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   1 /* Software floating-point emulation.
   2    Basic one-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 Library General Public License as
  12    published by the Free Software Foundation; either version 2 of the
  13    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    Library General Public License for more details.
  19
  20    You should have received a copy of the GNU Library General Public
  21    License along with the GNU C Library; see the file COPYING.LIB.  If
  22    not, write to the Free Software Foundation, Inc.,
  23    59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
  24
  25 #ifndef    __MATH_EMU_OP_1_H__
  26 #define    __MATH_EMU_OP_1_H__
  27
  28 #define _FP_FRAC_DECL_1(X)      _FP_W_TYPE X##_f=0
  29 #define _FP_FRAC_COPY_1(D,S)    (D##_f = S##_f)
  30 #define _FP_FRAC_SET_1(X,I)     (X##_f = I)
  31 #define _FP_FRAC_HIGH_1(X)      (X##_f)
  32 #define _FP_FRAC_LOW_1(X)       (X##_f)
  33 #define _FP_FRAC_WORD_1(X,w)    (X##_f)
  34
  35 #define _FP_FRAC_ADDI_1(X,I)    (X##_f += I)
  36 #define _FP_FRAC_SLL_1(X,N)                     \
  37   do {                                          \
  38     if (__builtin_constant_p(N) && (N) == 1)    \
  39       X##_f += X##_f;                           \
  40     else                                        \
  41       X##_f <<= (N);                            \
  42   } while (0)
  43 #define _FP_FRAC_SRL_1(X,N)     (X##_f >>= N)
  44
  45 /* Right shift with sticky-lsb.  */
  46 #define _FP_FRAC_SRS_1(X,N,sz)  __FP_FRAC_SRS_1(X##_f, N, sz)
  47
  48 #define __FP_FRAC_SRS_1(X,N,sz)                                         \
  49    (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1                \
  50                      ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
  51
  52 #define _FP_FRAC_ADD_1(R,X,Y)   (R##_f = X##_f + Y##_f)
  53 #define _FP_FRAC_SUB_1(R,X,Y)   (R##_f = X##_f - Y##_f)
  54 #define _FP_FRAC_DEC_1(X,Y)     (X##_f -= Y##_f)
  55 #define _FP_FRAC_CLZ_1(z, X)    __FP_CLZ(z, X##_f)
  56
  57 /* Predicates */
  58 #define _FP_FRAC_NEGP_1(X)      ((_FP_WS_TYPE)X##_f < 0)
  59 #define _FP_FRAC_ZEROP_1(X)     (X##_f == 0)
  60 #define _FP_FRAC_OVERP_1(fs,X)  (X##_f & _FP_OVERFLOW_##fs)
  61 #define _FP_FRAC_CLEAR_OVERP_1(fs,X)    (X##_f &= ~_FP_OVERFLOW_##fs)
  62 #define _FP_FRAC_EQ_1(X, Y)     (X##_f == Y##_f)
  63 #define _FP_FRAC_GE_1(X, Y)     (X##_f >= Y##_f)
  64 #define _FP_FRAC_GT_1(X, Y)     (X##_f > Y##_f)
  65
  66 #define _FP_ZEROFRAC_1          0
  67 #define _FP_MINFRAC_1           1
  68 #define _FP_MAXFRAC_1           (~(_FP_WS_TYPE)0)
  69
  70 /*
  71  * Unpack the raw bits of a native fp value.  Do not classify or
  72  * normalize the data.
  73  */
  74
  75 #define _FP_UNPACK_RAW_1(fs, X, val)                            \
  76   do {                                                          \
  77     union _FP_UNION_##fs _flo; _flo.flt = (val);                \
  78                                                                 \
  79     X##_f = _flo.bits.frac;                                     \
  80     X##_e = _flo.bits.exp;                                      \
  81     X##_s = _flo.bits.sign;                                     \
  82   } while (0)
  83
  84 #define _FP_UNPACK_RAW_1_P(fs, X, val)                          \
  85   do {                                                          \
  86     union _FP_UNION_##fs *_flo =                                \
  87       (union _FP_UNION_##fs *)(val);                            \
  88                                                                 \
  89     X##_f = _flo->bits.frac;                                    \
  90     X##_e = _flo->bits.exp;                                     \
  91     X##_s = _flo->bits.sign;                                    \
  92   } while (0)
  93
  94 /*
  95  * Repack the raw bits of a native fp value.
  96  */
  97
  98 #define _FP_PACK_RAW_1(fs, val, X)                              \
  99   do {                                                          \
 100     union _FP_UNION_##fs _flo;                                  \
 101                                                                 \
 102     _flo.bits.frac = X##_f;                                     \
 103     _flo.bits.exp  = X##_e;                                     \
 104     _flo.bits.sign = X##_s;                                     \
 105                                                                 \
 106     (val) = _flo.flt;                                           \
 107   } while (0)
 108
 109 #define _FP_PACK_RAW_1_P(fs, val, X)                            \
 110   do {                                                          \
 111     union _FP_UNION_##fs *_flo =                                \
 112       (union _FP_UNION_##fs *)(val);                            \
 113                                                                 \
 114     _flo->bits.frac = X##_f;                                    \
 115     _flo->bits.exp  = X##_e;                                    \
 116     _flo->bits.sign = X##_s;                                    \
 117   } while (0)
 118
 119
 120 /*
 121  * Multiplication algorithms:
 122  */
 123
 124 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 125    multiplication immediately.  */
 126
 127 #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y)                          \
 128   do {                                                                  \
 129     R##_f = X##_f * Y##_f;                                              \
 130     /* Normalize since we know where the msb of the multiplicands       \
 131        were (bit B), we know that the msb of the of the product is      \
 132        at either 2B or 2B-1.  */                                        \
 133     _FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits);                        \
 134   } while (0)
 135
 136 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
 137
 138 #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit)                   \
 139   do {                                                                  \
 140     _FP_W_TYPE _Z_f0, _Z_f1;                                            \
 141     doit(_Z_f1, _Z_f0, X##_f, Y##_f);                                   \
 142     /* Normalize since we know where the msb of the multiplicands       \
 143        were (bit B), we know that the msb of the of the product is      \
 144        at either 2B or 2B-1.  */                                        \
 145     _FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits);                       \
 146     R##_f = _Z_f0;                                                      \
 147   } while (0)
 148
 149 /* Finally, a simple widening multiply algorithm.  What fun!  */
 150
 151 #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y)                         \
 152   do {                                                                  \
 153     _FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1;          \
 154                                                                         \
 155     /* split the words in half */                                       \
 156     _xh = X##_f >> (_FP_W_TYPE_SIZE/2);                                 \
 157     _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
 158     _yh = Y##_f >> (_FP_W_TYPE_SIZE/2);                                 \
 159     _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
 160                                                                         \
 161     /* multiply the pieces */                                           \
 162     _z_f0 = _xl * _yl;                                                  \
 163     _a_f0 = _xh * _yl;                                                  \
 164     _a_f1 = _xl * _yh;                                                  \
 165     _z_f1 = _xh * _yh;                                                  \
 166                                                                         \
 167     /* reassemble into two full words */                                \
 168     if ((_a_f0 += _a_f1) < _a_f1)                                       \
 169       _z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2);                    \
 170     _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2);                               \
 171     _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2);                               \
 172     _FP_FRAC_ADD_2(_z, _z, _a);                                         \
 173                                                                         \
 174     /* normalize */                                                     \
 175     _FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits);                     \
 176     R##_f = _z_f0;                                                      \
 177   } while (0)
 178
 179
 180 /*
 181  * Division algorithms:
 182  */
 183
 184 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
 185    division immediately.  Give this macro either _FP_DIV_HELP_imm for
 186    C primitives or _FP_DIV_HELP_ldiv for the ISO function.  Which you
 187    choose will depend on what the compiler does with divrem4.  */
 188
 189 #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit)           \
 190   do {                                                  \
 191     _FP_W_TYPE _q, _r;                                  \
 192     X##_f <<= (X##_f < Y##_f                            \
 193                ? R##_e--, _FP_WFRACBITS_##fs            \
 194                : _FP_WFRACBITS_##fs - 1);               \
 195     doit(_q, _r, X##_f, Y##_f);                         \
 196     R##_f = _q | (_r != 0);                             \
 197   } while (0)
 198
 199 /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
 200    that may be useful in this situation.  This first is for a primitive
 201    that requires normalization, the second for one that does not.  Look
 202    for UDIV_NEEDS_NORMALIZATION to tell which your machine needs.  */
 203
 204 #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y)                           \
 205   do {                                                                  \
 206     _FP_W_TYPE _nh, _nl, _q, _r, _y;                                    \
 207                                                                         \
 208     /* Normalize Y -- i.e. make the most significant bit set.  */       \
 209     _y = Y##_f << _FP_WFRACXBITS_##fs;                                  \
 210                                                                         \
 211     /* Shift X op correspondingly high, that is, up one full word.  */  \
 212     if (X##_f < Y##_f)                                                  \
 213       {                                                                 \
 214         R##_e--;                                                        \
 215         _nl = 0;                                                        \
 216         _nh = X##_f;                                                    \
 217       }                                                                 \
 218     else                                                                \
 219       {                                                                 \
 220         _nl = X##_f << (_FP_W_TYPE_SIZE - 1);                           \
 221         _nh = X##_f >> 1;                                               \
 222       }                                                                 \
 223                                                                         \
 224     udiv_qrnnd(_q, _r, _nh, _nl, _y);                                   \
 225     R##_f = _q | (_r != 0);                                             \
 226   } while (0)
 227
 228 #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y)                \
 229   do {                                                  \
 230     _FP_W_TYPE _nh, _nl, _q, _r;                        \
 231     if (X##_f < Y##_f)                                  \
 232       {                                                 \
 233         R##_e--;                                        \
 234         _nl = X##_f << _FP_WFRACBITS_##fs;              \
 235         _nh = X##_f >> _FP_WFRACXBITS_##fs;             \
 236       }                                                 \
 237     else                                                \
 238       {                                                 \
 239         _nl = X##_f << (_FP_WFRACBITS_##fs - 1);        \
 240         _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1);       \
 241       }                                                 \
 242     udiv_qrnnd(_q, _r, _nh, _nl, Y##_f);                \
 243     R##_f = _q | (_r != 0);                             \
 244   } while (0)
 245
 246
 247 /*
 248  * Square root algorithms:
 249  * We have just one right now, maybe Newton approximation
 250  * should be added for those machines where division is fast.
 251  */
 252
 253 #define _FP_SQRT_MEAT_1(R, S, T, X, q)                  \
 254   do {                                                  \
 255     while (q != _FP_WORK_ROUND)                         \
 256       {                                                 \
 257         T##_f = S##_f + q;                              \
 258         if (T##_f <= X##_f)                             \
 259           {                                             \
 260             S##_f = T##_f + q;                          \
 261             X##_f -= T##_f;                             \
 262             R##_f += q;                                 \
 263           }                                             \
 264         _FP_FRAC_SLL_1(X, 1);                           \
 265         q >>= 1;                                        \
 266       }                                                 \
 267     if (X##_f)                                          \
 268       {                                                 \
 269         if (S##_f < X##_f)                              \
 270           R##_f |= _FP_WORK_ROUND;                      \
 271         R##_f |= _FP_WORK_STICKY;                       \
 272       }                                                 \
 273   } while (0)
 274
 275 /*
 276  * Assembly/disassembly for converting to/from integral types.
 277  * No shifting or overflow handled here.
 278  */
 279
 280 #define _FP_FRAC_ASSEMBLE_1(r, X, rsize)        (r = X##_f)
 281 #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize)     (X##_f = r)
 282
 283
 284 /*
 285  * Convert FP values between word sizes
 286  */
 287
 288 #define _FP_FRAC_CONV_1_1(dfs, sfs, D, S)                               \
 289   do {                                                                  \
 290     D##_f = S##_f;                                                      \
 291     if (_FP_WFRACBITS_##sfs > _FP_WFRACBITS_##dfs)                      \
 292       {                                                                 \
 293         if (S##_c != FP_CLS_NAN)                                        \
 294           _FP_FRAC_SRS_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs),  \
 295                          _FP_WFRACBITS_##sfs);                          \
 296         else                                                            \
 297           _FP_FRAC_SRL_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs)); \
 298       }                                                                 \
 299     else                                                                \
 300       D##_f <<= _FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs;              \
 301   } while (0)
 302
 303 #endif /* __MATH_EMU_OP_1_H__ */