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1/* Software floating-point emulation.
2 Definitions for IEEE Extended Precision.
3 Copyright (C) 1999 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5 Contributed by Jakub Jelinek (jj@ultra.linux.cz).
6
7 The GNU C Library is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Library General Public License as
9 published by the Free Software Foundation; either version 2 of the
10 License, or (at your option) any later version.
11
12 The GNU C Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Library General Public License for more details.
16
17 You should have received a copy of the GNU Library General Public
18 License along with the GNU C Library; see the file COPYING.LIB. If
19 not, write to the Free Software Foundation, Inc.,
20 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
21
22
23#ifndef __MATH_EMU_EXTENDED_H__
24#define __MATH_EMU_EXTENDED_H__
25
26#if _FP_W_TYPE_SIZE < 32
27#error "Here's a nickel, kid. Go buy yourself a real computer."
28#endif
29
30#if _FP_W_TYPE_SIZE < 64
31#define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE)
32#else
33#define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE)
34#endif
35
36#define _FP_FRACBITS_E 64
37#define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E)
38#define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E)
39#define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
40#define _FP_EXPBITS_E 15
41#define _FP_EXPBIAS_E 16383
42#define _FP_EXPMAX_E 32767
43
44#define _FP_QNANBIT_E \
45 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
46#define _FP_IMPLBIT_E \
47 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
48#define _FP_OVERFLOW_E \
49 ((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
50
51#if _FP_W_TYPE_SIZE < 64
52
53union _FP_UNION_E
54{
55 long double flt;
56 struct
57 {
58#if __BYTE_ORDER == __BIG_ENDIAN
59 unsigned long pad1 : _FP_W_TYPE_SIZE;
60 unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
61 unsigned long sign : 1;
62 unsigned long exp : _FP_EXPBITS_E;
63 unsigned long frac1 : _FP_W_TYPE_SIZE;
64 unsigned long frac0 : _FP_W_TYPE_SIZE;
65#else
66 unsigned long frac0 : _FP_W_TYPE_SIZE;
67 unsigned long frac1 : _FP_W_TYPE_SIZE;
68 unsigned exp : _FP_EXPBITS_E;
69 unsigned sign : 1;
70#endif /* not bigendian */
71 } bits __attribute__((packed));
72};
73
74
75#define FP_DECL_E(X) _FP_DECL(4,X)
76
77#define FP_UNPACK_RAW_E(X, val) \
78 do { \
79 union _FP_UNION_E _flo; _flo.flt = (val); \
80 \
81 X##_f[2] = 0; X##_f[3] = 0; \
82 X##_f[0] = _flo.bits.frac0; \
83 X##_f[1] = _flo.bits.frac1; \
84 X##_e = _flo.bits.exp; \
85 X##_s = _flo.bits.sign; \
86 if (!X##_e && (X##_f[1] || X##_f[0]) \
87 && !(X##_f[1] & _FP_IMPLBIT_E)) \
88 { \
89 X##_e++; \
90 FP_SET_EXCEPTION(FP_EX_DENORM); \
91 } \
92 } while (0)
93
94#define FP_UNPACK_RAW_EP(X, val) \
95 do { \
96 union _FP_UNION_E *_flo = \
97 (union _FP_UNION_E *)(val); \
98 \
99 X##_f[2] = 0; X##_f[3] = 0; \
100 X##_f[0] = _flo->bits.frac0; \
101 X##_f[1] = _flo->bits.frac1; \
102 X##_e = _flo->bits.exp; \
103 X##_s = _flo->bits.sign; \
104 if (!X##_e && (X##_f[1] || X##_f[0]) \
105 && !(X##_f[1] & _FP_IMPLBIT_E)) \
106 { \
107 X##_e++; \
108 FP_SET_EXCEPTION(FP_EX_DENORM); \
109 } \
110 } while (0)
111
112#define FP_PACK_RAW_E(val, X) \
113 do { \
114 union _FP_UNION_E _flo; \
115 \
116 if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
117 else X##_f[1] &= ~(_FP_IMPLBIT_E); \
118 _flo.bits.frac0 = X##_f[0]; \
119 _flo.bits.frac1 = X##_f[1]; \
120 _flo.bits.exp = X##_e; \
121 _flo.bits.sign = X##_s; \
122 \
123 (val) = _flo.flt; \
124 } while (0)
125
126#define FP_PACK_RAW_EP(val, X) \
127 do { \
128 if (!FP_INHIBIT_RESULTS) \
129 { \
130 union _FP_UNION_E *_flo = \
131 (union _FP_UNION_E *)(val); \
132 \
133 if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
134 else X##_f[1] &= ~(_FP_IMPLBIT_E); \
135 _flo->bits.frac0 = X##_f[0]; \
136 _flo->bits.frac1 = X##_f[1]; \
137 _flo->bits.exp = X##_e; \
138 _flo->bits.sign = X##_s; \
139 } \
140 } while (0)
141
142#define FP_UNPACK_E(X,val) \
143 do { \
144 FP_UNPACK_RAW_E(X,val); \
145 _FP_UNPACK_CANONICAL(E,4,X); \
146 } while (0)
147
148#define FP_UNPACK_EP(X,val) \
149 do { \
150 FP_UNPACK_RAW_2_P(X,val); \
151 _FP_UNPACK_CANONICAL(E,4,X); \
152 } while (0)
153
154#define FP_PACK_E(val,X) \
155 do { \
156 _FP_PACK_CANONICAL(E,4,X); \
157 FP_PACK_RAW_E(val,X); \
158 } while (0)
159
160#define FP_PACK_EP(val,X) \
161 do { \
162 _FP_PACK_CANONICAL(E,4,X); \
163 FP_PACK_RAW_EP(val,X); \
164 } while (0)
165
166#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,4,X)
167#define FP_NEG_E(R,X) _FP_NEG(E,4,R,X)
168#define FP_ADD_E(R,X,Y) _FP_ADD(E,4,R,X,Y)
169#define FP_SUB_E(R,X,Y) _FP_SUB(E,4,R,X,Y)
170#define FP_MUL_E(R,X,Y) _FP_MUL(E,4,R,X,Y)
171#define FP_DIV_E(R,X,Y) _FP_DIV(E,4,R,X,Y)
172#define FP_SQRT_E(R,X) _FP_SQRT(E,4,R,X)
173
174/*
175 * Square root algorithms:
176 * We have just one right now, maybe Newton approximation
177 * should be added for those machines where division is fast.
178 * This has special _E version because standard _4 square
179 * root would not work (it has to start normally with the
180 * second word and not the first), but as we have to do it
181 * anyway, we optimize it by doing most of the calculations
182 * in two UWtype registers instead of four.
183 */
184
185#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
186 do { \
187 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
188 _FP_FRAC_SRL_4(X, (_FP_WORKBITS)); \
189 while (q) \
190 { \
191 T##_f[1] = S##_f[1] + q; \
192 if (T##_f[1] <= X##_f[1]) \
193 { \
194 S##_f[1] = T##_f[1] + q; \
195 X##_f[1] -= T##_f[1]; \
196 R##_f[1] += q; \
197 } \
198 _FP_FRAC_SLL_2(X, 1); \
199 q >>= 1; \
200 } \
201 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
202 while (q) \
203 { \
204 T##_f[0] = S##_f[0] + q; \
205 T##_f[1] = S##_f[1]; \
206 if (T##_f[1] < X##_f[1] || \
207 (T##_f[1] == X##_f[1] && \
208 T##_f[0] <= X##_f[0])) \
209 { \
210 S##_f[0] = T##_f[0] + q; \
211 S##_f[1] += (T##_f[0] > S##_f[0]); \
212 _FP_FRAC_DEC_2(X, T); \
213 R##_f[0] += q; \
214 } \
215 _FP_FRAC_SLL_2(X, 1); \
216 q >>= 1; \
217 } \
218 _FP_FRAC_SLL_4(R, (_FP_WORKBITS)); \
219 if (X##_f[0] | X##_f[1]) \
220 { \
221 if (S##_f[1] < X##_f[1] || \
222 (S##_f[1] == X##_f[1] && \
223 S##_f[0] < X##_f[0])) \
224 R##_f[0] |= _FP_WORK_ROUND; \
225 R##_f[0] |= _FP_WORK_STICKY; \
226 } \
227 } while (0)
228
229#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un)
230#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y)
231
232#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,4,r,X,rsz,rsg)
233#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,4,r,X,rsz,rsg)
234#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,4,X,r,rs,rt)
235
236#define _FP_FRAC_HIGH_E(X) (X##_f[2])
237#define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
238
239#else /* not _FP_W_TYPE_SIZE < 64 */
240union _FP_UNION_E
241{
242 long double flt /* __attribute__((mode(TF))) */ ;
243 struct {
244#if __BYTE_ORDER == __BIG_ENDIAN
245 unsigned long pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
246 unsigned sign : 1;
247 unsigned exp : _FP_EXPBITS_E;
248 unsigned long frac : _FP_W_TYPE_SIZE;
249#else
250 unsigned long frac : _FP_W_TYPE_SIZE;
251 unsigned exp : _FP_EXPBITS_E;
252 unsigned sign : 1;
253#endif
254 } bits;
255};
256
257#define FP_DECL_E(X) _FP_DECL(2,X)
258
259#define FP_UNPACK_RAW_E(X, val) \
260 do { \
261 union _FP_UNION_E _flo; _flo.flt = (val); \
262 \
263 X##_f0 = _flo.bits.frac; \
264 X##_f1 = 0; \
265 X##_e = _flo.bits.exp; \
266 X##_s = _flo.bits.sign; \
267 if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
268 { \
269 X##_e++; \
270 FP_SET_EXCEPTION(FP_EX_DENORM); \
271 } \
272 } while (0)
273
274#define FP_UNPACK_RAW_EP(X, val) \
275 do { \
276 union _FP_UNION_E *_flo = \
277 (union _FP_UNION_E *)(val); \
278 \
279 X##_f0 = _flo->bits.frac; \
280 X##_f1 = 0; \
281 X##_e = _flo->bits.exp; \
282 X##_s = _flo->bits.sign; \
283 if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
284 { \
285 X##_e++; \
286 FP_SET_EXCEPTION(FP_EX_DENORM); \
287 } \
288 } while (0)
289
290#define FP_PACK_RAW_E(val, X) \
291 do { \
292 union _FP_UNION_E _flo; \
293 \
294 if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
295 else X##_f0 &= ~(_FP_IMPLBIT_E); \
296 _flo.bits.frac = X##_f0; \
297 _flo.bits.exp = X##_e; \
298 _flo.bits.sign = X##_s; \
299 \
300 (val) = _flo.flt; \
301 } while (0)
302
303#define FP_PACK_RAW_EP(fs, val, X) \
304 do { \
305 if (!FP_INHIBIT_RESULTS) \
306 { \
307 union _FP_UNION_E *_flo = \
308 (union _FP_UNION_E *)(val); \
309 \
310 if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
311 else X##_f0 &= ~(_FP_IMPLBIT_E); \
312 _flo->bits.frac = X##_f0; \
313 _flo->bits.exp = X##_e; \
314 _flo->bits.sign = X##_s; \
315 } \
316 } while (0)
317
318
319#define FP_UNPACK_E(X,val) \
320 do { \
321 FP_UNPACK_RAW_E(X,val); \
322 _FP_UNPACK_CANONICAL(E,2,X); \
323 } while (0)
324
325#define FP_UNPACK_EP(X,val) \
326 do { \
327 FP_UNPACK_RAW_EP(X,val); \
328 _FP_UNPACK_CANONICAL(E,2,X); \
329 } while (0)
330
331#define FP_PACK_E(val,X) \
332 do { \
333 _FP_PACK_CANONICAL(E,2,X); \
334 FP_PACK_RAW_E(val,X); \
335 } while (0)
336
337#define FP_PACK_EP(val,X) \
338 do { \
339 _FP_PACK_CANONICAL(E,2,X); \
340 FP_PACK_RAW_EP(val,X); \
341 } while (0)
342
343#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,2,X)
344#define FP_NEG_E(R,X) _FP_NEG(E,2,R,X)
345#define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y)
346#define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y)
347#define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y)
348#define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y)
349#define FP_SQRT_E(R,X) _FP_SQRT(E,2,R,X)
350
351/*
352 * Square root algorithms:
353 * We have just one right now, maybe Newton approximation
354 * should be added for those machines where division is fast.
355 * We optimize it by doing most of the calculations
356 * in one UWtype registers instead of two, although we don't
357 * have to.
358 */
359#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
360 do { \
361 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
362 _FP_FRAC_SRL_2(X, (_FP_WORKBITS)); \
363 while (q) \
364 { \
365 T##_f0 = S##_f0 + q; \
366 if (T##_f0 <= X##_f0) \
367 { \
368 S##_f0 = T##_f0 + q; \
369 X##_f0 -= T##_f0; \
370 R##_f0 += q; \
371 } \
372 _FP_FRAC_SLL_1(X, 1); \
373 q >>= 1; \
374 } \
375 _FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \
376 if (X##_f0) \
377 { \
378 if (S##_f0 < X##_f0) \
379 R##_f0 |= _FP_WORK_ROUND; \
380 R##_f0 |= _FP_WORK_STICKY; \
381 } \
382 } while (0)
383
384#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un)
385#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y)
386
387#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg)
388#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,2,r,X,rsz,rsg)
389#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt)
390
391#define _FP_FRAC_HIGH_E(X) (X##_f1)
392#define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
393
394#endif /* not _FP_W_TYPE_SIZE < 64 */
395
396#endif /* __MATH_EMU_EXTENDED_H__ */
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