1 | /* Software floating-point emulation. |
2 | Basic two-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_2_H__ |
26 | #define __MATH_EMU_OP_2_H__ |
27 | |
28 | #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0 = 0, X##_f1 = 0 |
29 | #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1) |
30 | #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I) |
31 | #define _FP_FRAC_HIGH_2(X) (X##_f1) |
32 | #define _FP_FRAC_LOW_2(X) (X##_f0) |
33 | #define _FP_FRAC_WORD_2(X,w) (X##_f##w) |
34 | #define _FP_FRAC_SLL_2(X, N) ( \ |
35 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
36 | ? ({ \ |
37 | if (__builtin_constant_p(N) && (N) == 1) { \ |
38 | X##_f1 = X##_f1 + X##_f1 + \ |
39 | (((_FP_WS_TYPE) (X##_f0)) < 0); \ |
40 | X##_f0 += X##_f0; \ |
41 | } else { \ |
42 | X##_f1 = X##_f1 << (N) | X##_f0 >> \ |
43 | (_FP_W_TYPE_SIZE - (N)); \ |
44 | X##_f0 <<= (N); \ |
45 | } \ |
46 | 0; \ |
47 | }) \ |
48 | : ({ \ |
49 | X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ |
50 | X##_f0 = 0; \ |
51 | }))) |
52 | |
53 | |
54 | #define _FP_FRAC_SRL_2(X, N) ( \ |
55 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
56 | ? ({ \ |
57 | X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ |
58 | X##_f1 >>= (N); \ |
59 | }) \ |
60 | : ({ \ |
61 | X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ |
62 | X##_f1 = 0; \ |
63 | }))) |
64 | |
65 | |
66 | /* Right shift with sticky-lsb. */ |
67 | #define _FP_FRAC_SRS_2(X, N, sz) ( \ |
68 | (void) (((N) < _FP_W_TYPE_SIZE) \ |
69 | ? ({ \ |
70 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ |
71 | | (__builtin_constant_p(N) && (N) == 1 \ |
72 | ? X##_f0 & 1 \ |
73 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ |
74 | X##_f1 >>= (N); \ |
75 | }) \ |
76 | : ({ \ |
77 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ |
78 | | ((((N) == _FP_W_TYPE_SIZE \ |
79 | ? 0 \ |
80 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ |
81 | | X##_f0) != 0)); \ |
82 | X##_f1 = 0; \ |
83 | }))) |
84 | |
85 | #define _FP_FRAC_ADDI_2(X,I) \ |
86 | __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) |
87 | |
88 | #define _FP_FRAC_ADD_2(R,X,Y) \ |
89 | __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
90 | |
91 | #define _FP_FRAC_SUB_2(R,X,Y) \ |
92 | __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) |
93 | |
94 | #define _FP_FRAC_DEC_2(X,Y) \ |
95 | __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0) |
96 | |
97 | #define _FP_FRAC_CLZ_2(R,X) \ |
98 | do { \ |
99 | if (X##_f1) \ |
100 | __FP_CLZ(R,X##_f1); \ |
101 | else \ |
102 | { \ |
103 | __FP_CLZ(R,X##_f0); \ |
104 | R += _FP_W_TYPE_SIZE; \ |
105 | } \ |
106 | } while(0) |
107 | |
108 | /* Predicates */ |
109 | #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) |
110 | #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) |
111 | #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) |
112 | #define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs) |
113 | #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) |
114 | #define _FP_FRAC_GT_2(X, Y) \ |
115 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) |
116 | #define _FP_FRAC_GE_2(X, Y) \ |
117 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) |
118 | |
119 | #define _FP_ZEROFRAC_2 0, 0 |
120 | #define _FP_MINFRAC_2 0, 1 |
121 | #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) |
122 | |
123 | /* |
124 | * Internals |
125 | */ |
126 | |
127 | #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) |
128 | |
129 | #define __FP_CLZ_2(R, xh, xl) \ |
130 | do { \ |
131 | if (xh) \ |
132 | __FP_CLZ(R,xh); \ |
133 | else \ |
134 | { \ |
135 | __FP_CLZ(R,xl); \ |
136 | R += _FP_W_TYPE_SIZE; \ |
137 | } \ |
138 | } while(0) |
139 | |
140 | #if 0 |
141 | |
142 | #ifndef __FP_FRAC_ADDI_2 |
143 | #define __FP_FRAC_ADDI_2(xh, xl, i) \ |
144 | (xh += ((xl += i) < i)) |
145 | #endif |
146 | #ifndef __FP_FRAC_ADD_2 |
147 | #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ |
148 | (rh = xh + yh + ((rl = xl + yl) < xl)) |
149 | #endif |
150 | #ifndef __FP_FRAC_SUB_2 |
151 | #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ |
152 | (rh = xh - yh - ((rl = xl - yl) > xl)) |
153 | #endif |
154 | #ifndef __FP_FRAC_DEC_2 |
155 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
156 | do { \ |
157 | UWtype _t = xl; \ |
158 | xh -= yh + ((xl -= yl) > _t); \ |
159 | } while (0) |
160 | #endif |
161 | |
162 | #else |
163 | |
164 | #undef __FP_FRAC_ADDI_2 |
165 | #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) |
166 | #undef __FP_FRAC_ADD_2 |
167 | #define __FP_FRAC_ADD_2 add_ssaaaa |
168 | #undef __FP_FRAC_SUB_2 |
169 | #define __FP_FRAC_SUB_2 sub_ddmmss |
170 | #undef __FP_FRAC_DEC_2 |
171 | #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl) |
172 | |
173 | #endif |
174 | |
175 | /* |
176 | * Unpack the raw bits of a native fp value. Do not classify or |
177 | * normalize the data. |
178 | */ |
179 | |
180 | #define _FP_UNPACK_RAW_2(fs, X, val) \ |
181 | do { \ |
182 | union _FP_UNION_##fs _flo; _flo.flt = (val); \ |
183 | \ |
184 | X##_f0 = _flo.bits.frac0; \ |
185 | X##_f1 = _flo.bits.frac1; \ |
186 | X##_e = _flo.bits.exp; \ |
187 | X##_s = _flo.bits.sign; \ |
188 | } while (0) |
189 | |
190 | #define _FP_UNPACK_RAW_2_P(fs, X, val) \ |
191 | do { \ |
192 | union _FP_UNION_##fs *_flo = \ |
193 | (union _FP_UNION_##fs *)(val); \ |
194 | \ |
195 | X##_f0 = _flo->bits.frac0; \ |
196 | X##_f1 = _flo->bits.frac1; \ |
197 | X##_e = _flo->bits.exp; \ |
198 | X##_s = _flo->bits.sign; \ |
199 | } while (0) |
200 | |
201 | |
202 | /* |
203 | * Repack the raw bits of a native fp value. |
204 | */ |
205 | |
206 | #define _FP_PACK_RAW_2(fs, val, X) \ |
207 | do { \ |
208 | union _FP_UNION_##fs _flo; \ |
209 | \ |
210 | _flo.bits.frac0 = X##_f0; \ |
211 | _flo.bits.frac1 = X##_f1; \ |
212 | _flo.bits.exp = X##_e; \ |
213 | _flo.bits.sign = X##_s; \ |
214 | \ |
215 | (val) = _flo.flt; \ |
216 | } while (0) |
217 | |
218 | #define _FP_PACK_RAW_2_P(fs, val, X) \ |
219 | do { \ |
220 | union _FP_UNION_##fs *_flo = \ |
221 | (union _FP_UNION_##fs *)(val); \ |
222 | \ |
223 | _flo->bits.frac0 = X##_f0; \ |
224 | _flo->bits.frac1 = X##_f1; \ |
225 | _flo->bits.exp = X##_e; \ |
226 | _flo->bits.sign = X##_s; \ |
227 | } while (0) |
228 | |
229 | |
230 | /* |
231 | * Multiplication algorithms: |
232 | */ |
233 | |
234 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
235 | |
236 | #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ |
237 | do { \ |
238 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ |
239 | \ |
240 | doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ |
241 | doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ |
242 | doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ |
243 | doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ |
244 | \ |
245 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
246 | _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \ |
247 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
248 | _FP_FRAC_WORD_4(_z,1)); \ |
249 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
250 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \ |
251 | _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
252 | _FP_FRAC_WORD_4(_z,1)); \ |
253 | \ |
254 | /* Normalize since we know where the msb of the multiplicands \ |
255 | were (bit B), we know that the msb of the of the product is \ |
256 | at either 2B or 2B-1. */ \ |
257 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ |
258 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \ |
259 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \ |
260 | } while (0) |
261 | |
262 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. |
263 | Do only 3 multiplications instead of four. This one is for machines |
264 | where multiplication is much more expensive than subtraction. */ |
265 | |
266 | #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
267 | do { \ |
268 | _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ |
269 | _FP_W_TYPE _d; \ |
270 | int _c1, _c2; \ |
271 | \ |
272 | _b_f0 = X##_f0 + X##_f1; \ |
273 | _c1 = _b_f0 < X##_f0; \ |
274 | _b_f1 = Y##_f0 + Y##_f1; \ |
275 | _c2 = _b_f1 < Y##_f0; \ |
276 | doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ |
277 | doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \ |
278 | doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ |
279 | \ |
280 | _b_f0 &= -_c2; \ |
281 | _b_f1 &= -_c1; \ |
282 | __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
283 | _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \ |
284 | 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \ |
285 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
286 | _b_f0); \ |
287 | __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
288 | _b_f1); \ |
289 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
290 | _FP_FRAC_WORD_4(_z,1), \ |
291 | 0, _d, _FP_FRAC_WORD_4(_z,0)); \ |
292 | __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ |
293 | _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \ |
294 | __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \ |
295 | _c_f1, _c_f0, \ |
296 | _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \ |
297 | \ |
298 | /* Normalize since we know where the msb of the multiplicands \ |
299 | were (bit B), we know that the msb of the of the product is \ |
300 | at either 2B or 2B-1. */ \ |
301 | _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ |
302 | R##_f0 = _FP_FRAC_WORD_4(_z,0); \ |
303 | R##_f1 = _FP_FRAC_WORD_4(_z,1); \ |
304 | } while (0) |
305 | |
306 | #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ |
307 | do { \ |
308 | _FP_FRAC_DECL_4(_z); \ |
309 | _FP_W_TYPE _x[2], _y[2]; \ |
310 | _x[0] = X##_f0; _x[1] = X##_f1; \ |
311 | _y[0] = Y##_f0; _y[1] = Y##_f1; \ |
312 | \ |
313 | mpn_mul_n(_z_f, _x, _y, 2); \ |
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_4(_z, wfracbits-1, 2*wfracbits); \ |
319 | R##_f0 = _z_f[0]; \ |
320 | R##_f1 = _z_f[1]; \ |
321 | } while (0) |
322 | |
323 | /* Do at most 120x120=240 bits multiplication using double floating |
324 | point multiplication. This is useful if floating point |
325 | multiplication has much bigger throughput than integer multiply. |
326 | It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits |
327 | between 106 and 120 only. |
328 | Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. |
329 | SETFETZ is a macro which will disable all FPU exceptions and set rounding |
330 | towards zero, RESETFE should optionally reset it back. */ |
331 | |
332 | #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ |
333 | do { \ |
334 | static const double _const[] = { \ |
335 | /* 2^-24 */ 5.9604644775390625e-08, \ |
336 | /* 2^-48 */ 3.5527136788005009e-15, \ |
337 | /* 2^-72 */ 2.1175823681357508e-22, \ |
338 | /* 2^-96 */ 1.2621774483536189e-29, \ |
339 | /* 2^28 */ 2.68435456e+08, \ |
340 | /* 2^4 */ 1.600000e+01, \ |
341 | /* 2^-20 */ 9.5367431640625e-07, \ |
342 | /* 2^-44 */ 5.6843418860808015e-14, \ |
343 | /* 2^-68 */ 3.3881317890172014e-21, \ |
344 | /* 2^-92 */ 2.0194839173657902e-28, \ |
345 | /* 2^-116 */ 1.2037062152420224e-35}; \ |
346 | double _a240, _b240, _c240, _d240, _e240, _f240, \ |
347 | _g240, _h240, _i240, _j240, _k240; \ |
348 | union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ |
349 | _p240, _q240, _r240, _s240; \ |
350 | UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ |
351 | \ |
352 | if (wfracbits < 106 || wfracbits > 120) \ |
353 | abort(); \ |
354 | \ |
355 | setfetz; \ |
356 | \ |
357 | _e240 = (double)(long)(X##_f0 & 0xffffff); \ |
358 | _j240 = (double)(long)(Y##_f0 & 0xffffff); \ |
359 | _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ |
360 | _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ |
361 | _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ |
362 | _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ |
363 | _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ |
364 | _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ |
365 | _a240 = (double)(long)(X##_f1 >> 32); \ |
366 | _f240 = (double)(long)(Y##_f1 >> 32); \ |
367 | _e240 *= _const[3]; \ |
368 | _j240 *= _const[3]; \ |
369 | _d240 *= _const[2]; \ |
370 | _i240 *= _const[2]; \ |
371 | _c240 *= _const[1]; \ |
372 | _h240 *= _const[1]; \ |
373 | _b240 *= _const[0]; \ |
374 | _g240 *= _const[0]; \ |
375 | _s240.d = _e240*_j240;\ |
376 | _r240.d = _d240*_j240 + _e240*_i240;\ |
377 | _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\ |
378 | _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\ |
379 | _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\ |
380 | _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ |
381 | _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ |
382 | _l240.d = _a240*_g240 + _b240*_f240; \ |
383 | _k240 = _a240*_f240; \ |
384 | _r240.d += _s240.d; \ |
385 | _q240.d += _r240.d; \ |
386 | _p240.d += _q240.d; \ |
387 | _o240.d += _p240.d; \ |
388 | _n240.d += _o240.d; \ |
389 | _m240.d += _n240.d; \ |
390 | _l240.d += _m240.d; \ |
391 | _k240 += _l240.d; \ |
392 | _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ |
393 | _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ |
394 | _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ |
395 | _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ |
396 | _o240.d += _const[7]; \ |
397 | _n240.d += _const[6]; \ |
398 | _m240.d += _const[5]; \ |
399 | _l240.d += _const[4]; \ |
400 | if (_s240.d != 0.0) _y240 = 1; \ |
401 | if (_r240.d != 0.0) _y240 = 1; \ |
402 | if (_q240.d != 0.0) _y240 = 1; \ |
403 | if (_p240.d != 0.0) _y240 = 1; \ |
404 | _t240 = (DItype)_k240; \ |
405 | _u240 = _l240.i; \ |
406 | _v240 = _m240.i; \ |
407 | _w240 = _n240.i; \ |
408 | _x240 = _o240.i; \ |
409 | R##_f1 = (_t240 << (128 - (wfracbits - 1))) \ |
410 | | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \ |
411 | R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ |
412 | | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ |
413 | | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ |
414 | | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ |
415 | | _y240; \ |
416 | resetfe; \ |
417 | } while (0) |
418 | |
419 | /* |
420 | * Division algorithms: |
421 | */ |
422 | |
423 | #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ |
424 | do { \ |
425 | _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ |
426 | if (_FP_FRAC_GT_2(X, Y)) \ |
427 | { \ |
428 | _n_f2 = X##_f1 >> 1; \ |
429 | _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ |
430 | _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ |
431 | } \ |
432 | else \ |
433 | { \ |
434 | R##_e--; \ |
435 | _n_f2 = X##_f1; \ |
436 | _n_f1 = X##_f0; \ |
437 | _n_f0 = 0; \ |
438 | } \ |
439 | \ |
440 | /* Normalize, i.e. make the most significant bit of the \ |
441 | denominator set. */ \ |
442 | _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ |
443 | \ |
444 | udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ |
445 | umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ |
446 | _r_f0 = _n_f0; \ |
447 | if (_FP_FRAC_GT_2(_m, _r)) \ |
448 | { \ |
449 | R##_f1--; \ |
450 | _FP_FRAC_ADD_2(_r, Y, _r); \ |
451 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ |
452 | { \ |
453 | R##_f1--; \ |
454 | _FP_FRAC_ADD_2(_r, Y, _r); \ |
455 | } \ |
456 | } \ |
457 | _FP_FRAC_DEC_2(_r, _m); \ |
458 | \ |
459 | if (_r_f1 == Y##_f1) \ |
460 | { \ |
461 | /* This is a special case, not an optimization \ |
462 | (_r/Y##_f1 would not fit into UWtype). \ |
463 | As _r is guaranteed to be < Y, R##_f0 can be either \ |
464 | (UWtype)-1 or (UWtype)-2. But as we know what kind \ |
465 | of bits it is (sticky, guard, round), we don't care. \ |
466 | We also don't care what the reminder is, because the \ |
467 | guard bit will be set anyway. -jj */ \ |
468 | R##_f0 = -1; \ |
469 | } \ |
470 | else \ |
471 | { \ |
472 | udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ |
473 | umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ |
474 | _r_f0 = 0; \ |
475 | if (_FP_FRAC_GT_2(_m, _r)) \ |
476 | { \ |
477 | R##_f0--; \ |
478 | _FP_FRAC_ADD_2(_r, Y, _r); \ |
479 | if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ |
480 | { \ |
481 | R##_f0--; \ |
482 | _FP_FRAC_ADD_2(_r, Y, _r); \ |
483 | } \ |
484 | } \ |
485 | if (!_FP_FRAC_EQ_2(_r, _m)) \ |
486 | R##_f0 |= _FP_WORK_STICKY; \ |
487 | } \ |
488 | } while (0) |
489 | |
490 | |
491 | #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ |
492 | do { \ |
493 | _FP_W_TYPE _x[4], _y[2], _z[4]; \ |
494 | _y[0] = Y##_f0; _y[1] = Y##_f1; \ |
495 | _x[0] = _x[3] = 0; \ |
496 | if (_FP_FRAC_GT_2(X, Y)) \ |
497 | { \ |
498 | R##_e++; \ |
499 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ |
500 | X##_f1 >> (_FP_W_TYPE_SIZE - \ |
501 | (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ |
502 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ |
503 | } \ |
504 | else \ |
505 | { \ |
506 | _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ |
507 | X##_f1 >> (_FP_W_TYPE_SIZE - \ |
508 | (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ |
509 | _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ |
510 | } \ |
511 | \ |
512 | (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ |
513 | R##_f1 = _z[1]; \ |
514 | R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ |
515 | } while (0) |
516 | |
517 | |
518 | /* |
519 | * Square root algorithms: |
520 | * We have just one right now, maybe Newton approximation |
521 | * should be added for those machines where division is fast. |
522 | */ |
523 | |
524 | #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ |
525 | do { \ |
526 | while (q) \ |
527 | { \ |
528 | T##_f1 = S##_f1 + q; \ |
529 | if (T##_f1 <= X##_f1) \ |
530 | { \ |
531 | S##_f1 = T##_f1 + q; \ |
532 | X##_f1 -= T##_f1; \ |
533 | R##_f1 += q; \ |
534 | } \ |
535 | _FP_FRAC_SLL_2(X, 1); \ |
536 | q >>= 1; \ |
537 | } \ |
538 | q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ |
539 | while (q != _FP_WORK_ROUND) \ |
540 | { \ |
541 | T##_f0 = S##_f0 + q; \ |
542 | T##_f1 = S##_f1; \ |
543 | if (T##_f1 < X##_f1 || \ |
544 | (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ |
545 | { \ |
546 | S##_f0 = T##_f0 + q; \ |
547 | S##_f1 += (T##_f0 > S##_f0); \ |
548 | _FP_FRAC_DEC_2(X, T); \ |
549 | R##_f0 += q; \ |
550 | } \ |
551 | _FP_FRAC_SLL_2(X, 1); \ |
552 | q >>= 1; \ |
553 | } \ |
554 | if (X##_f0 | X##_f1) \ |
555 | { \ |
556 | if (S##_f1 < X##_f1 || \ |
557 | (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ |
558 | R##_f0 |= _FP_WORK_ROUND; \ |
559 | R##_f0 |= _FP_WORK_STICKY; \ |
560 | } \ |
561 | } while (0) |
562 | |
563 | |
564 | /* |
565 | * Assembly/disassembly for converting to/from integral types. |
566 | * No shifting or overflow handled here. |
567 | */ |
568 | |
569 | #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ |
570 | (void) (((rsize) <= _FP_W_TYPE_SIZE) \ |
571 | ? ({ (r) = X##_f0; }) \ |
572 | : ({ \ |
573 | (r) = X##_f1; \ |
574 | (r) <<= _FP_W_TYPE_SIZE; \ |
575 | (r) += X##_f0; \ |
576 | })) |
577 | |
578 | #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ |
579 | do { \ |
580 | X##_f0 = r; \ |
581 | X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ |
582 | } while (0) |
583 | |
584 | /* |
585 | * Convert FP values between word sizes |
586 | */ |
587 | |
588 | #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \ |
589 | do { \ |
590 | if (S##_c != FP_CLS_NAN) \ |
591 | _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ |
592 | _FP_WFRACBITS_##sfs); \ |
593 | else \ |
594 | _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ |
595 | D##_f = S##_f0; \ |
596 | } while (0) |
597 | |
598 | #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ |
599 | do { \ |
600 | D##_f0 = S##_f; \ |
601 | D##_f1 = 0; \ |
602 | _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ |
603 | } while (0) |
604 | |
605 | #endif |
606 | |