soft-fp/op-1.h

   1 /* Software floating-point emulation.
   2    Basic one-word fraction declaration and manipulation.
   3    Copyright (C) 1997-2014 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    In addition to the permissions in the GNU Lesser General Public
  16    License, the Free Software Foundation gives you unlimited
  17    permission to link the compiled version of this file into
  18    combinations with other programs, and to distribute those
  19    combinations without any restriction coming from the use of this
  20    file.  (The Lesser General Public License restrictions do apply in
  21    other respects; for example, they cover modification of the file,
  22    and distribution when not linked into a combine executable.)
  23
  24    The GNU C Library is distributed in the hope that it will be useful,
  25    but WITHOUT ANY WARRANTY; without even the implied warranty of
  26    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  27    Lesser General Public License for more details.
  28
  29    You should have received a copy of the GNU Lesser General Public
  30    License along with the GNU C Library; if not, see
  31    <http://www.gnu.org/licenses/>.  */
  32
  33 #define _FP_FRAC_DECL_1(X)      _FP_W_TYPE X##_f
  34 #define _FP_FRAC_COPY_1(D, S)   (D##_f = S##_f)
  35 #define _FP_FRAC_SET_1(X, I)    (X##_f = I)
  36 #define _FP_FRAC_HIGH_1(X)      (X##_f)
  37 #define _FP_FRAC_LOW_1(X)       (X##_f)
  38 #define _FP_FRAC_WORD_1(X, w)   (X##_f)
  39
  40 #define _FP_FRAC_ADDI_1(X, I)   (X##_f += I)
  41 #define _FP_FRAC_SLL_1(X, N)                    \
  42   do                                            \
  43     {                                           \
  44       if (__builtin_constant_p (N) && (N) == 1) \
  45         X##_f += X##_f;                         \
  46       else                                      \
  47         X##_f <<= (N);                          \
  48     }                                           \
  49   while (0)
  50 #define _FP_FRAC_SRL_1(X, N)    (X##_f >>= N)
  51
  52 /* Right shift with sticky-lsb.  */
  53 #define _FP_FRAC_SRST_1(X, S, N, sz)    __FP_FRAC_SRST_1 (X##_f, S, N, sz)
  54 #define _FP_FRAC_SRS_1(X, N, sz)        __FP_FRAC_SRS_1 (X##_f, N, sz)
  55
  56 #define __FP_FRAC_SRST_1(X, S, N, sz)                   \
  57   do                                                    \
  58     {                                                   \
  59       S = (__builtin_constant_p (N) && (N) == 1         \
  60            ? X & 1                                      \
  61            : (X << (_FP_W_TYPE_SIZE - (N))) != 0);      \
  62       X = X >> (N);                                     \
  63     }                                                   \
  64   while (0)
  65
  66 #define __FP_FRAC_SRS_1(X, N, sz)                               \
  67   (X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1        \
  68                     ? X & 1                                     \
  69                     : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
  70
  71 #define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f)
  72 #define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f)
  73 #define _FP_FRAC_DEC_1(X, Y)    (X##_f -= Y##_f)
  74 #define _FP_FRAC_CLZ_1(z, X)    __FP_CLZ (z, X##_f)
  75
  76 /* Predicates */
  77 #define _FP_FRAC_NEGP_1(X)      ((_FP_WS_TYPE) X##_f < 0)
  78 #define _FP_FRAC_ZEROP_1(X)     (X##_f == 0)
  79 #define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs)
  80 #define _FP_FRAC_CLEAR_OVERP_1(fs, X)   (X##_f &= ~_FP_OVERFLOW_##fs)
  81 #define _FP_FRAC_HIGHBIT_DW_1(fs, X)    (X##_f & _FP_HIGHBIT_DW_##fs)
  82 #define _FP_FRAC_EQ_1(X, Y)     (X##_f == Y##_f)
  83 #define _FP_FRAC_GE_1(X, Y)     (X##_f >= Y##_f)
  84 #define _FP_FRAC_GT_1(X, Y)     (X##_f > Y##_f)
  85
  86 #define _FP_ZEROFRAC_1          0
  87 #define _FP_MINFRAC_1           1
  88 #define _FP_MAXFRAC_1           (~(_FP_WS_TYPE) 0)
  89
  90 /*
  91  * Unpack the raw bits of a native fp value.  Do not classify or
  92  * normalize the data.
  93  */
  94
  95 #define _FP_UNPACK_RAW_1(fs, X, val)            \
  96   do                                            \
  97     {                                           \
  98       union _FP_UNION_##fs _flo;                \
  99       _flo.flt = (val);                         \
 100                                                 \
 101       X##_f = _flo.bits.frac;                   \
 102       X##_e = _flo.bits.exp;                    \
 103       X##_s = _flo.bits.sign;                   \
 104     }                                           \
 105   while (0)
 106
 107 #define _FP_UNPACK_RAW_1_P(fs, X, val)                                  \
 108   do                                                                    \
 109     {                                                                   \
 110       union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *) (val);      \
 111                                                                         \
 112       X##_f = _flo->bits.frac;                                          \
 113       X##_e = _flo->bits.exp;                                           \
 114       X##_s = _flo->bits.sign;                                          \
 115     }                                                                   \
 116   while (0)
 117
 118 /*
 119  * Repack the raw bits of a native fp value.
 120  */
 121
 122 #define _FP_PACK_RAW_1(fs, val, X)              \
 123   do                                            \
 124     {                                           \
 125       union _FP_UNION_##fs _flo;                \
 126                                                 \
 127       _flo.bits.frac = X##_f;                   \
 128       _flo.bits.exp  = X##_e;                   \
 129       _flo.bits.sign = X##_s;                   \
 130                                                 \
 131       (val) = _flo.flt;                         \
 132     }                                           \
 133   while (0)
 134
 135 #define _FP_PACK_RAW_1_P(fs, val, X)                                    \
 136   do                                                                    \
 137     {                                                                   \
 138       union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *) (val);      \
 139                                                                         \
 140       _flo->bits.frac = X##_f;                                          \
 141       _flo->bits.exp  = X##_e;                                          \
 142       _flo->bits.sign = X##_s;                                          \
 143     }                                                                   \
 144   while (0)
 145
 146
 147 /*
 148  * Multiplication algorithms:
 149  */
 150
 151 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 152    multiplication immediately.  */
 153
 154 #define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y)       \
 155   do                                                    \
 156     {                                                   \
 157       R##_f = X##_f * Y##_f;                            \
 158     }                                                   \
 159   while (0)
 160
 161 #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y)                          \
 162   do                                                                    \
 163     {                                                                   \
 164       _FP_MUL_MEAT_DW_1_imm (wfracbits, R, X, Y);                       \
 165       /* Normalize since we know where the msb of the multiplicands     \
 166          were (bit B), we know that the msb of the of the product is    \
 167          at either 2B or 2B-1.  */                                      \
 168       _FP_FRAC_SRS_1 (R, wfracbits-1, 2*wfracbits);                     \
 169     }                                                                   \
 170   while (0)
 171
 172 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 173
 174 #define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit)        \
 175   do                                                            \
 176     {                                                           \
 177       doit (R##_f1, R##_f0, X##_f, Y##_f);                      \
 178     }                                                           \
 179   while (0)
 180
 181 #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit)                   \
 182   do                                                                    \
 183     {                                                                   \
 184       _FP_FRAC_DECL_2 (_Z);                                             \
 185       _FP_MUL_MEAT_DW_1_wide (wfracbits, _Z, X, Y, doit);               \
 186       /* Normalize since we know where the msb of the multiplicands     \
 187          were (bit B), we know that the msb of the of the product is    \
 188          at either 2B or 2B-1.  */                                      \
 189       _FP_FRAC_SRS_2 (_Z, wfracbits-1, 2*wfracbits);                    \
 190       R##_f = _Z_f0;                                                    \
 191     }                                                                   \
 192   while (0)
 193
 194 /* Finally, a simple widening multiply algorithm.  What fun!  */
 195
 196 #define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y)                      \
 197   do                                                                    \
 198     {                                                                   \
 199       _FP_W_TYPE _xh, _xl, _yh, _yl;                                    \
 200       _FP_FRAC_DECL_2 (_a);                                             \
 201                                                                         \
 202       /* split the words in half */                                     \
 203       _xh = X##_f >> (_FP_W_TYPE_SIZE/2);                               \
 204       _xl = X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1);      \
 205       _yh = Y##_f >> (_FP_W_TYPE_SIZE/2);                               \
 206       _yl = Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1);      \
 207                                                                         \
 208       /* multiply the pieces */                                         \
 209       R##_f0 = _xl * _yl;                                               \
 210       _a_f0 = _xh * _yl;                                                \
 211       _a_f1 = _xl * _yh;                                                \
 212       R##_f1 = _xh * _yh;                                               \
 213                                                                         \
 214       /* reassemble into two full words */                              \
 215       if ((_a_f0 += _a_f1) < _a_f1)                                     \
 216         R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2);                \
 217       _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2);                             \
 218       _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2);                             \
 219       _FP_FRAC_ADD_2 (R, R, _a);                                        \
 220     }                                                                   \
 221   while (0)
 222
 223 #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y)         \
 224   do                                                    \
 225     {                                                   \
 226       _FP_FRAC_DECL_2 (_z);                             \
 227       _FP_MUL_MEAT_DW_1_hard (wfracbits, _z, X, Y);     \
 228                                                         \
 229       /* normalize */                                   \
 230       _FP_FRAC_SRS_2 (_z, wfracbits - 1, 2*wfracbits);  \
 231       R##_f = _z_f0;                                    \
 232     }                                                   \
 233   while (0)
 234
 235
 236 /*
 237  * Division algorithms:
 238  */
 239
 240 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 241    division immediately.  Give this macro either _FP_DIV_HELP_imm for
 242    C primitives or _FP_DIV_HELP_ldiv for the ISO function.  Which you
 243    choose will depend on what the compiler does with divrem4.  */
 244
 245 #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit)   \
 246   do                                            \
 247     {                                           \
 248       _FP_W_TYPE _q, _r;                        \
 249       X##_f <<= (X##_f < Y##_f                  \
 250                  ? R##_e--, _FP_WFRACBITS_##fs  \
 251                  : _FP_WFRACBITS_##fs - 1);     \
 252       doit (_q, _r, X##_f, Y##_f);              \
 253       R##_f = _q | (_r != 0);                   \
 254     }                                           \
 255   while (0)
 256
 257 /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
 258    that may be useful in this situation.  This first is for a primitive
 259    that requires normalization, the second for one that does not.  Look
 260    for UDIV_NEEDS_NORMALIZATION to tell which your machine needs.  */
 261
 262 #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y)                           \
 263   do                                                                    \
 264     {                                                                   \
 265       _FP_W_TYPE _nh, _nl, _q, _r, _y;                                  \
 266                                                                         \
 267       /* Normalize Y -- i.e. make the most significant bit set.  */     \
 268       _y = Y##_f << _FP_WFRACXBITS_##fs;                                \
 269                                                                         \
 270       /* Shift X op correspondingly high, that is, up one full word.  */ \
 271       if (X##_f < Y##_f)                                                \
 272         {                                                               \
 273           R##_e--;                                                      \
 274           _nl = 0;                                                      \
 275           _nh = X##_f;                                                  \
 276         }                                                               \
 277       else                                                              \
 278         {                                                               \
 279           _nl = X##_f << (_FP_W_TYPE_SIZE - 1);                         \
 280           _nh = X##_f >> 1;                                             \
 281         }                                                               \
 282                                                                         \
 283       udiv_qrnnd (_q, _r, _nh, _nl, _y);                                \
 284       R##_f = _q | (_r != 0);                                           \
 285     }                                                                   \
 286   while (0)
 287
 288 #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y)                \
 289   do                                                    \
 290     {                                                   \
 291       _FP_W_TYPE _nh, _nl, _q, _r;                      \
 292       if (X##_f < Y##_f)                                \
 293         {                                               \
 294           R##_e--;                                      \
 295           _nl = X##_f << _FP_WFRACBITS_##fs;            \
 296           _nh = X##_f >> _FP_WFRACXBITS_##fs;           \
 297         }                                               \
 298       else                                              \
 299         {                                               \
 300           _nl = X##_f << (_FP_WFRACBITS_##fs - 1);      \
 301           _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1);     \
 302         }                                               \
 303       udiv_qrnnd (_q, _r, _nh, _nl, Y##_f);             \
 304       R##_f = _q | (_r != 0);                           \
 305     }                                                   \
 306   while (0)
 307
 308
 309 /*
 310  * Square root algorithms:
 311  * We have just one right now, maybe Newton approximation
 312  * should be added for those machines where division is fast.
 313  */
 314
 315 #define _FP_SQRT_MEAT_1(R, S, T, X, q)          \
 316   do                                            \
 317     {                                           \
 318       while (q != _FP_WORK_ROUND)               \
 319         {                                       \
 320           T##_f = S##_f + q;                    \
 321           if (T##_f <= X##_f)                   \
 322             {                                   \
 323               S##_f = T##_f + q;                \
 324               X##_f -= T##_f;                   \
 325               R##_f += q;                       \
 326             }                                   \
 327           _FP_FRAC_SLL_1 (X, 1);                \
 328           q >>= 1;                              \
 329         }                                       \
 330       if (X##_f)                                \
 331         {                                       \
 332           if (S##_f < X##_f)                    \
 333             R##_f |= _FP_WORK_ROUND;            \
 334           R##_f |= _FP_WORK_STICKY;             \
 335         }                                       \
 336     }                                           \
 337   while (0)
 338
 339 /*
 340  * Assembly/disassembly for converting to/from integral types.
 341  * No shifting or overflow handled here.
 342  */
 343
 344 #define _FP_FRAC_ASSEMBLE_1(r, X, rsize)        (r = X##_f)
 345 #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize)     (X##_f = r)
 346
 347
 348 /*
 349  * Convert FP values between word sizes
 350  */
 351
 352 #define _FP_FRAC_COPY_1_1(D, S)         (D##_f = S##_f)