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op-2.h

/* Software floating-point emulation.
   Basic two-word fraction declaration and manipulation.
   Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Richard Henderson (rth@cygnus.com),
              Jakub Jelinek (jj@ultra.linux.cz),
              David S. Miller (davem@redhat.com) and
              Peter Maydell (pmaydell@chiark.greenend.org.uk).

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#define _FP_FRAC_DECL_2(X)    _FP_W_TYPE X##_f0, X##_f1
#define _FP_FRAC_COPY_2(D,S)  (D##_f0 = S##_f0, D##_f1 = S##_f1)
#define _FP_FRAC_SET_2(X,I)   __FP_FRAC_SET_2(X, I)
#define _FP_FRAC_HIGH_2(X)    (X##_f1)
#define _FP_FRAC_LOW_2(X)     (X##_f0)
#define _FP_FRAC_WORD_2(X,w)  (X##_f##w)

#define _FP_FRAC_SLL_2(X,N)                                 \
  do {                                                      \
    if ((N) < _FP_W_TYPE_SIZE)                                    \
      {                                                     \
      if (__builtin_constant_p(N) && (N) == 1)              \
        {                                             \
          X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0);     \
          X##_f0 += X##_f0;                                 \
        }                                             \
      else                                            \
        {                                             \
          X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N));   \
          X##_f0 <<= (N);                                   \
        }                                             \
      }                                                     \
    else                                              \
      {                                                     \
      X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE);                 \
      X##_f0 = 0;                                     \
      }                                                     \
  } while (0)

#define _FP_FRAC_SRL_2(X,N)                                 \
  do {                                                      \
    if ((N) < _FP_W_TYPE_SIZE)                                    \
      {                                                     \
      X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
      X##_f1 >>= (N);                                       \
      }                                                     \
    else                                              \
      {                                                     \
      X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE);                 \
      X##_f1 = 0;                                     \
      }                                                     \
  } while (0)

/* Right shift with sticky-lsb.  */
#define _FP_FRAC_SRS_2(X,N,sz)                                    \
  do {                                                      \
    if ((N) < _FP_W_TYPE_SIZE)                                    \
      {                                                     \
      X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) |     \
              (__builtin_constant_p(N) && (N) == 1                \
               ? X##_f0 & 1                                 \
               : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0));      \
      X##_f1 >>= (N);                                       \
      }                                                     \
    else                                              \
      {                                                     \
      X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) |               \
              (((X##_f1 << (2*_FP_W_TYPE_SIZE - (N))) |           \
                X##_f0) != 0));                             \
      X##_f1 = 0;                                     \
      }                                                     \
  } while (0)

#define _FP_FRAC_ADDI_2(X,I)  \
  __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)

#define _FP_FRAC_ADD_2(R,X,Y) \
  __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_SUB_2(R,X,Y) \
  __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_DEC_2(X,Y)   \
  __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_CLZ_2(R,X)   \
  do {                        \
    if (X##_f1)               \
      __FP_CLZ(R,X##_f1);     \
    else                \
    {                   \
      __FP_CLZ(R,X##_f0);     \
      R += _FP_W_TYPE_SIZE;   \
    }                   \
  } while(0)

/* Predicates */
#define _FP_FRAC_NEGP_2(X)    ((_FP_WS_TYPE)X##_f1 < 0)
#define _FP_FRAC_ZEROP_2(X)   ((X##_f1 | X##_f0) == 0)
#define _FP_FRAC_OVERP_2(fs,X)      (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
#define _FP_FRAC_CLEAR_OVERP_2(fs,X)      (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
#define _FP_FRAC_EQ_2(X, Y)   (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
#define _FP_FRAC_GT_2(X, Y)   \
  (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 > Y##_f0)
#define _FP_FRAC_GE_2(X, Y)   \
  (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)

#define _FP_ZEROFRAC_2        0, 0
#define _FP_MINFRAC_2         0, 1
#define _FP_MAXFRAC_2         (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)

/*
 * Internals 
 */

#define __FP_FRAC_SET_2(X,I1,I0)    (X##_f0 = I0, X##_f1 = I1)

#define __FP_CLZ_2(R, xh, xl) \
  do {                        \
    if (xh)             \
      __FP_CLZ(R,xh);         \
    else                \
    {                   \
      __FP_CLZ(R,xl);         \
      R += _FP_W_TYPE_SIZE;   \
    }                   \
  } while(0)

#if 0

#ifndef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) \
  (xh += ((xl += i) < i))
#endif
#ifndef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
  (rh = xh + yh + ((rl = xl + yl) < xl))
#endif
#ifndef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
  (rh = xh - yh - ((rl = xl - yl) > xl))
#endif
#ifndef __FP_FRAC_DEC_2
#define __FP_FRAC_DEC_2(xh, xl, yh, yl)   \
  do {                              \
    UWtype _t = xl;                 \
    xh -= yh + ((xl -= yl) > _t);   \
  } while (0)
#endif

#else

#undef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
#undef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2             add_ssaaaa
#undef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2             sub_ddmmss
#undef __FP_FRAC_DEC_2
#define __FP_FRAC_DEC_2(xh, xl, yh, yl)   sub_ddmmss(xh, xl, xh, xl, yh, yl)

#endif

/*
 * Unpack the raw bits of a native fp value.  Do not classify or
 * normalize the data.
 */

#define _FP_UNPACK_RAW_2(fs, X, val)                  \
  do {                                          \
    union _FP_UNION_##fs _flo; _flo.flt = (val);      \
                                          \
    X##_f0 = _flo.bits.frac0;                   \
    X##_f1 = _flo.bits.frac1;                   \
    X##_e  = _flo.bits.exp;                     \
    X##_s  = _flo.bits.sign;                    \
  } while (0)

#define _FP_UNPACK_RAW_2_P(fs, X, val)                \
  do {                                          \
    union _FP_UNION_##fs *_flo =                \
      (union _FP_UNION_##fs *)(val);                  \
                                          \
    X##_f0 = _flo->bits.frac0;                        \
    X##_f1 = _flo->bits.frac1;                        \
    X##_e  = _flo->bits.exp;                    \
    X##_s  = _flo->bits.sign;                   \
  } while (0)


/*
 * Repack the raw bits of a native fp value.
 */

#define _FP_PACK_RAW_2(fs, val, X)              \
  do {                                          \
    union _FP_UNION_##fs _flo;                        \
                                          \
    _flo.bits.frac0 = X##_f0;                   \
    _flo.bits.frac1 = X##_f1;                   \
    _flo.bits.exp   = X##_e;                    \
    _flo.bits.sign  = X##_s;                    \
                                          \
    (val) = _flo.flt;                           \
  } while (0)

#define _FP_PACK_RAW_2_P(fs, val, X)                  \
  do {                                          \
    union _FP_UNION_##fs *_flo =                \
      (union _FP_UNION_##fs *)(val);                  \
                                          \
    _flo->bits.frac0 = X##_f0;                        \
    _flo->bits.frac1 = X##_f1;                        \
    _flo->bits.exp   = X##_e;                   \
    _flo->bits.sign  = X##_s;                   \
  } while (0)


/*
 * Multiplication algorithms:
 */

/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */

#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit)             \
  do {                                                      \
    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);      \
                                                      \
    doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
    doit(_b_f1, _b_f0, X##_f0, Y##_f1);                           \
    doit(_c_f1, _c_f0, X##_f1, Y##_f0);                           \
    doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
                                                      \
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),  \
                _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0,           \
                _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),      \
                _FP_FRAC_WORD_4(_z,1));                     \
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),  \
                _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0,           \
                _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),      \
                _FP_FRAC_WORD_4(_z,1));                     \
                                                      \
    /* Normalize since we know where the msb of the multiplicands \
       were (bit B), we know that the msb of the of the product is      \
       at either 2B or 2B-1.  */                            \
    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);                 \
    R##_f0 = _FP_FRAC_WORD_4(_z,0);                         \
    R##_f1 = _FP_FRAC_WORD_4(_z,1);                         \
  } while (0)

/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
   Do only 3 multiplications instead of four. This one is for machines
   where multiplication is much more expensive than subtraction.  */

#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit)        \
  do {                                                      \
    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);      \
    _FP_W_TYPE _d;                                          \
    int _c1, _c2;                                     \
                                                      \
    _b_f0 = X##_f0 + X##_f1;                                \
    _c1 = _b_f0 < X##_f0;                                   \
    _b_f1 = Y##_f0 + Y##_f1;                                \
    _c2 = _b_f1 < Y##_f0;                                   \
    doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0);              \
    doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1);   \
    doit(_c_f1, _c_f0, X##_f1, Y##_f1);                           \
                                                      \
    _b_f0 &= -_c2;                                          \
    _b_f1 &= -_c1;                                          \
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),  \
                _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d,        \
                0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \
    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
                 _b_f0);                                    \
    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
                 _b_f1);                                    \
    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),  \
                _FP_FRAC_WORD_4(_z,1),                      \
                0, _d, _FP_FRAC_WORD_4(_z,0));              \
    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),  \
                _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0);          \
    __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \
                _c_f1, _c_f0,                         \
                _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2));    \
                                                      \
    /* Normalize since we know where the msb of the multiplicands \
       were (bit B), we know that the msb of the of the product is      \
       at either 2B or 2B-1.  */                            \
    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);                 \
    R##_f0 = _FP_FRAC_WORD_4(_z,0);                         \
    R##_f1 = _FP_FRAC_WORD_4(_z,1);                         \
  } while (0)

#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y)                    \
  do {                                                      \
    _FP_FRAC_DECL_4(_z);                                    \
    _FP_W_TYPE _x[2], _y[2];                                \
    _x[0] = X##_f0; _x[1] = X##_f1;                         \
    _y[0] = Y##_f0; _y[1] = Y##_f1;                         \
                                                      \
    mpn_mul_n(_z_f, _x, _y, 2);                                   \
                                                      \
    /* Normalize since we know where the msb of the multiplicands \
       were (bit B), we know that the msb of the of the product is      \
       at either 2B or 2B-1.  */                            \
    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);                 \
    R##_f0 = _z_f[0];                                       \
    R##_f1 = _z_f[1];                                       \
  } while (0)

/* Do at most 120x120=240 bits multiplication using double floating
   point multiplication.  This is useful if floating point
   multiplication has much bigger throughput than integer multiply.
   It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
   between 106 and 120 only.  
   Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
   SETFETZ is a macro which will disable all FPU exceptions and set rounding
   towards zero,  RESETFE should optionally reset it back.  */

#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe)   \
  do {                                                            \
    static const double _const[] = {                                    \
      /* 2^-24 */ 5.9604644775390625e-08,                         \
      /* 2^-48 */ 3.5527136788005009e-15,                         \
      /* 2^-72 */ 2.1175823681357508e-22,                         \
      /* 2^-96 */ 1.2621774483536189e-29,                         \
      /* 2^28 */ 2.68435456e+08,                                  \
      /* 2^4 */ 1.600000e+01,                                     \
      /* 2^-20 */ 9.5367431640625e-07,                                  \
      /* 2^-44 */ 5.6843418860808015e-14,                         \
      /* 2^-68 */ 3.3881317890172014e-21,                         \
      /* 2^-92 */ 2.0194839173657902e-28,                         \
      /* 2^-116 */ 1.2037062152420224e-35};                             \
    double _a240, _b240, _c240, _d240, _e240, _f240,                    \
         _g240, _h240, _i240, _j240, _k240;                             \
    union { double d; UDItype i; } _l240, _m240, _n240, _o240,                \
                           _p240, _q240, _r240, _s240;                  \
    UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0;               \
                                                            \
    if (wfracbits < 106 || wfracbits > 120)                             \
      abort();                                                    \
                                                            \
    setfetz;                                                      \
                                                            \
    _e240 = (double)(long)(X##_f0 & 0xffffff);                          \
    _j240 = (double)(long)(Y##_f0 & 0xffffff);                          \
    _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff);                        \
    _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff);                        \
    _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48));     \
    _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48));     \
    _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff);                   \
    _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff);                   \
    _a240 = (double)(long)(X##_f1 >> 32);                         \
    _f240 = (double)(long)(Y##_f1 >> 32);                         \
    _e240 *= _const[3];                                           \
    _j240 *= _const[3];                                           \
    _d240 *= _const[2];                                           \
    _i240 *= _const[2];                                           \
    _c240 *= _const[1];                                           \
    _h240 *= _const[1];                                           \
    _b240 *= _const[0];                                           \
    _g240 *= _const[0];                                           \
    _s240.d =                                               _e240*_j240;\
    _r240.d =                                   _d240*_j240 + _e240*_i240;\
    _q240.d =                         _c240*_j240 + _d240*_i240 + _e240*_h240;\
    _p240.d =               _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
    _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
    _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240;          \
    _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240;                        \
    _l240.d = _a240*_g240 + _b240*_f240;                          \
    _k240 =   _a240*_f240;                                        \
    _r240.d += _s240.d;                                           \
    _q240.d += _r240.d;                                           \
    _p240.d += _q240.d;                                           \
    _o240.d += _p240.d;                                           \
    _n240.d += _o240.d;                                           \
    _m240.d += _n240.d;                                           \
    _l240.d += _m240.d;                                           \
    _k240 += _l240.d;                                             \
    _s240.d -= ((_const[10]+_s240.d)-_const[10]);                       \
    _r240.d -= ((_const[9]+_r240.d)-_const[9]);                         \
    _q240.d -= ((_const[8]+_q240.d)-_const[8]);                         \
    _p240.d -= ((_const[7]+_p240.d)-_const[7]);                         \
    _o240.d += _const[7];                                         \
    _n240.d += _const[6];                                         \
    _m240.d += _const[5];                                         \
    _l240.d += _const[4];                                         \
    if (_s240.d != 0.0) _y240 = 1;                                \
    if (_r240.d != 0.0) _y240 = 1;                                \
    if (_q240.d != 0.0) _y240 = 1;                                \
    if (_p240.d != 0.0) _y240 = 1;                                \
    _t240 = (DItype)_k240;                                        \
    _u240 = _l240.i;                                              \
    _v240 = _m240.i;                                              \
    _w240 = _n240.i;                                              \
    _x240 = _o240.i;                                              \
    R##_f1 = (_t240 << (128 - (wfracbits - 1)))                         \
           | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104));                 \
    R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1)))                  \
           | ((_v240 & 0xffffff) << (144 - (wfracbits - 1)))                  \
           | ((_w240 & 0xffffff) << (120 - (wfracbits - 1)))                  \
           | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96))             \
           | _y240;                                               \
    resetfe;                                                      \
  } while (0)

/*
 * Division algorithms:
 */

#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y)                    \
  do {                                                      \
    _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0;         \
    if (_FP_FRAC_GT_2(X, Y))                                \
      {                                                     \
      _n_f2 = X##_f1 >> 1;                                  \
      _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1;            \
      _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1);              \
      }                                                     \
    else                                              \
      {                                                     \
      R##_e--;                                        \
      _n_f2 = X##_f1;                                       \
      _n_f1 = X##_f0;                                       \
      _n_f0 = 0;                                      \
      }                                                     \
                                                      \
    /* Normalize, i.e. make the most significant bit of the             \
       denominator set. */                                  \
    _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs);                       \
                                                      \
    udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1);              \
    umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0);                      \
    _r_f0 = _n_f0;                                          \
    if (_FP_FRAC_GT_2(_m, _r))                                    \
      {                                                     \
      R##_f1--;                                       \
      _FP_FRAC_ADD_2(_r, Y, _r);                            \
      if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))          \
        {                                             \
          R##_f1--;                                         \
          _FP_FRAC_ADD_2(_r, Y, _r);                              \
        }                                             \
      }                                                     \
    _FP_FRAC_DEC_2(_r, _m);                                 \
                                                      \
    if (_r_f1 == Y##_f1)                                    \
      {                                                     \
      /* This is a special case, not an optimization              \
         (_r/Y##_f1 would not fit into UWtype).             \
         As _r is guaranteed to be < Y,  R##_f0 can be either           \
         (UWtype)-1 or (UWtype)-2.  But as we know what kind            \
         of bits it is (sticky, guard, round),  we don't care.    \
         We also don't care what the reminder is,  because the    \
         guard bit will be set anyway.  -jj */              \
      R##_f0 = -1;                                          \
      }                                                     \
    else                                              \
      {                                                     \
      udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1);            \
      umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0);              \
      _r_f0 = 0;                                      \
      if (_FP_FRAC_GT_2(_m, _r))                            \
        {                                             \
          R##_f0--;                                         \
          _FP_FRAC_ADD_2(_r, Y, _r);                              \
          if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))            \
            {                                               \
            R##_f0--;                                 \
            _FP_FRAC_ADD_2(_r, Y, _r);                      \
            }                                               \
        }                                             \
      if (!_FP_FRAC_EQ_2(_r, _m))                           \
        R##_f0 |= _FP_WORK_STICKY;                          \
      }                                                     \
  } while (0)


#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y)                           \
  do {                                                      \
    _FP_W_TYPE _x[4], _y[2], _z[4];                         \
    _y[0] = Y##_f0; _y[1] = Y##_f1;                         \
    _x[0] = _x[3] = 0;                                      \
    if (_FP_FRAC_GT_2(X, Y))                                \
      {                                                     \
      R##_e++;                                        \
      _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) |     \
             X##_f1 >> (_FP_W_TYPE_SIZE -                   \
                      (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \
      _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \
      }                                                     \
    else                                              \
      {                                                     \
      _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \
             X##_f1 >> (_FP_W_TYPE_SIZE -                   \
                      (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE)));   \
      _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE);   \
      }                                                     \
                                                      \
    (void) mpn_divrem (_z, 0, _x, 4, _y, 2);                      \
    R##_f1 = _z[1];                                         \
    R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0);                      \
  } while (0)


/*
 * Square root algorithms:
 * We have just one right now, maybe Newton approximation
 * should be added for those machines where division is fast.
 */
 
#define _FP_SQRT_MEAT_2(R, S, T, X, q)                \
  do {                                          \
    while (q)                                   \
      {                                         \
      T##_f1 = S##_f1 + q;                      \
      if (T##_f1 <= X##_f1)                     \
        {                                 \
          S##_f1 = T##_f1 + q;                  \
          X##_f1 -= T##_f1;                     \
          R##_f1 += q;                    \
        }                                 \
      _FP_FRAC_SLL_2(X, 1);                     \
      q >>= 1;                            \
      }                                         \
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);       \
    while (q != _FP_WORK_ROUND)                       \
      {                                         \
      T##_f0 = S##_f0 + q;                      \
      T##_f1 = S##_f1;                    \
      if (T##_f1 < X##_f1 ||                    \
          (T##_f1 == X##_f1 && T##_f0 <= X##_f0))     \
        {                                 \
          S##_f0 = T##_f0 + q;                  \
          S##_f1 += (T##_f0 > S##_f0);          \
          _FP_FRAC_DEC_2(X, T);                 \
          R##_f0 += q;                    \
        }                                 \
      _FP_FRAC_SLL_2(X, 1);                     \
      q >>= 1;                            \
      }                                         \
    if (X##_f0 | X##_f1)                        \
      {                                         \
      if (S##_f1 < X##_f1 ||                    \
          (S##_f1 == X##_f1 && S##_f0 < X##_f0))      \
        R##_f0 |= _FP_WORK_ROUND;               \
      R##_f0 |= _FP_WORK_STICKY;                \
      }                                         \
  } while (0)


/*
 * Assembly/disassembly for converting to/from integral types.  
 * No shifting or overflow handled here.
 */

#define _FP_FRAC_ASSEMBLE_2(r, X, rsize)  \
  do {                                    \
    if (rsize <= _FP_W_TYPE_SIZE)         \
      r = X##_f0;                   \
    else                            \
      {                                   \
      r = X##_f1;                   \
      r <<= _FP_W_TYPE_SIZE;              \
      r += X##_f0;                        \
      }                                   \
  } while (0)

#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize)                       \
  do {                                                      \
    X##_f0 = r;                                             \
    X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);     \
  } while (0)

/*
 * Convert FP values between word sizes
 */

#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S)                   \
  do {                                                      \
    if (S##_c != FP_CLS_NAN)                                \
      _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),    \
                 _FP_WFRACBITS_##sfs);                      \
    else                                              \
      _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));   \
    D##_f = S##_f0;                                         \
  } while (0)

#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S)                   \
  do {                                                      \
    D##_f0 = S##_f;                                         \
    D##_f1 = 0;                                             \
    _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));     \
  } while (0)


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