soft-fp/op-4.h

   1 /* Software floating-point emulation.
   2    Basic four-word fraction declaration and manipulation.
   3    Copyright (C) 1997,1998,1999,2006 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 Lesser General Public
  12    License as published by the Free Software Foundation; either
  13    version 2.1 of the 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    Lesser General Public License for more details.
  19
  20    You should have received a copy of the GNU Lesser General Public
  21    License along with the GNU C Library; if not, write to the Free
  22    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  23    02111-1307 USA.  */
  24
  25 #define _FP_FRAC_DECL_4(X)      _FP_W_TYPE X##_f[4]
  26 #define _FP_FRAC_COPY_4(D,S)                    \
  27   (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1],    \
  28    D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
  29 #define _FP_FRAC_SET_4(X,I)     __FP_FRAC_SET_4(X, I)
  30 #define _FP_FRAC_HIGH_4(X)      (X##_f[3])
  31 #define _FP_FRAC_LOW_4(X)       (X##_f[0])
  32 #define _FP_FRAC_WORD_4(X,w)    (X##_f[w])
  33
  34 #define _FP_FRAC_SLL_4(X,N)                                             \
  35   do {                                                                  \
  36     _FP_I_TYPE _up, _down, _skip, _i;                                   \
  37     _skip = (N) / _FP_W_TYPE_SIZE;                                      \
  38     _up = (N) % _FP_W_TYPE_SIZE;                                        \
  39     _down = _FP_W_TYPE_SIZE - _up;                                      \
  40     if (!_up)                                                           \
  41       for (_i = 3; _i >= _skip; --_i)                                   \
  42         X##_f[_i] = X##_f[_i-_skip];                                    \
  43     else                                                                \
  44       {                                                                 \
  45         for (_i = 3; _i > _skip; --_i)                                  \
  46           X##_f[_i] = X##_f[_i-_skip] << _up                            \
  47                       | X##_f[_i-_skip-1] >> _down;                     \
  48         X##_f[_i--] = X##_f[0] << _up;                                  \
  49       }                                                                 \
  50     for (; _i >= 0; --_i)                                               \
  51       X##_f[_i] = 0;                                                    \
  52   } while (0)
  53
  54 /* This one was broken too */
  55 #define _FP_FRAC_SRL_4(X,N)                                             \
  56   do {                                                                  \
  57     _FP_I_TYPE _up, _down, _skip, _i;                                   \
  58     _skip = (N) / _FP_W_TYPE_SIZE;                                      \
  59     _down = (N) % _FP_W_TYPE_SIZE;                                      \
  60     _up = _FP_W_TYPE_SIZE - _down;                                      \
  61     if (!_down)                                                         \
  62       for (_i = 0; _i <= 3-_skip; ++_i)                                 \
  63         X##_f[_i] = X##_f[_i+_skip];                                    \
  64     else                                                                \
  65       {                                                                 \
  66         for (_i = 0; _i < 3-_skip; ++_i)                                \
  67           X##_f[_i] = X##_f[_i+_skip] >> _down                          \
  68                       | X##_f[_i+_skip+1] << _up;                       \
  69         X##_f[_i++] = X##_f[3] >> _down;                                \
  70       }                                                                 \
  71     for (; _i < 4; ++_i)                                                \
  72       X##_f[_i] = 0;                                                    \
  73   } while (0)
  74
  75
  76 /* Right shift with sticky-lsb.
  77  * What this actually means is that we do a standard right-shift,
  78  * but that if any of the bits that fall off the right hand side
  79  * were one then we always set the LSbit.
  80  */
  81 #define _FP_FRAC_SRST_4(X,S,N,size)                     \
  82   do {                                                  \
  83     _FP_I_TYPE _up, _down, _skip, _i;                   \
  84     _FP_W_TYPE _s;                                      \
  85     _skip = (N) / _FP_W_TYPE_SIZE;                      \
  86     _down = (N) % _FP_W_TYPE_SIZE;                      \
  87     _up = _FP_W_TYPE_SIZE - _down;                      \
  88     for (_s = _i = 0; _i < _skip; ++_i)                 \
  89       _s |= X##_f[_i];                                  \
  90     if (!_down)                                         \
  91       for (_i = 0; _i <= 3-_skip; ++_i)                 \
  92         X##_f[_i] = X##_f[_i+_skip];                    \
  93     else                                                \
  94       {                                                 \
  95         _s |= X##_f[_i] << _up;                         \
  96         for (_i = 0; _i < 3-_skip; ++_i)                \
  97           X##_f[_i] = X##_f[_i+_skip] >> _down          \
  98                       | X##_f[_i+_skip+1] << _up;       \
  99         X##_f[_i++] = X##_f[3] >> _down;                \
 100       }                                                 \
 101     for (; _i < 4; ++_i)                                \
 102       X##_f[_i] = 0;                                    \
 103     S = (_s != 0);                                      \
 104   } while (0)
 105
 106 #define _FP_FRAC_SRS_4(X,N,size)                \
 107   do {                                          \
 108     int _sticky;                                \
 109     _FP_FRAC_SRST_4(X, _sticky, N, size);       \
 110     X##_f[0] |= _sticky;                        \
 111   } while (0)
 112
 113 #define _FP_FRAC_ADD_4(R,X,Y)                                           \
 114   __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],               \
 115                   X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 116                   Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 117
 118 #define _FP_FRAC_SUB_4(R,X,Y)                                           \
 119   __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],               \
 120                   X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 121                   Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 122
 123 #define _FP_FRAC_DEC_4(X,Y)                                             \
 124   __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 125                   Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 126
 127 #define _FP_FRAC_ADDI_4(X,I)                                            \
 128   __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
 129
 130 #define _FP_ZEROFRAC_4  0,0,0,0
 131 #define _FP_MINFRAC_4   0,0,0,1
 132 #define _FP_MAXFRAC_4   (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
 133
 134 #define _FP_FRAC_ZEROP_4(X)     ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
 135 #define _FP_FRAC_NEGP_4(X)      ((_FP_WS_TYPE)X##_f[3] < 0)
 136 #define _FP_FRAC_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
 137 #define _FP_FRAC_CLEAR_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
 138
 139 #define _FP_FRAC_EQ_4(X,Y)                              \
 140  (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1]          \
 141   && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
 142
 143 #define _FP_FRAC_GT_4(X,Y)                              \
 144  (X##_f[3] > Y##_f[3] ||                                \
 145   (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 146    (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 147     (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0])       \
 148    ))                                                   \
 149   ))                                                    \
 150  )
 151
 152 #define _FP_FRAC_GE_4(X,Y)                              \
 153  (X##_f[3] > Y##_f[3] ||                                \
 154   (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 155    (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 156     (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0])      \
 157    ))                                                   \
 158   ))                                                    \
 159  )
 160
 161
 162 #define _FP_FRAC_CLZ_4(R,X)             \
 163   do {                                  \
 164     if (X##_f[3])                       \
 165     {                                   \
 166         __FP_CLZ(R,X##_f[3]);           \
 167     }                                   \
 168     else if (X##_f[2])                  \
 169     {                                   \
 170         __FP_CLZ(R,X##_f[2]);           \
 171         R += _FP_W_TYPE_SIZE;           \
 172     }                                   \
 173     else if (X##_f[1])                  \
 174     {                                   \
 175         __FP_CLZ(R,X##_f[1]);           \
 176         R += _FP_W_TYPE_SIZE*2;         \
 177     }                                   \
 178     else                                \
 179     {                                   \
 180         __FP_CLZ(R,X##_f[0]);           \
 181         R += _FP_W_TYPE_SIZE*3;         \
 182     }                                   \
 183   } while(0)
 184
 185
 186 #define _FP_UNPACK_RAW_4(fs, X, val)                            \
 187   do {                                                          \
 188     union _FP_UNION_##fs _flo; _flo.flt = (val);                \
 189     X##_f[0] = _flo.bits.frac0;                                 \
 190     X##_f[1] = _flo.bits.frac1;                                 \
 191     X##_f[2] = _flo.bits.frac2;                                 \
 192     X##_f[3] = _flo.bits.frac3;                                 \
 193     X##_e  = _flo.bits.exp;                                     \
 194     X##_s  = _flo.bits.sign;                                    \
 195   } while (0)
 196
 197 #define _FP_UNPACK_RAW_4_P(fs, X, val)                          \
 198   do {                                                          \
 199     union _FP_UNION_##fs *_flo =                                \
 200       (union _FP_UNION_##fs *)(val);                            \
 201                                                                 \
 202     X##_f[0] = _flo->bits.frac0;                                \
 203     X##_f[1] = _flo->bits.frac1;                                \
 204     X##_f[2] = _flo->bits.frac2;                                \
 205     X##_f[3] = _flo->bits.frac3;                                \
 206     X##_e  = _flo->bits.exp;                                    \
 207     X##_s  = _flo->bits.sign;                                   \
 208   } while (0)
 209
 210 #define _FP_PACK_RAW_4(fs, val, X)                              \
 211   do {                                                          \
 212     union _FP_UNION_##fs _flo;                                  \
 213     _flo.bits.frac0 = X##_f[0];                                 \
 214     _flo.bits.frac1 = X##_f[1];                                 \
 215     _flo.bits.frac2 = X##_f[2];                                 \
 216     _flo.bits.frac3 = X##_f[3];                                 \
 217     _flo.bits.exp   = X##_e;                                    \
 218     _flo.bits.sign  = X##_s;                                    \
 219     (val) = _flo.flt;                                           \
 220   } while (0)
 221
 222 #define _FP_PACK_RAW_4_P(fs, val, X)                            \
 223   do {                                                          \
 224     union _FP_UNION_##fs *_flo =                                \
 225       (union _FP_UNION_##fs *)(val);                            \
 226                                                                 \
 227     _flo->bits.frac0 = X##_f[0];                                \
 228     _flo->bits.frac1 = X##_f[1];                                \
 229     _flo->bits.frac2 = X##_f[2];                                \
 230     _flo->bits.frac3 = X##_f[3];                                \
 231     _flo->bits.exp   = X##_e;                                   \
 232     _flo->bits.sign  = X##_s;                                   \
 233   } while (0)
 234
 235 /*
 236  * Multiplication algorithms:
 237  */
 238
 239 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 240
 241 #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit)                       \
 242   do {                                                                      \
 243     _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);          \
 244     _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f);          \
 245                                                                             \
 246     doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
 247     doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]);                                 \
 248     doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]);                                 \
 249     doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]);                                 \
 250     doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]);                                 \
 251     doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]);                                 \
 252     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 253                     _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0,                   \
 254                     0,0,_FP_FRAC_WORD_8(_z,1));                             \
 255     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 256                     _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0,                   \
 257                     _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 258                     _FP_FRAC_WORD_8(_z,1));                                 \
 259     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 260                     _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0,                   \
 261                     0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2));         \
 262     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 263                     _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0,                   \
 264                     _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 265                     _FP_FRAC_WORD_8(_z,2));                                 \
 266     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 267                     _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0,                   \
 268                     _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 269                     _FP_FRAC_WORD_8(_z,2));                                 \
 270     doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]);                                 \
 271     doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]);                                 \
 272     doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]);                                 \
 273     doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]);                                 \
 274     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 275                     _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0,                   \
 276                     0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3));         \
 277     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 278                     _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0,                   \
 279                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 280                     _FP_FRAC_WORD_8(_z,3));                                 \
 281     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 282                     _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0,                   \
 283                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 284                     _FP_FRAC_WORD_8(_z,3));                                 \
 285     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 286                     _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0,                   \
 287                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 288                     _FP_FRAC_WORD_8(_z,3));                                 \
 289     doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]);                                 \
 290     doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]);                                 \
 291     doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]);                                 \
 292     doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]);                                 \
 293     doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]);                                 \
 294     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 295                     _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0,                   \
 296                     0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4));         \
 297     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 298                     _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0,                   \
 299                     _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 300                     _FP_FRAC_WORD_8(_z,4));                                 \
 301     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 302                     _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0,                   \
 303                     _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 304                     _FP_FRAC_WORD_8(_z,4));                                 \
 305     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 306                     _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0,                   \
 307                     0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5));         \
 308     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 309                     _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0,                   \
 310                     _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 311                     _FP_FRAC_WORD_8(_z,5));                                 \
 312     doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]);                                 \
 313     __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 314                     _b_f1,_b_f0,                                            \
 315                     _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6));           \
 316                                                                             \
 317     /* Normalize since we know where the msb of the multiplicands           \
 318        were (bit B), we know that the msb of the of the product is          \
 319        at either 2B or 2B-1.  */                                            \
 320     _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 321     __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 322                     _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 323   } while (0)
 324
 325 #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y)                              \
 326   do {                                                                      \
 327     _FP_FRAC_DECL_8(_z);                                                    \
 328                                                                             \
 329     mpn_mul_n(_z_f, _x_f, _y_f, 4);                                         \
 330                                                                             \
 331     /* Normalize since we know where the msb of the multiplicands           \
 332        were (bit B), we know that the msb of the of the product is          \
 333        at either 2B or 2B-1.  */                                            \
 334     _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 335     __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 336                     _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 337   } while (0)
 338
 339 /*
 340  * Helper utility for _FP_DIV_MEAT_4_udiv:
 341  * pppp = m * nnn
 342  */
 343 #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0)                               \
 344   do {                                                                      \
 345     UWtype _t;                                                              \
 346     umul_ppmm(p1,p0,m,n0);                                                  \
 347     umul_ppmm(p2,_t,m,n1);                                                  \
 348     __FP_FRAC_ADDI_2(p2,p1,_t);                                             \
 349     umul_ppmm(p3,_t,m,n2);                                                  \
 350     __FP_FRAC_ADDI_2(p3,p2,_t);                                             \
 351   } while (0)
 352
 353 /*
 354  * Division algorithms:
 355  */
 356
 357 #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y)                                    \
 358   do {                                                                      \
 359     int _i;                                                                 \
 360     _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m);                               \
 361     _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4);                                     \
 362     if (_FP_FRAC_GT_4(X, Y))                                                \
 363       {                                                                     \
 364         _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1);                        \
 365         _FP_FRAC_SRL_4(X, 1);                                               \
 366       }                                                                     \
 367     else                                                                    \
 368       R##_e--;                                                              \
 369                                                                             \
 370     /* Normalize, i.e. make the most significant bit of the                 \
 371        denominator set. */                                                  \
 372     _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs);                                 \
 373                                                                             \
 374     for (_i = 3; ; _i--)                                                    \
 375       {                                                                     \
 376         if (X##_f[3] == Y##_f[3])                                           \
 377           {                                                                 \
 378             /* This is a special case, not an optimization                  \
 379                (X##_f[3]/Y##_f[3] would not fit into UWtype).               \
 380                As X## is guaranteed to be < Y,  R##_f[_i] can be either     \
 381                (UWtype)-1 or (UWtype)-2.  */                                \
 382             R##_f[_i] = -1;                                                 \
 383             if (!_i)                                                        \
 384               break;                                                        \
 385             __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],         \
 386                             Y##_f[2], Y##_f[1], Y##_f[0], 0,                \
 387                             X##_f[2], X##_f[1], X##_f[0], _n_f[_i]);        \
 388             _FP_FRAC_SUB_4(X, Y, X);                                        \
 389             if (X##_f[3] > Y##_f[3])                                        \
 390               {                                                             \
 391                 R##_f[_i] = -2;                                             \
 392                 _FP_FRAC_ADD_4(X, Y, X);                                    \
 393               }                                                             \
 394           }                                                                 \
 395         else                                                                \
 396           {                                                                 \
 397             udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]);  \
 398             umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0],               \
 399                           R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]);         \
 400             X##_f[2] = X##_f[1];                                            \
 401             X##_f[1] = X##_f[0];                                            \
 402             X##_f[0] = _n_f[_i];                                            \
 403             if (_FP_FRAC_GT_4(_m, X))                                       \
 404               {                                                             \
 405                 R##_f[_i]--;                                                \
 406                 _FP_FRAC_ADD_4(X, Y, X);                                    \
 407                 if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X))            \
 408                   {                                                         \
 409                     R##_f[_i]--;                                            \
 410                     _FP_FRAC_ADD_4(X, Y, X);                                \
 411                   }                                                         \
 412               }                                                             \
 413             _FP_FRAC_DEC_4(X, _m);                                          \
 414             if (!_i)                                                        \
 415               {                                                             \
 416                 if (!_FP_FRAC_EQ_4(X, _m))                                  \
 417                   R##_f[0] |= _FP_WORK_STICKY;                              \
 418                 break;                                                      \
 419               }                                                             \
 420           }                                                                 \
 421       }                                                                     \
 422   } while (0)
 423
 424
 425 /*
 426  * Square root algorithms:
 427  * We have just one right now, maybe Newton approximation
 428  * should be added for those machines where division is fast.
 429  */
 430
 431 #define _FP_SQRT_MEAT_4(R, S, T, X, q)                          \
 432   do {                                                          \
 433     while (q)                                                   \
 434       {                                                         \
 435         T##_f[3] = S##_f[3] + q;                                \
 436         if (T##_f[3] <= X##_f[3])                               \
 437           {                                                     \
 438             S##_f[3] = T##_f[3] + q;                            \
 439             X##_f[3] -= T##_f[3];                               \
 440             R##_f[3] += q;                                      \
 441           }                                                     \
 442         _FP_FRAC_SLL_4(X, 1);                                   \
 443         q >>= 1;                                                \
 444       }                                                         \
 445     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 446     while (q)                                                   \
 447       {                                                         \
 448         T##_f[2] = S##_f[2] + q;                                \
 449         T##_f[3] = S##_f[3];                                    \
 450         if (T##_f[3] < X##_f[3] ||                              \
 451             (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2]))     \
 452           {                                                     \
 453             S##_f[2] = T##_f[2] + q;                            \
 454             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 455             __FP_FRAC_DEC_2(X##_f[3], X##_f[2],                 \
 456                             T##_f[3], T##_f[2]);                \
 457             R##_f[2] += q;                                      \
 458           }                                                     \
 459         _FP_FRAC_SLL_4(X, 1);                                   \
 460         q >>= 1;                                                \
 461       }                                                         \
 462     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 463     while (q)                                                   \
 464       {                                                         \
 465         T##_f[1] = S##_f[1] + q;                                \
 466         T##_f[2] = S##_f[2];                                    \
 467         T##_f[3] = S##_f[3];                                    \
 468         if (T##_f[3] < X##_f[3] ||                              \
 469             (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] ||    \
 470              (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1]))))  \
 471           {                                                     \
 472             S##_f[1] = T##_f[1] + q;                            \
 473             S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 474             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 475             __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1],       \
 476                             T##_f[3], T##_f[2], T##_f[1]);      \
 477             R##_f[1] += q;                                      \
 478           }                                                     \
 479         _FP_FRAC_SLL_4(X, 1);                                   \
 480         q >>= 1;                                                \
 481       }                                                         \
 482     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 483     while (q != _FP_WORK_ROUND)                                 \
 484       {                                                         \
 485         T##_f[0] = S##_f[0] + q;                                \
 486         T##_f[1] = S##_f[1];                                    \
 487         T##_f[2] = S##_f[2];                                    \
 488         T##_f[3] = S##_f[3];                                    \
 489         if (_FP_FRAC_GE_4(X,T))                                 \
 490           {                                                     \
 491             S##_f[0] = T##_f[0] + q;                            \
 492             S##_f[1] += (T##_f[0] > S##_f[0]);                  \
 493             S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 494             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 495             _FP_FRAC_DEC_4(X, T);                               \
 496             R##_f[0] += q;                                      \
 497           }                                                     \
 498         _FP_FRAC_SLL_4(X, 1);                                   \
 499         q >>= 1;                                                \
 500       }                                                         \
 501     if (!_FP_FRAC_ZEROP_4(X))                                   \
 502       {                                                         \
 503         if (_FP_FRAC_GT_4(X,S))                                 \
 504           R##_f[0] |= _FP_WORK_ROUND;                           \
 505         R##_f[0] |= _FP_WORK_STICKY;                            \
 506       }                                                         \
 507   } while (0)
 508
 509
 510 /*
 511  * Internals
 512  */
 513
 514 #define __FP_FRAC_SET_4(X,I3,I2,I1,I0)                                  \
 515   (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
 516
 517 #ifndef __FP_FRAC_ADD_3
 518 #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 519   do {                                                          \
 520     _FP_W_TYPE _c1, _c2;                                        \
 521     r0 = x0 + y0;                                               \
 522     _c1 = r0 < x0;                                              \
 523     r1 = x1 + y1;                                               \
 524     _c2 = r1 < x1;                                              \
 525     r1 += _c1;                                                  \
 526     _c2 |= r1 < _c1;                                            \
 527     r2 = x2 + y2 + _c2;                                         \
 528   } while (0)
 529 #endif
 530
 531 #ifndef __FP_FRAC_ADD_4
 532 #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 533   do {                                                          \
 534     _FP_W_TYPE _c1, _c2, _c3;                                   \
 535     r0 = x0 + y0;                                               \
 536     _c1 = r0 < x0;                                              \
 537     r1 = x1 + y1;                                               \
 538     _c2 = r1 < x1;                                              \
 539     r1 += _c1;                                                  \
 540     _c2 |= r1 < _c1;                                            \
 541     r2 = x2 + y2;                                               \
 542     _c3 = r2 < x2;                                              \
 543     r2 += _c2;                                                  \
 544     _c3 |= r2 < _c2;                                            \
 545     r3 = x3 + y3 + _c3;                                         \
 546   } while (0)
 547 #endif
 548
 549 #ifndef __FP_FRAC_SUB_3
 550 #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 551   do {                                                          \
 552     _FP_W_TYPE _c1, _c2;                                        \
 553     r0 = x0 - y0;                                               \
 554     _c1 = r0 > x0;                                              \
 555     r1 = x1 - y1;                                               \
 556     _c2 = r1 > x1;                                              \
 557     r1 -= _c1;                                                  \
 558     _c2 |= r1 > _c1;                                            \
 559     r2 = x2 - y2 - _c2;                                         \
 560   } while (0)
 561 #endif
 562
 563 #ifndef __FP_FRAC_SUB_4
 564 #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 565   do {                                                          \
 566     _FP_W_TYPE _c1, _c2, _c3;                                   \
 567     r0 = x0 - y0;                                               \
 568     _c1 = r0 > x0;                                              \
 569     r1 = x1 - y1;                                               \
 570     _c2 = r1 > x1;                                              \
 571     r1 -= _c1;                                                  \
 572     _c2 |= r1 > _c1;                                            \
 573     r2 = x2 - y2;                                               \
 574     _c3 = r2 > x2;                                              \
 575     r2 -= _c2;                                                  \
 576     _c3 |= r2 > _c2;                                            \
 577     r3 = x3 - y3 - _c3;                                         \
 578   } while (0)
 579 #endif
 580
 581 #ifndef __FP_FRAC_DEC_3
 582 #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0)                              \
 583   do {                                                                  \
 584     UWtype _t0, _t1, _t2;                                               \
 585     _t0 = x0, _t1 = x1, _t2 = x2;                                       \
 586     __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0);            \
 587   } while (0)
 588 #endif
 589
 590 #ifndef __FP_FRAC_DEC_4
 591 #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0)                        \
 592   do {                                                                  \
 593     UWtype _t0, _t1, _t2, _t3;                                          \
 594     _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3;                             \
 595     __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0);         \
 596   } while (0)
 597 #endif
 598
 599 #ifndef __FP_FRAC_ADDI_4
 600 #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i)                                 \
 601   do {                                                                  \
 602     UWtype _t;                                                          \
 603     _t = ((x0 += i) < i);                                               \
 604     x1 += _t; _t = (x1 < _t);                                           \
 605     x2 += _t; _t = (x2 < _t);                                           \
 606     x3 += _t;                                                           \
 607   } while (0)
 608 #endif
 609
 610 /* Convert FP values between word sizes. This appears to be more
 611  * complicated than I'd have expected it to be, so these might be
 612  * wrong... These macros are in any case somewhat bogus because they
 613  * use information about what various FRAC_n variables look like
 614  * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
 615  * the ones in op-2.h and op-1.h.
 616  */
 617 #define _FP_FRAC_COPY_1_4(D, S)         (D##_f = S##_f[0])
 618
 619 #define _FP_FRAC_COPY_2_4(D, S)                 \
 620 do {                                            \
 621   D##_f0 = S##_f[0];                            \
 622   D##_f1 = S##_f[1];                            \
 623 } while (0)
 624
 625 /* Assembly/disassembly for converting to/from integral types.
 626  * No shifting or overflow handled here.
 627  */
 628 /* Put the FP value X into r, which is an integer of size rsize. */
 629 #define _FP_FRAC_ASSEMBLE_4(r, X, rsize)                                \
 630   do {                                                                  \
 631     if (rsize <= _FP_W_TYPE_SIZE)                                       \
 632       r = X##_f[0];                                                     \
 633     else if (rsize <= 2*_FP_W_TYPE_SIZE)                                \
 634     {                                                                   \
 635       r = X##_f[1];                                                     \
 636       r <<= _FP_W_TYPE_SIZE;                                            \
 637       r += X##_f[0];                                                    \
 638     }                                                                   \
 639     else                                                                \
 640     {                                                                   \
 641       /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \
 642       /* and int == 4words as a single case.                     */     \
 643       r = X##_f[3];                                                     \
 644       r <<= _FP_W_TYPE_SIZE;                                            \
 645       r += X##_f[2];                                                    \
 646       r <<= _FP_W_TYPE_SIZE;                                            \
 647       r += X##_f[1];                                                    \
 648       r <<= _FP_W_TYPE_SIZE;                                            \
 649       r += X##_f[0];                                                    \
 650     }                                                                   \
 651   } while (0)
 652
 653 /* "No disassemble Number Five!" */
 654 /* move an integer of size rsize into X's fractional part. We rely on
 655  * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
 656  * having to mask the values we store into it.
 657  */
 658 #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize)                             \
 659   do {                                                                  \
 660     X##_f[0] = r;                                                       \
 661     X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);   \
 662     X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
 663     X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
 664   } while (0);
 665
 666 #define _FP_FRAC_COPY_4_1(D, S)                 \
 667 do {                                            \
 668   D##_f[0] = S##_f;                             \
 669   D##_f[1] = D##_f[2] = D##_f[3] = 0;           \
 670 } while (0)
 671
 672 #define _FP_FRAC_COPY_4_2(D, S)                 \
 673 do {                                            \
 674   D##_f[0] = S##_f0;                            \
 675   D##_f[1] = S##_f1;                            \
 676   D##_f[2] = D##_f[3] = 0;                      \
 677 } while (0)