soft-fp/op-1.h

   1 /* Software floating-point emulation.
   2    Basic one-word fraction declaration and manipulation.
   3    Copyright (C) 1997-2013 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     if (__builtin_constant_p(N) && (N) == 1)    \
  44       X##_f += X##_f;                           \
  45     else                                        \
  46       X##_f <<= (N);                            \
  47   } while (0)
  48 #define _FP_FRAC_SRL_1(X,N)     (X##_f >>= N)
  49
  50 /* Right shift with sticky-lsb.  */
  51 #define _FP_FRAC_SRST_1(X,S,N,sz)       __FP_FRAC_SRST_1(X##_f, S, N, sz)
  52 #define _FP_FRAC_SRS_1(X,N,sz)  __FP_FRAC_SRS_1(X##_f, N, sz)
  53
  54 #define __FP_FRAC_SRST_1(X,S,N,sz)                      \
  55 do {                                                    \
  56   S = (__builtin_constant_p(N) && (N) == 1              \
  57        ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0);  \
  58   X = X >> (N);                                         \
  59 } while (0)
  60
  61 #define __FP_FRAC_SRS_1(X,N,sz)                                         \
  62    (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1                \
  63                      ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
  64
  65 #define _FP_FRAC_ADD_1(R,X,Y)   (R##_f = X##_f + Y##_f)
  66 #define _FP_FRAC_SUB_1(R,X,Y)   (R##_f = X##_f - Y##_f)
  67 #define _FP_FRAC_DEC_1(X,Y)     (X##_f -= Y##_f)
  68 #define _FP_FRAC_CLZ_1(z, X)    __FP_CLZ(z, X##_f)
  69
  70 /* Predicates */
  71 #define _FP_FRAC_NEGP_1(X)      ((_FP_WS_TYPE)X##_f < 0)
  72 #define _FP_FRAC_ZEROP_1(X)     (X##_f == 0)
  73 #define _FP_FRAC_OVERP_1(fs,X)  (X##_f & _FP_OVERFLOW_##fs)
  74 #define _FP_FRAC_CLEAR_OVERP_1(fs,X)    (X##_f &= ~_FP_OVERFLOW_##fs)
  75 #define _FP_FRAC_HIGHBIT_DW_1(fs,X)     (X##_f & _FP_HIGHBIT_DW_##fs)
  76 #define _FP_FRAC_EQ_1(X, Y)     (X##_f == Y##_f)
  77 #define _FP_FRAC_GE_1(X, Y)     (X##_f >= Y##_f)
  78 #define _FP_FRAC_GT_1(X, Y)     (X##_f > Y##_f)
  79
  80 #define _FP_ZEROFRAC_1          0
  81 #define _FP_MINFRAC_1           1
  82 #define _FP_MAXFRAC_1           (~(_FP_WS_TYPE)0)
  83
  84 /*
  85  * Unpack the raw bits of a native fp value.  Do not classify or
  86  * normalize the data.
  87  */
  88
  89 #define _FP_UNPACK_RAW_1(fs, X, val)                            \
  90   do {                                                          \
  91     union _FP_UNION_##fs _flo; _flo.flt = (val);                \
  92                                                                 \
  93     X##_f = _flo.bits.frac;                                     \
  94     X##_e = _flo.bits.exp;                                      \
  95     X##_s = _flo.bits.sign;                                     \
  96   } while (0)
  97
  98 #define _FP_UNPACK_RAW_1_P(fs, X, val)                          \
  99   do {                                                          \
 100     union _FP_UNION_##fs *_flo =                                \
 101       (union _FP_UNION_##fs *)(val);                            \
 102                                                                 \
 103     X##_f = _flo->bits.frac;                                    \
 104     X##_e = _flo->bits.exp;                                     \
 105     X##_s = _flo->bits.sign;                                    \
 106   } while (0)
 107
 108 /*
 109  * Repack the raw bits of a native fp value.
 110  */
 111
 112 #define _FP_PACK_RAW_1(fs, val, X)                              \
 113   do {                                                          \
 114     union _FP_UNION_##fs _flo;                                  \
 115                                                                 \
 116     _flo.bits.frac = X##_f;                                     \
 117     _flo.bits.exp  = X##_e;                                     \
 118     _flo.bits.sign = X##_s;                                     \
 119                                                                 \
 120     (val) = _flo.flt;                                           \
 121   } while (0)
 122
 123 #define _FP_PACK_RAW_1_P(fs, val, X)                            \
 124   do {                                                          \
 125     union _FP_UNION_##fs *_flo =                                \
 126       (union _FP_UNION_##fs *)(val);                            \
 127                                                                 \
 128     _flo->bits.frac = X##_f;                                    \
 129     _flo->bits.exp  = X##_e;                                    \
 130     _flo->bits.sign = X##_s;                                    \
 131   } while (0)
 132
 133
 134 /*
 135  * Multiplication algorithms:
 136  */
 137
 138 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 139    multiplication immediately.  */
 140
 141 #define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y)                       \
 142   do {                                                                  \
 143     R##_f = X##_f * Y##_f;                                              \
 144   } while (0)
 145
 146 #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y)                          \
 147   do {                                                                  \
 148     _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y);                          \
 149     /* Normalize since we know where the msb of the multiplicands       \
 150        were (bit B), we know that the msb of the of the product is      \
 151        at either 2B or 2B-1.  */                                        \
 152     _FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits);                        \
 153   } while (0)
 154
 155 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 156
 157 #define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit)                \
 158   do {                                                                  \
 159     doit(R##_f1, R##_f0, X##_f, Y##_f);                                 \
 160   } while (0)
 161
 162 #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit)                   \
 163   do {                                                                  \
 164     _FP_FRAC_DECL_2(_Z);                                                \
 165     _FP_MUL_MEAT_DW_1_wide(wfracbits, _Z, X, Y, doit);                  \
 166     /* Normalize since we know where the msb of the multiplicands       \
 167        were (bit B), we know that the msb of the of the product is      \
 168        at either 2B or 2B-1.  */                                        \
 169     _FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits);                       \
 170     R##_f = _Z_f0;                                                      \
 171   } while (0)
 172
 173 /* Finally, a simple widening multiply algorithm.  What fun!  */
 174
 175 #define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y)                      \
 176   do {                                                                  \
 177     _FP_W_TYPE _xh, _xl, _yh, _yl;                                      \
 178     _FP_FRAC_DECL_2(_a);                                                \
 179                                                                         \
 180     /* split the words in half */                                       \
 181     _xh = X##_f >> (_FP_W_TYPE_SIZE/2);                                 \
 182     _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
 183     _yh = Y##_f >> (_FP_W_TYPE_SIZE/2);                                 \
 184     _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
 185                                                                         \
 186     /* multiply the pieces */                                           \
 187     R##_f0 = _xl * _yl;                                                 \
 188     _a_f0 = _xh * _yl;                                                  \
 189     _a_f1 = _xl * _yh;                                                  \
 190     R##_f1 = _xh * _yh;                                                 \
 191                                                                         \
 192     /* reassemble into two full words */                                \
 193     if ((_a_f0 += _a_f1) < _a_f1)                                       \
 194       R##_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2);                   \
 195     _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2);                               \
 196     _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2);                               \
 197     _FP_FRAC_ADD_2(R, R, _a);                                           \
 198   } while (0)
 199
 200 #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y)                         \
 201   do {                                                                  \
 202     _FP_FRAC_DECL_2(_z);                                                \
 203     _FP_MUL_MEAT_DW_1_hard(wfracbits, _z, X, Y);                        \
 204                                                                         \
 205     /* normalize */                                                     \
 206     _FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits);                     \
 207     R##_f = _z_f0;                                                      \
 208   } while (0)
 209
 210
 211 /*
 212  * Division algorithms:
 213  */
 214
 215 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 216    division immediately.  Give this macro either _FP_DIV_HELP_imm for
 217    C primitives or _FP_DIV_HELP_ldiv for the ISO function.  Which you
 218    choose will depend on what the compiler does with divrem4.  */
 219
 220 #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit)           \
 221   do {                                                  \
 222     _FP_W_TYPE _q, _r;                                  \
 223     X##_f <<= (X##_f < Y##_f                            \
 224                ? R##_e--, _FP_WFRACBITS_##fs            \
 225                : _FP_WFRACBITS_##fs - 1);               \
 226     doit(_q, _r, X##_f, Y##_f);                         \
 227     R##_f = _q | (_r != 0);                             \
 228   } while (0)
 229
 230 /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
 231    that may be useful in this situation.  This first is for a primitive
 232    that requires normalization, the second for one that does not.  Look
 233    for UDIV_NEEDS_NORMALIZATION to tell which your machine needs.  */
 234
 235 #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y)                           \
 236   do {                                                                  \
 237     _FP_W_TYPE _nh, _nl, _q, _r, _y;                                    \
 238                                                                         \
 239     /* Normalize Y -- i.e. make the most significant bit set.  */       \
 240     _y = Y##_f << _FP_WFRACXBITS_##fs;                                  \
 241                                                                         \
 242     /* Shift X op correspondingly high, that is, up one full word.  */  \
 243     if (X##_f < Y##_f)                                                  \
 244       {                                                                 \
 245         R##_e--;                                                        \
 246         _nl = 0;                                                        \
 247         _nh = X##_f;                                                    \
 248       }                                                                 \
 249     else                                                                \
 250       {                                                                 \
 251         _nl = X##_f << (_FP_W_TYPE_SIZE - 1);                           \
 252         _nh = X##_f >> 1;                                               \
 253       }                                                                 \
 254                                                                         \
 255     udiv_qrnnd(_q, _r, _nh, _nl, _y);                                   \
 256     R##_f = _q | (_r != 0);                                             \
 257   } while (0)
 258
 259 #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y)                \
 260   do {                                                  \
 261     _FP_W_TYPE _nh, _nl, _q, _r;                        \
 262     if (X##_f < Y##_f)                                  \
 263       {                                                 \
 264         R##_e--;                                        \
 265         _nl = X##_f << _FP_WFRACBITS_##fs;              \
 266         _nh = X##_f >> _FP_WFRACXBITS_##fs;             \
 267       }                                                 \
 268     else                                                \
 269       {                                                 \
 270         _nl = X##_f << (_FP_WFRACBITS_##fs - 1);        \
 271         _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1);       \
 272       }                                                 \
 273     udiv_qrnnd(_q, _r, _nh, _nl, Y##_f);                \
 274     R##_f = _q | (_r != 0);                             \
 275   } while (0)
 276
 277
 278 /*
 279  * Square root algorithms:
 280  * We have just one right now, maybe Newton approximation
 281  * should be added for those machines where division is fast.
 282  */
 283
 284 #define _FP_SQRT_MEAT_1(R, S, T, X, q)                  \
 285   do {                                                  \
 286     while (q != _FP_WORK_ROUND)                         \
 287       {                                                 \
 288         T##_f = S##_f + q;                              \
 289         if (T##_f <= X##_f)                             \
 290           {                                             \
 291             S##_f = T##_f + q;                          \
 292             X##_f -= T##_f;                             \
 293             R##_f += q;                                 \
 294           }                                             \
 295         _FP_FRAC_SLL_1(X, 1);                           \
 296         q >>= 1;                                        \
 297       }                                                 \
 298     if (X##_f)                                          \
 299       {                                                 \
 300         if (S##_f < X##_f)                              \
 301           R##_f |= _FP_WORK_ROUND;                      \
 302         R##_f |= _FP_WORK_STICKY;                       \
 303       }                                                 \
 304   } while (0)
 305
 306 /*
 307  * Assembly/disassembly for converting to/from integral types.
 308  * No shifting or overflow handled here.
 309  */
 310
 311 #define _FP_FRAC_ASSEMBLE_1(r, X, rsize)        (r = X##_f)
 312 #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize)     (X##_f = r)
 313
 314
 315 /*
 316  * Convert FP values between word sizes
 317  */
 318
 319 #define _FP_FRAC_COPY_1_1(D, S)         (D##_f = S##_f)