linux/include/math-emu/op-4.h
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   1/* Software floating-point emulation.
   2   Basic four-word fraction declaration and manipulation.
   3   Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
   4   This file is part of the GNU C Library.
   5   Contributed by Richard Henderson (rth@cygnus.com),
   6                  Jakub Jelinek (jj@ultra.linux.cz),
   7                  David S. Miller (davem@redhat.com) and
   8                  Peter Maydell (pmaydell@chiark.greenend.org.uk).
   9
  10   The GNU C Library is free software; you can redistribute it and/or
  11   modify it under the terms of the GNU Library General Public License as
  12   published by the Free Software Foundation; either version 2 of the
  13   License, or (at your option) any later version.
  14
  15   The GNU C Library is distributed in the hope that it will be useful,
  16   but WITHOUT ANY WARRANTY; without even the implied warranty of
  17   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  18   Library General Public License for more details.
  19
  20   You should have received a copy of the GNU Library General Public
  21   License along with the GNU C Library; see the file COPYING.LIB.  If
  22   not, write to the Free Software Foundation, Inc.,
  23   59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
  24
  25#ifndef __MATH_EMU_OP_4_H__
  26#define __MATH_EMU_OP_4_H__
  27
  28#define _FP_FRAC_DECL_4(X)      _FP_W_TYPE X##_f[4]
  29#define _FP_FRAC_COPY_4(D,S)                    \
  30  (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1],    \
  31   D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
  32#define _FP_FRAC_SET_4(X,I)     __FP_FRAC_SET_4(X, I)
  33#define _FP_FRAC_HIGH_4(X)      (X##_f[3])
  34#define _FP_FRAC_LOW_4(X)       (X##_f[0])
  35#define _FP_FRAC_WORD_4(X,w)    (X##_f[w])
  36
  37#define _FP_FRAC_SLL_4(X,N)                                             \
  38  do {                                                                  \
  39    _FP_I_TYPE _up, _down, _skip, _i;                                   \
  40    _skip = (N) / _FP_W_TYPE_SIZE;                                      \
  41    _up = (N) % _FP_W_TYPE_SIZE;                                        \
  42    _down = _FP_W_TYPE_SIZE - _up;                                      \
  43    if (!_up)                                                           \
  44      for (_i = 3; _i >= _skip; --_i)                                   \
  45        X##_f[_i] = X##_f[_i-_skip];                                    \
  46    else                                                                \
  47      {                                                                 \
  48        for (_i = 3; _i > _skip; --_i)                                  \
  49          X##_f[_i] = X##_f[_i-_skip] << _up                            \
  50                      | X##_f[_i-_skip-1] >> _down;                     \
  51        X##_f[_i--] = X##_f[0] << _up;                                  \
  52      }                                                                 \
  53    for (; _i >= 0; --_i)                                               \
  54      X##_f[_i] = 0;                                                    \
  55  } while (0)
  56
  57/* This one was broken too */
  58#define _FP_FRAC_SRL_4(X,N)                                             \
  59  do {                                                                  \
  60    _FP_I_TYPE _up, _down, _skip, _i;                                   \
  61    _skip = (N) / _FP_W_TYPE_SIZE;                                      \
  62    _down = (N) % _FP_W_TYPE_SIZE;                                      \
  63    _up = _FP_W_TYPE_SIZE - _down;                                      \
  64    if (!_down)                                                         \
  65      for (_i = 0; _i <= 3-_skip; ++_i)                                 \
  66        X##_f[_i] = X##_f[_i+_skip];                                    \
  67    else                                                                \
  68      {                                                                 \
  69        for (_i = 0; _i < 3-_skip; ++_i)                                \
  70          X##_f[_i] = X##_f[_i+_skip] >> _down                          \
  71                      | X##_f[_i+_skip+1] << _up;                       \
  72        X##_f[_i++] = X##_f[3] >> _down;                                \
  73      }                                                                 \
  74    for (; _i < 4; ++_i)                                                \
  75      X##_f[_i] = 0;                                                    \
  76  } while (0)
  77
  78
  79/* Right shift with sticky-lsb. 
  80 * What this actually means is that we do a standard right-shift,
  81 * but that if any of the bits that fall off the right hand side
  82 * were one then we always set the LSbit.
  83 */
  84#define _FP_FRAC_SRS_4(X,N,size)                                        \
  85  do {                                                                  \
  86    _FP_I_TYPE _up, _down, _skip, _i;                                   \
  87    _FP_W_TYPE _s;                                                      \
  88    _skip = (N) / _FP_W_TYPE_SIZE;                                      \
  89    _down = (N) % _FP_W_TYPE_SIZE;                                      \
  90    _up = _FP_W_TYPE_SIZE - _down;                                      \
  91    for (_s = _i = 0; _i < _skip; ++_i)                                 \
  92      _s |= X##_f[_i];                                                  \
  93    _s |= X##_f[_i] << _up;                                             \
  94/* s is now != 0 if we want to set the LSbit */                         \
  95    if (!_down)                                                         \
  96      for (_i = 0; _i <= 3-_skip; ++_i)                                 \
  97        X##_f[_i] = X##_f[_i+_skip];                                    \
  98    else                                                                \
  99      {                                                                 \
 100        for (_i = 0; _i < 3-_skip; ++_i)                                \
 101          X##_f[_i] = X##_f[_i+_skip] >> _down                          \
 102                      | X##_f[_i+_skip+1] << _up;                       \
 103        X##_f[_i++] = X##_f[3] >> _down;                                \
 104      }                                                                 \
 105    for (; _i < 4; ++_i)                                                \
 106      X##_f[_i] = 0;                                                    \
 107    /* don't fix the LSB until the very end when we're sure f[0] is stable */   \
 108    X##_f[0] |= (_s != 0);                                              \
 109  } while (0)
 110
 111#define _FP_FRAC_ADD_4(R,X,Y)                                           \
 112  __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],               \
 113                  X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 114                  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 115
 116#define _FP_FRAC_SUB_4(R,X,Y)                                           \
 117  __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],               \
 118                  X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 119                  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 120
 121#define _FP_FRAC_DEC_4(X,Y)                                             \
 122  __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 123                  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 124
 125#define _FP_FRAC_ADDI_4(X,I)                                            \
 126  __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
 127
 128#define _FP_ZEROFRAC_4  0,0,0,0
 129#define _FP_MINFRAC_4   0,0,0,1
 130#define _FP_MAXFRAC_4   (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
 131
 132#define _FP_FRAC_ZEROP_4(X)     ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
 133#define _FP_FRAC_NEGP_4(X)      ((_FP_WS_TYPE)X##_f[3] < 0)
 134#define _FP_FRAC_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
 135#define _FP_FRAC_CLEAR_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
 136
 137#define _FP_FRAC_EQ_4(X,Y)                              \
 138 (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1]          \
 139  && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
 140
 141#define _FP_FRAC_GT_4(X,Y)                              \
 142 (X##_f[3] > Y##_f[3] ||                                \
 143  (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 144   (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 145    (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0])       \
 146   ))                                                   \
 147  ))                                                    \
 148 )
 149
 150#define _FP_FRAC_GE_4(X,Y)                              \
 151 (X##_f[3] > Y##_f[3] ||                                \
 152  (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 153   (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 154    (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0])      \
 155   ))                                                   \
 156  ))                                                    \
 157 )
 158
 159
 160#define _FP_FRAC_CLZ_4(R,X)             \
 161  do {                                  \
 162    if (X##_f[3])                       \
 163    {                                   \
 164        __FP_CLZ(R,X##_f[3]);           \
 165    }                                   \
 166    else if (X##_f[2])                  \
 167    {                                   \
 168        __FP_CLZ(R,X##_f[2]);           \
 169        R += _FP_W_TYPE_SIZE;           \
 170    }                                   \
 171    else if (X##_f[1])                  \
 172    {                                   \
 173        __FP_CLZ(R,X##_f[2]);           \
 174        R += _FP_W_TYPE_SIZE*2;         \
 175    }                                   \
 176    else                                \
 177    {                                   \
 178        __FP_CLZ(R,X##_f[0]);           \
 179        R += _FP_W_TYPE_SIZE*3;         \
 180    }                                   \
 181  } while(0)
 182
 183
 184#define _FP_UNPACK_RAW_4(fs, X, val)                            \
 185  do {                                                          \
 186    union _FP_UNION_##fs _flo; _flo.flt = (val);                \
 187    X##_f[0] = _flo.bits.frac0;                                 \
 188    X##_f[1] = _flo.bits.frac1;                                 \
 189    X##_f[2] = _flo.bits.frac2;                                 \
 190    X##_f[3] = _flo.bits.frac3;                                 \
 191    X##_e  = _flo.bits.exp;                                     \
 192    X##_s  = _flo.bits.sign;                                    \
 193  } while (0)
 194
 195#define _FP_UNPACK_RAW_4_P(fs, X, val)                          \
 196  do {                                                          \
 197    union _FP_UNION_##fs *_flo =                                \
 198      (union _FP_UNION_##fs *)(val);                            \
 199                                                                \
 200    X##_f[0] = _flo->bits.frac0;                                \
 201    X##_f[1] = _flo->bits.frac1;                                \
 202    X##_f[2] = _flo->bits.frac2;                                \
 203    X##_f[3] = _flo->bits.frac3;                                \
 204    X##_e  = _flo->bits.exp;                                    \
 205    X##_s  = _flo->bits.sign;                                   \
 206  } while (0)
 207
 208#define _FP_PACK_RAW_4(fs, val, X)                              \
 209  do {                                                          \
 210    union _FP_UNION_##fs _flo;                                  \
 211    _flo.bits.frac0 = X##_f[0];                                 \
 212    _flo.bits.frac1 = X##_f[1];                                 \
 213    _flo.bits.frac2 = X##_f[2];                                 \
 214    _flo.bits.frac3 = X##_f[3];                                 \
 215    _flo.bits.exp   = X##_e;                                    \
 216    _flo.bits.sign  = X##_s;                                    \
 217    (val) = _flo.flt;                                           \
 218  } while (0)
 219
 220#define _FP_PACK_RAW_4_P(fs, val, X)                            \
 221  do {                                                          \
 222    union _FP_UNION_##fs *_flo =                                \
 223      (union _FP_UNION_##fs *)(val);                            \
 224                                                                \
 225    _flo->bits.frac0 = X##_f[0];                                \
 226    _flo->bits.frac1 = X##_f[1];                                \
 227    _flo->bits.frac2 = X##_f[2];                                \
 228    _flo->bits.frac3 = X##_f[3];                                \
 229    _flo->bits.exp   = X##_e;                                   \
 230    _flo->bits.sign  = X##_s;                                   \
 231  } while (0)
 232
 233/*
 234 * Multiplication algorithms:
 235 */
 236
 237/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 238
 239#define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit)                       \
 240  do {                                                                      \
 241    _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);          \
 242    _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f);          \
 243                                                                            \
 244    doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
 245    doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]);                                 \
 246    doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]);                                 \
 247    doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]);                                 \
 248    doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]);                                 \
 249    doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]);                                 \
 250    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 251                    _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0,                   \
 252                    0,0,_FP_FRAC_WORD_8(_z,1));                             \
 253    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 254                    _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0,                   \
 255                    _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 256                    _FP_FRAC_WORD_8(_z,1));                                 \
 257    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 258                    _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0,                   \
 259                    0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2));         \
 260    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 261                    _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0,                   \
 262                    _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 263                    _FP_FRAC_WORD_8(_z,2));                                 \
 264    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 265                    _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0,                   \
 266                    _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 267                    _FP_FRAC_WORD_8(_z,2));                                 \
 268    doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]);                                 \
 269    doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]);                                 \
 270    doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]);                                 \
 271    doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]);                                 \
 272    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 273                    _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0,                   \
 274                    0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3));         \
 275    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 276                    _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0,                   \
 277                    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 278                    _FP_FRAC_WORD_8(_z,3));                                 \
 279    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 280                    _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0,                   \
 281                    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 282                    _FP_FRAC_WORD_8(_z,3));                                 \
 283    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 284                    _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0,                   \
 285                    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 286                    _FP_FRAC_WORD_8(_z,3));                                 \
 287    doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]);                                 \
 288    doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]);                                 \
 289    doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]);                                 \
 290    doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]);                                 \
 291    doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]);                                 \
 292    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 293                    _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0,                   \
 294                    0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4));         \
 295    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 296                    _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0,                   \
 297                    _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 298                    _FP_FRAC_WORD_8(_z,4));                                 \
 299    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 300                    _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0,                   \
 301                    _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 302                    _FP_FRAC_WORD_8(_z,4));                                 \
 303    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 304                    _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0,                   \
 305                    0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5));         \
 306    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 307                    _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0,                   \
 308                    _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 309                    _FP_FRAC_WORD_8(_z,5));                                 \
 310    doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]);                                 \
 311    __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 312                    _b_f1,_b_f0,                                            \
 313                    _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6));           \
 314                                                                            \
 315    /* Normalize since we know where the msb of the multiplicands           \
 316       were (bit B), we know that the msb of the of the product is          \
 317       at either 2B or 2B-1.  */                                            \
 318    _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 319    __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 320                    _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 321  } while (0)
 322
 323#define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y)                              \
 324  do {                                                                      \
 325    _FP_FRAC_DECL_8(_z);                                                    \
 326                                                                            \
 327    mpn_mul_n(_z_f, _x_f, _y_f, 4);                                         \
 328                                                                            \
 329    /* Normalize since we know where the msb of the multiplicands           \
 330       were (bit B), we know that the msb of the of the product is          \
 331       at either 2B or 2B-1.  */                                            \
 332    _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 333    __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 334                    _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 335  } while (0)
 336
 337/*
 338 * Helper utility for _FP_DIV_MEAT_4_udiv:
 339 * pppp = m * nnn
 340 */
 341#define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0)                               \
 342  do {                                                                      \
 343    UWtype _t;                                                              \
 344    umul_ppmm(p1,p0,m,n0);                                                  \
 345    umul_ppmm(p2,_t,m,n1);                                                  \
 346    __FP_FRAC_ADDI_2(p2,p1,_t);                                             \
 347    umul_ppmm(p3,_t,m,n2);                                                  \
 348    __FP_FRAC_ADDI_2(p3,p2,_t);                                             \
 349  } while (0)
 350
 351/*
 352 * Division algorithms:
 353 */
 354
 355#define _FP_DIV_MEAT_4_udiv(fs, R, X, Y)                                    \
 356  do {                                                                      \
 357    int _i;                                                                 \
 358    _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m);                               \
 359    _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4);                                     \
 360    if (_FP_FRAC_GT_4(X, Y))                                                \
 361      {                                                                     \
 362        _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1);                        \
 363        _FP_FRAC_SRL_4(X, 1);                                               \
 364      }                                                                     \
 365    else                                                                    \
 366      R##_e--;                                                              \
 367                                                                            \
 368    /* Normalize, i.e. make the most significant bit of the                 \
 369       denominator set. */                                                  \
 370    _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs);                                 \
 371                                                                            \
 372    for (_i = 3; ; _i--)                                                    \
 373      {                                                                     \
 374        if (X##_f[3] == Y##_f[3])                                           \
 375          {                                                                 \
 376            /* This is a special case, not an optimization                  \
 377               (X##_f[3]/Y##_f[3] would not fit into UWtype).               \
 378               As X## is guaranteed to be < Y,  R##_f[_i] can be either     \
 379               (UWtype)-1 or (UWtype)-2.  */                                \
 380            R##_f[_i] = -1;                                                 \
 381            if (!_i)                                                        \
 382              break;                                                        \
 383            __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],         \
 384                            Y##_f[2], Y##_f[1], Y##_f[0], 0,                \
 385                            X##_f[2], X##_f[1], X##_f[0], _n_f[_i]);        \
 386            _FP_FRAC_SUB_4(X, Y, X);                                        \
 387            if (X##_f[3] > Y##_f[3])                                        \
 388              {                                                             \
 389                R##_f[_i] = -2;                                             \
 390                _FP_FRAC_ADD_4(X, Y, X);                                    \
 391              }                                                             \
 392          }                                                                 \
 393        else                                                                \
 394          {                                                                 \
 395            udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]);  \
 396            umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0],               \
 397                          R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]);         \
 398            X##_f[2] = X##_f[1];                                            \
 399            X##_f[1] = X##_f[0];                                            \
 400            X##_f[0] = _n_f[_i];                                            \
 401            if (_FP_FRAC_GT_4(_m, X))                                       \
 402              {                                                             \
 403                R##_f[_i]--;                                                \
 404                _FP_FRAC_ADD_4(X, Y, X);                                    \
 405                if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X))            \
 406                  {                                                         \
 407                    R##_f[_i]--;                                            \
 408                    _FP_FRAC_ADD_4(X, Y, X);                                \
 409                  }                                                         \
 410              }                                                             \
 411            _FP_FRAC_DEC_4(X, _m);                                          \
 412            if (!_i)                                                        \
 413              {                                                             \
 414                if (!_FP_FRAC_EQ_4(X, _m))                                  \
 415                  R##_f[0] |= _FP_WORK_STICKY;                              \
 416                break;                                                      \
 417              }                                                             \
 418          }                                                                 \
 419      }                                                                     \
 420  } while (0)
 421
 422
 423/*
 424 * Square root algorithms:
 425 * We have just one right now, maybe Newton approximation
 426 * should be added for those machines where division is fast.
 427 */
 428 
 429#define _FP_SQRT_MEAT_4(R, S, T, X, q)                          \
 430  do {                                                          \
 431    while (q)                                                   \
 432      {                                                         \
 433        T##_f[3] = S##_f[3] + q;                                \
 434        if (T##_f[3] <= X##_f[3])                               \
 435          {                                                     \
 436            S##_f[3] = T##_f[3] + q;                            \
 437            X##_f[3] -= T##_f[3];                               \
 438            R##_f[3] += q;                                      \
 439          }                                                     \
 440        _FP_FRAC_SLL_4(X, 1);                                   \
 441        q >>= 1;                                                \
 442      }                                                         \
 443    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 444    while (q)                                                   \
 445      {                                                         \
 446        T##_f[2] = S##_f[2] + q;                                \
 447        T##_f[3] = S##_f[3];                                    \
 448        if (T##_f[3] < X##_f[3] ||                              \
 449            (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2]))     \
 450          {                                                     \
 451            S##_f[2] = T##_f[2] + q;                            \
 452            S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 453            __FP_FRAC_DEC_2(X##_f[3], X##_f[2],                 \
 454                            T##_f[3], T##_f[2]);                \
 455            R##_f[2] += q;                                      \
 456          }                                                     \
 457        _FP_FRAC_SLL_4(X, 1);                                   \
 458        q >>= 1;                                                \
 459      }                                                         \
 460    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 461    while (q)                                                   \
 462      {                                                         \
 463        T##_f[1] = S##_f[1] + q;                                \
 464        T##_f[2] = S##_f[2];                                    \
 465        T##_f[3] = S##_f[3];                                    \
 466        if (T##_f[3] < X##_f[3] ||                              \
 467            (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] ||    \
 468             (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1]))))  \
 469          {                                                     \
 470            S##_f[1] = T##_f[1] + q;                            \
 471            S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 472            S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 473            __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1],       \
 474                            T##_f[3], T##_f[2], T##_f[1]);      \
 475            R##_f[1] += q;                                      \
 476          }                                                     \
 477        _FP_FRAC_SLL_4(X, 1);                                   \
 478        q >>= 1;                                                \
 479      }                                                         \
 480    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 481    while (q != _FP_WORK_ROUND)                                 \
 482      {                                                         \
 483        T##_f[0] = S##_f[0] + q;                                \
 484        T##_f[1] = S##_f[1];                                    \
 485        T##_f[2] = S##_f[2];                                    \
 486        T##_f[3] = S##_f[3];                                    \
 487        if (_FP_FRAC_GE_4(X,T))                                 \
 488          {                                                     \
 489            S##_f[0] = T##_f[0] + q;                            \
 490            S##_f[1] += (T##_f[0] > S##_f[0]);                  \
 491            S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 492            S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 493            _FP_FRAC_DEC_4(X, T);                               \
 494            R##_f[0] += q;                                      \
 495          }                                                     \
 496        _FP_FRAC_SLL_4(X, 1);                                   \
 497        q >>= 1;                                                \
 498      }                                                         \
 499    if (!_FP_FRAC_ZEROP_4(X))                                   \
 500      {                                                         \
 501        if (_FP_FRAC_GT_4(X,S))                                 \
 502          R##_f[0] |= _FP_WORK_ROUND;                           \
 503        R##_f[0] |= _FP_WORK_STICKY;                            \
 504      }                                                         \
 505  } while (0)
 506
 507
 508/*
 509 * Internals 
 510 */
 511
 512#define __FP_FRAC_SET_4(X,I3,I2,I1,I0)                                  \
 513  (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
 514
 515#ifndef __FP_FRAC_ADD_3
 516#define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 517  do {                                                          \
 518    int _c1, _c2;                                                       \
 519    r0 = x0 + y0;                                               \
 520    _c1 = r0 < x0;                                              \
 521    r1 = x1 + y1;                                               \
 522    _c2 = r1 < x1;                                              \
 523    r1 += _c1;                                                  \
 524    _c2 |= r1 < _c1;                                            \
 525    r2 = x2 + y2 + _c2;                                         \
 526  } while (0)
 527#endif
 528
 529#ifndef __FP_FRAC_ADD_4
 530#define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 531  do {                                                          \
 532    int _c1, _c2, _c3;                                          \
 533    r0 = x0 + y0;                                               \
 534    _c1 = r0 < x0;                                              \
 535    r1 = x1 + y1;                                               \
 536    _c2 = r1 < x1;                                              \
 537    r1 += _c1;                                                  \
 538    _c2 |= r1 < _c1;                                            \
 539    r2 = x2 + y2;                                               \
 540    _c3 = r2 < x2;                                              \
 541    r2 += _c2;                                                  \
 542    _c3 |= r2 < _c2;                                            \
 543    r3 = x3 + y3 + _c3;                                         \
 544  } while (0)
 545#endif
 546
 547#ifndef __FP_FRAC_SUB_3
 548#define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 549  do {                                                          \
 550    int _c1, _c2;                                                       \
 551    r0 = x0 - y0;                                               \
 552    _c1 = r0 > x0;                                              \
 553    r1 = x1 - y1;                                               \
 554    _c2 = r1 > x1;                                              \
 555    r1 -= _c1;                                                  \
 556    _c2 |= r1 > _c1;                                            \
 557    r2 = x2 - y2 - _c2;                                         \
 558  } while (0)
 559#endif
 560
 561#ifndef __FP_FRAC_SUB_4
 562#define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 563  do {                                                          \
 564    int _c1, _c2, _c3;                                          \
 565    r0 = x0 - y0;                                               \
 566    _c1 = r0 > x0;                                              \
 567    r1 = x1 - y1;                                               \
 568    _c2 = r1 > x1;                                              \
 569    r1 -= _c1;                                                  \
 570    _c2 |= r1 > _c1;                                            \
 571    r2 = x2 - y2;                                               \
 572    _c3 = r2 > x2;                                              \
 573    r2 -= _c2;                                                  \
 574    _c3 |= r2 > _c2;                                            \
 575    r3 = x3 - y3 - _c3;                                         \
 576  } while (0)
 577#endif
 578
 579#ifndef __FP_FRAC_DEC_3
 580#define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0)                              \
 581  do {                                                                  \
 582    UWtype _t0, _t1, _t2;                                               \
 583    _t0 = x0, _t1 = x1, _t2 = x2;                                       \
 584    __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0);            \
 585  } while (0)
 586#endif
 587
 588#ifndef __FP_FRAC_DEC_4
 589#define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0)                        \
 590  do {                                                                  \
 591    UWtype _t0, _t1, _t2, _t3;                                          \
 592    _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3;                             \
 593    __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0);         \
 594  } while (0)
 595#endif
 596
 597#ifndef __FP_FRAC_ADDI_4
 598#define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i)                                 \
 599  do {                                                                  \
 600    UWtype _t;                                                          \
 601    _t = ((x0 += i) < i);                                               \
 602    x1 += _t; _t = (x1 < _t);                                           \
 603    x2 += _t; _t = (x2 < _t);                                           \
 604    x3 += _t;                                                           \
 605  } while (0)
 606#endif
 607
 608/* Convert FP values between word sizes. This appears to be more
 609 * complicated than I'd have expected it to be, so these might be
 610 * wrong... These macros are in any case somewhat bogus because they
 611 * use information about what various FRAC_n variables look like 
 612 * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
 613 * the ones in op-2.h and op-1.h. 
 614 */
 615#define _FP_FRAC_CONV_1_4(dfs, sfs, D, S)                               \
 616   do {                                                                 \
 617     if (S##_c != FP_CLS_NAN)                                           \
 618       _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),   \
 619                          _FP_WFRACBITS_##sfs);                         \
 620     else                                                               \
 621       _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));  \
 622     D##_f = S##_f[0];                                                  \
 623  } while (0)
 624
 625#define _FP_FRAC_CONV_2_4(dfs, sfs, D, S)                               \
 626   do {                                                                 \
 627     if (S##_c != FP_CLS_NAN)                                           \
 628       _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),   \
 629                      _FP_WFRACBITS_##sfs);                             \
 630     else                                                               \
 631       _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));  \
 632     D##_f0 = S##_f[0];                                                 \
 633     D##_f1 = S##_f[1];                                                 \
 634  } while (0)
 635
 636/* Assembly/disassembly for converting to/from integral types.  
 637 * No shifting or overflow handled here.
 638 */
 639/* Put the FP value X into r, which is an integer of size rsize. */
 640#define _FP_FRAC_ASSEMBLE_4(r, X, rsize)                                \
 641  do {                                                                  \
 642    if (rsize <= _FP_W_TYPE_SIZE)                                       \
 643      r = X##_f[0];                                                     \
 644    else if (rsize <= 2*_FP_W_TYPE_SIZE)                                \
 645    {                                                                   \
 646      r = X##_f[1];                                                     \
 647      r <<= _FP_W_TYPE_SIZE;                                            \
 648      r += X##_f[0];                                                    \
 649    }                                                                   \
 650    else                                                                \
 651    {                                                                   \
 652      /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \
 653      /* and int == 4words as a single case.                     */     \
 654      r = X##_f[3];                                                     \
 655      r <<= _FP_W_TYPE_SIZE;                                            \
 656      r += X##_f[2];                                                    \
 657      r <<= _FP_W_TYPE_SIZE;                                            \
 658      r += X##_f[1];                                                    \
 659      r <<= _FP_W_TYPE_SIZE;                                            \
 660      r += X##_f[0];                                                    \
 661    }                                                                   \
 662  } while (0)
 663
 664/* "No disassemble Number Five!" */
 665/* move an integer of size rsize into X's fractional part. We rely on
 666 * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
 667 * having to mask the values we store into it.
 668 */
 669#define _FP_FRAC_DISASSEMBLE_4(X, r, rsize)                             \
 670  do {                                                                  \
 671    X##_f[0] = r;                                                       \
 672    X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);   \
 673    X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
 674    X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
 675  } while (0)
 676
 677#define _FP_FRAC_CONV_4_1(dfs, sfs, D, S)                               \
 678   do {                                                                 \
 679     D##_f[0] = S##_f;                                                  \
 680     D##_f[1] = D##_f[2] = D##_f[3] = 0;                                \
 681     _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));    \
 682   } while (0)
 683
 684#define _FP_FRAC_CONV_4_2(dfs, sfs, D, S)                               \
 685   do {                                                                 \
 686     D##_f[0] = S##_f0;                                                 \
 687     D##_f[1] = S##_f1;                                                 \
 688     D##_f[2] = D##_f[3] = 0;                                           \
 689     _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));    \
 690   } while (0)
 691
 692#endif
 693
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