linux/include/math-emu/op-common.h
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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 truly 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)                                 \
  37do {                                                                    \
  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)                           \
  90do {                                                            \
  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)                                \
 230do {                                                                         \
 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)                        \
 394do {                                                    \
 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)                        \
 457do {                                                    \
 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)                                          \
 587do {                                                                    \
 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__ */
 872
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