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