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op-common.h

#define _FP_DECL(wc, X)             \
  _FP_I_TYPE X##_c, X##_s, X##_e;   \
  _FP_FRAC_DECL_##wc(X)

/*
 * Finish truely unpacking a native fp value by classifying the kind
 * of fp value and normalizing both the exponent and the fraction.
 */

#define _FP_UNPACK_CANONICAL(fs, wc, X)                           \
do {                                                  \
  switch (X##_e)                                      \
  {                                                   \
  default:                                            \
    _FP_FRAC_HIGH_##wc(X) |= _FP_IMPLBIT_##fs;                    \
    _FP_FRAC_SLL_##wc(X, _FP_WORKBITS);                           \
    X##_e -= _FP_EXPBIAS_##fs;                                    \
    X##_c = FP_CLS_NORMAL;                                  \
    break;                                            \
                                                      \
  case 0:                                             \
    if (_FP_FRAC_ZEROP_##wc(X))                                   \
      X##_c = FP_CLS_ZERO;                                  \
    else                                              \
      {                                                     \
      /* a denormalized number */                           \
      _FP_I_TYPE _shift;                                    \
      _FP_FRAC_CLZ_##wc(_shift, X);                         \
      _shift -= _FP_FRACXBITS_##fs;                         \
      _FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS));                \
      X##_e -= _FP_EXPBIAS_##fs - 1 + _shift;                     \
      X##_c = FP_CLS_NORMAL;                                \
      }                                                     \
    break;                                            \
                                                      \
  case _FP_EXPMAX_##fs:                                     \
    if (_FP_FRAC_ZEROP_##wc(X))                                   \
      X##_c = FP_CLS_INF;                                   \
    else                                              \
      /* we don't differentiate between signaling and quiet nans */     \
      X##_c = FP_CLS_NAN;                                   \
    break;                                            \
  }                                                   \
} while (0)


/*
 * Before packing the bits back into the native fp result, take care
 * of such mundane things as rounding and overflow.  Also, for some
 * kinds of fp values, the original parts may not have been fully
 * extracted -- but that is ok, we can regenerate them now.
 */

#define _FP_PACK_CANONICAL(fs, wc, X)                       \
({int __ret = 0;                                \
  switch (X##_c)                                \
  {                                             \
  case FP_CLS_NORMAL:                                 \
    X##_e += _FP_EXPBIAS_##fs;                              \
    if (X##_e > 0)                                    \
      {                                               \
      __ret |= _FP_ROUND(wc, X);                      \
      if (_FP_FRAC_OVERP_##wc(fs, X))                       \
        {                                       \
          _FP_FRAC_SRL_##wc(X, (_FP_WORKBITS+1));           \
          X##_e++;                                    \
        }                                       \
      else                                      \
        _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);                 \
      if (X##_e >= _FP_EXPMAX_##fs)                   \
        {                                       \
          /* overflow to infinity */                        \
          X##_e = _FP_EXPMAX_##fs;                    \
          _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);          \
            __ret |= EFLAG_OVERFLOW;                        \
        }                                       \
      }                                               \
    else                                        \
      {                                               \
      /* we've got a denormalized number */                 \
      X##_e = -X##_e + 1;                             \
      if (X##_e <= _FP_WFRACBITS_##fs)                \
        {                                       \
          _FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs);  \
          _FP_FRAC_SLL_##wc(X, 1);                    \
          if (_FP_FRAC_OVERP_##wc(fs, X))             \
            {                                         \
              X##_e = 1;                              \
              _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);      \
            }                                         \
          else                                  \
            {                                         \
            X##_e = 0;                          \
            _FP_FRAC_SRL_##wc(X, _FP_WORKBITS+1);           \
                __ret |= EFLAG_UNDERFLOW;             \
            }                                         \
        }                                       \
      else                                      \
        {                                       \
          /* underflow to zero */                     \
          X##_e = 0;                                  \
          _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);          \
            __ret |= EFLAG_UNDERFLOW;                       \
        }                                       \
      }                                               \
    break;                                      \
                                                \
  case FP_CLS_ZERO:                                   \
    X##_e = 0;                                        \
    _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                \
    break;                                      \
                                                \
  case FP_CLS_INF:                                    \
    X##_e = _FP_EXPMAX_##fs;                          \
    _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                \
    break;                                      \
                                                \
  case FP_CLS_NAN:                                    \
    X##_e = _FP_EXPMAX_##fs;                          \
    if (!_FP_KEEPNANFRACP)                            \
      {                                               \
      _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs);               \
      X##_s = 0;                                \
      }                                               \
    else                                        \
      _FP_FRAC_HIGH_##wc(X) |= _FP_QNANBIT_##fs;            \
    break;                                      \
  }                                             \
  __ret;                                        \
})


/*
 * Main addition routine.  The input values should be cooked.
 */

#define _FP_ADD(fs, wc, R, X, Y)                                 \
do {                                                       \
  switch (_FP_CLS_COMBINE(X##_c, Y##_c))                         \
  {                                                        \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):                   \
    {                                                      \
      /* shift the smaller number so that its exponent matches the larger */ \
      _FP_I_TYPE diff = X##_e - Y##_e;                                 \
                                                           \
      if (diff < 0)                                              \
      {                                                    \
        diff = -diff;                                            \
        if (diff <= _FP_WFRACBITS_##fs)                          \
          _FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs);              \
        else if (!_FP_FRAC_ZEROP_##wc(X))                        \
          _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc);                      \
        else                                                     \
          _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);                     \
        R##_e = Y##_e;                                     \
      }                                                    \
      else                                                 \
      {                                                    \
        if (diff > 0)                                            \
          {                                                \
            if (diff <= _FP_WFRACBITS_##fs)                            \
              _FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs);                \
            else if (!_FP_FRAC_ZEROP_##wc(Y))                          \
              _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc);                  \
            else                                           \
              _FP_FRAC_SET_##wc(Y, _FP_ZEROFRAC_##wc);                 \
          }                                                \
        R##_e = X##_e;                                     \
      }                                                    \
                                                           \
      R##_c = FP_CLS_NORMAL;                                     \
                                                           \
      if (X##_s == Y##_s)                                        \
      {                                                    \
        R##_s = X##_s;                                     \
        _FP_FRAC_ADD_##wc(R, X, Y);                              \
        if (_FP_FRAC_OVERP_##wc(fs, R))                          \
          {                                                \
            _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);               \
            R##_e++;                                             \
          }                                                \
      }                                                    \
      else                                                 \
      {                                                    \
        R##_s = X##_s;                                     \
        _FP_FRAC_SUB_##wc(R, X, Y);                              \
        if (_FP_FRAC_ZEROP_##wc(R))                              \
          {                                                \
            /* return an exact zero */                           \
            if (FP_ROUNDMODE == FP_RND_MINF)                           \
            R##_s |= Y##_s;                                      \
            else                                           \
            R##_s &= Y##_s;                                      \
            R##_c = FP_CLS_ZERO;                                 \
          }                                                \
        else                                                     \
          {                                                \
            if (_FP_FRAC_NEGP_##wc(R))                           \
            {                                              \
              _FP_FRAC_SUB_##wc(R, Y, X);                        \
              R##_s = Y##_s;                               \
            }                                              \
                                                           \
            /* renormalize after subtraction */                  \
            _FP_FRAC_CLZ_##wc(diff, R);                          \
            diff -= _FP_WFRACXBITS_##fs;                         \
            if (diff)                                            \
            {                                              \
              R##_e -= diff;                               \
              _FP_FRAC_SLL_##wc(R, diff);                        \
            }                                              \
          }                                                \
      }                                                    \
      break;                                                     \
    }                                                      \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):                         \
    _FP_CHOOSENAN(fs, wc, R, X, Y);                              \
    break;                                                 \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):                     \
    R##_e = X##_e;                                               \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):                      \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):                         \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):                        \
    _FP_FRAC_COPY_##wc(R, X);                                    \
    R##_s = X##_s;                                               \
    R##_c = X##_c;                                               \
    break;                                                 \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):                     \
    R##_e = Y##_e;                                               \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):                      \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):                         \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):                        \
    _FP_FRAC_COPY_##wc(R, Y);                                    \
    R##_s = Y##_s;                                               \
    R##_c = Y##_c;                                               \
    break;                                                 \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):                         \
    if (X##_s != Y##_s)                                          \
      {                                                          \
      /* +INF + -INF => NAN */                                   \
      _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);                          \
      R##_s = X##_s ^ Y##_s;                                     \
      R##_c = FP_CLS_NAN;                                        \
      break;                                                     \
      }                                                          \
    /* FALLTHRU */                                               \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):                      \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):                        \
    R##_s = X##_s;                                               \
    R##_c = FP_CLS_INF;                                          \
    break;                                                 \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):                      \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):                        \
    R##_s = Y##_s;                                               \
    R##_c = FP_CLS_INF;                                          \
    break;                                                 \
                                                           \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):                       \
    /* make sure the sign is correct */                                \
    if (FP_ROUNDMODE == FP_RND_MINF)                                   \
      R##_s = X##_s | Y##_s;                                     \
    else                                                   \
      R##_s = X##_s & Y##_s;                                     \
    R##_c = FP_CLS_ZERO;                                         \
    break;                                                 \
                                                           \
  default:                                                 \
    abort();                                                     \
  }                                                        \
} while (0)


/*
 * Main negation routine.  FIXME -- when we care about setting exception
 * bits reliably, this will not do.  We should examine all of the fp classes.
 */

#define _FP_NEG(fs, wc, R, X)       \
  do {                              \
    _FP_FRAC_COPY_##wc(R, X);       \
    R##_c = X##_c;                  \
    R##_e = X##_e;                  \
    R##_s = 1 ^ X##_s;              \
  } while (0)


/*
 * Main multiplication routine.  The input values should be cooked.
 */

#define _FP_MUL(fs, wc, R, X, Y)                \
do {                                      \
  R##_s = X##_s ^ Y##_s;                        \
  switch (_FP_CLS_COMBINE(X##_c, Y##_c))        \
  {                                       \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):  \
    R##_c = FP_CLS_NORMAL;                      \
    R##_e = X##_e + Y##_e + 1;                        \
                                          \
    _FP_MUL_MEAT_##fs(R,X,Y);                   \
                                          \
    if (_FP_FRAC_OVERP_##wc(fs, R))             \
      _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs);    \
    else                                  \
      R##_e--;                                  \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):        \
    _FP_CHOOSENAN(fs, wc, R, X, Y);             \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):     \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):        \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):       \
    R##_s = X##_s;                              \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):        \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):     \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):    \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):      \
    _FP_FRAC_COPY_##wc(R, X);                   \
    R##_c = X##_c;                              \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):     \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):        \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):       \
    R##_s = Y##_s;                              \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):     \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):    \
    _FP_FRAC_COPY_##wc(R, Y);                   \
    R##_c = Y##_c;                              \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):       \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):       \
    R##_c = FP_CLS_NAN;                         \
    _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);           \
    break;                                \
                                          \
  default:                                \
    abort();                                    \
  }                                       \
} while (0)


/*
 * Main division routine.  The input values should be cooked.
 */

#define _FP_DIV(fs, wc, R, X, Y)                \
do {                                      \
  R##_s = X##_s ^ Y##_s;                        \
  switch (_FP_CLS_COMBINE(X##_c, Y##_c))        \
  {                                       \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL):  \
    R##_c = FP_CLS_NORMAL;                      \
    R##_e = X##_e - Y##_e;                      \
                                          \
    _FP_DIV_MEAT_##fs(R,X,Y);                   \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN):        \
    _FP_CHOOSENAN(fs, wc, R, X, Y);             \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL):     \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF):        \
  case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO):       \
    R##_s = X##_s;                              \
    _FP_FRAC_COPY_##wc(R, X);                   \
    R##_c = X##_c;                              \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN):     \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN):        \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN):       \
    R##_s = Y##_s;                              \
    _FP_FRAC_COPY_##wc(R, Y);                   \
    R##_c = Y##_c;                              \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF):     \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF):       \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL):    \
    R##_c = FP_CLS_ZERO;                        \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO):    \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO):       \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL):     \
    R##_c = FP_CLS_INF;                         \
    break;                                \
                                          \
  case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF):        \
  case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO):      \
    R##_c = FP_CLS_NAN;                         \
    _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs);           \
    break;                                \
                                          \
  default:                                \
    abort();                                    \
  }                                       \
} while (0)


/*
 * Main differential comparison routine.  The inputs should be raw not
 * cooked.  The return is -1,0,1 for normal values, 2 otherwise.
 */

#define _FP_CMP(fs, wc, ret, X, Y, un)                            \
  do {                                                      \
    /* NANs are unordered */                                \
    if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))           \
      || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))   \
      {                                                     \
      ret = un;                                       \
      }                                                     \
    else                                              \
      {                                                     \
        int __x_zero = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0;      \
        int __y_zero = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0;      \
                                                      \
      if (__x_zero && __y_zero)                             \
        ret = 0;                                      \
      else if (__x_zero)                                    \
        ret = Y##_s ? 1 : -1;                               \
      else if (__y_zero)                                    \
        ret = X##_s ? -1 : 1;                               \
      else if (X##_s != Y##_s)                              \
        ret = X##_s ? -1 : 1;                               \
      else if (X##_e > Y##_e)                               \
        ret = X##_s ? -1 : 1;                               \
      else if (X##_e < Y##_e)                               \
        ret = X##_s ? 1 : -1;                               \
      else if (_FP_FRAC_GT_##wc(X, Y))                      \
        ret = X##_s ? -1 : 1;                               \
      else if (_FP_FRAC_GT_##wc(Y, X))                      \
        ret = X##_s ? 1 : -1;                               \
      else                                            \
        ret = 0;                                      \
      }                                                     \
  } while (0)


/* Simplification for strict equality.  */

#define _FP_CMP_EQ(fs, wc, ret, X, Y)                               \
  do {                                                        \
    /* NANs are unordered */                                  \
    if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X))             \
      || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y)))     \
      {                                                       \
      ret = 1;                                          \
      }                                                       \
    else                                                \
      {                                                       \
      ret = !(X##_e == Y##_e                                  \
            && _FP_FRAC_EQ_##wc(X, Y)                         \
            && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
      }                                                       \
  } while (0)

/*
 * Main square root routine.  The input value should be cooked.
 */

#define _FP_SQRT(fs, wc, R, X)                                    \
do {                                                  \
    _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S);                 \
    _FP_W_TYPE q;                                     \
    switch (X##_c)                                          \
    {                                                 \
    case FP_CLS_NAN:                                        \
      R##_s = 0;                                      \
      R##_c = FP_CLS_NAN;                                   \
      _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc);              \
      break;                                                \
    case FP_CLS_INF:                                        \
      if (X##_s)                                      \
        {                                             \
          R##_s = 0;                                        \
          R##_c = FP_CLS_NAN; /* sNAN */                    \
        }                                             \
      else                                            \
        {                                             \
          R##_s = 0;                                        \
          R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */             \
        }                                             \
      break;                                                \
    case FP_CLS_ZERO:                                       \
      R##_s = X##_s;                                        \
      R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */                  \
      break;                                                \
    case FP_CLS_NORMAL:                                     \
      R##_s = 0;                                      \
        if (X##_s)                                          \
          {                                           \
          R##_c = FP_CLS_NAN; /* sNAN */                    \
          break;                                      \
          }                                           \
      R##_c = FP_CLS_NORMAL;                                \
        if (X##_e & 1)                                      \
          _FP_FRAC_SLL_##wc(X, 1);                          \
        R##_e = X##_e >> 1;                                 \
        _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc);                  \
        _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc);                  \
        q = _FP_OVERFLOW_##fs;                                    \
        _FP_FRAC_SLL_##wc(X, 1);                            \
        _FP_SQRT_MEAT_##wc(R, S, T, X, q);                        \
        _FP_FRAC_SRL_##wc(R, 1);                            \
    }                                                 \
  } while (0)

/*
 * Convert from FP to integer
 */

/* "When a NaN, infinity, large positive argument >= 2147483648.0, or
 * large negative argument <= -2147483649.0 is converted to an integer,
 * the invalid_current bit...should be set and fp_exception_IEEE_754 should
 * be raised. If the floating point invalid trap is disabled, no trap occurs
 * and a numerical result is generated: if the sign bit of the operand
 * is 0, the result is 2147483647; if the sign bit of the operand is 1,
 * the result is -2147483648."
 * Similarly for conversion to extended ints, except that the boundaries
 * are >= 2^63, <= -(2^63 + 1), and the results are 2^63 + 1 for s=0 and
 * -2^63 for s=1.
 * -- SPARC Architecture Manual V9, Appendix B, which specifies how
 * SPARCs resolve implementation dependencies in the IEEE-754 spec.
 * I don't believe that the code below follows this. I'm not even sure
 * it's right!
 * It doesn't cope with needing to convert to an n bit integer when there
 * is no n bit integer type. Fortunately gcc provides long long so this
 * isn't a problem for sparc32.
 * I have, however, fixed its NaN handling to conform as above.
 *         -- PMM 02/1998
 * NB: rsigned is not 'is r declared signed?' but 'should the value stored
 * in r be signed or unsigned?'. r is always(?) declared unsigned.
 * Comments below are mine, BTW -- PMM
 */
#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned)                  \
  do {                                                      \
    switch (X##_c)                                          \
      {                                                     \
      case FP_CLS_NORMAL:                                   \
      if (X##_e < 0)                                        \
        {                                             \
        /* case FP_CLS_NAN: see above! */                   \
        case FP_CLS_ZERO:                                   \
          r = 0;                                      \
        }                                             \
      else if (X##_e >= rsize - (rsigned != 0))             \
        {   /* overflow */                                  \
        case FP_CLS_NAN:                                              \
          case FP_CLS_INF:                                  \
          if (rsigned)                                \
            {                                               \
            r = 1;                                          \
            r <<= rsize - 1;                          \
            r -= 1 - X##_s;                                 \
            }                                               \
          else                                        \
            {                                               \
            r = 0;                                          \
            if (!X##_s)                               \
              r = ~r;                                 \
            }                                               \
        }                                             \
      else                                            \
        {                                             \
          if (_FP_W_TYPE_SIZE*wc < rsize)                   \
            {                                               \
            _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                  \
            r <<= X##_e - _FP_WFRACBITS_##fs;               \
            }                                               \
          else                                        \
            {                                               \
            if (X##_e >= _FP_WFRACBITS_##fs)                \
              _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1));\
            else                                      \
              _FP_FRAC_SRL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));\
            _FP_FRAC_ASSEMBLE_##wc(r, X, rsize);                  \
            }                                               \
          if (rsigned && X##_s)                             \
            r = -r;                                         \
        }                                             \
      break;                                                \
      }                                                     \
  } while (0)

#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype)                  \
  do {                                                      \
    if (r)                                            \
      {                                                     \
      X##_c = FP_CLS_NORMAL;                                \
                                                      \
      if ((X##_s = (r < 0)))                                \
        r = -r;                                       \
      /* Note that `r' is now considered unsigned, so we don't have     \
         to worry about the single signed overflow case.  */            \
                                                      \
      if (rsize <= _FP_W_TYPE_SIZE)                         \
        __FP_CLZ(X##_e, r);                                 \
      else                                            \
        __FP_CLZ_2(X##_e, (_FP_W_TYPE)(r >> _FP_W_TYPE_SIZE),     \
                 (_FP_W_TYPE)r);                            \
      if (rsize < _FP_W_TYPE_SIZE)                          \
            X##_e -= (_FP_W_TYPE_SIZE - rsize);             \
      X##_e = rsize - X##_e - 1;                            \
                                                      \
      if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e)      \
        __FP_FRAC_SRS_1(r, (X##_e - _FP_WFRACBITS_##fs), rsize);  \
      r &= ~((_FP_W_TYPE)1 << X##_e);                             \
      _FP_FRAC_DISASSEMBLE_##wc(X, ((unsigned rtype)r), rsize);   \
      _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1));           \
      }                                                     \
    else                                              \
      {                                                     \
      X##_c = FP_CLS_ZERO, X##_s = 0;                             \
      }                                                     \
  } while (0)


#define FP_CONV(dfs,sfs,dwc,swc,D,S)                  \
  do {                                          \
    _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S);      \
    D##_e = S##_e;                              \
    D##_c = S##_c;                              \
    D##_s = S##_s;                              \
  } while (0)

/*
 * Helper primitives.
 */

/* Count leading zeros in a word.  */

#ifndef __FP_CLZ
#if _FP_W_TYPE_SIZE < 64
/* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
#define __FP_CLZ(r, x)                    \
  do {                                    \
    _FP_W_TYPE _t = (x);                  \
    r = _FP_W_TYPE_SIZE - 1;              \
    if (_t > 0xffff) r -= 16;             \
    if (_t > 0xffff) _t >>= 16;                 \
    if (_t > 0xff) r -= 8;                \
    if (_t > 0xff) _t >>= 8;              \
    if (_t & 0xf0) r -= 4;                \
    if (_t & 0xf0) _t >>= 4;              \
    if (_t & 0xc) r -= 2;                 \
    if (_t & 0xc) _t >>= 2;               \
    if (_t & 0x2) r -= 1;                 \
  } while (0)
#else /* not _FP_W_TYPE_SIZE < 64 */
#define __FP_CLZ(r, x)                    \
  do {                                    \
    _FP_W_TYPE _t = (x);                  \
    r = _FP_W_TYPE_SIZE - 1;              \
    if (_t > 0xffffffff) r -= 32;         \
    if (_t > 0xffffffff) _t >>= 32;       \
    if (_t > 0xffff) r -= 16;             \
    if (_t > 0xffff) _t >>= 16;                 \
    if (_t > 0xff) r -= 8;                \
    if (_t > 0xff) _t >>= 8;              \
    if (_t & 0xf0) r -= 4;                \
    if (_t & 0xf0) _t >>= 4;              \
    if (_t & 0xc) r -= 2;                 \
    if (_t & 0xc) _t >>= 2;               \
    if (_t & 0x2) r -= 1;                 \
  } while (0)
#endif /* not _FP_W_TYPE_SIZE < 64 */
#endif /* ndef __FP_CLZ */

#define _FP_DIV_HELP_imm(q, r, n, d)            \
  do {                                    \
    q = n / d, r = n % d;                 \
  } while (0)


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