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   1 /* Software floating-point emulation. Common operations.
   2    Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Richard Henderson (rth@cygnus.com),
   5                   Jakub Jelinek (jj@ultra.linux.cz),
   6                   David S. Miller (davem@redhat.com) and
   7                   Peter Maydell (pmaydell@chiark.greenend.org.uk).
   8
   9    The GNU C Library is free software; you can redistribute it and/or
  10    modify it under the terms of the GNU Library General Public License as
  11    published by the Free Software Foundation; either version 2 of the
  12    License, or (at your option) any later version.
  13
  14    The GNU C Library is distributed in the hope that it will be useful,
  15    but WITHOUT ANY WARRANTY; without even the implied warranty of
  16    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  17    Library General Public License for more details.
  18
  19    You should have received a copy of the GNU Library General Public
  20    License along with the GNU C Library; see the file COPYING.LIB.  If
  21    not, write to the Free Software Foundation, Inc.,
  22    59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
  23
  24 #ifndef __MATH_EMU_OP_COMMON_H__
  25 #define __MATH_EMU_OP_COMMON_H__
  26
  27 #define _FP_DECL(wc, X)                 \
  28   _FP_I_TYPE X##_c=0, X##_s=0, X##_e=0; \
  29   _FP_FRAC_DECL_##wc(X)
  30
  31 /*
  32  * Finish truely unpacking a native fp value by classifying the kind
  33  * of fp value and normalizing both the exponent and the fraction.
  34  */
  35
  36 #define _FP_UNPACK_CANONICAL(fs, wc, X)                                 \
  37 do {                                                                    \
  38   switch (X##_e)                                                        \
  39   {                                                                     \
  40   default:                                                              \
  41     _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs;                      \
  42     _FP_FRAC_SLL_##wc(X, _FP_WORKBITS);                                 \
  43     X##_e -= _FP_EXPBIAS_##fs;                                          \
  44     X##_c = FP_CLS_NORMAL;                                              \
  45     break;                                                              \
  46                                                                         \
  47   case 0:                                                               \
  48     if (_FP_FRAC_ZEROP_##wc(X))                                         \
  49       X##_c = FP_CLS_ZERO;                                              \
  50     else                                                                \
  51       {                                                                 \
  52         /* a denormalized number */                                     \
  53         _FP_I_TYPE _shift;                                              \
  54         _FP_FRAC_CLZ_##wc(_shift, X);                                   \
  55         _shift -= _FP_FRACXBITS_##fs;                                   \
  56         _FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS));                    \
  57         X##_e -= _FP_EXPBIAS_##fs - 1 + _shift;                         \
  58         X##_c = FP_CLS_NORMAL;                                          \
  59         FP_SET_EXCEPTION(FP_EX_DENORM);                                 \
  60         if (FP_DENORM_ZERO)                                             \
  61           {                                                             \
  62             FP_SET_EXCEPTION(FP_EX_INEXACT);                            \
  63             X##_c = FP_CLS_ZERO;                                        \
  64           }                                                             \
  65       }                                                                 \
  66     break;                                                              \
  67                                                                         \
  68   case _FP_EXPMAX_##fs:                                                 \
  69     if (_FP_FRAC_ZEROP_##wc(X))                                         \
  70       X##_c = FP_CLS_INF;                                               \
  71     else                                                                \
  72       {                                                                 \
  73         X##_c = FP_CLS_NAN;                                             \
  74         /* Check for signaling NaN */                                   \
  75         if (!(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))            \
  76           FP_SET_EXCEPTION(FP_EX_INVALID | 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             if (_FP_FRAC_HIGH_##fs(X)                           \
 143                 & (_FP_OVERFLOW_##fs >> 1))                     \
 144               {                                                 \
 145                 X##_e = 1;                                      \
 146                 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);        \
 147               }                                                 \
 148             else                                                \
 149               {                                                 \
 150                 _FP_ROUND(wc, X);                               \
 151                 if (_FP_FRAC_HIGH_##fs(X)                       \
 152                    & (_FP_OVERFLOW_##fs >> 1))                  \
 153                   {                                             \
 154                     X##_e = 1;                                  \
 155                     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);    \
 156                     FP_SET_EXCEPTION(FP_EX_INEXACT);            \
 157                   }                                             \
 158                 else                                            \
 159                   {                                             \
 160                     X##_e = 0;                                  \
 161                     _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);         \
 162                   }                                             \
 163               }                                                 \
 164             if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) ||          \
 165                 (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW))     \
 166                 FP_SET_EXCEPTION(FP_EX_UNDERFLOW);              \
 167           }                                                     \
 168         else                                                    \
 169           {                                                     \
 170             /* underflow to zero */                             \
 171             X##_e = 0;                                          \
 172             if (!_FP_FRAC_ZEROP_##wc(X))                        \
 173               {                                                 \
 174                 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);         \
 175                 _FP_ROUND(wc, X);                               \
 176                 _FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS);        \
 177               }                                                 \
 178             FP_SET_EXCEPTION(FP_EX_UNDERFLOW);                  \
 179           }                                                     \
 180       }                                                         \
 181     break;                                                      \
 182                                                                 \
 183   case FP_CLS_ZERO:                                             \
 184     X##_e = 0;                                                  \
 185     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 186     break;                                                      \
 187                                                                 \
 188   case FP_CLS_INF:                                              \
 189     X##_e = _FP_EXPMAX_##fs;                                    \
 190     _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                    \
 191     break;                                                      \
 192                                                                 \
 193   case FP_CLS_NAN:                                              \
 194     X##_e = _FP_EXPMAX_##fs;                                    \
 195     if (!_FP_KEEPNANFRACP)                                      \
 196       {                                                         \
 197         _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs);                 \
 198         X##_s = _FP_NANSIGN_##fs;                               \
 199       }                                                         \
 200     else                                                        \
 201       _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs;            \
 202     break;                                                      \
 203   }                                                             \
 204 } while (0)
 205
 206 /* This one accepts raw argument and not cooked,  returns
 207  * 1 if X is a signaling NaN.
 208  */
 209 #define _FP_ISSIGNAN(fs, wc, X)                                 \
 210 ({                                                              \
 211   int __ret = 0;                                                \
 212   if (X##_e == _FP_EXPMAX_##fs)                                 \
 213     {                                                           \
 214       if (!_FP_FRAC_ZEROP_##wc(X)                               \
 215           && !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))   \
 216         __ret = 1;                                              \
 217     }                                                           \
 218   __ret;                                                        \
 219 })
 220
 221
 222
 223
 224
 225 /*
 226  * Main addition routine.  The input values should be cooked.
 227  */
 228
 229 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP)                                \
 230 do {                                                                         \
 231   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                                     \
 232   {                                                                          \
 233   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):                         \
 234     {                                                                        \
 235       /* shift the smaller number so that its exponent matches the larger */ \
 236       _FP_I_TYPE diff = X##_e - Y##_e;                                       \
 237                                                                              \
 238       if (diff < 0)                                                          \
 239         {                                                                    \
 240           diff = -diff;                                                      \
 241           if (diff <= _FP_WFRACBITS_##fs)                                    \
 242             _FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs);                  \
 243           else if (!_FP_FRAC_ZEROP_##wc(X))                                  \
 244             _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                          \
 245           R##_e = Y##_e;                                                     \
 246         }                                                                    \
 247       else                                                                   \
 248         {                                                                    \
 249           if (diff > 0)                                                      \
 250             {                                                                \
 251               if (diff <= _FP_WFRACBITS_##fs)                                \
 252                 _FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs);              \
 253               else if (!_FP_FRAC_ZEROP_##wc(Y))                              \
 254                 _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc);                      \
 255             }                                                                \
 256           R##_e = X##_e;                                                     \
 257         }                                                                    \
 258                                                                              \
 259       R##_c = FP_CLS_NORMAL;                                                 \
 260                                                                              \
 261       if (X##_s == Y##_s)                                                    \
 262         {                                                                    \
 263           R##_s = X##_s;                                                     \
 264           _FP_FRAC_ADD_##wc(R, X, Y);                                        \
 265           if (_FP_FRAC_OVERP_##wc(fs, R))                                    \
 266             {                                                                \
 267               _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);                   \
 268               R##_e++;                                                       \
 269             }                                                                \
 270         }                                                                    \
 271       else                                                                   \
 272         {                                                                    \
 273           R##_s = X##_s;                                                     \
 274           _FP_FRAC_SUB_##wc(R, X, Y);                                        \
 275           if (_FP_FRAC_ZEROP_##wc(R))                                        \
 276             {                                                                \
 277               /* return an exact zero */                                     \
 278               if (FP_ROUNDMODE == FP_RND_MINF)                               \
 279                 R##_s |= Y##_s;                                              \
 280               else                                                           \
 281                 R##_s &= Y##_s;                                              \
 282               R##_c = FP_CLS_ZERO;                                           \
 283             }                                                                \
 284           else                                                               \
 285             {                                                                \
 286               if (_FP_FRAC_NEGP_##wc(R))                                     \
 287                 {                                                            \
 288                   _FP_FRAC_SUB_##wc(R, Y, X);                                \
 289                   R##_s = Y##_s;                                             \
 290                 }                                                            \
 291                                                                              \
 292               /* renormalize after subtraction */                            \
 293               _FP_FRAC_CLZ_##wc(diff, R);                                    \
 294               diff -= _FP_WFRACXBITS_##fs;                                   \
 295               if (diff)                                                      \
 296                 {                                                            \
 297                   R##_e -= diff;                                             \
 298                   _FP_FRAC_SLL_##wc(R, diff);                                \
 299                 }                                                            \
 300             }                                                                \
 301         }                                                                    \
 302       break;                                                                 \
 303     }                                                                        \
 304                                                                              \
 305   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):                               \
 306     _FP_CHOOSENAN(fs, wc, R, X, Y, OP);                                      \
 307     break;                                                                   \
 308                                                                              \
 309   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):                           \
 310     R##_e = X##_e;                                                           \
 311   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):                            \
 312   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):                               \
 313   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):                              \
 314     _FP_FRAC_COPY_##wc(R, X);                                                \
 315     R##_s = X##_s;                                                           \
 316     R##_c = X##_c;                                                           \
 317     break;                                                                   \
 318                                                                              \
 319   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):                           \
 320     R##_e = Y##_e;                                                           \
 321   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):                            \
 322   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):                               \
 323   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):                              \
 324     _FP_FRAC_COPY_##wc(R, Y);                                                \
 325     R##_s = Y##_s;                                                           \
 326     R##_c = Y##_c;                                                           \
 327     break;                                                                   \
 328                                                                              \
 329   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):                               \
 330     if (X##_s != Y##_s)                                                      \
 331       {                                                                      \
 332         /* +INF + -INF => NAN */                                             \
 333         _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                              \
 334         R##_s = _FP_NANSIGN_##fs;                                            \
 335         R##_c = FP_CLS_NAN;                                                  \
 336         FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_ISI);                 \
 337         break;                                                               \
 338       }                                                                      \
 339     /* FALLTHRU */                                                           \
 340                                                                              \
 341   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):                            \
 342   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):                              \
 343     R##_s = X##_s;                                                           \
 344     R##_c = FP_CLS_INF;                                                      \
 345     break;                                                                   \
 346                                                                              \
 347   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):                            \
 348   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):                              \
 349     R##_s = Y##_s;                                                           \
 350     R##_c = FP_CLS_INF;                                                      \
 351     break;                                                                   \
 352                                                                              \
 353   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):                             \
 354     /* make sure the sign is correct */                                      \
 355     if (FP_ROUNDMODE == FP_RND_MINF)                                         \
 356       R##_s = X##_s | Y##_s;                                                 \
 357     else                                                                     \
 358       R##_s = X##_s & Y##_s;                                                 \
 359     R##_c = FP_CLS_ZERO;                                                     \
 360     break;                                                                   \
 361                                                                              \
 362   default:                                                                   \
 363     abort();                                                                 \
 364   }                                                                          \
 365 } while (0)
 366
 367 #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
 368 #define _FP_SUB(fs, wc, R, X, Y)                                             \
 369   do {                                                                       \
 370     if (Y##_c != FP_CLS_NAN) Y##_s ^= 1;                                     \
 371     _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-');                                  \
 372   } while (0)
 373
 374
 375 /*
 376  * Main negation routine.  FIXME -- when we care about setting exception
 377  * bits reliably, this will not do.  We should examine all of the fp classes.
 378  */
 379
 380 #define _FP_NEG(fs, wc, R, X)           \
 381   do {                                  \
 382     _FP_FRAC_COPY_##wc(R, X);           \
 383     R##_c = X##_c;                      \
 384     R##_e = X##_e;                      \
 385     R##_s = 1 ^ X##_s;                  \
 386   } while (0)
 387
 388
 389 /*
 390  * Main multiplication routine.  The input values should be cooked.
 391  */
 392
 393 #define _FP_MUL(fs, wc, R, X, Y)                        \
 394 do {                                                    \
 395   R##_s = X##_s ^ Y##_s;                                \
 396   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 397   {                                                     \
 398   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 399     R##_c = FP_CLS_NORMAL;                              \
 400     R##_e = X##_e + Y##_e + 1;                          \
 401                                                         \
 402     _FP_MUL_MEAT_##fs(R,X,Y);                           \
 403                                                         \
 404     if (_FP_FRAC_OVERP_##wc(fs, R))                     \
 405       _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);      \
 406     else                                                \
 407       R##_e--;                                          \
 408     break;                                              \
 409                                                         \
 410   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 411     _FP_CHOOSENAN(fs, wc, R, X, Y, '*');                \
 412     break;                                              \
 413                                                         \
 414   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 415   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 416   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 417     R##_s = X##_s;                                      \
 418                                                         \
 419   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 420   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 421   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 422   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 423     _FP_FRAC_COPY_##wc(R, X);                           \
 424     R##_c = X##_c;                                      \
 425     break;                                              \
 426                                                         \
 427   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 428   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 429   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 430     R##_s = Y##_s;                                      \
 431                                                         \
 432   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 433   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 434     _FP_FRAC_COPY_##wc(R, Y);                           \
 435     R##_c = Y##_c;                                      \
 436     break;                                              \
 437                                                         \
 438   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 439   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 440     R##_s = _FP_NANSIGN_##fs;                           \
 441     R##_c = FP_CLS_NAN;                                 \
 442     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 443     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_IMZ);\
 444     break;                                              \
 445                                                         \
 446   default:                                              \
 447     abort();                                            \
 448   }                                                     \
 449 } while (0)
 450
 451
 452 /*
 453  * Main division routine.  The input values should be cooked.
 454  */
 455
 456 #define _FP_DIV(fs, wc, R, X, Y)                        \
 457 do {                                                    \
 458   R##_s = X##_s ^ Y##_s;                                \
 459   switch (_FP_CLS_COMBINE(X##_c, Y##_c))                \
 460   {                                                     \
 461   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):    \
 462     R##_c = FP_CLS_NORMAL;                              \
 463     R##_e = X##_e - Y##_e;                              \
 464                                                         \
 465     _FP_DIV_MEAT_##fs(R,X,Y);                           \
 466     break;                                              \
 467                                                         \
 468   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):          \
 469     _FP_CHOOSENAN(fs, wc, R, X, Y, '/');                \
 470     break;                                              \
 471                                                         \
 472   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):       \
 473   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):          \
 474   case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):         \
 475     R##_s = X##_s;                                      \
 476     _FP_FRAC_COPY_##wc(R, X);                           \
 477     R##_c = X##_c;                                      \
 478     break;                                              \
 479                                                         \
 480   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):       \
 481   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):          \
 482   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):         \
 483     R##_s = Y##_s;                                      \
 484     _FP_FRAC_COPY_##wc(R, Y);                           \
 485     R##_c = Y##_c;                                      \
 486     break;                                              \
 487                                                         \
 488   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):       \
 489   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):         \
 490   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):      \
 491     R##_c = FP_CLS_ZERO;                                \
 492     break;                                              \
 493                                                         \
 494   case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):      \
 495     FP_SET_EXCEPTION(FP_EX_DIVZERO);                    \
 496   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):         \
 497   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):       \
 498     R##_c = FP_CLS_INF;                                 \
 499     break;                                              \
 500                                                         \
 501   case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):          \
 502     R##_s = _FP_NANSIGN_##fs;                           \
 503     R##_c = FP_CLS_NAN;                                 \
 504     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 505     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_IDI);\
 506     break;                                              \
 507                                                         \
 508   case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):        \
 509     R##_s = _FP_NANSIGN_##fs;                           \
 510     R##_c = FP_CLS_NAN;                                 \
 511     _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);             \
 512     FP_SET_EXCEPTION(FP_EX_INVALID | FP_EX_INVALID_ZDZ);\
 513     break;                                              \
 514                                                         \
 515   default:                                              \
 516     abort();                                            \
 517   }                                                     \
 518 } while (0)
 519
 520
 521 /*
 522  * Main differential comparison routine.  The inputs should be raw not
 523  * cooked.  The return is -1,0,1 for normal values, 2 otherwise.
 524  */
 525
 526 #define _FP_CMP(fs, wc, ret, X, Y, un)                                  \
 527   do {                                                                  \
 528     /* NANs are unordered */                                            \
 529     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))           \
 530         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))       \
 531       {                                                                 \
 532         ret = un;                                                       \
 533       }                                                                 \
 534     else                                                                \
 535       {                                                                 \
 536         int __is_zero_x;                                                \
 537         int __is_zero_y;                                                \
 538                                                                         \
 539         __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0;       \
 540         __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0;       \
 541                                                                         \
 542         if (__is_zero_x && __is_zero_y)                                 \
 543                 ret = 0;                                                \
 544         else if (__is_zero_x)                                           \
 545                 ret = Y##_s ? 1 : -1;                                   \
 546         else if (__is_zero_y)                                           \
 547                 ret = X##_s ? -1 : 1;                                   \
 548         else if (X##_s != Y##_s)                                        \
 549           ret = X##_s ? -1 : 1;                                         \
 550         else if (X##_e > Y##_e)                                         \
 551           ret = X##_s ? -1 : 1;                                         \
 552         else if (X##_e < Y##_e)                                         \
 553           ret = X##_s ? 1 : -1;                                         \
 554         else if (_FP_FRAC_GT_##wc(X, Y))                                \
 555           ret = X##_s ? -1 : 1;                                         \
 556         else if (_FP_FRAC_GT_##wc(Y, X))                                \
 557           ret = X##_s ? 1 : -1;                                         \
 558         else                                                            \
 559           ret = 0;                                                      \
 560       }                                                                 \
 561   } while (0)
 562
 563
 564 /* Simplification for strict equality.  */
 565
 566 #define _FP_CMP_EQ(fs, wc, ret, X, Y)                                     \
 567   do {                                                                    \
 568     /* NANs are unordered */                                              \
 569     if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))             \
 570         || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))         \
 571       {                                                                   \
 572         ret = 1;                                                          \
 573       }                                                                   \
 574     else                                                                  \
 575       {                                                                   \
 576         ret = !(X##_e == Y##_e                                            \
 577                 && _FP_FRAC_EQ_##wc(X, Y)                                 \
 578                 && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
 579       }                                                                   \
 580   } while (0)
 581
 582 /*
 583  * Main square root routine.  The input value should be cooked.
 584  */
 585
 586 #define _FP_SQRT(fs, wc, R, X)                                          \
 587 do {                                                                    \
 588     _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S);                       \
 589     _FP_W_TYPE q;                                                       \
 590     switch (X##_c)                                                      \
 591     {                                                                   \
 592     case FP_CLS_NAN:                                                    \
 593         _FP_FRAC_COPY_##wc(R, X);                                       \
 594         R##_s = X##_s;                                                  \
 595         R##_c = FP_CLS_NAN;                                             \
 596         break;                                                          \
 597     case FP_CLS_INF:                                                    \
 598         if (X##_s)                                                      \
 599           {                                                             \
 600             R##_s = _FP_NANSIGN_##fs;                                   \
 601             R##_c = FP_CLS_NAN; /* NAN */                               \
 602             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 603             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 604           }                                                             \
 605         else                                                            \
 606           {                                                             \
 607             R##_s = 0;                                                  \
 608             R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */                 \
 609           }                                                             \
 610         break;                                                          \
 611     case FP_CLS_ZERO:                                                   \
 612         R##_s = X##_s;                                                  \
 613         R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */                      \
 614         break;                                                          \
 615     case FP_CLS_NORMAL:                                                 \
 616         R##_s = 0;                                                      \
 617         if (X##_s)                                                      \
 618           {                                                             \
 619             R##_c = FP_CLS_NAN; /* sNAN */                              \
 620             R##_s = _FP_NANSIGN_##fs;                                   \
 621             _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                     \
 622             FP_SET_EXCEPTION(FP_EX_INVALID);                            \
 623             break;                                                      \
 624           }                                                             \
 625         R##_c = FP_CLS_NORMAL;                                          \
 626         if (X##_e & 1)                                                  \
 627           _FP_FRAC_SLL_##wc(X, 1);                                      \
 628         R##_e = X##_e >> 1;                                             \
 629         _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc);                        \
 630         _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc);                        \
 631         q = _FP_OVERFLOW_##fs >> 1;                                     \
 632         _FP_SQRT_MEAT_##wc(R, S, T, X, q);                              \
 633     }                                                                   \
 634   } while (0)
 635
 636 /*
 637  * Convert from FP to integer
 638  */
 639
 640 /* RSIGNED can have following values:
 641  * 0:  the number is required to be 0..(2^rsize)-1, if not, NV is set plus
 642  *     the result is either 0 or (2^rsize)-1 depending on the sign in such case.
 643  * 1:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 644  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 645  *     on the sign in such case.
 646  * 2:  the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
 647  *     set plus the result is truncated to fit into destination.
 648  * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
 649  *     set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
 650  *     on the sign in such case.
 651  */
 652 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned)                                \
 653   do {                                                                          \
 654     switch (X##_c)                                                              \
 655       {                                                                         \
 656       case FP_CLS_NORMAL:                                                       \
 657         if (X##_e < 0)                                                          \
 658           {                                                                     \
 659             FP_SET_EXCEPTION(FP_EX_INEXACT);                                    \
 660           case FP_CLS_ZERO:                                                     \
 661             r = 0;                                                              \
 662           }                                                                     \
 663         else if (X##_e >= rsize - (rsigned > 0 || X##_s)                        \
 664                  || (!rsigned && X##_s))                                        \
 665           {     /* overflow */                                                  \
 666           case FP_CLS_NAN:                                                      \
 667           case FP_CLS_INF:                                                      \
 668             if (rsigned == 2)                                                   \
 669               {                                                                 \
 670                 if (X##_c != FP_CLS_NORMAL                                      \
 671                     || X##_e >= rsize - 1 + _FP_WFRACBITS_##fs)                 \
 672                   r = 0;                                                        \
 673                 else                                                            \
 674                   {                                                             \
 675                     _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));     \
 676                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 677                   }                                                             \
 678               }                                                                 \
 679             else if (rsigned)                                                   \
 680               {                                                                 \
 681                 r = 1;                                                          \
 682                 r <<= rsize - 1;                                                \
 683                 r -= 1 - X##_s;                                                 \
 684               }                                                                 \
 685             else                                                                \
 686               {                                                                 \
 687                 r = 0;                                                          \
 688                 if (X##_s)                                                      \
 689                   r = ~r;                                                       \
 690               }                                                                 \
 691             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 692           }                                                                     \
 693         else                                                                    \
 694           {                                                                     \
 695             if (_FP_W_TYPE_SIZE*wc < rsize)                                     \
 696               {                                                                 \
 697                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 698                 r <<= X##_e - _FP_WFRACBITS_##fs;                               \
 699               }                                                                 \
 700             else                                                                \
 701               {                                                                 \
 702                 if (X##_e >= _FP_WFRACBITS_##fs)                                \
 703                   _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));       \
 704                 else if (X##_e < _FP_WFRACBITS_##fs - 1)                        \
 705                   {                                                             \
 706                     _FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2),      \
 707                                       _FP_WFRACBITS_##fs);                      \
 708                     if (_FP_FRAC_LOW_##wc(X) & 1)                               \
 709                       FP_SET_EXCEPTION(FP_EX_INEXACT);                          \
 710                     _FP_FRAC_SRL_##wc(X, 1);                                    \
 711                   }                                                             \
 712                 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                            \
 713               }                                                                 \
 714             if (rsigned && X##_s)                                               \
 715               r = -r;                                                           \
 716           }                                                                     \
 717         break;                                                                  \
 718       }                                                                         \
 719   } while (0)
 720
 721 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned)                          \
 722   do {                                                                          \
 723     r = 0;                                                                      \
 724     switch (X##_c)                                                              \
 725       {                                                                         \
 726       case FP_CLS_NORMAL:                                                       \
 727         if (X##_e >= _FP_FRACBITS_##fs - 1)                                     \
 728           {                                                                     \
 729             if (X##_e < rsize - 1 + _FP_WFRACBITS_##fs)                         \
 730               {                                                                 \
 731                 if (X##_e >= _FP_WFRACBITS_##fs - 1)                            \
 732                   {                                                             \
 733                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 734                     r <<= X##_e - _FP_WFRACBITS_##fs + 1;                       \
 735                   }                                                             \
 736                 else                                                            \
 737                   {                                                             \
 738                     _FP_FRAC_SRL_##wc(X, _FP_WORKBITS - X##_e                   \
 739                                       + _FP_FRACBITS_##fs - 1);                 \
 740                     _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                        \
 741                   }                                                             \
 742               }                                                                 \
 743           }                                                                     \
 744         else                                                                    \
 745           {                                                                     \
 746             if (X##_e <= -_FP_WORKBITS - 1)                                     \
 747               _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                           \
 748             else                                                                \
 749               _FP_FRAC_SRS_##wc(X, _FP_FRACBITS_##fs - 1 - X##_e,               \
 750                                 _FP_WFRACBITS_##fs);                            \
 751             _FP_ROUND(wc, X);                                                   \
 752             _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                                 \
 753             _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                                \
 754           }                                                                     \
 755         if (rsigned && X##_s)                                                   \
 756           r = -r;                                                               \
 757         if (X##_e >= rsize - (rsigned > 0 || X##_s)                             \
 758             || (!rsigned && X##_s))                                             \
 759           {     /* overflow */                                                  \
 760           case FP_CLS_NAN:                                                      \
 761           case FP_CLS_INF:                                                      \
 762             if (!rsigned)                                                       \
 763               {                                                                 \
 764                 r = 0;                                                          \
 765                 if (X##_s)                                                      \
 766                   r = ~r;                                                       \
 767               }                                                                 \
 768             else if (rsigned != 2)                                              \
 769               {                                                                 \
 770                 r = 1;                                                          \
 771                 r <<= rsize - 1;                                                \
 772                 r -= 1 - X##_s;                                                 \
 773               }                                                                 \
 774             FP_SET_EXCEPTION(FP_EX_INVALID);                                    \
 775           }                                                                     \
 776         break;                                                                  \
 777       case FP_CLS_ZERO:                                                         \
 778         break;                                                                  \
 779       }                                                                         \
 780   } while (0)
 781
 782 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype)                        \
 783   do {                                                                  \
 784     if (r)                                                              \
 785       {                                                                 \
 786         unsigned rtype ur_;                                             \
 787         X##_c = FP_CLS_NORMAL;                                          \
 788                                                                         \
 789         if ((X##_s = (r < 0)))                                          \
 790           ur_ = (unsigned rtype) -r;                                    \
 791         else                                                            \
 792           ur_ = (unsigned rtype) r;                                     \
 793         if (rsize <= _FP_W_TYPE_SIZE)                                   \
 794           __FP_CLZ(X##_e, ur_);                                         \
 795         else                                                            \
 796           __FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE),       \
 797                      (_FP_W_TYPE)ur_);                                  \
 798         if (rsize < _FP_W_TYPE_SIZE)                                    \
 799                 X##_e -= (_FP_W_TYPE_SIZE - rsize);                     \
 800         X##_e = rsize - X##_e - 1;                                      \
 801                                                                         \
 802         if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e)    \
 803           __FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\
 804         _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize);                       \
 805         if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0)                       \
 806           _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));       \
 807       }                                                                 \
 808     else                                                                \
 809       {                                                                 \
 810         X##_c = FP_CLS_ZERO, X##_s = 0;                                 \
 811       }                                                                 \
 812   } while (0)
 813
 814
 815 #define FP_CONV(dfs,sfs,dwc,swc,D,S)                    \
 816   do {                                                  \
 817     _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S);        \
 818     D##_e = S##_e;                                      \
 819     D##_c = S##_c;                                      \
 820     D##_s = S##_s;                                      \
 821   } while (0)
 822
 823 /*
 824  * Helper primitives.
 825  */
 826
 827 /* Count leading zeros in a word.  */
 828
 829 #ifndef __FP_CLZ
 830 #if _FP_W_TYPE_SIZE < 64
 831 /* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
 832 #define __FP_CLZ(r, x)                          \
 833   do {                                          \
 834     _FP_W_TYPE _t = (x);                        \
 835     r = _FP_W_TYPE_SIZE - 1;                    \
 836     if (_t > 0xffff) r -= 16;                   \
 837     if (_t > 0xffff) _t >>= 16;                 \
 838     if (_t > 0xff) r -= 8;                      \
 839     if (_t > 0xff) _t >>= 8;                    \
 840     if (_t & 0xf0) r -= 4;                      \
 841     if (_t & 0xf0) _t >>= 4;                    \
 842     if (_t & 0xc) r -= 2;                       \
 843     if (_t & 0xc) _t >>= 2;                     \
 844     if (_t & 0x2) r -= 1;                       \
 845   } while (0)
 846 #else /* not _FP_W_TYPE_SIZE < 64 */
 847 #define __FP_CLZ(r, x)                          \
 848   do {                                          \
 849     _FP_W_TYPE _t = (x);                        \
 850     r = _FP_W_TYPE_SIZE - 1;                    \
 851     if (_t > 0xffffffff) r -= 32;               \
 852     if (_t > 0xffffffff) _t >>= 32;             \
 853     if (_t > 0xffff) r -= 16;                   \
 854     if (_t > 0xffff) _t >>= 16;                 \
 855     if (_t > 0xff) r -= 8;                      \
 856     if (_t > 0xff) _t >>= 8;                    \
 857     if (_t & 0xf0) r -= 4;                      \
 858     if (_t & 0xf0) _t >>= 4;                    \
 859     if (_t & 0xc) r -= 2;                       \
 860     if (_t & 0xc) _t >>= 2;                     \
 861     if (_t & 0x2) r -= 1;                       \
 862   } while (0)
 863 #endif /* not _FP_W_TYPE_SIZE < 64 */
 864 #endif /* ndef __FP_CLZ */
 865
 866 #define _FP_DIV_HELP_imm(q, r, n, d)            \
 867   do {                                          \
 868     q = n / d, r = n % d;                       \
 869   } while (0)
 870
 871 #endif /* __MATH_EMU_OP_COMMON_H__ */