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d876f532 UD |
1 | /* Software floating-point emulation. |
2 | Basic four-word fraction declaration and manipulation. | |
568035b7 | 3 | Copyright (C) 1997-2013 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 | 29 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 PE |
30 | License along with the GNU C Library; if not, see |
31 | <http://www.gnu.org/licenses/>. */ | |
d876f532 UD |
32 | |
33 | #define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4] | |
34 | #define _FP_FRAC_COPY_4(D,S) \ | |
35 | (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \ | |
36 | D##_f[2] = S##_f[2], D##_f[3] = S##_f[3]) | |
37 | #define _FP_FRAC_SET_4(X,I) __FP_FRAC_SET_4(X, I) | |
38 | #define _FP_FRAC_HIGH_4(X) (X##_f[3]) | |
39 | #define _FP_FRAC_LOW_4(X) (X##_f[0]) | |
40 | #define _FP_FRAC_WORD_4(X,w) (X##_f[w]) | |
41 | ||
42 | #define _FP_FRAC_SLL_4(X,N) \ | |
43 | do { \ | |
44 | _FP_I_TYPE _up, _down, _skip, _i; \ | |
45 | _skip = (N) / _FP_W_TYPE_SIZE; \ | |
46 | _up = (N) % _FP_W_TYPE_SIZE; \ | |
47 | _down = _FP_W_TYPE_SIZE - _up; \ | |
48 | if (!_up) \ | |
49 | for (_i = 3; _i >= _skip; --_i) \ | |
50 | X##_f[_i] = X##_f[_i-_skip]; \ | |
51 | else \ | |
52 | { \ | |
53 | for (_i = 3; _i > _skip; --_i) \ | |
54 | X##_f[_i] = X##_f[_i-_skip] << _up \ | |
55 | | X##_f[_i-_skip-1] >> _down; \ | |
56 | X##_f[_i--] = X##_f[0] << _up; \ | |
57 | } \ | |
58 | for (; _i >= 0; --_i) \ | |
59 | X##_f[_i] = 0; \ | |
60 | } while (0) | |
61 | ||
62 | /* This one was broken too */ | |
63 | #define _FP_FRAC_SRL_4(X,N) \ | |
64 | do { \ | |
65 | _FP_I_TYPE _up, _down, _skip, _i; \ | |
66 | _skip = (N) / _FP_W_TYPE_SIZE; \ | |
67 | _down = (N) % _FP_W_TYPE_SIZE; \ | |
68 | _up = _FP_W_TYPE_SIZE - _down; \ | |
69 | if (!_down) \ | |
70 | for (_i = 0; _i <= 3-_skip; ++_i) \ | |
71 | X##_f[_i] = X##_f[_i+_skip]; \ | |
72 | else \ | |
73 | { \ | |
74 | for (_i = 0; _i < 3-_skip; ++_i) \ | |
75 | X##_f[_i] = X##_f[_i+_skip] >> _down \ | |
76 | | X##_f[_i+_skip+1] << _up; \ | |
77 | X##_f[_i++] = X##_f[3] >> _down; \ | |
78 | } \ | |
79 | for (; _i < 4; ++_i) \ | |
80 | X##_f[_i] = 0; \ | |
81 | } while (0) | |
82 | ||
83 | ||
9c84384c | 84 | /* Right shift with sticky-lsb. |
d876f532 UD |
85 | * What this actually means is that we do a standard right-shift, |
86 | * but that if any of the bits that fall off the right hand side | |
87 | * were one then we always set the LSbit. | |
88 | */ | |
fe0b1e85 RM |
89 | #define _FP_FRAC_SRST_4(X,S,N,size) \ |
90 | do { \ | |
91 | _FP_I_TYPE _up, _down, _skip, _i; \ | |
92 | _FP_W_TYPE _s; \ | |
93 | _skip = (N) / _FP_W_TYPE_SIZE; \ | |
94 | _down = (N) % _FP_W_TYPE_SIZE; \ | |
95 | _up = _FP_W_TYPE_SIZE - _down; \ | |
96 | for (_s = _i = 0; _i < _skip; ++_i) \ | |
97 | _s |= X##_f[_i]; \ | |
98 | if (!_down) \ | |
99 | for (_i = 0; _i <= 3-_skip; ++_i) \ | |
100 | X##_f[_i] = X##_f[_i+_skip]; \ | |
101 | else \ | |
102 | { \ | |
103 | _s |= X##_f[_i] << _up; \ | |
104 | for (_i = 0; _i < 3-_skip; ++_i) \ | |
105 | X##_f[_i] = X##_f[_i+_skip] >> _down \ | |
106 | | X##_f[_i+_skip+1] << _up; \ | |
107 | X##_f[_i++] = X##_f[3] >> _down; \ | |
108 | } \ | |
109 | for (; _i < 4; ++_i) \ | |
110 | X##_f[_i] = 0; \ | |
111 | S = (_s != 0); \ | |
112 | } while (0) | |
113 | ||
114 | #define _FP_FRAC_SRS_4(X,N,size) \ | |
115 | do { \ | |
116 | int _sticky; \ | |
117 | _FP_FRAC_SRST_4(X, _sticky, N, size); \ | |
118 | X##_f[0] |= _sticky; \ | |
d876f532 UD |
119 | } while (0) |
120 | ||
121 | #define _FP_FRAC_ADD_4(R,X,Y) \ | |
122 | __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ | |
123 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ | |
124 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) | |
125 | ||
126 | #define _FP_FRAC_SUB_4(R,X,Y) \ | |
127 | __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ | |
128 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ | |
129 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) | |
130 | ||
131 | #define _FP_FRAC_DEC_4(X,Y) \ | |
132 | __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ | |
133 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) | |
134 | ||
135 | #define _FP_FRAC_ADDI_4(X,I) \ | |
136 | __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I) | |
137 | ||
138 | #define _FP_ZEROFRAC_4 0,0,0,0 | |
139 | #define _FP_MINFRAC_4 0,0,0,1 | |
140 | #define _FP_MAXFRAC_4 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) | |
141 | ||
142 | #define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0) | |
143 | #define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE)X##_f[3] < 0) | |
144 | #define _FP_FRAC_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) | |
cf299341 | 145 | #define _FP_FRAC_CLEAR_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs) |
d876f532 UD |
146 | |
147 | #define _FP_FRAC_EQ_4(X,Y) \ | |
148 | (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \ | |
149 | && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3]) | |
150 | ||
151 | #define _FP_FRAC_GT_4(X,Y) \ | |
152 | (X##_f[3] > Y##_f[3] || \ | |
153 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \ | |
154 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \ | |
155 | (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0]) \ | |
156 | )) \ | |
157 | )) \ | |
158 | ) | |
159 | ||
160 | #define _FP_FRAC_GE_4(X,Y) \ | |
161 | (X##_f[3] > Y##_f[3] || \ | |
162 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \ | |
163 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \ | |
164 | (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0]) \ | |
165 | )) \ | |
166 | )) \ | |
167 | ) | |
168 | ||
169 | ||
170 | #define _FP_FRAC_CLZ_4(R,X) \ | |
171 | do { \ | |
172 | if (X##_f[3]) \ | |
173 | { \ | |
174 | __FP_CLZ(R,X##_f[3]); \ | |
175 | } \ | |
176 | else if (X##_f[2]) \ | |
177 | { \ | |
178 | __FP_CLZ(R,X##_f[2]); \ | |
179 | R += _FP_W_TYPE_SIZE; \ | |
180 | } \ | |
181 | else if (X##_f[1]) \ | |
182 | { \ | |
52e1b618 | 183 | __FP_CLZ(R,X##_f[1]); \ |
d876f532 UD |
184 | R += _FP_W_TYPE_SIZE*2; \ |
185 | } \ | |
186 | else \ | |
187 | { \ | |
188 | __FP_CLZ(R,X##_f[0]); \ | |
189 | R += _FP_W_TYPE_SIZE*3; \ | |
190 | } \ | |
191 | } while(0) | |
192 | ||
193 | ||
194 | #define _FP_UNPACK_RAW_4(fs, X, val) \ | |
195 | do { \ | |
196 | union _FP_UNION_##fs _flo; _flo.flt = (val); \ | |
197 | X##_f[0] = _flo.bits.frac0; \ | |
198 | X##_f[1] = _flo.bits.frac1; \ | |
199 | X##_f[2] = _flo.bits.frac2; \ | |
200 | X##_f[3] = _flo.bits.frac3; \ | |
201 | X##_e = _flo.bits.exp; \ | |
202 | X##_s = _flo.bits.sign; \ | |
203 | } while (0) | |
204 | ||
205 | #define _FP_UNPACK_RAW_4_P(fs, X, val) \ | |
206 | do { \ | |
207 | union _FP_UNION_##fs *_flo = \ | |
208 | (union _FP_UNION_##fs *)(val); \ | |
209 | \ | |
210 | X##_f[0] = _flo->bits.frac0; \ | |
211 | X##_f[1] = _flo->bits.frac1; \ | |
212 | X##_f[2] = _flo->bits.frac2; \ | |
213 | X##_f[3] = _flo->bits.frac3; \ | |
214 | X##_e = _flo->bits.exp; \ | |
215 | X##_s = _flo->bits.sign; \ | |
216 | } while (0) | |
217 | ||
218 | #define _FP_PACK_RAW_4(fs, val, X) \ | |
219 | do { \ | |
220 | union _FP_UNION_##fs _flo; \ | |
221 | _flo.bits.frac0 = X##_f[0]; \ | |
222 | _flo.bits.frac1 = X##_f[1]; \ | |
223 | _flo.bits.frac2 = X##_f[2]; \ | |
224 | _flo.bits.frac3 = X##_f[3]; \ | |
225 | _flo.bits.exp = X##_e; \ | |
226 | _flo.bits.sign = X##_s; \ | |
227 | (val) = _flo.flt; \ | |
228 | } while (0) | |
229 | ||
230 | #define _FP_PACK_RAW_4_P(fs, val, X) \ | |
231 | do { \ | |
232 | union _FP_UNION_##fs *_flo = \ | |
233 | (union _FP_UNION_##fs *)(val); \ | |
234 | \ | |
235 | _flo->bits.frac0 = X##_f[0]; \ | |
236 | _flo->bits.frac1 = X##_f[1]; \ | |
237 | _flo->bits.frac2 = X##_f[2]; \ | |
238 | _flo->bits.frac3 = X##_f[3]; \ | |
239 | _flo->bits.exp = X##_e; \ | |
240 | _flo->bits.sign = X##_s; \ | |
241 | } while (0) | |
242 | ||
243 | /* | |
244 | * Multiplication algorithms: | |
245 | */ | |
246 | ||
247 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ | |
248 | ||
249 | #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \ | |
250 | do { \ | |
251 | _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ | |
252 | _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f); \ | |
253 | \ | |
254 | doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \ | |
255 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]); \ | |
256 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]); \ | |
257 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]); \ | |
258 | doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]); \ | |
259 | doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]); \ | |
260 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ | |
261 | _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \ | |
262 | 0,0,_FP_FRAC_WORD_8(_z,1)); \ | |
263 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ | |
264 | _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \ | |
265 | _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ | |
266 | _FP_FRAC_WORD_8(_z,1)); \ | |
267 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ | |
268 | _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \ | |
269 | 0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \ | |
270 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ | |
271 | _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \ | |
272 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ | |
273 | _FP_FRAC_WORD_8(_z,2)); \ | |
274 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ | |
275 | _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \ | |
276 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ | |
277 | _FP_FRAC_WORD_8(_z,2)); \ | |
278 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]); \ | |
279 | doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]); \ | |
280 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]); \ | |
281 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]); \ | |
282 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
283 | _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \ | |
284 | 0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \ | |
285 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
286 | _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \ | |
287 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
288 | _FP_FRAC_WORD_8(_z,3)); \ | |
289 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
290 | _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \ | |
291 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
292 | _FP_FRAC_WORD_8(_z,3)); \ | |
293 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
294 | _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \ | |
295 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ | |
296 | _FP_FRAC_WORD_8(_z,3)); \ | |
297 | doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]); \ | |
298 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]); \ | |
299 | doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]); \ | |
300 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]); \ | |
301 | doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]); \ | |
302 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ | |
303 | _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \ | |
304 | 0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \ | |
305 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ | |
306 | _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \ | |
307 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ | |
308 | _FP_FRAC_WORD_8(_z,4)); \ | |
309 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ | |
310 | _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \ | |
311 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ | |
312 | _FP_FRAC_WORD_8(_z,4)); \ | |
313 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ | |
314 | _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \ | |
315 | 0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \ | |
316 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ | |
317 | _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \ | |
318 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ | |
319 | _FP_FRAC_WORD_8(_z,5)); \ | |
320 | doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \ | |
321 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ | |
322 | _b_f1,_b_f0, \ | |
323 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \ | |
324 | \ | |
325 | /* Normalize since we know where the msb of the multiplicands \ | |
326 | were (bit B), we know that the msb of the of the product is \ | |
327 | at either 2B or 2B-1. */ \ | |
328 | _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \ | |
329 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \ | |
330 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \ | |
331 | } while (0) | |
332 | ||
333 | #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \ | |
334 | do { \ | |
335 | _FP_FRAC_DECL_8(_z); \ | |
336 | \ | |
337 | mpn_mul_n(_z_f, _x_f, _y_f, 4); \ | |
338 | \ | |
339 | /* Normalize since we know where the msb of the multiplicands \ | |
340 | were (bit B), we know that the msb of the of the product is \ | |
341 | at either 2B or 2B-1. */ \ | |
342 | _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \ | |
343 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \ | |
344 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \ | |
345 | } while (0) | |
346 | ||
347 | /* | |
348 | * Helper utility for _FP_DIV_MEAT_4_udiv: | |
349 | * pppp = m * nnn | |
350 | */ | |
351 | #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0) \ | |
352 | do { \ | |
353 | UWtype _t; \ | |
354 | umul_ppmm(p1,p0,m,n0); \ | |
355 | umul_ppmm(p2,_t,m,n1); \ | |
356 | __FP_FRAC_ADDI_2(p2,p1,_t); \ | |
357 | umul_ppmm(p3,_t,m,n2); \ | |
358 | __FP_FRAC_ADDI_2(p3,p2,_t); \ | |
359 | } while (0) | |
360 | ||
361 | /* | |
362 | * Division algorithms: | |
363 | */ | |
364 | ||
365 | #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \ | |
366 | do { \ | |
367 | int _i; \ | |
368 | _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m); \ | |
369 | _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4); \ | |
370 | if (_FP_FRAC_GT_4(X, Y)) \ | |
371 | { \ | |
372 | _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \ | |
373 | _FP_FRAC_SRL_4(X, 1); \ | |
374 | } \ | |
375 | else \ | |
376 | R##_e--; \ | |
377 | \ | |
378 | /* Normalize, i.e. make the most significant bit of the \ | |
379 | denominator set. */ \ | |
380 | _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs); \ | |
381 | \ | |
382 | for (_i = 3; ; _i--) \ | |
383 | { \ | |
384 | if (X##_f[3] == Y##_f[3]) \ | |
385 | { \ | |
386 | /* This is a special case, not an optimization \ | |
387 | (X##_f[3]/Y##_f[3] would not fit into UWtype). \ | |
388 | As X## is guaranteed to be < Y, R##_f[_i] can be either \ | |
389 | (UWtype)-1 or (UWtype)-2. */ \ | |
390 | R##_f[_i] = -1; \ | |
391 | if (!_i) \ | |
392 | break; \ | |
393 | __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ | |
394 | Y##_f[2], Y##_f[1], Y##_f[0], 0, \ | |
395 | X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \ | |
396 | _FP_FRAC_SUB_4(X, Y, X); \ | |
397 | if (X##_f[3] > Y##_f[3]) \ | |
398 | { \ | |
399 | R##_f[_i] = -2; \ | |
400 | _FP_FRAC_ADD_4(X, Y, X); \ | |
401 | } \ | |
402 | } \ | |
403 | else \ | |
404 | { \ | |
405 | udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \ | |
406 | umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0], \ | |
407 | R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \ | |
408 | X##_f[2] = X##_f[1]; \ | |
409 | X##_f[1] = X##_f[0]; \ | |
410 | X##_f[0] = _n_f[_i]; \ | |
411 | if (_FP_FRAC_GT_4(_m, X)) \ | |
412 | { \ | |
413 | R##_f[_i]--; \ | |
414 | _FP_FRAC_ADD_4(X, Y, X); \ | |
415 | if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X)) \ | |
416 | { \ | |
417 | R##_f[_i]--; \ | |
418 | _FP_FRAC_ADD_4(X, Y, X); \ | |
419 | } \ | |
420 | } \ | |
421 | _FP_FRAC_DEC_4(X, _m); \ | |
422 | if (!_i) \ | |
423 | { \ | |
424 | if (!_FP_FRAC_EQ_4(X, _m)) \ | |
425 | R##_f[0] |= _FP_WORK_STICKY; \ | |
426 | break; \ | |
427 | } \ | |
428 | } \ | |
429 | } \ | |
430 | } while (0) | |
431 | ||
432 | ||
433 | /* | |
434 | * Square root algorithms: | |
435 | * We have just one right now, maybe Newton approximation | |
436 | * should be added for those machines where division is fast. | |
437 | */ | |
9c84384c | 438 | |
d876f532 UD |
439 | #define _FP_SQRT_MEAT_4(R, S, T, X, q) \ |
440 | do { \ | |
441 | while (q) \ | |
442 | { \ | |
443 | T##_f[3] = S##_f[3] + q; \ | |
444 | if (T##_f[3] <= X##_f[3]) \ | |
445 | { \ | |
446 | S##_f[3] = T##_f[3] + q; \ | |
447 | X##_f[3] -= T##_f[3]; \ | |
448 | R##_f[3] += q; \ | |
449 | } \ | |
450 | _FP_FRAC_SLL_4(X, 1); \ | |
451 | q >>= 1; \ | |
452 | } \ | |
453 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ | |
454 | while (q) \ | |
455 | { \ | |
456 | T##_f[2] = S##_f[2] + q; \ | |
457 | T##_f[3] = S##_f[3]; \ | |
458 | if (T##_f[3] < X##_f[3] || \ | |
459 | (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \ | |
460 | { \ | |
461 | S##_f[2] = T##_f[2] + q; \ | |
462 | S##_f[3] += (T##_f[2] > S##_f[2]); \ | |
463 | __FP_FRAC_DEC_2(X##_f[3], X##_f[2], \ | |
464 | T##_f[3], T##_f[2]); \ | |
465 | R##_f[2] += q; \ | |
466 | } \ | |
467 | _FP_FRAC_SLL_4(X, 1); \ | |
468 | q >>= 1; \ | |
469 | } \ | |
470 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ | |
471 | while (q) \ | |
472 | { \ | |
473 | T##_f[1] = S##_f[1] + q; \ | |
474 | T##_f[2] = S##_f[2]; \ | |
475 | T##_f[3] = S##_f[3]; \ | |
476 | if (T##_f[3] < X##_f[3] || \ | |
477 | (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] || \ | |
478 | (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1])))) \ | |
479 | { \ | |
480 | S##_f[1] = T##_f[1] + q; \ | |
481 | S##_f[2] += (T##_f[1] > S##_f[1]); \ | |
482 | S##_f[3] += (T##_f[2] > S##_f[2]); \ | |
483 | __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1], \ | |
350635a5 | 484 | T##_f[3], T##_f[2], T##_f[1]); \ |
d876f532 UD |
485 | R##_f[1] += q; \ |
486 | } \ | |
487 | _FP_FRAC_SLL_4(X, 1); \ | |
488 | q >>= 1; \ | |
489 | } \ | |
490 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ | |
491 | while (q != _FP_WORK_ROUND) \ | |
492 | { \ | |
493 | T##_f[0] = S##_f[0] + q; \ | |
494 | T##_f[1] = S##_f[1]; \ | |
495 | T##_f[2] = S##_f[2]; \ | |
496 | T##_f[3] = S##_f[3]; \ | |
497 | if (_FP_FRAC_GE_4(X,T)) \ | |
498 | { \ | |
499 | S##_f[0] = T##_f[0] + q; \ | |
500 | S##_f[1] += (T##_f[0] > S##_f[0]); \ | |
501 | S##_f[2] += (T##_f[1] > S##_f[1]); \ | |
502 | S##_f[3] += (T##_f[2] > S##_f[2]); \ | |
503 | _FP_FRAC_DEC_4(X, T); \ | |
504 | R##_f[0] += q; \ | |
505 | } \ | |
506 | _FP_FRAC_SLL_4(X, 1); \ | |
507 | q >>= 1; \ | |
508 | } \ | |
509 | if (!_FP_FRAC_ZEROP_4(X)) \ | |
510 | { \ | |
511 | if (_FP_FRAC_GT_4(X,S)) \ | |
512 | R##_f[0] |= _FP_WORK_ROUND; \ | |
513 | R##_f[0] |= _FP_WORK_STICKY; \ | |
514 | } \ | |
515 | } while (0) | |
516 | ||
517 | ||
518 | /* | |
9c84384c | 519 | * Internals |
d876f532 UD |
520 | */ |
521 | ||
522 | #define __FP_FRAC_SET_4(X,I3,I2,I1,I0) \ | |
523 | (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0) | |
524 | ||
525 | #ifndef __FP_FRAC_ADD_3 | |
1a8aaf91 UD |
526 | #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ |
527 | do { \ | |
fe0b1e85 | 528 | _FP_W_TYPE _c1, _c2; \ |
1a8aaf91 UD |
529 | r0 = x0 + y0; \ |
530 | _c1 = r0 < x0; \ | |
531 | r1 = x1 + y1; \ | |
532 | _c2 = r1 < x1; \ | |
533 | r1 += _c1; \ | |
534 | _c2 |= r1 < _c1; \ | |
535 | r2 = x2 + y2 + _c2; \ | |
536 | } while (0) | |
d876f532 UD |
537 | #endif |
538 | ||
539 | #ifndef __FP_FRAC_ADD_4 | |
1a8aaf91 UD |
540 | #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ |
541 | do { \ | |
fe0b1e85 | 542 | _FP_W_TYPE _c1, _c2, _c3; \ |
1a8aaf91 UD |
543 | r0 = x0 + y0; \ |
544 | _c1 = r0 < x0; \ | |
545 | r1 = x1 + y1; \ | |
546 | _c2 = r1 < x1; \ | |
547 | r1 += _c1; \ | |
548 | _c2 |= r1 < _c1; \ | |
549 | r2 = x2 + y2; \ | |
550 | _c3 = r2 < x2; \ | |
551 | r2 += _c2; \ | |
552 | _c3 |= r2 < _c2; \ | |
553 | r3 = x3 + y3 + _c3; \ | |
554 | } while (0) | |
d876f532 UD |
555 | #endif |
556 | ||
557 | #ifndef __FP_FRAC_SUB_3 | |
1a8aaf91 UD |
558 | #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ |
559 | do { \ | |
fe0b1e85 | 560 | _FP_W_TYPE _c1, _c2; \ |
1a8aaf91 UD |
561 | r0 = x0 - y0; \ |
562 | _c1 = r0 > x0; \ | |
563 | r1 = x1 - y1; \ | |
564 | _c2 = r1 > x1; \ | |
565 | r1 -= _c1; \ | |
d68f5d2c | 566 | _c2 |= _c1 && (y1 == x1); \ |
1a8aaf91 UD |
567 | r2 = x2 - y2 - _c2; \ |
568 | } while (0) | |
d876f532 UD |
569 | #endif |
570 | ||
571 | #ifndef __FP_FRAC_SUB_4 | |
1a8aaf91 UD |
572 | #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ |
573 | do { \ | |
fe0b1e85 | 574 | _FP_W_TYPE _c1, _c2, _c3; \ |
1a8aaf91 UD |
575 | r0 = x0 - y0; \ |
576 | _c1 = r0 > x0; \ | |
577 | r1 = x1 - y1; \ | |
578 | _c2 = r1 > x1; \ | |
579 | r1 -= _c1; \ | |
d68f5d2c | 580 | _c2 |= _c1 && (y1 == x1); \ |
1a8aaf91 UD |
581 | r2 = x2 - y2; \ |
582 | _c3 = r2 > x2; \ | |
583 | r2 -= _c2; \ | |
d68f5d2c | 584 | _c3 |= _c2 && (y2 == x2); \ |
1a8aaf91 UD |
585 | r3 = x3 - y3 - _c3; \ |
586 | } while (0) | |
d876f532 UD |
587 | #endif |
588 | ||
589 | #ifndef __FP_FRAC_DEC_3 | |
590 | #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0) \ | |
591 | do { \ | |
1a8aaf91 UD |
592 | UWtype _t0, _t1, _t2; \ |
593 | _t0 = x0, _t1 = x1, _t2 = x2; \ | |
594 | __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \ | |
d876f532 UD |
595 | } while (0) |
596 | #endif | |
597 | ||
598 | #ifndef __FP_FRAC_DEC_4 | |
599 | #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0) \ | |
600 | do { \ | |
1a8aaf91 UD |
601 | UWtype _t0, _t1, _t2, _t3; \ |
602 | _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \ | |
603 | __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0); \ | |
d876f532 UD |
604 | } while (0) |
605 | #endif | |
606 | ||
607 | #ifndef __FP_FRAC_ADDI_4 | |
608 | #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i) \ | |
609 | do { \ | |
610 | UWtype _t; \ | |
611 | _t = ((x0 += i) < i); \ | |
612 | x1 += _t; _t = (x1 < _t); \ | |
613 | x2 += _t; _t = (x2 < _t); \ | |
614 | x3 += _t; \ | |
615 | } while (0) | |
616 | #endif | |
617 | ||
618 | /* Convert FP values between word sizes. This appears to be more | |
619 | * complicated than I'd have expected it to be, so these might be | |
620 | * wrong... These macros are in any case somewhat bogus because they | |
9c84384c | 621 | * use information about what various FRAC_n variables look like |
d876f532 | 622 | * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do |
9c84384c | 623 | * the ones in op-2.h and op-1.h. |
d876f532 | 624 | */ |
fe0b1e85 | 625 | #define _FP_FRAC_COPY_1_4(D, S) (D##_f = S##_f[0]) |
d876f532 | 626 | |
fe0b1e85 RM |
627 | #define _FP_FRAC_COPY_2_4(D, S) \ |
628 | do { \ | |
629 | D##_f0 = S##_f[0]; \ | |
630 | D##_f1 = S##_f[1]; \ | |
631 | } while (0) | |
d876f532 | 632 | |
9c84384c | 633 | /* Assembly/disassembly for converting to/from integral types. |
d876f532 UD |
634 | * No shifting or overflow handled here. |
635 | */ | |
636 | /* Put the FP value X into r, which is an integer of size rsize. */ | |
637 | #define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \ | |
638 | do { \ | |
639 | if (rsize <= _FP_W_TYPE_SIZE) \ | |
640 | r = X##_f[0]; \ | |
641 | else if (rsize <= 2*_FP_W_TYPE_SIZE) \ | |
642 | { \ | |
643 | r = X##_f[1]; \ | |
644 | r <<= _FP_W_TYPE_SIZE; \ | |
645 | r += X##_f[0]; \ | |
646 | } \ | |
647 | else \ | |
648 | { \ | |
649 | /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \ | |
650 | /* and int == 4words as a single case. */ \ | |
651 | r = X##_f[3]; \ | |
652 | r <<= _FP_W_TYPE_SIZE; \ | |
653 | r += X##_f[2]; \ | |
654 | r <<= _FP_W_TYPE_SIZE; \ | |
655 | r += X##_f[1]; \ | |
656 | r <<= _FP_W_TYPE_SIZE; \ | |
657 | r += X##_f[0]; \ | |
658 | } \ | |
659 | } while (0) | |
660 | ||
661 | /* "No disassemble Number Five!" */ | |
662 | /* move an integer of size rsize into X's fractional part. We rely on | |
663 | * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid | |
664 | * having to mask the values we store into it. | |
665 | */ | |
666 | #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \ | |
667 | do { \ | |
668 | X##_f[0] = r; \ | |
669 | X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ | |
670 | X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \ | |
671 | X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \ | |
672 | } while (0); | |
673 | ||
fe0b1e85 RM |
674 | #define _FP_FRAC_COPY_4_1(D, S) \ |
675 | do { \ | |
676 | D##_f[0] = S##_f; \ | |
677 | D##_f[1] = D##_f[2] = D##_f[3] = 0; \ | |
678 | } while (0) | |
679 | ||
680 | #define _FP_FRAC_COPY_4_2(D, S) \ | |
681 | do { \ | |
682 | D##_f[0] = S##_f0; \ | |
683 | D##_f[1] = S##_f1; \ | |
684 | D##_f[2] = D##_f[3] = 0; \ | |
685 | } while (0) | |
37002cbc JJ |
686 | |
687 | #define _FP_FRAC_COPY_4_4(D,S) _FP_FRAC_COPY_4(D,S) |