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d876f532 UD |
1 | /* Software floating-point emulation. |
2 | Basic two-word fraction declaration and manipulation. | |
fe0b1e85 | 3 | Copyright (C) 1997,1998,1999,2006 Free Software Foundation, Inc. |
d876f532 UD |
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 | |
41bdb6e2 AJ |
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. | |
d876f532 | 14 | |
638a783c RM |
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 | ||
d876f532 UD |
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 | |
41bdb6e2 | 27 | Lesser General Public License for more details. |
d876f532 | 28 | |
41bdb6e2 AJ |
29 | You should have received a copy of the GNU Lesser General Public |
30 | License along with the GNU C Library; if not, write to the Free | |
638a783c RM |
31 | Software Foundation, 51 Franklin Street, Fifth Floor, Boston, |
32 | MA 02110-1301, USA. */ | |
d876f532 UD |
33 | |
34 | #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1 | |
35 | #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1) | |
36 | #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I) | |
37 | #define _FP_FRAC_HIGH_2(X) (X##_f1) | |
38 | #define _FP_FRAC_LOW_2(X) (X##_f0) | |
39 | #define _FP_FRAC_WORD_2(X,w) (X##_f##w) | |
40 | ||
fe0b1e85 RM |
41 | #define _FP_FRAC_SLL_2(X,N) \ |
42 | (void)(((N) < _FP_W_TYPE_SIZE) \ | |
43 | ? ({ \ | |
44 | if (__builtin_constant_p(N) && (N) == 1) \ | |
45 | { \ | |
46 | X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \ | |
47 | X##_f0 += X##_f0; \ | |
48 | } \ | |
49 | else \ | |
50 | { \ | |
51 | X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ | |
52 | X##_f0 <<= (N); \ | |
53 | } \ | |
54 | 0; \ | |
55 | }) \ | |
56 | : ({ \ | |
57 | X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ | |
58 | X##_f0 = 0; \ | |
59 | })) | |
60 | ||
d876f532 UD |
61 | |
62 | #define _FP_FRAC_SRL_2(X,N) \ | |
fe0b1e85 RM |
63 | (void)(((N) < _FP_W_TYPE_SIZE) \ |
64 | ? ({ \ | |
65 | X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ | |
66 | X##_f1 >>= (N); \ | |
67 | }) \ | |
68 | : ({ \ | |
69 | X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ | |
70 | X##_f1 = 0; \ | |
71 | })) | |
d876f532 UD |
72 | |
73 | /* Right shift with sticky-lsb. */ | |
fe0b1e85 RM |
74 | #define _FP_FRAC_SRST_2(X,S, N,sz) \ |
75 | (void)(((N) < _FP_W_TYPE_SIZE) \ | |
76 | ? ({ \ | |
77 | S = (__builtin_constant_p(N) && (N) == 1 \ | |
78 | ? X##_f0 & 1 \ | |
79 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ | |
80 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ | |
81 | X##_f1 >>= (N); \ | |
82 | }) \ | |
83 | : ({ \ | |
84 | S = ((((N) == _FP_W_TYPE_SIZE \ | |
85 | ? 0 \ | |
86 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ | |
87 | | X##_f0) != 0); \ | |
88 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ | |
89 | X##_f1 = 0; \ | |
90 | })) | |
91 | ||
92 | #define _FP_FRAC_SRS_2(X,N,sz) \ | |
93 | (void)(((N) < _FP_W_TYPE_SIZE) \ | |
94 | ? ({ \ | |
95 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \ | |
96 | (__builtin_constant_p(N) && (N) == 1 \ | |
97 | ? X##_f0 & 1 \ | |
98 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ | |
99 | X##_f1 >>= (N); \ | |
100 | }) \ | |
101 | : ({ \ | |
102 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \ | |
103 | ((((N) == _FP_W_TYPE_SIZE \ | |
104 | ? 0 \ | |
105 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ | |
106 | | X##_f0) != 0)); \ | |
107 | X##_f1 = 0; \ | |
108 | })) | |
d876f532 UD |
109 | |
110 | #define _FP_FRAC_ADDI_2(X,I) \ | |
111 | __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) | |
112 | ||
113 | #define _FP_FRAC_ADD_2(R,X,Y) \ | |
114 | __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) | |
115 | ||
116 | #define _FP_FRAC_SUB_2(R,X,Y) \ | |
117 | __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) | |
118 | ||
119 | #define _FP_FRAC_DEC_2(X,Y) \ | |
120 | __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0) | |
121 | ||
122 | #define _FP_FRAC_CLZ_2(R,X) \ | |
123 | do { \ | |
124 | if (X##_f1) \ | |
125 | __FP_CLZ(R,X##_f1); \ | |
126 | else \ | |
127 | { \ | |
128 | __FP_CLZ(R,X##_f0); \ | |
129 | R += _FP_W_TYPE_SIZE; \ | |
130 | } \ | |
131 | } while(0) | |
132 | ||
133 | /* Predicates */ | |
134 | #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) | |
135 | #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) | |
136 | #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) | |
cf299341 | 137 | #define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs) |
d876f532 UD |
138 | #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) |
139 | #define _FP_FRAC_GT_2(X, Y) \ | |
fe0b1e85 | 140 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) |
d876f532 | 141 | #define _FP_FRAC_GE_2(X, Y) \ |
fe0b1e85 | 142 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) |
d876f532 UD |
143 | |
144 | #define _FP_ZEROFRAC_2 0, 0 | |
145 | #define _FP_MINFRAC_2 0, 1 | |
146 | #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) | |
147 | ||
148 | /* | |
149 | * Internals | |
150 | */ | |
151 | ||
152 | #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) | |
153 | ||
154 | #define __FP_CLZ_2(R, xh, xl) \ | |
155 | do { \ | |
156 | if (xh) \ | |
157 | __FP_CLZ(R,xh); \ | |
158 | else \ | |
159 | { \ | |
160 | __FP_CLZ(R,xl); \ | |
161 | R += _FP_W_TYPE_SIZE; \ | |
162 | } \ | |
163 | } while(0) | |
164 | ||
165 | #if 0 | |
166 | ||
167 | #ifndef __FP_FRAC_ADDI_2 | |
168 | #define __FP_FRAC_ADDI_2(xh, xl, i) \ | |
169 | (xh += ((xl += i) < i)) | |
170 | #endif | |
171 | #ifndef __FP_FRAC_ADD_2 | |
172 | #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ | |
173 | (rh = xh + yh + ((rl = xl + yl) < xl)) | |
174 | #endif | |
175 | #ifndef __FP_FRAC_SUB_2 | |
176 | #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ | |
177 | (rh = xh - yh - ((rl = xl - yl) > xl)) | |
178 | #endif | |
179 | #ifndef __FP_FRAC_DEC_2 | |
180 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ | |
181 | do { \ | |
182 | UWtype _t = xl; \ | |
183 | xh -= yh + ((xl -= yl) > _t); \ | |
184 | } while (0) | |
185 | #endif | |
186 | ||
187 | #else | |
188 | ||
189 | #undef __FP_FRAC_ADDI_2 | |
190 | #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) | |
191 | #undef __FP_FRAC_ADD_2 | |
192 | #define __FP_FRAC_ADD_2 add_ssaaaa | |
193 | #undef __FP_FRAC_SUB_2 | |
194 | #define __FP_FRAC_SUB_2 sub_ddmmss | |
195 | #undef __FP_FRAC_DEC_2 | |
196 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl) | |
197 | ||
198 | #endif | |
199 | ||
200 | /* | |
201 | * Unpack the raw bits of a native fp value. Do not classify or | |
202 | * normalize the data. | |
203 | */ | |
204 | ||
205 | #define _FP_UNPACK_RAW_2(fs, X, val) \ | |
206 | do { \ | |
207 | union _FP_UNION_##fs _flo; _flo.flt = (val); \ | |
208 | \ | |
209 | X##_f0 = _flo.bits.frac0; \ | |
210 | X##_f1 = _flo.bits.frac1; \ | |
211 | X##_e = _flo.bits.exp; \ | |
212 | X##_s = _flo.bits.sign; \ | |
213 | } while (0) | |
214 | ||
215 | #define _FP_UNPACK_RAW_2_P(fs, X, val) \ | |
216 | do { \ | |
217 | union _FP_UNION_##fs *_flo = \ | |
218 | (union _FP_UNION_##fs *)(val); \ | |
219 | \ | |
220 | X##_f0 = _flo->bits.frac0; \ | |
221 | X##_f1 = _flo->bits.frac1; \ | |
222 | X##_e = _flo->bits.exp; \ | |
223 | X##_s = _flo->bits.sign; \ | |
224 | } while (0) | |
225 | ||
226 | ||
227 | /* | |
228 | * Repack the raw bits of a native fp value. | |
229 | */ | |
230 | ||
231 | #define _FP_PACK_RAW_2(fs, val, X) \ | |
232 | do { \ | |
233 | union _FP_UNION_##fs _flo; \ | |
234 | \ | |
235 | _flo.bits.frac0 = X##_f0; \ | |
236 | _flo.bits.frac1 = X##_f1; \ | |
237 | _flo.bits.exp = X##_e; \ | |
238 | _flo.bits.sign = X##_s; \ | |
239 | \ | |
240 | (val) = _flo.flt; \ | |
241 | } while (0) | |
242 | ||
243 | #define _FP_PACK_RAW_2_P(fs, val, X) \ | |
244 | do { \ | |
245 | union _FP_UNION_##fs *_flo = \ | |
246 | (union _FP_UNION_##fs *)(val); \ | |
247 | \ | |
248 | _flo->bits.frac0 = X##_f0; \ | |
249 | _flo->bits.frac1 = X##_f1; \ | |
250 | _flo->bits.exp = X##_e; \ | |
251 | _flo->bits.sign = X##_s; \ | |
252 | } while (0) | |
253 | ||
254 | ||
255 | /* | |
256 | * Multiplication algorithms: | |
257 | */ | |
258 | ||
259 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ | |
260 | ||
261 | #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ | |
262 | do { \ | |
263 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ | |
264 | \ | |
265 | doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ | |
266 | doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ | |
267 | doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ | |
268 | doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ | |
269 | \ | |
270 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
271 | _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \ | |
272 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
273 | _FP_FRAC_WORD_4(_z,1)); \ | |
274 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
275 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \ | |
276 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
277 | _FP_FRAC_WORD_4(_z,1)); \ | |
278 | \ | |
279 | /* Normalize since we know where the msb of the multiplicands \ | |
280 | were (bit B), we know that the msb of the of the product is \ | |
281 | at either 2B or 2B-1. */ \ | |
282 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ | |
283 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \ | |
284 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \ | |
285 | } while (0) | |
286 | ||
287 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. | |
288 | Do only 3 multiplications instead of four. This one is for machines | |
289 | where multiplication is much more expensive than subtraction. */ | |
290 | ||
291 | #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ | |
292 | do { \ | |
293 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ | |
294 | _FP_W_TYPE _d; \ | |
295 | int _c1, _c2; \ | |
296 | \ | |
297 | _b_f0 = X##_f0 + X##_f1; \ | |
298 | _c1 = _b_f0 < X##_f0; \ | |
299 | _b_f1 = Y##_f0 + Y##_f1; \ | |
300 | _c2 = _b_f1 < Y##_f0; \ | |
301 | doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ | |
302 | doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \ | |
303 | doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ | |
304 | \ | |
305 | _b_f0 &= -_c2; \ | |
306 | _b_f1 &= -_c1; \ | |
307 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
308 | _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \ | |
309 | 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \ | |
310 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
311 | _b_f0); \ | |
312 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
313 | _b_f1); \ | |
314 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
315 | _FP_FRAC_WORD_4(_z,1), \ | |
316 | 0, _d, _FP_FRAC_WORD_4(_z,0)); \ | |
317 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ | |
318 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \ | |
319 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \ | |
320 | _c_f1, _c_f0, \ | |
321 | _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \ | |
322 | \ | |
323 | /* Normalize since we know where the msb of the multiplicands \ | |
324 | were (bit B), we know that the msb of the of the product is \ | |
325 | at either 2B or 2B-1. */ \ | |
326 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ | |
327 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \ | |
328 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \ | |
329 | } while (0) | |
330 | ||
331 | #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ | |
332 | do { \ | |
333 | _FP_FRAC_DECL_4(_z); \ | |
334 | _FP_W_TYPE _x[2], _y[2]; \ | |
335 | _x[0] = X##_f0; _x[1] = X##_f1; \ | |
336 | _y[0] = Y##_f0; _y[1] = Y##_f1; \ | |
337 | \ | |
338 | mpn_mul_n(_z_f, _x, _y, 2); \ | |
339 | \ | |
340 | /* Normalize since we know where the msb of the multiplicands \ | |
341 | were (bit B), we know that the msb of the of the product is \ | |
342 | at either 2B or 2B-1. */ \ | |
343 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ | |
344 | R##_f0 = _z_f[0]; \ | |
345 | R##_f1 = _z_f[1]; \ | |
346 | } while (0) | |
347 | ||
348 | /* Do at most 120x120=240 bits multiplication using double floating | |
349 | point multiplication. This is useful if floating point | |
350 | multiplication has much bigger throughput than integer multiply. | |
351 | It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits | |
352 | between 106 and 120 only. | |
353 | Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. | |
354 | SETFETZ is a macro which will disable all FPU exceptions and set rounding | |
355 | towards zero, RESETFE should optionally reset it back. */ | |
356 | ||
357 | #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ | |
358 | do { \ | |
359 | static const double _const[] = { \ | |
360 | /* 2^-24 */ 5.9604644775390625e-08, \ | |
361 | /* 2^-48 */ 3.5527136788005009e-15, \ | |
362 | /* 2^-72 */ 2.1175823681357508e-22, \ | |
363 | /* 2^-96 */ 1.2621774483536189e-29, \ | |
364 | /* 2^28 */ 2.68435456e+08, \ | |
365 | /* 2^4 */ 1.600000e+01, \ | |
366 | /* 2^-20 */ 9.5367431640625e-07, \ | |
367 | /* 2^-44 */ 5.6843418860808015e-14, \ | |
368 | /* 2^-68 */ 3.3881317890172014e-21, \ | |
369 | /* 2^-92 */ 2.0194839173657902e-28, \ | |
370 | /* 2^-116 */ 1.2037062152420224e-35}; \ | |
371 | double _a240, _b240, _c240, _d240, _e240, _f240, \ | |
372 | _g240, _h240, _i240, _j240, _k240; \ | |
373 | union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ | |
374 | _p240, _q240, _r240, _s240; \ | |
375 | UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ | |
376 | \ | |
377 | if (wfracbits < 106 || wfracbits > 120) \ | |
378 | abort(); \ | |
379 | \ | |
380 | setfetz; \ | |
381 | \ | |
382 | _e240 = (double)(long)(X##_f0 & 0xffffff); \ | |
383 | _j240 = (double)(long)(Y##_f0 & 0xffffff); \ | |
384 | _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ | |
385 | _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ | |
386 | _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ | |
387 | _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ | |
388 | _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ | |
389 | _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ | |
390 | _a240 = (double)(long)(X##_f1 >> 32); \ | |
391 | _f240 = (double)(long)(Y##_f1 >> 32); \ | |
392 | _e240 *= _const[3]; \ | |
393 | _j240 *= _const[3]; \ | |
394 | _d240 *= _const[2]; \ | |
395 | _i240 *= _const[2]; \ | |
396 | _c240 *= _const[1]; \ | |
397 | _h240 *= _const[1]; \ | |
398 | _b240 *= _const[0]; \ | |
399 | _g240 *= _const[0]; \ | |
400 | _s240.d = _e240*_j240;\ | |
401 | _r240.d = _d240*_j240 + _e240*_i240;\ | |
402 | _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\ | |
403 | _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\ | |
404 | _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\ | |
405 | _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ | |
406 | _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ | |
407 | _l240.d = _a240*_g240 + _b240*_f240; \ | |
408 | _k240 = _a240*_f240; \ | |
409 | _r240.d += _s240.d; \ | |
410 | _q240.d += _r240.d; \ | |
411 | _p240.d += _q240.d; \ | |
412 | _o240.d += _p240.d; \ | |
413 | _n240.d += _o240.d; \ | |
414 | _m240.d += _n240.d; \ | |
415 | _l240.d += _m240.d; \ | |
416 | _k240 += _l240.d; \ | |
417 | _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ | |
418 | _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ | |
419 | _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ | |
420 | _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ | |
421 | _o240.d += _const[7]; \ | |
422 | _n240.d += _const[6]; \ | |
423 | _m240.d += _const[5]; \ | |
424 | _l240.d += _const[4]; \ | |
425 | if (_s240.d != 0.0) _y240 = 1; \ | |
426 | if (_r240.d != 0.0) _y240 = 1; \ | |
427 | if (_q240.d != 0.0) _y240 = 1; \ | |
428 | if (_p240.d != 0.0) _y240 = 1; \ | |
429 | _t240 = (DItype)_k240; \ | |
430 | _u240 = _l240.i; \ | |
431 | _v240 = _m240.i; \ | |
432 | _w240 = _n240.i; \ | |
433 | _x240 = _o240.i; \ | |
434 | R##_f1 = (_t240 << (128 - (wfracbits - 1))) \ | |
435 | | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \ | |
436 | R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ | |
437 | | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ | |
438 | | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ | |
439 | | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ | |
440 | | _y240; \ | |
441 | resetfe; \ | |
442 | } while (0) | |
443 | ||
444 | /* | |
445 | * Division algorithms: | |
446 | */ | |
447 | ||
448 | #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ | |
449 | do { \ | |
450 | _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ | |
451 | if (_FP_FRAC_GT_2(X, Y)) \ | |
452 | { \ | |
453 | _n_f2 = X##_f1 >> 1; \ | |
454 | _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ | |
455 | _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ | |
456 | } \ | |
457 | else \ | |
458 | { \ | |
459 | R##_e--; \ | |
460 | _n_f2 = X##_f1; \ | |
461 | _n_f1 = X##_f0; \ | |
462 | _n_f0 = 0; \ | |
463 | } \ | |
464 | \ | |
465 | /* Normalize, i.e. make the most significant bit of the \ | |
466 | denominator set. */ \ | |
467 | _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ | |
468 | \ | |
469 | udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ | |
470 | umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ | |
471 | _r_f0 = _n_f0; \ | |
472 | if (_FP_FRAC_GT_2(_m, _r)) \ | |
473 | { \ | |
474 | R##_f1--; \ | |
475 | _FP_FRAC_ADD_2(_r, Y, _r); \ | |
476 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ | |
477 | { \ | |
478 | R##_f1--; \ | |
479 | _FP_FRAC_ADD_2(_r, Y, _r); \ | |
480 | } \ | |
481 | } \ | |
482 | _FP_FRAC_DEC_2(_r, _m); \ | |
483 | \ | |
484 | if (_r_f1 == Y##_f1) \ | |
485 | { \ | |
486 | /* This is a special case, not an optimization \ | |
487 | (_r/Y##_f1 would not fit into UWtype). \ | |
488 | As _r is guaranteed to be < Y, R##_f0 can be either \ | |
489 | (UWtype)-1 or (UWtype)-2. But as we know what kind \ | |
490 | of bits it is (sticky, guard, round), we don't care. \ | |
491 | We also don't care what the reminder is, because the \ | |
492 | guard bit will be set anyway. -jj */ \ | |
493 | R##_f0 = -1; \ | |
494 | } \ | |
495 | else \ | |
496 | { \ | |
497 | udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ | |
498 | umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ | |
499 | _r_f0 = 0; \ | |
500 | if (_FP_FRAC_GT_2(_m, _r)) \ | |
501 | { \ | |
502 | R##_f0--; \ | |
503 | _FP_FRAC_ADD_2(_r, Y, _r); \ | |
504 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ | |
505 | { \ | |
506 | R##_f0--; \ | |
507 | _FP_FRAC_ADD_2(_r, Y, _r); \ | |
508 | } \ | |
509 | } \ | |
510 | if (!_FP_FRAC_EQ_2(_r, _m)) \ | |
511 | R##_f0 |= _FP_WORK_STICKY; \ | |
512 | } \ | |
513 | } while (0) | |
514 | ||
515 | ||
516 | #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ | |
517 | do { \ | |
518 | _FP_W_TYPE _x[4], _y[2], _z[4]; \ | |
519 | _y[0] = Y##_f0; _y[1] = Y##_f1; \ | |
520 | _x[0] = _x[3] = 0; \ | |
521 | if (_FP_FRAC_GT_2(X, Y)) \ | |
522 | { \ | |
523 | R##_e++; \ | |
524 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ | |
525 | X##_f1 >> (_FP_W_TYPE_SIZE - \ | |
526 | (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ | |
527 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ | |
528 | } \ | |
529 | else \ | |
530 | { \ | |
531 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ | |
532 | X##_f1 >> (_FP_W_TYPE_SIZE - \ | |
533 | (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ | |
534 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ | |
535 | } \ | |
536 | \ | |
537 | (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ | |
538 | R##_f1 = _z[1]; \ | |
539 | R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ | |
540 | } while (0) | |
541 | ||
542 | ||
543 | /* | |
544 | * Square root algorithms: | |
545 | * We have just one right now, maybe Newton approximation | |
546 | * should be added for those machines where division is fast. | |
547 | */ | |
548 | ||
549 | #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ | |
550 | do { \ | |
551 | while (q) \ | |
552 | { \ | |
553 | T##_f1 = S##_f1 + q; \ | |
554 | if (T##_f1 <= X##_f1) \ | |
555 | { \ | |
556 | S##_f1 = T##_f1 + q; \ | |
557 | X##_f1 -= T##_f1; \ | |
558 | R##_f1 += q; \ | |
559 | } \ | |
560 | _FP_FRAC_SLL_2(X, 1); \ | |
561 | q >>= 1; \ | |
562 | } \ | |
563 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ | |
564 | while (q != _FP_WORK_ROUND) \ | |
565 | { \ | |
566 | T##_f0 = S##_f0 + q; \ | |
567 | T##_f1 = S##_f1; \ | |
568 | if (T##_f1 < X##_f1 || \ | |
569 | (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ | |
570 | { \ | |
571 | S##_f0 = T##_f0 + q; \ | |
572 | S##_f1 += (T##_f0 > S##_f0); \ | |
573 | _FP_FRAC_DEC_2(X, T); \ | |
574 | R##_f0 += q; \ | |
575 | } \ | |
576 | _FP_FRAC_SLL_2(X, 1); \ | |
577 | q >>= 1; \ | |
578 | } \ | |
579 | if (X##_f0 | X##_f1) \ | |
580 | { \ | |
581 | if (S##_f1 < X##_f1 || \ | |
582 | (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ | |
583 | R##_f0 |= _FP_WORK_ROUND; \ | |
584 | R##_f0 |= _FP_WORK_STICKY; \ | |
585 | } \ | |
586 | } while (0) | |
587 | ||
588 | ||
589 | /* | |
590 | * Assembly/disassembly for converting to/from integral types. | |
591 | * No shifting or overflow handled here. | |
592 | */ | |
593 | ||
594 | #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ | |
fe0b1e85 RM |
595 | (void)((rsize <= _FP_W_TYPE_SIZE) \ |
596 | ? ({ r = X##_f0; }) \ | |
597 | : ({ \ | |
598 | r = X##_f1; \ | |
599 | r <<= _FP_W_TYPE_SIZE; \ | |
600 | r += X##_f0; \ | |
601 | })) | |
d876f532 UD |
602 | |
603 | #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ | |
604 | do { \ | |
605 | X##_f0 = r; \ | |
606 | X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ | |
607 | } while (0) | |
608 | ||
609 | /* | |
610 | * Convert FP values between word sizes | |
611 | */ | |
612 | ||
fe0b1e85 | 613 | #define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0) |
d876f532 | 614 | |
fe0b1e85 | 615 | #define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0)) |