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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