soft-fp/op-4.h

   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 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_SRS_4(X,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     _s |= X##_f[_i] << _up;                                             \
  91 /* s is now != 0 if we want to set the LSbit */                         \
  92     if (!_down)                                                         \
  93       for (_i = 0; _i <= 3-_skip; ++_i)                                 \
  94         X##_f[_i] = X##_f[_i+_skip];                                    \
  95     else                                                                \
  96       {                                                                 \
  97         for (_i = 0; _i < 3-_skip; ++_i)                                \
  98           X##_f[_i] = X##_f[_i+_skip] >> _down                          \
  99                       | X##_f[_i+_skip+1] << _up;                       \
 100         X##_f[_i++] = X##_f[3] >> _down;                                \
 101       }                                                                 \
 102     for (; _i < 4; ++_i)                                                \
 103       X##_f[_i] = 0;                                                    \
 104     /* don't fix the LSB until the very end when we're sure f[0] is stable */   \
 105     X##_f[0] |= (_s != 0);                                              \
 106   } while (0)
 107
 108 #define _FP_FRAC_ADD_4(R,X,Y)                                           \
 109   __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],               \
 110                   X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 111                   Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 112
 113 #define _FP_FRAC_SUB_4(R,X,Y)                                           \
 114   __FP_FRAC_SUB_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_DEC_4(X,Y)                                             \
 119   __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],               \
 120                   Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
 121
 122 #define _FP_FRAC_ADDI_4(X,I)                                            \
 123   __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
 124
 125 #define _FP_ZEROFRAC_4  0,0,0,0
 126 #define _FP_MINFRAC_4   0,0,0,1
 127 #define _FP_MAXFRAC_4   (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
 128
 129 #define _FP_FRAC_ZEROP_4(X)     ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
 130 #define _FP_FRAC_NEGP_4(X)      ((_FP_WS_TYPE)X##_f[3] < 0)
 131 #define _FP_FRAC_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
 132 #define _FP_FRAC_CLEAR_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
 133
 134 #define _FP_FRAC_EQ_4(X,Y)                              \
 135  (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1]          \
 136   && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
 137
 138 #define _FP_FRAC_GT_4(X,Y)                              \
 139  (X##_f[3] > Y##_f[3] ||                                \
 140   (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 141    (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 142     (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0])       \
 143    ))                                                   \
 144   ))                                                    \
 145  )
 146
 147 #define _FP_FRAC_GE_4(X,Y)                              \
 148  (X##_f[3] > Y##_f[3] ||                                \
 149   (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||      \
 150    (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||     \
 151     (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0])      \
 152    ))                                                   \
 153   ))                                                    \
 154  )
 155
 156
 157 #define _FP_FRAC_CLZ_4(R,X)             \
 158   do {                                  \
 159     if (X##_f[3])                       \
 160     {                                   \
 161         __FP_CLZ(R,X##_f[3]);           \
 162     }                                   \
 163     else if (X##_f[2])                  \
 164     {                                   \
 165         __FP_CLZ(R,X##_f[2]);           \
 166         R += _FP_W_TYPE_SIZE;           \
 167     }                                   \
 168     else if (X##_f[1])                  \
 169     {                                   \
 170         __FP_CLZ(R,X##_f[1]);           \
 171         R += _FP_W_TYPE_SIZE*2;         \
 172     }                                   \
 173     else                                \
 174     {                                   \
 175         __FP_CLZ(R,X##_f[0]);           \
 176         R += _FP_W_TYPE_SIZE*3;         \
 177     }                                   \
 178   } while(0)
 179
 180
 181 #define _FP_UNPACK_RAW_4(fs, X, val)                            \
 182   do {                                                          \
 183     union _FP_UNION_##fs _flo; _flo.flt = (val);                \
 184     X##_f[0] = _flo.bits.frac0;                                 \
 185     X##_f[1] = _flo.bits.frac1;                                 \
 186     X##_f[2] = _flo.bits.frac2;                                 \
 187     X##_f[3] = _flo.bits.frac3;                                 \
 188     X##_e  = _flo.bits.exp;                                     \
 189     X##_s  = _flo.bits.sign;                                    \
 190   } while (0)
 191
 192 #define _FP_UNPACK_RAW_4_P(fs, X, val)                          \
 193   do {                                                          \
 194     union _FP_UNION_##fs *_flo =                                \
 195       (union _FP_UNION_##fs *)(val);                            \
 196                                                                 \
 197     X##_f[0] = _flo->bits.frac0;                                \
 198     X##_f[1] = _flo->bits.frac1;                                \
 199     X##_f[2] = _flo->bits.frac2;                                \
 200     X##_f[3] = _flo->bits.frac3;                                \
 201     X##_e  = _flo->bits.exp;                                    \
 202     X##_s  = _flo->bits.sign;                                   \
 203   } while (0)
 204
 205 #define _FP_PACK_RAW_4(fs, val, X)                              \
 206   do {                                                          \
 207     union _FP_UNION_##fs _flo;                                  \
 208     _flo.bits.frac0 = X##_f[0];                                 \
 209     _flo.bits.frac1 = X##_f[1];                                 \
 210     _flo.bits.frac2 = X##_f[2];                                 \
 211     _flo.bits.frac3 = X##_f[3];                                 \
 212     _flo.bits.exp   = X##_e;                                    \
 213     _flo.bits.sign  = X##_s;                                    \
 214     (val) = _flo.flt;                                           \
 215   } while (0)
 216
 217 #define _FP_PACK_RAW_4_P(fs, val, X)                            \
 218   do {                                                          \
 219     union _FP_UNION_##fs *_flo =                                \
 220       (union _FP_UNION_##fs *)(val);                            \
 221                                                                 \
 222     _flo->bits.frac0 = X##_f[0];                                \
 223     _flo->bits.frac1 = X##_f[1];                                \
 224     _flo->bits.frac2 = X##_f[2];                                \
 225     _flo->bits.frac3 = X##_f[3];                                \
 226     _flo->bits.exp   = X##_e;                                   \
 227     _flo->bits.sign  = X##_s;                                   \
 228   } while (0)
 229
 230 /*
 231  * Multiplication algorithms:
 232  */
 233
 234 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 235
 236 #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit)                       \
 237   do {                                                                      \
 238     _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);          \
 239     _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f);          \
 240                                                                             \
 241     doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
 242     doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]);                                 \
 243     doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]);                                 \
 244     doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]);                                 \
 245     doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]);                                 \
 246     doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]);                                 \
 247     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 248                     _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0,                   \
 249                     0,0,_FP_FRAC_WORD_8(_z,1));                             \
 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,_c_f1,_c_f0,                   \
 252                     _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),            \
 253                     _FP_FRAC_WORD_8(_z,1));                                 \
 254     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 255                     _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0,                   \
 256                     0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2));         \
 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,_e_f1,_e_f0,                   \
 259                     _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 260                     _FP_FRAC_WORD_8(_z,2));                                 \
 261     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 262                     _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0,                   \
 263                     _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),            \
 264                     _FP_FRAC_WORD_8(_z,2));                                 \
 265     doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]);                                 \
 266     doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]);                                 \
 267     doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]);                                 \
 268     doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]);                                 \
 269     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 270                     _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0,                   \
 271                     0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3));         \
 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,_c_f1,_c_f0,                   \
 274                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 275                     _FP_FRAC_WORD_8(_z,3));                                 \
 276     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 277                     _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0,                   \
 278                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 279                     _FP_FRAC_WORD_8(_z,3));                                 \
 280     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 281                     _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0,                   \
 282                     _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),            \
 283                     _FP_FRAC_WORD_8(_z,3));                                 \
 284     doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]);                                 \
 285     doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]);                                 \
 286     doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]);                                 \
 287     doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]);                                 \
 288     doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]);                                 \
 289     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 290                     _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0,                   \
 291                     0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4));         \
 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,_c_f1,_c_f0,                   \
 294                     _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 295                     _FP_FRAC_WORD_8(_z,4));                                 \
 296     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 297                     _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0,                   \
 298                     _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),            \
 299                     _FP_FRAC_WORD_8(_z,4));                                 \
 300     __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 301                     _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0,                   \
 302                     0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5));         \
 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,_f_f1,_f_f0,                   \
 305                     _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 306                     _FP_FRAC_WORD_8(_z,5));                                 \
 307     doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]);                                 \
 308     __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),            \
 309                     _b_f1,_b_f0,                                            \
 310                     _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6));           \
 311                                                                             \
 312     /* Normalize since we know where the msb of the multiplicands           \
 313        were (bit B), we know that the msb of the of the product is          \
 314        at either 2B or 2B-1.  */                                            \
 315     _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 316     __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 317                     _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 318   } while (0)
 319
 320 #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y)                              \
 321   do {                                                                      \
 322     _FP_FRAC_DECL_8(_z);                                                    \
 323                                                                             \
 324     mpn_mul_n(_z_f, _x_f, _y_f, 4);                                         \
 325                                                                             \
 326     /* Normalize since we know where the msb of the multiplicands           \
 327        were (bit B), we know that the msb of the of the product is          \
 328        at either 2B or 2B-1.  */                                            \
 329     _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);                           \
 330     __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),        \
 331                     _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));          \
 332   } while (0)
 333
 334 /*
 335  * Helper utility for _FP_DIV_MEAT_4_udiv:
 336  * pppp = m * nnn
 337  */
 338 #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0)                               \
 339   do {                                                                      \
 340     UWtype _t;                                                              \
 341     umul_ppmm(p1,p0,m,n0);                                                  \
 342     umul_ppmm(p2,_t,m,n1);                                                  \
 343     __FP_FRAC_ADDI_2(p2,p1,_t);                                             \
 344     umul_ppmm(p3,_t,m,n2);                                                  \
 345     __FP_FRAC_ADDI_2(p3,p2,_t);                                             \
 346   } while (0)
 347
 348 /*
 349  * Division algorithms:
 350  */
 351
 352 #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y)                                    \
 353   do {                                                                      \
 354     int _i;                                                                 \
 355     _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m);                               \
 356     _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4);                                     \
 357     if (_FP_FRAC_GT_4(X, Y))                                                \
 358       {                                                                     \
 359         _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1);                        \
 360         _FP_FRAC_SRL_4(X, 1);                                               \
 361       }                                                                     \
 362     else                                                                    \
 363       R##_e--;                                                              \
 364                                                                             \
 365     /* Normalize, i.e. make the most significant bit of the                 \
 366        denominator set. */                                                  \
 367     _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs);                                 \
 368                                                                             \
 369     for (_i = 3; ; _i--)                                                    \
 370       {                                                                     \
 371         if (X##_f[3] == Y##_f[3])                                           \
 372           {                                                                 \
 373             /* This is a special case, not an optimization                  \
 374                (X##_f[3]/Y##_f[3] would not fit into UWtype).               \
 375                As X## is guaranteed to be < Y,  R##_f[_i] can be either     \
 376                (UWtype)-1 or (UWtype)-2.  */                                \
 377             R##_f[_i] = -1;                                                 \
 378             if (!_i)                                                        \
 379               break;                                                        \
 380             __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],         \
 381                             Y##_f[2], Y##_f[1], Y##_f[0], 0,                \
 382                             X##_f[2], X##_f[1], X##_f[0], _n_f[_i]);        \
 383             _FP_FRAC_SUB_4(X, Y, X);                                        \
 384             if (X##_f[3] > Y##_f[3])                                        \
 385               {                                                             \
 386                 R##_f[_i] = -2;                                             \
 387                 _FP_FRAC_ADD_4(X, Y, X);                                    \
 388               }                                                             \
 389           }                                                                 \
 390         else                                                                \
 391           {                                                                 \
 392             udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]);  \
 393             umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0],               \
 394                           R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]);         \
 395             X##_f[2] = X##_f[1];                                            \
 396             X##_f[1] = X##_f[0];                                            \
 397             X##_f[0] = _n_f[_i];                                            \
 398             if (_FP_FRAC_GT_4(_m, X))                                       \
 399               {                                                             \
 400                 R##_f[_i]--;                                                \
 401                 _FP_FRAC_ADD_4(X, Y, X);                                    \
 402                 if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X))            \
 403                   {                                                         \
 404                     R##_f[_i]--;                                            \
 405                     _FP_FRAC_ADD_4(X, Y, X);                                \
 406                   }                                                         \
 407               }                                                             \
 408             _FP_FRAC_DEC_4(X, _m);                                          \
 409             if (!_i)                                                        \
 410               {                                                             \
 411                 if (!_FP_FRAC_EQ_4(X, _m))                                  \
 412                   R##_f[0] |= _FP_WORK_STICKY;                              \
 413                 break;                                                      \
 414               }                                                             \
 415           }                                                                 \
 416       }                                                                     \
 417   } while (0)
 418
 419
 420 /*
 421  * Square root algorithms:
 422  * We have just one right now, maybe Newton approximation
 423  * should be added for those machines where division is fast.
 424  */
 425
 426 #define _FP_SQRT_MEAT_4(R, S, T, X, q)                          \
 427   do {                                                          \
 428     while (q)                                                   \
 429       {                                                         \
 430         T##_f[3] = S##_f[3] + q;                                \
 431         if (T##_f[3] <= X##_f[3])                               \
 432           {                                                     \
 433             S##_f[3] = T##_f[3] + q;                            \
 434             X##_f[3] -= T##_f[3];                               \
 435             R##_f[3] += q;                                      \
 436           }                                                     \
 437         _FP_FRAC_SLL_4(X, 1);                                   \
 438         q >>= 1;                                                \
 439       }                                                         \
 440     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 441     while (q)                                                   \
 442       {                                                         \
 443         T##_f[2] = S##_f[2] + q;                                \
 444         T##_f[3] = S##_f[3];                                    \
 445         if (T##_f[3] < X##_f[3] ||                              \
 446             (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2]))     \
 447           {                                                     \
 448             S##_f[2] = T##_f[2] + q;                            \
 449             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 450             __FP_FRAC_DEC_2(X##_f[3], X##_f[2],                 \
 451                             T##_f[3], T##_f[2]);                \
 452             R##_f[2] += q;                                      \
 453           }                                                     \
 454         _FP_FRAC_SLL_4(X, 1);                                   \
 455         q >>= 1;                                                \
 456       }                                                         \
 457     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 458     while (q)                                                   \
 459       {                                                         \
 460         T##_f[1] = S##_f[1] + q;                                \
 461         T##_f[2] = S##_f[2];                                    \
 462         T##_f[3] = S##_f[3];                                    \
 463         if (T##_f[3] < X##_f[3] ||                              \
 464             (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] ||    \
 465              (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1]))))  \
 466           {                                                     \
 467             S##_f[1] = T##_f[1] + q;                            \
 468             S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 469             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 470             __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1],       \
 471                             T##_f[3], T##_f[2], T##_f[1]);      \
 472             R##_f[1] += q;                                      \
 473           }                                                     \
 474         _FP_FRAC_SLL_4(X, 1);                                   \
 475         q >>= 1;                                                \
 476       }                                                         \
 477     q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);                 \
 478     while (q != _FP_WORK_ROUND)                                 \
 479       {                                                         \
 480         T##_f[0] = S##_f[0] + q;                                \
 481         T##_f[1] = S##_f[1];                                    \
 482         T##_f[2] = S##_f[2];                                    \
 483         T##_f[3] = S##_f[3];                                    \
 484         if (_FP_FRAC_GE_4(X,T))                                 \
 485           {                                                     \
 486             S##_f[0] = T##_f[0] + q;                            \
 487             S##_f[1] += (T##_f[0] > S##_f[0]);                  \
 488             S##_f[2] += (T##_f[1] > S##_f[1]);                  \
 489             S##_f[3] += (T##_f[2] > S##_f[2]);                  \
 490             _FP_FRAC_DEC_4(X, T);                               \
 491             R##_f[0] += q;                                      \
 492           }                                                     \
 493         _FP_FRAC_SLL_4(X, 1);                                   \
 494         q >>= 1;                                                \
 495       }                                                         \
 496     if (!_FP_FRAC_ZEROP_4(X))                                   \
 497       {                                                         \
 498         if (_FP_FRAC_GT_4(X,S))                                 \
 499           R##_f[0] |= _FP_WORK_ROUND;                           \
 500         R##_f[0] |= _FP_WORK_STICKY;                            \
 501       }                                                         \
 502   } while (0)
 503
 504
 505 /*
 506  * Internals
 507  */
 508
 509 #define __FP_FRAC_SET_4(X,I3,I2,I1,I0)                                  \
 510   (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
 511
 512 #ifndef __FP_FRAC_ADD_3
 513 #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 514   do {                                                          \
 515     int _c1, _c2;                                                       \
 516     r0 = x0 + y0;                                               \
 517     _c1 = r0 < x0;                                              \
 518     r1 = x1 + y1;                                               \
 519     _c2 = r1 < x1;                                              \
 520     r1 += _c1;                                                  \
 521     _c2 |= r1 < _c1;                                            \
 522     r2 = x2 + y2 + _c2;                                         \
 523   } while (0)
 524 #endif
 525
 526 #ifndef __FP_FRAC_ADD_4
 527 #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 528   do {                                                          \
 529     int _c1, _c2, _c3;                                          \
 530     r0 = x0 + y0;                                               \
 531     _c1 = r0 < x0;                                              \
 532     r1 = x1 + y1;                                               \
 533     _c2 = r1 < x1;                                              \
 534     r1 += _c1;                                                  \
 535     _c2 |= r1 < _c1;                                            \
 536     r2 = x2 + y2;                                               \
 537     _c3 = r2 < x2;                                              \
 538     r2 += _c2;                                                  \
 539     _c3 |= r2 < _c2;                                            \
 540     r3 = x3 + y3 + _c3;                                         \
 541   } while (0)
 542 #endif
 543
 544 #ifndef __FP_FRAC_SUB_3
 545 #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)             \
 546   do {                                                          \
 547     int _c1, _c2;                                                       \
 548     r0 = x0 - y0;                                               \
 549     _c1 = r0 > x0;                                              \
 550     r1 = x1 - y1;                                               \
 551     _c2 = r1 > x1;                                              \
 552     r1 -= _c1;                                                  \
 553     _c2 |= r1 > _c1;                                            \
 554     r2 = x2 - y2 - _c2;                                         \
 555   } while (0)
 556 #endif
 557
 558 #ifndef __FP_FRAC_SUB_4
 559 #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)    \
 560   do {                                                          \
 561     int _c1, _c2, _c3;                                          \
 562     r0 = x0 - y0;                                               \
 563     _c1 = r0 > x0;                                              \
 564     r1 = x1 - y1;                                               \
 565     _c2 = r1 > x1;                                              \
 566     r1 -= _c1;                                                  \
 567     _c2 |= r1 > _c1;                                            \
 568     r2 = x2 - y2;                                               \
 569     _c3 = r2 > x2;                                              \
 570     r2 -= _c2;                                                  \
 571     _c3 |= r2 > _c2;                                            \
 572     r3 = x3 - y3 - _c3;                                         \
 573   } while (0)
 574 #endif
 575
 576 #ifndef __FP_FRAC_DEC_3
 577 #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0)                              \
 578   do {                                                                  \
 579     UWtype _t0, _t1, _t2;                                               \
 580     _t0 = x0, _t1 = x1, _t2 = x2;                                       \
 581     __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0);            \
 582   } while (0)
 583 #endif
 584
 585 #ifndef __FP_FRAC_DEC_4
 586 #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0)                        \
 587   do {                                                                  \
 588     UWtype _t0, _t1, _t2, _t3;                                          \
 589     _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3;                             \
 590     __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0);         \
 591   } while (0)
 592 #endif
 593
 594 #ifndef __FP_FRAC_ADDI_4
 595 #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i)                                 \
 596   do {                                                                  \
 597     UWtype _t;                                                          \
 598     _t = ((x0 += i) < i);                                               \
 599     x1 += _t; _t = (x1 < _t);                                           \
 600     x2 += _t; _t = (x2 < _t);                                           \
 601     x3 += _t;                                                           \
 602   } while (0)
 603 #endif
 604
 605 /* Convert FP values between word sizes. This appears to be more
 606  * complicated than I'd have expected it to be, so these might be
 607  * wrong... These macros are in any case somewhat bogus because they
 608  * use information about what various FRAC_n variables look like
 609  * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
 610  * the ones in op-2.h and op-1.h.
 611  */
 612 #define _FP_FRAC_CONV_1_4(dfs, sfs, D, S)                               \
 613    do {                                                                 \
 614      if (S##_c != FP_CLS_NAN)                                           \
 615        _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),   \
 616                           _FP_WFRACBITS_##sfs);                         \
 617      else                                                               \
 618        _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));  \
 619      D##_f = S##_f[0];                                                  \
 620   } while (0)
 621
 622 #define _FP_FRAC_CONV_2_4(dfs, sfs, D, S)                               \
 623    do {                                                                 \
 624      if (S##_c != FP_CLS_NAN)                                           \
 625        _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),   \
 626                       _FP_WFRACBITS_##sfs);                             \
 627      else                                                               \
 628        _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));  \
 629      D##_f0 = S##_f[0];                                                 \
 630      D##_f1 = S##_f[1];                                                 \
 631   } while (0)
 632
 633 /* Assembly/disassembly for converting to/from integral types.
 634  * No shifting or overflow handled here.
 635  */
 636 /* Put the FP value X into r, which is an integer of size rsize. */
 637 #define _FP_FRAC_ASSEMBLE_4(r, X, rsize)                                \
 638   do {                                                                  \
 639     if (rsize <= _FP_W_TYPE_SIZE)                                       \
 640       r = X##_f[0];                                                     \
 641     else if (rsize <= 2*_FP_W_TYPE_SIZE)                                \
 642     {                                                                   \
 643       r = X##_f[1];                                                     \
 644       r <<= _FP_W_TYPE_SIZE;                                            \
 645       r += X##_f[0];                                                    \
 646     }                                                                   \
 647     else                                                                \
 648     {                                                                   \
 649       /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \
 650       /* and int == 4words as a single case.                     */     \
 651       r = X##_f[3];                                                     \
 652       r <<= _FP_W_TYPE_SIZE;                                            \
 653       r += X##_f[2];                                                    \
 654       r <<= _FP_W_TYPE_SIZE;                                            \
 655       r += X##_f[1];                                                    \
 656       r <<= _FP_W_TYPE_SIZE;                                            \
 657       r += X##_f[0];                                                    \
 658     }                                                                   \
 659   } while (0)
 660
 661 /* "No disassemble Number Five!" */
 662 /* move an integer of size rsize into X's fractional part. We rely on
 663  * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
 664  * having to mask the values we store into it.
 665  */
 666 #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize)                             \
 667   do {                                                                  \
 668     X##_f[0] = r;                                                       \
 669     X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);   \
 670     X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
 671     X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
 672   } while (0);
 673
 674 #define _FP_FRAC_CONV_4_1(dfs, sfs, D, S)                               \
 675    do {                                                                 \
 676      D##_f[0] = S##_f;                                                  \
 677      D##_f[1] = D##_f[2] = D##_f[3] = 0;                                \
 678      _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));    \
 679    } while (0)
 680
 681 #define _FP_FRAC_CONV_4_2(dfs, sfs, D, S)                               \
 682    do {                                                                 \
 683      D##_f[0] = S##_f0;                                                 \
 684      D##_f[1] = S##_f1;                                                 \
 685      D##_f[2] = D##_f[3] = 0;                                           \
 686      _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));    \
 687    } while (0)
 688