if (_FP_FRAC_LOW_##wc(X) & 1)                               \
 694                       FP_SET_EXCEPTION(FP_EX_INEXACT);                          \
 695                     _FP_FRAC_SRL_##wc(X, 1);                                    \
 696                   }                                                             \
 697                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 698               }                                                                 \
 699             if (rsigned && X##_s)                                               \
 700               r = -r;                                                           \
 701           }                                                                     \
 702         break;                                                                  \
 703       }                                                                         \
 704   } while (0)
 705
 706 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned)                          \
 707   do {                                                                          \
 708     r = 0;                                                                      \
 709     switch (X##_c)                                                              \
 710       {                                                                         \
 711       case FP_CLS_NORMAL:                                                       \
 712         if (X##_e >= _FP_FRACBITS_##fs - 1)                                     \
 713           {                                                                     \
 714             if (X##_e < rsize - 1 + _FP_WFRACBITS_##fs)                         \
 715               {                                                                 \
 716                 if (X##_e >= _FP_WFRACBITS_##fs - 1)                            \
 717                   {                                                             \
 718                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 719                     r <<= X##_e - _FP_WFRACBITS_##fs + 1;                       \
 720                   }                                                             \
 721                 else                                                            \
 722                   {                                                             \
 723                     _FP_FRAC_SRL_##wc(X, _FP_WORKBITS - X##_e                   \
 724                                       + _FP_FRACBITS_##fs - 1);                 \
 725                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 726                   }                                                             \
 727               }                                                                 \
 728           }                                                                     \
 729         else                                                                    \
 730           {                                                                     \
 731             if (X##_e <= -_FP_WORKBITS - 1)                                     \
 732               _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                           \
 733             else                                                                \
 734               _FP_FRAC_SRS_##wc(X, _FP_FRACBITS_##fs - 1 - X##_e,               \
 735                                 _FP_WFRACBITS_##fs);                            \
 736             _FP_ROUND(wc, X);                                                   \
 737             _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                                 \
 738             _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                                \
 739           }                                                                     \
 740         if (rsigned && X##_s)                                                   \
 741           r = -r;                                                               \
 742         if (X##_e >= rsize - (rsigned > 0 || X##_s)                             \
 743             || (!rsigned && X##_s))                                             \
 744           {     /* overflow */                                                  \
 745           case FP_CLS_NAN:                                                      \
 746           case FP_CLS_INF:                                                      \
 747             if (!rsigned)                                                       \
 748               {                                                                 \
 749                 r = 0;                                                          \
 750                 if (X##_s)                                                      \
 751                   r = ~r;                                                       \
 752               }                                                                 \
 753             else if (rsigned != 2)                                              \
 754               {                                                                 \
 755                 r = 1;                                                          \
 756                 r <<= rsize - 1;                                                \
 757                 r -= 1 - X##_s;                                                 \
 758               }                                                                 \
 759             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 760           }                                                                     \
 761         break;                                                                  \
 762       case FP_CLS_ZERO:                                                         \
 763         break;                                                                  \
 764       }                                                                         \
 765   } while (0)
 766
 767 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype)                        \
 768   do {                                                                  \
 769     if (r)                                                              \
 770       {                                                                 \
 771         unsigned rtype ur_;                                             \
 772         X##_c = FP_CLS_NORMAL;                                          \
 773                                                                         \
 774         if ((X##_s = (r < 0)))                                          \
 775           ur_ = (unsigned rtype) -r;                                    \
 776         else                                                            \
 777           ur_ = (unsigned rtype) r;                                     \
 778         if (rsize <= _FP_W_TYPE_SIZE)                                   \
 779           __FP_CLZ(X##_e, ur_);                                         \
 780         else                                                            \
 781           __FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE),       \
 782                      (_FP_W_TYPE)ur_);                                  \
 783         if (rsize < _FP_W_TYPE_SIZE)                                    \
 784                 X##_e -= (_FP_W_TYPE_SIZE - rsize);                     \
 785         X##_e = rsize - X##_e - 1;                                      \
 786                                                                         \
 787         if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e)    \
 788           __FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\
 789         _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize);                       \
 790         if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0)                       \
 791           _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));       \
 792       }                                                                 \
 793     else                                                                \
 794       {                                                                 \
 795         X##_c = FP_CLS_ZERO, X##_s = 0;                                 \
 796       }                                                                 \
 797   } while (0)
 798
 799
 800 #define FP_CONV(dfs,sfs,dwc,swc,D,S)                    \
 801   do {                                                  \
 802     _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S);        \
 803     D##_e = S##_e;                                      \
 804     D##_c = S##_c;                                      \
 805     D##_s = S##_s;                                      \
 806   } while (0)
 807
 808 /*
 809  * Helper primitives.
 810  */
 811
 812 /* Count leading zeros in a word.  */
 813
 814 #ifndef __FP_CLZ
 815 #if _FP_W_TYPE_SIZE < 64
 816 /* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
 817 #define __FP_CLZ(r, x)                          \
 818   do {                                          \
 819     _FP_W_TYPE _t = (x);                        \
 820     r = _FP_W_TYPE_SIZE - 1;                    \
 821     if (_t > 0xffff) r -= 16;                   \
 822     if (_t > 0xffff) _t >>= 16;                 \
 823     if (_t > 0xff) r -= 8;                      \
 824     if (_t > 0xff) _t >>= 8;                    \
 825     if (_t & 0xf0) r -= 4;                      \
 826     if (_t & 0xf0) _t >>= 4;                    \
 827     if (_t & 0xc) r -= 2;                       \
 828     if (_t & 0xc) _t >>= 2;                     \
 829     if (_t & 0x2) r -= 1;                       \
 830   } while (0)
 831 #else /* not _FP_W_TYPE_SIZE < 64 */
 832 #define __FP_CLZ(r, x)                          \
 833   do {                                          \
 834     _FP_W_TYPE _t = (x);                        \
 835     r = _FP_W_TYPE_SIZE - 1;                    \
 836     if (_t > 0xffffffff) r -= 32;               \
 837     if (_t > 0xffffffff) _t >>= 32;             \
 838     if (_t > 0xffff) r -= 16;                   \
 839     if (_t > 0xffff) _t >>= 16;                 \
 840     if (_t > 0xff) r -= 8;                      \
 841     if (_t > 0xff) _t >>= 8;                    \
 842     if (_t & 0xf0) r -= 4;                      \
 843     if (_t & 0xf0) _t >>= 4;                    \
 844     if (_t & 0xc) r -= 2;                       \
 845     if (_t & 0xc) _t >>= 2;                     \
 846     if (_t & 0x2) r -= 1;                       \
 847   } while (0)
 848 #endif /* not _FP_W_TYPE_SIZE < 64 */
 849 #endif /* ndef __FP_CLZ */
 850
 851 #define _FP_DIV_HELP_imm(q, r, n, d)            \
 852   do {                                          \
 853     q = n / d, r = n % d;                       \
 854   } while (0)
 855
 856 #endif /* __MATH_EMU_OP_COMMON_H__ */