1 | /* Software floating-point emulation. |
2 | Basic four-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_4_H__ |
26 | #define __MATH_EMU_OP_4_H__ |
27 | |
28 | #define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4] |
29 | #define _FP_FRAC_COPY_4(D,S) \ |
30 | (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \ |
31 | D##_f[2] = S##_f[2], D##_f[3] = S##_f[3]) |
32 | #define _FP_FRAC_SET_4(X,I) __FP_FRAC_SET_4(X, I) |
33 | #define _FP_FRAC_HIGH_4(X) (X##_f[3]) |
34 | #define _FP_FRAC_LOW_4(X) (X##_f[0]) |
35 | #define _FP_FRAC_WORD_4(X,w) (X##_f[w]) |
36 | |
37 | #define _FP_FRAC_SLL_4(X,N) \ |
38 | do { \ |
39 | _FP_I_TYPE _up, _down, _skip, _i; \ |
40 | _skip = (N) / _FP_W_TYPE_SIZE; \ |
41 | _up = (N) % _FP_W_TYPE_SIZE; \ |
42 | _down = _FP_W_TYPE_SIZE - _up; \ |
43 | if (!_up) \ |
44 | for (_i = 3; _i >= _skip; --_i) \ |
45 | X##_f[_i] = X##_f[_i-_skip]; \ |
46 | else \ |
47 | { \ |
48 | for (_i = 3; _i > _skip; --_i) \ |
49 | X##_f[_i] = X##_f[_i-_skip] << _up \ |
50 | | X##_f[_i-_skip-1] >> _down; \ |
51 | X##_f[_i--] = X##_f[0] << _up; \ |
52 | } \ |
53 | for (; _i >= 0; --_i) \ |
54 | X##_f[_i] = 0; \ |
55 | } while (0) |
56 | |
57 | /* This one was broken too */ |
58 | #define _FP_FRAC_SRL_4(X,N) \ |
59 | do { \ |
60 | _FP_I_TYPE _up, _down, _skip, _i; \ |
61 | _skip = (N) / _FP_W_TYPE_SIZE; \ |
62 | _down = (N) % _FP_W_TYPE_SIZE; \ |
63 | _up = _FP_W_TYPE_SIZE - _down; \ |
64 | if (!_down) \ |
65 | for (_i = 0; _i <= 3-_skip; ++_i) \ |
66 | X##_f[_i] = X##_f[_i+_skip]; \ |
67 | else \ |
68 | { \ |
69 | for (_i = 0; _i < 3-_skip; ++_i) \ |
70 | X##_f[_i] = X##_f[_i+_skip] >> _down \ |
71 | | X##_f[_i+_skip+1] << _up; \ |
72 | X##_f[_i++] = X##_f[3] >> _down; \ |
73 | } \ |
74 | for (; _i < 4; ++_i) \ |
75 | X##_f[_i] = 0; \ |
76 | } while (0) |
77 | |
78 | |
79 | /* Right shift with sticky-lsb. |
80 | * What this actually means is that we do a standard right-shift, |
81 | * but that if any of the bits that fall off the right hand side |
82 | * were one then we always set the LSbit. |
83 | */ |
84 | #define _FP_FRAC_SRS_4(X,N,size) \ |
85 | do { \ |
86 | _FP_I_TYPE _up, _down, _skip, _i; \ |
87 | _FP_W_TYPE _s; \ |
88 | _skip = (N) / _FP_W_TYPE_SIZE; \ |
89 | _down = (N) % _FP_W_TYPE_SIZE; \ |
90 | _up = _FP_W_TYPE_SIZE - _down; \ |
91 | for (_s = _i = 0; _i < _skip; ++_i) \ |
92 | _s |= X##_f[_i]; \ |
93 | _s |= X##_f[_i] << _up; \ |
94 | /* s is now != 0 if we want to set the LSbit */ \ |
95 | if (!_down) \ |
96 | for (_i = 0; _i <= 3-_skip; ++_i) \ |
97 | X##_f[_i] = X##_f[_i+_skip]; \ |
98 | else \ |
99 | { \ |
100 | for (_i = 0; _i < 3-_skip; ++_i) \ |
101 | X##_f[_i] = X##_f[_i+_skip] >> _down \ |
102 | | X##_f[_i+_skip+1] << _up; \ |
103 | X##_f[_i++] = X##_f[3] >> _down; \ |
104 | } \ |
105 | for (; _i < 4; ++_i) \ |
106 | X##_f[_i] = 0; \ |
107 | /* don't fix the LSB until the very end when we're sure f[0] is stable */ \ |
108 | X##_f[0] |= (_s != 0); \ |
109 | } while (0) |
110 | |
111 | #define _FP_FRAC_ADD_4(R,X,Y) \ |
112 | __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ |
113 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
114 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
115 | |
116 | #define _FP_FRAC_SUB_4(R,X,Y) \ |
117 | __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \ |
118 | X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
119 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
120 | |
121 | #define _FP_FRAC_DEC_4(X,Y) \ |
122 | __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
123 | Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0]) |
124 | |
125 | #define _FP_FRAC_ADDI_4(X,I) \ |
126 | __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I) |
127 | |
128 | #define _FP_ZEROFRAC_4 0,0,0,0 |
129 | #define _FP_MINFRAC_4 0,0,0,1 |
130 | #define _FP_MAXFRAC_4 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) |
131 | |
132 | #define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0) |
133 | #define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE)X##_f[3] < 0) |
134 | #define _FP_FRAC_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) |
135 | #define _FP_FRAC_CLEAR_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs) |
136 | |
137 | #define _FP_FRAC_EQ_4(X,Y) \ |
138 | (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \ |
139 | && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3]) |
140 | |
141 | #define _FP_FRAC_GT_4(X,Y) \ |
142 | (X##_f[3] > Y##_f[3] || \ |
143 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \ |
144 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \ |
145 | (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0]) \ |
146 | )) \ |
147 | )) \ |
148 | ) |
149 | |
150 | #define _FP_FRAC_GE_4(X,Y) \ |
151 | (X##_f[3] > Y##_f[3] || \ |
152 | (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \ |
153 | (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \ |
154 | (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0]) \ |
155 | )) \ |
156 | )) \ |
157 | ) |
158 | |
159 | |
160 | #define _FP_FRAC_CLZ_4(R,X) \ |
161 | do { \ |
162 | if (X##_f[3]) \ |
163 | { \ |
164 | __FP_CLZ(R,X##_f[3]); \ |
165 | } \ |
166 | else if (X##_f[2]) \ |
167 | { \ |
168 | __FP_CLZ(R,X##_f[2]); \ |
169 | R += _FP_W_TYPE_SIZE; \ |
170 | } \ |
171 | else if (X##_f[1]) \ |
172 | { \ |
173 | __FP_CLZ(R,X##_f[2]); \ |
174 | R += _FP_W_TYPE_SIZE*2; \ |
175 | } \ |
176 | else \ |
177 | { \ |
178 | __FP_CLZ(R,X##_f[0]); \ |
179 | R += _FP_W_TYPE_SIZE*3; \ |
180 | } \ |
181 | } while(0) |
182 | |
183 | |
184 | #define _FP_UNPACK_RAW_4(fs, X, val) \ |
185 | do { \ |
186 | union _FP_UNION_##fs _flo; _flo.flt = (val); \ |
187 | X##_f[0] = _flo.bits.frac0; \ |
188 | X##_f[1] = _flo.bits.frac1; \ |
189 | X##_f[2] = _flo.bits.frac2; \ |
190 | X##_f[3] = _flo.bits.frac3; \ |
191 | X##_e = _flo.bits.exp; \ |
192 | X##_s = _flo.bits.sign; \ |
193 | } while (0) |
194 | |
195 | #define _FP_UNPACK_RAW_4_P(fs, X, val) \ |
196 | do { \ |
197 | union _FP_UNION_##fs *_flo = \ |
198 | (union _FP_UNION_##fs *)(val); \ |
199 | \ |
200 | X##_f[0] = _flo->bits.frac0; \ |
201 | X##_f[1] = _flo->bits.frac1; \ |
202 | X##_f[2] = _flo->bits.frac2; \ |
203 | X##_f[3] = _flo->bits.frac3; \ |
204 | X##_e = _flo->bits.exp; \ |
205 | X##_s = _flo->bits.sign; \ |
206 | } while (0) |
207 | |
208 | #define _FP_PACK_RAW_4(fs, val, X) \ |
209 | do { \ |
210 | union _FP_UNION_##fs _flo; \ |
211 | _flo.bits.frac0 = X##_f[0]; \ |
212 | _flo.bits.frac1 = X##_f[1]; \ |
213 | _flo.bits.frac2 = X##_f[2]; \ |
214 | _flo.bits.frac3 = X##_f[3]; \ |
215 | _flo.bits.exp = X##_e; \ |
216 | _flo.bits.sign = X##_s; \ |
217 | (val) = _flo.flt; \ |
218 | } while (0) |
219 | |
220 | #define _FP_PACK_RAW_4_P(fs, val, X) \ |
221 | do { \ |
222 | union _FP_UNION_##fs *_flo = \ |
223 | (union _FP_UNION_##fs *)(val); \ |
224 | \ |
225 | _flo->bits.frac0 = X##_f[0]; \ |
226 | _flo->bits.frac1 = X##_f[1]; \ |
227 | _flo->bits.frac2 = X##_f[2]; \ |
228 | _flo->bits.frac3 = X##_f[3]; \ |
229 | _flo->bits.exp = X##_e; \ |
230 | _flo->bits.sign = X##_s; \ |
231 | } while (0) |
232 | |
233 | /* |
234 | * Multiplication algorithms: |
235 | */ |
236 | |
237 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
238 | |
239 | #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \ |
240 | do { \ |
241 | _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ |
242 | _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f); \ |
243 | \ |
244 | doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \ |
245 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]); \ |
246 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]); \ |
247 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]); \ |
248 | doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]); \ |
249 | doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]); \ |
250 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
251 | _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \ |
252 | 0,0,_FP_FRAC_WORD_8(_z,1)); \ |
253 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
254 | _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \ |
255 | _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \ |
256 | _FP_FRAC_WORD_8(_z,1)); \ |
257 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
258 | _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \ |
259 | 0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \ |
260 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
261 | _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \ |
262 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
263 | _FP_FRAC_WORD_8(_z,2)); \ |
264 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
265 | _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \ |
266 | _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \ |
267 | _FP_FRAC_WORD_8(_z,2)); \ |
268 | doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]); \ |
269 | doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]); \ |
270 | doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]); \ |
271 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]); \ |
272 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
273 | _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \ |
274 | 0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \ |
275 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
276 | _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \ |
277 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
278 | _FP_FRAC_WORD_8(_z,3)); \ |
279 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
280 | _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \ |
281 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
282 | _FP_FRAC_WORD_8(_z,3)); \ |
283 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
284 | _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \ |
285 | _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \ |
286 | _FP_FRAC_WORD_8(_z,3)); \ |
287 | doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]); \ |
288 | doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]); \ |
289 | doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]); \ |
290 | doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]); \ |
291 | doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]); \ |
292 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
293 | _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \ |
294 | 0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \ |
295 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
296 | _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \ |
297 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
298 | _FP_FRAC_WORD_8(_z,4)); \ |
299 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
300 | _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \ |
301 | _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \ |
302 | _FP_FRAC_WORD_8(_z,4)); \ |
303 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
304 | _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \ |
305 | 0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \ |
306 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
307 | _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \ |
308 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
309 | _FP_FRAC_WORD_8(_z,5)); \ |
310 | doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \ |
311 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \ |
312 | _b_f1,_b_f0, \ |
313 | _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \ |
314 | \ |
315 | /* Normalize since we know where the msb of the multiplicands \ |
316 | were (bit B), we know that the msb of the of the product is \ |
317 | at either 2B or 2B-1. */ \ |
318 | _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \ |
319 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \ |
320 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \ |
321 | } while (0) |
322 | |
323 | #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \ |
324 | do { \ |
325 | _FP_FRAC_DECL_8(_z); \ |
326 | \ |
327 | mpn_mul_n(_z_f, _x_f, _y_f, 4); \ |
328 | \ |
329 | /* Normalize since we know where the msb of the multiplicands \ |
330 | were (bit B), we know that the msb of the of the product is \ |
331 | at either 2B or 2B-1. */ \ |
332 | _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \ |
333 | __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \ |
334 | _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \ |
335 | } while (0) |
336 | |
337 | /* |
338 | * Helper utility for _FP_DIV_MEAT_4_udiv: |
339 | * pppp = m * nnn |
340 | */ |
341 | #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0) \ |
342 | do { \ |
343 | UWtype _t; \ |
344 | umul_ppmm(p1,p0,m,n0); \ |
345 | umul_ppmm(p2,_t,m,n1); \ |
346 | __FP_FRAC_ADDI_2(p2,p1,_t); \ |
347 | umul_ppmm(p3,_t,m,n2); \ |
348 | __FP_FRAC_ADDI_2(p3,p2,_t); \ |
349 | } while (0) |
350 | |
351 | /* |
352 | * Division algorithms: |
353 | */ |
354 | |
355 | #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \ |
356 | do { \ |
357 | int _i; \ |
358 | _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m); \ |
359 | _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4); \ |
360 | if (_FP_FRAC_GT_4(X, Y)) \ |
361 | { \ |
362 | _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \ |
363 | _FP_FRAC_SRL_4(X, 1); \ |
364 | } \ |
365 | else \ |
366 | R##_e--; \ |
367 | \ |
368 | /* Normalize, i.e. make the most significant bit of the \ |
369 | denominator set. */ \ |
370 | _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs); \ |
371 | \ |
372 | for (_i = 3; ; _i--) \ |
373 | { \ |
374 | if (X##_f[3] == Y##_f[3]) \ |
375 | { \ |
376 | /* This is a special case, not an optimization \ |
377 | (X##_f[3]/Y##_f[3] would not fit into UWtype). \ |
378 | As X## is guaranteed to be < Y, R##_f[_i] can be either \ |
379 | (UWtype)-1 or (UWtype)-2. */ \ |
380 | R##_f[_i] = -1; \ |
381 | if (!_i) \ |
382 | break; \ |
383 | __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \ |
384 | Y##_f[2], Y##_f[1], Y##_f[0], 0, \ |
385 | X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \ |
386 | _FP_FRAC_SUB_4(X, Y, X); \ |
387 | if (X##_f[3] > Y##_f[3]) \ |
388 | { \ |
389 | R##_f[_i] = -2; \ |
390 | _FP_FRAC_ADD_4(X, Y, X); \ |
391 | } \ |
392 | } \ |
393 | else \ |
394 | { \ |
395 | udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \ |
396 | umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0], \ |
397 | R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \ |
398 | X##_f[2] = X##_f[1]; \ |
399 | X##_f[1] = X##_f[0]; \ |
400 | X##_f[0] = _n_f[_i]; \ |
401 | if (_FP_FRAC_GT_4(_m, X)) \ |
402 | { \ |
403 | R##_f[_i]--; \ |
404 | _FP_FRAC_ADD_4(X, Y, X); \ |
405 | if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X)) \ |
406 | { \ |
407 | R##_f[_i]--; \ |
408 | _FP_FRAC_ADD_4(X, Y, X); \ |
409 | } \ |
410 | } \ |
411 | _FP_FRAC_DEC_4(X, _m); \ |
412 | if (!_i) \ |
413 | { \ |
414 | if (!_FP_FRAC_EQ_4(X, _m)) \ |
415 | R##_f[0] |= _FP_WORK_STICKY; \ |
416 | break; \ |
417 | } \ |
418 | } \ |
419 | } \ |
420 | } while (0) |
421 | |
422 | |
423 | /* |
424 | * Square root algorithms: |
425 | * We have just one right now, maybe Newton approximation |
426 | * should be added for those machines where division is fast. |
427 | */ |
428 | |
429 | #define _FP_SQRT_MEAT_4(R, S, T, X, q) \ |
430 | do { \ |
431 | while (q) \ |
432 | { \ |
433 | T##_f[3] = S##_f[3] + q; \ |
434 | if (T##_f[3] <= X##_f[3]) \ |
435 | { \ |
436 | S##_f[3] = T##_f[3] + q; \ |
437 | X##_f[3] -= T##_f[3]; \ |
438 | R##_f[3] += q; \ |
439 | } \ |
440 | _FP_FRAC_SLL_4(X, 1); \ |
441 | q >>= 1; \ |
442 | } \ |
443 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ |
444 | while (q) \ |
445 | { \ |
446 | T##_f[2] = S##_f[2] + q; \ |
447 | T##_f[3] = S##_f[3]; \ |
448 | if (T##_f[3] < X##_f[3] || \ |
449 | (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \ |
450 | { \ |
451 | S##_f[2] = T##_f[2] + q; \ |
452 | S##_f[3] += (T##_f[2] > S##_f[2]); \ |
453 | __FP_FRAC_DEC_2(X##_f[3], X##_f[2], \ |
454 | T##_f[3], T##_f[2]); \ |
455 | R##_f[2] += q; \ |
456 | } \ |
457 | _FP_FRAC_SLL_4(X, 1); \ |
458 | q >>= 1; \ |
459 | } \ |
460 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ |
461 | while (q) \ |
462 | { \ |
463 | T##_f[1] = S##_f[1] + q; \ |
464 | T##_f[2] = S##_f[2]; \ |
465 | T##_f[3] = S##_f[3]; \ |
466 | if (T##_f[3] < X##_f[3] || \ |
467 | (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] || \ |
468 | (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1])))) \ |
469 | { \ |
470 | S##_f[1] = T##_f[1] + q; \ |
471 | S##_f[2] += (T##_f[1] > S##_f[1]); \ |
472 | S##_f[3] += (T##_f[2] > S##_f[2]); \ |
473 | __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1], \ |
474 | T##_f[3], T##_f[2], T##_f[1]); \ |
475 | R##_f[1] += q; \ |
476 | } \ |
477 | _FP_FRAC_SLL_4(X, 1); \ |
478 | q >>= 1; \ |
479 | } \ |
480 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ |
481 | while (q != _FP_WORK_ROUND) \ |
482 | { \ |
483 | T##_f[0] = S##_f[0] + q; \ |
484 | T##_f[1] = S##_f[1]; \ |
485 | T##_f[2] = S##_f[2]; \ |
486 | T##_f[3] = S##_f[3]; \ |
487 | if (_FP_FRAC_GE_4(X,T)) \ |
488 | { \ |
489 | S##_f[0] = T##_f[0] + q; \ |
490 | S##_f[1] += (T##_f[0] > S##_f[0]); \ |
491 | S##_f[2] += (T##_f[1] > S##_f[1]); \ |
492 | S##_f[3] += (T##_f[2] > S##_f[2]); \ |
493 | _FP_FRAC_DEC_4(X, T); \ |
494 | R##_f[0] += q; \ |
495 | } \ |
496 | _FP_FRAC_SLL_4(X, 1); \ |
497 | q >>= 1; \ |
498 | } \ |
499 | if (!_FP_FRAC_ZEROP_4(X)) \ |
500 | { \ |
501 | if (_FP_FRAC_GT_4(X,S)) \ |
502 | R##_f[0] |= _FP_WORK_ROUND; \ |
503 | R##_f[0] |= _FP_WORK_STICKY; \ |
504 | } \ |
505 | } while (0) |
506 | |
507 | |
508 | /* |
509 | * Internals |
510 | */ |
511 | |
512 | #define __FP_FRAC_SET_4(X,I3,I2,I1,I0) \ |
513 | (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0) |
514 | |
515 | #ifndef __FP_FRAC_ADD_3 |
516 | #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ |
517 | do { \ |
518 | int _c1, _c2; \ |
519 | r0 = x0 + y0; \ |
520 | _c1 = r0 < x0; \ |
521 | r1 = x1 + y1; \ |
522 | _c2 = r1 < x1; \ |
523 | r1 += _c1; \ |
524 | _c2 |= r1 < _c1; \ |
525 | r2 = x2 + y2 + _c2; \ |
526 | } while (0) |
527 | #endif |
528 | |
529 | #ifndef __FP_FRAC_ADD_4 |
530 | #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ |
531 | do { \ |
532 | int _c1, _c2, _c3; \ |
533 | r0 = x0 + y0; \ |
534 | _c1 = r0 < x0; \ |
535 | r1 = x1 + y1; \ |
536 | _c2 = r1 < x1; \ |
537 | r1 += _c1; \ |
538 | _c2 |= r1 < _c1; \ |
539 | r2 = x2 + y2; \ |
540 | _c3 = r2 < x2; \ |
541 | r2 += _c2; \ |
542 | _c3 |= r2 < _c2; \ |
543 | r3 = x3 + y3 + _c3; \ |
544 | } while (0) |
545 | #endif |
546 | |
547 | #ifndef __FP_FRAC_SUB_3 |
548 | #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ |
549 | do { \ |
550 | int _c1, _c2; \ |
551 | r0 = x0 - y0; \ |
552 | _c1 = r0 > x0; \ |
553 | r1 = x1 - y1; \ |
554 | _c2 = r1 > x1; \ |
555 | r1 -= _c1; \ |
556 | _c2 |= r1 > _c1; \ |
557 | r2 = x2 - y2 - _c2; \ |
558 | } while (0) |
559 | #endif |
560 | |
561 | #ifndef __FP_FRAC_SUB_4 |
562 | #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ |
563 | do { \ |
564 | int _c1, _c2, _c3; \ |
565 | r0 = x0 - y0; \ |
566 | _c1 = r0 > x0; \ |
567 | r1 = x1 - y1; \ |
568 | _c2 = r1 > x1; \ |
569 | r1 -= _c1; \ |
570 | _c2 |= r1 > _c1; \ |
571 | r2 = x2 - y2; \ |
572 | _c3 = r2 > x2; \ |
573 | r2 -= _c2; \ |
574 | _c3 |= r2 > _c2; \ |
575 | r3 = x3 - y3 - _c3; \ |
576 | } while (0) |
577 | #endif |
578 | |
579 | #ifndef __FP_FRAC_DEC_3 |
580 | #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0) \ |
581 | do { \ |
582 | UWtype _t0, _t1, _t2; \ |
583 | _t0 = x0, _t1 = x1, _t2 = x2; \ |
584 | __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \ |
585 | } while (0) |
586 | #endif |
587 | |
588 | #ifndef __FP_FRAC_DEC_4 |
589 | #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0) \ |
590 | do { \ |
591 | UWtype _t0, _t1, _t2, _t3; \ |
592 | _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \ |
593 | __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0); \ |
594 | } while (0) |
595 | #endif |
596 | |
597 | #ifndef __FP_FRAC_ADDI_4 |
598 | #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i) \ |
599 | do { \ |
600 | UWtype _t; \ |
601 | _t = ((x0 += i) < i); \ |
602 | x1 += _t; _t = (x1 < _t); \ |
603 | x2 += _t; _t = (x2 < _t); \ |
604 | x3 += _t; \ |
605 | } while (0) |
606 | #endif |
607 | |
608 | /* Convert FP values between word sizes. This appears to be more |
609 | * complicated than I'd have expected it to be, so these might be |
610 | * wrong... These macros are in any case somewhat bogus because they |
611 | * use information about what various FRAC_n variables look like |
612 | * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do |
613 | * the ones in op-2.h and op-1.h. |
614 | */ |
615 | #define _FP_FRAC_CONV_1_4(dfs, sfs, D, S) \ |
616 | do { \ |
617 | if (S##_c != FP_CLS_NAN) \ |
618 | _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
619 | _FP_WFRACBITS_##sfs); \ |
620 | else \ |
621 | _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
622 | D##_f = S##_f[0]; \ |
623 | } while (0) |
624 | |
625 | #define _FP_FRAC_CONV_2_4(dfs, sfs, D, S) \ |
626 | do { \ |
627 | if (S##_c != FP_CLS_NAN) \ |
628 | _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
629 | _FP_WFRACBITS_##sfs); \ |
630 | else \ |
631 | _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
632 | D##_f0 = S##_f[0]; \ |
633 | D##_f1 = S##_f[1]; \ |
634 | } while (0) |
635 | |
636 | /* Assembly/disassembly for converting to/from integral types. |
637 | * No shifting or overflow handled here. |
638 | */ |
639 | /* Put the FP value X into r, which is an integer of size rsize. */ |
640 | #define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \ |
641 | do { \ |
642 | if (rsize <= _FP_W_TYPE_SIZE) \ |
643 | r = X##_f[0]; \ |
644 | else if (rsize <= 2*_FP_W_TYPE_SIZE) \ |
645 | { \ |
646 | r = X##_f[1]; \ |
647 | r <<= _FP_W_TYPE_SIZE; \ |
648 | r += X##_f[0]; \ |
649 | } \ |
650 | else \ |
651 | { \ |
652 | /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \ |
653 | /* and int == 4words as a single case. */ \ |
654 | r = X##_f[3]; \ |
655 | r <<= _FP_W_TYPE_SIZE; \ |
656 | r += X##_f[2]; \ |
657 | r <<= _FP_W_TYPE_SIZE; \ |
658 | r += X##_f[1]; \ |
659 | r <<= _FP_W_TYPE_SIZE; \ |
660 | r += X##_f[0]; \ |
661 | } \ |
662 | } while (0) |
663 | |
664 | /* "No disassemble Number Five!" */ |
665 | /* move an integer of size rsize into X's fractional part. We rely on |
666 | * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid |
667 | * having to mask the values we store into it. |
668 | */ |
669 | #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \ |
670 | do { \ |
671 | X##_f[0] = r; \ |
672 | X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ |
673 | X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \ |
674 | X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \ |
675 | } while (0) |
676 | |
677 | #define _FP_FRAC_CONV_4_1(dfs, sfs, D, S) \ |
678 | do { \ |
679 | D##_f[0] = S##_f; \ |
680 | D##_f[1] = D##_f[2] = D##_f[3] = 0; \ |
681 | _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
682 | } while (0) |
683 | |
684 | #define _FP_FRAC_CONV_4_2(dfs, sfs, D, S) \ |
685 | do { \ |
686 | D##_f[0] = S##_f0; \ |
687 | D##_f[1] = S##_f1; \ |
688 | D##_f[2] = D##_f[3] = 0; \ |
689 | _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
690 | } while (0) |
691 | |
692 | #endif |
693 | |