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op-1.h
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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 ([email protected]),
6  Jakub Jelinek ([email protected]),
7  David S. Miller ([email protected]) and
8  Peter Maydell ([email protected]).
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__ */
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