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d876f532 UD |
1 | /* Software floating-point emulation. |
2 | Basic two-word fraction declaration and manipulation. | |
04277e02 | 3 | Copyright (C) 1997-2019 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 | 32 | |
a2f8be9c JM |
33 | #ifndef SOFT_FP_OP_2_H |
34 | #define SOFT_FP_OP_2_H 1 | |
35 | ||
b838844b JM |
36 | #define _FP_FRAC_DECL_2(X) \ |
37 | _FP_W_TYPE X##_f0 _FP_ZERO_INIT, X##_f1 _FP_ZERO_INIT | |
51ca9e29 JM |
38 | #define _FP_FRAC_COPY_2(D, S) (D##_f0 = S##_f0, D##_f1 = S##_f1) |
39 | #define _FP_FRAC_SET_2(X, I) __FP_FRAC_SET_2 (X, I) | |
d876f532 UD |
40 | #define _FP_FRAC_HIGH_2(X) (X##_f1) |
41 | #define _FP_FRAC_LOW_2(X) (X##_f0) | |
51ca9e29 JM |
42 | #define _FP_FRAC_WORD_2(X, w) (X##_f##w) |
43 | ||
44 | #define _FP_FRAC_SLL_2(X, N) \ | |
45 | (void) (((N) < _FP_W_TYPE_SIZE) \ | |
46 | ? ({ \ | |
47 | if (__builtin_constant_p (N) && (N) == 1) \ | |
48 | { \ | |
49 | X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE) (X##_f0)) < 0); \ | |
50 | X##_f0 += X##_f0; \ | |
51 | } \ | |
52 | else \ | |
53 | { \ | |
54 | X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ | |
55 | X##_f0 <<= (N); \ | |
56 | } \ | |
57 | 0; \ | |
58 | }) \ | |
59 | : ({ \ | |
60 | X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ | |
61 | X##_f0 = 0; \ | |
62 | })) | |
63 | ||
64 | ||
65 | #define _FP_FRAC_SRL_2(X, N) \ | |
66 | (void) (((N) < _FP_W_TYPE_SIZE) \ | |
67 | ? ({ \ | |
68 | X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ | |
69 | X##_f1 >>= (N); \ | |
70 | }) \ | |
71 | : ({ \ | |
72 | X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ | |
73 | X##_f1 = 0; \ | |
74 | })) | |
d876f532 UD |
75 | |
76 | /* Right shift with sticky-lsb. */ | |
51ca9e29 JM |
77 | #define _FP_FRAC_SRST_2(X, S, N, sz) \ |
78 | (void) (((N) < _FP_W_TYPE_SIZE) \ | |
79 | ? ({ \ | |
80 | S = (__builtin_constant_p (N) && (N) == 1 \ | |
81 | ? X##_f0 & 1 \ | |
82 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ | |
83 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ | |
84 | X##_f1 >>= (N); \ | |
85 | }) \ | |
86 | : ({ \ | |
87 | S = ((((N) == _FP_W_TYPE_SIZE \ | |
88 | ? 0 \ | |
89 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ | |
90 | | X##_f0) != 0); \ | |
91 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ | |
92 | X##_f1 = 0; \ | |
93 | })) | |
94 | ||
95 | #define _FP_FRAC_SRS_2(X, N, sz) \ | |
96 | (void) (((N) < _FP_W_TYPE_SIZE) \ | |
97 | ? ({ \ | |
98 | X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ | |
99 | | (__builtin_constant_p (N) && (N) == 1 \ | |
100 | ? X##_f0 & 1 \ | |
101 | : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ | |
102 | X##_f1 >>= (N); \ | |
103 | }) \ | |
104 | : ({ \ | |
105 | X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ | |
106 | | ((((N) == _FP_W_TYPE_SIZE \ | |
107 | ? 0 \ | |
108 | : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ | |
109 | | X##_f0) != 0)); \ | |
110 | X##_f1 = 0; \ | |
111 | })) | |
112 | ||
113 | #define _FP_FRAC_ADDI_2(X, I) \ | |
114 | __FP_FRAC_ADDI_2 (X##_f1, X##_f0, I) | |
115 | ||
116 | #define _FP_FRAC_ADD_2(R, X, Y) \ | |
117 | __FP_FRAC_ADD_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) | |
118 | ||
119 | #define _FP_FRAC_SUB_2(R, X, Y) \ | |
120 | __FP_FRAC_SUB_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) | |
121 | ||
122 | #define _FP_FRAC_DEC_2(X, Y) \ | |
123 | __FP_FRAC_DEC_2 (X##_f1, X##_f0, Y##_f1, Y##_f0) | |
124 | ||
125 | #define _FP_FRAC_CLZ_2(R, X) \ | |
1e145589 JM |
126 | do \ |
127 | { \ | |
128 | if (X##_f1) \ | |
5c0508a3 | 129 | __FP_CLZ ((R), X##_f1); \ |
1e145589 JM |
130 | else \ |
131 | { \ | |
5c0508a3 JM |
132 | __FP_CLZ ((R), X##_f0); \ |
133 | (R) += _FP_W_TYPE_SIZE; \ | |
1e145589 JM |
134 | } \ |
135 | } \ | |
51ca9e29 | 136 | while (0) |
d876f532 | 137 | |
c4fe3ea7 | 138 | /* Predicates. */ |
51ca9e29 | 139 | #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE) X##_f1 < 0) |
d876f532 | 140 | #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) |
51ca9e29 JM |
141 | #define _FP_FRAC_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs) |
142 | #define _FP_FRAC_CLEAR_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs) | |
143 | #define _FP_FRAC_HIGHBIT_DW_2(fs, X) \ | |
144 | (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs) | |
d876f532 UD |
145 | #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) |
146 | #define _FP_FRAC_GT_2(X, Y) \ | |
fe0b1e85 | 147 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) |
d876f532 | 148 | #define _FP_FRAC_GE_2(X, Y) \ |
fe0b1e85 | 149 | (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) |
d876f532 UD |
150 | |
151 | #define _FP_ZEROFRAC_2 0, 0 | |
152 | #define _FP_MINFRAC_2 0, 1 | |
51ca9e29 | 153 | #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0) |
d876f532 | 154 | |
c4fe3ea7 | 155 | /* Internals. */ |
d876f532 | 156 | |
51ca9e29 | 157 | #define __FP_FRAC_SET_2(X, I1, I0) (X##_f0 = I0, X##_f1 = I1) |
d876f532 | 158 | |
1e145589 JM |
159 | #define __FP_CLZ_2(R, xh, xl) \ |
160 | do \ | |
161 | { \ | |
162 | if (xh) \ | |
5c0508a3 | 163 | __FP_CLZ ((R), xh); \ |
1e145589 JM |
164 | else \ |
165 | { \ | |
5c0508a3 JM |
166 | __FP_CLZ ((R), xl); \ |
167 | (R) += _FP_W_TYPE_SIZE; \ | |
1e145589 JM |
168 | } \ |
169 | } \ | |
51ca9e29 | 170 | while (0) |
d876f532 UD |
171 | |
172 | #if 0 | |
173 | ||
71b4dea7 JM |
174 | # ifndef __FP_FRAC_ADDI_2 |
175 | # define __FP_FRAC_ADDI_2(xh, xl, i) \ | |
d876f532 | 176 | (xh += ((xl += i) < i)) |
71b4dea7 JM |
177 | # endif |
178 | # ifndef __FP_FRAC_ADD_2 | |
179 | # define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ | |
d876f532 | 180 | (rh = xh + yh + ((rl = xl + yl) < xl)) |
71b4dea7 JM |
181 | # endif |
182 | # ifndef __FP_FRAC_SUB_2 | |
183 | # define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ | |
d876f532 | 184 | (rh = xh - yh - ((rl = xl - yl) > xl)) |
71b4dea7 JM |
185 | # endif |
186 | # ifndef __FP_FRAC_DEC_2 | |
3a6e9887 JM |
187 | # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ |
188 | do \ | |
189 | { \ | |
190 | UWtype __FP_FRAC_DEC_2_t = xl; \ | |
191 | xh -= yh + ((xl -= yl) > __FP_FRAC_DEC_2_t); \ | |
192 | } \ | |
1e145589 | 193 | while (0) |
71b4dea7 | 194 | # endif |
d876f532 UD |
195 | |
196 | #else | |
197 | ||
71b4dea7 | 198 | # undef __FP_FRAC_ADDI_2 |
51ca9e29 | 199 | # define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa (xh, xl, xh, xl, 0, i) |
71b4dea7 JM |
200 | # undef __FP_FRAC_ADD_2 |
201 | # define __FP_FRAC_ADD_2 add_ssaaaa | |
202 | # undef __FP_FRAC_SUB_2 | |
203 | # define __FP_FRAC_SUB_2 sub_ddmmss | |
204 | # undef __FP_FRAC_DEC_2 | |
205 | # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ | |
51ca9e29 | 206 | sub_ddmmss (xh, xl, xh, xl, yh, yl) |
d876f532 UD |
207 | |
208 | #endif | |
209 | ||
c4fe3ea7 JM |
210 | /* Unpack the raw bits of a native fp value. Do not classify or |
211 | normalize the data. */ | |
d876f532 | 212 | |
3a6e9887 JM |
213 | #define _FP_UNPACK_RAW_2(fs, X, val) \ |
214 | do \ | |
215 | { \ | |
216 | union _FP_UNION_##fs _FP_UNPACK_RAW_2_flo; \ | |
217 | _FP_UNPACK_RAW_2_flo.flt = (val); \ | |
218 | \ | |
219 | X##_f0 = _FP_UNPACK_RAW_2_flo.bits.frac0; \ | |
220 | X##_f1 = _FP_UNPACK_RAW_2_flo.bits.frac1; \ | |
221 | X##_e = _FP_UNPACK_RAW_2_flo.bits.exp; \ | |
222 | X##_s = _FP_UNPACK_RAW_2_flo.bits.sign; \ | |
223 | } \ | |
1e145589 JM |
224 | while (0) |
225 | ||
3a6e9887 JM |
226 | #define _FP_UNPACK_RAW_2_P(fs, X, val) \ |
227 | do \ | |
228 | { \ | |
229 | union _FP_UNION_##fs *_FP_UNPACK_RAW_2_P_flo \ | |
230 | = (union _FP_UNION_##fs *) (val); \ | |
231 | \ | |
232 | X##_f0 = _FP_UNPACK_RAW_2_P_flo->bits.frac0; \ | |
233 | X##_f1 = _FP_UNPACK_RAW_2_P_flo->bits.frac1; \ | |
234 | X##_e = _FP_UNPACK_RAW_2_P_flo->bits.exp; \ | |
235 | X##_s = _FP_UNPACK_RAW_2_P_flo->bits.sign; \ | |
236 | } \ | |
1e145589 | 237 | while (0) |
d876f532 UD |
238 | |
239 | ||
c4fe3ea7 | 240 | /* Repack the raw bits of a native fp value. */ |
d876f532 | 241 | |
1e145589 JM |
242 | #define _FP_PACK_RAW_2(fs, val, X) \ |
243 | do \ | |
244 | { \ | |
3a6e9887 | 245 | union _FP_UNION_##fs _FP_PACK_RAW_2_flo; \ |
1e145589 | 246 | \ |
3a6e9887 JM |
247 | _FP_PACK_RAW_2_flo.bits.frac0 = X##_f0; \ |
248 | _FP_PACK_RAW_2_flo.bits.frac1 = X##_f1; \ | |
249 | _FP_PACK_RAW_2_flo.bits.exp = X##_e; \ | |
250 | _FP_PACK_RAW_2_flo.bits.sign = X##_s; \ | |
1e145589 | 251 | \ |
3a6e9887 | 252 | (val) = _FP_PACK_RAW_2_flo.flt; \ |
1e145589 JM |
253 | } \ |
254 | while (0) | |
255 | ||
3a6e9887 JM |
256 | #define _FP_PACK_RAW_2_P(fs, val, X) \ |
257 | do \ | |
258 | { \ | |
259 | union _FP_UNION_##fs *_FP_PACK_RAW_2_P_flo \ | |
260 | = (union _FP_UNION_##fs *) (val); \ | |
261 | \ | |
262 | _FP_PACK_RAW_2_P_flo->bits.frac0 = X##_f0; \ | |
263 | _FP_PACK_RAW_2_P_flo->bits.frac1 = X##_f1; \ | |
264 | _FP_PACK_RAW_2_P_flo->bits.exp = X##_e; \ | |
265 | _FP_PACK_RAW_2_P_flo->bits.sign = X##_s; \ | |
266 | } \ | |
1e145589 | 267 | while (0) |
d876f532 UD |
268 | |
269 | ||
c4fe3ea7 | 270 | /* Multiplication algorithms: */ |
d876f532 UD |
271 | |
272 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ | |
273 | ||
77f01ab5 | 274 | #define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit) \ |
1e145589 JM |
275 | do \ |
276 | { \ | |
3a6e9887 JM |
277 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_b); \ |
278 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_c); \ | |
d876f532 | 279 | \ |
3a6e9887 JM |
280 | doit (_FP_FRAC_WORD_4 (R, 1), _FP_FRAC_WORD_4 (R, 0), \ |
281 | X##_f0, Y##_f0); \ | |
282 | doit (_FP_MUL_MEAT_DW_2_wide_b_f1, _FP_MUL_MEAT_DW_2_wide_b_f0, \ | |
283 | X##_f0, Y##_f1); \ | |
284 | doit (_FP_MUL_MEAT_DW_2_wide_c_f1, _FP_MUL_MEAT_DW_2_wide_c_f0, \ | |
285 | X##_f1, Y##_f0); \ | |
286 | doit (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ | |
287 | X##_f1, Y##_f1); \ | |
d876f532 | 288 | \ |
51ca9e29 | 289 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
3a6e9887 JM |
290 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
291 | _FP_MUL_MEAT_DW_2_wide_b_f1, \ | |
292 | _FP_MUL_MEAT_DW_2_wide_b_f0, \ | |
51ca9e29 JM |
293 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
294 | _FP_FRAC_WORD_4 (R, 1)); \ | |
295 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ | |
3a6e9887 JM |
296 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
297 | _FP_MUL_MEAT_DW_2_wide_c_f1, \ | |
298 | _FP_MUL_MEAT_DW_2_wide_c_f0, \ | |
51ca9e29 JM |
299 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
300 | _FP_FRAC_WORD_4 (R, 1)); \ | |
1e145589 JM |
301 | } \ |
302 | while (0) | |
77f01ab5 JM |
303 | |
304 | #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ | |
1e145589 JM |
305 | do \ |
306 | { \ | |
3a6e9887 | 307 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_z); \ |
77f01ab5 | 308 | \ |
5c0508a3 | 309 | _FP_MUL_MEAT_DW_2_wide ((wfracbits), _FP_MUL_MEAT_2_wide_z, \ |
3a6e9887 | 310 | X, Y, doit); \ |
d876f532 | 311 | \ |
1e145589 JM |
312 | /* Normalize since we know where the msb of the multiplicands \ |
313 | were (bit B), we know that the msb of the of the product is \ | |
314 | at either 2B or 2B-1. */ \ | |
5c0508a3 JM |
315 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_z, (wfracbits)-1, \ |
316 | 2*(wfracbits)); \ | |
3a6e9887 JM |
317 | R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 0); \ |
318 | R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 1); \ | |
1e145589 JM |
319 | } \ |
320 | while (0) | |
d876f532 UD |
321 | |
322 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. | |
323 | Do only 3 multiplications instead of four. This one is for machines | |
324 | where multiplication is much more expensive than subtraction. */ | |
325 | ||
77f01ab5 | 326 | #define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit) \ |
1e145589 JM |
327 | do \ |
328 | { \ | |
3a6e9887 JM |
329 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_b); \ |
330 | _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_c); \ | |
331 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_wide_3mul_d; \ | |
332 | int _FP_MUL_MEAT_DW_2_wide_3mul_c1; \ | |
333 | int _FP_MUL_MEAT_DW_2_wide_3mul_c2; \ | |
d876f532 | 334 | \ |
3a6e9887 JM |
335 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 = X##_f0 + X##_f1; \ |
336 | _FP_MUL_MEAT_DW_2_wide_3mul_c1 \ | |
337 | = _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 < X##_f0; \ | |
338 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 = Y##_f0 + Y##_f1; \ | |
339 | _FP_MUL_MEAT_DW_2_wide_3mul_c2 \ | |
340 | = _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 < Y##_f0; \ | |
341 | doit (_FP_MUL_MEAT_DW_2_wide_3mul_d, _FP_FRAC_WORD_4 (R, 0), \ | |
342 | X##_f0, Y##_f0); \ | |
343 | doit (_FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1), \ | |
344 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0, \ | |
345 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ | |
346 | doit (_FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ | |
347 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, X##_f1, Y##_f1); \ | |
d876f532 | 348 | \ |
3a6e9887 JM |
349 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 \ |
350 | &= -_FP_MUL_MEAT_DW_2_wide_3mul_c2; \ | |
351 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 \ | |
352 | &= -_FP_MUL_MEAT_DW_2_wide_3mul_c1; \ | |
51ca9e29 | 353 | __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
3a6e9887 JM |
354 | _FP_FRAC_WORD_4 (R, 1), \ |
355 | (_FP_MUL_MEAT_DW_2_wide_3mul_c1 \ | |
356 | & _FP_MUL_MEAT_DW_2_wide_3mul_c2), 0, \ | |
357 | _FP_MUL_MEAT_DW_2_wide_3mul_d, \ | |
51ca9e29 JM |
358 | 0, _FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1)); \ |
359 | __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ | |
3a6e9887 | 360 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f0); \ |
51ca9e29 | 361 | __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
3a6e9887 | 362 | _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \ |
51ca9e29 JM |
363 | __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
364 | _FP_FRAC_WORD_4 (R, 1), \ | |
3a6e9887 JM |
365 | 0, _FP_MUL_MEAT_DW_2_wide_3mul_d, \ |
366 | _FP_FRAC_WORD_4 (R, 0)); \ | |
51ca9e29 | 367 | __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
3a6e9887 JM |
368 | _FP_FRAC_WORD_4 (R, 1), 0, \ |
369 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ | |
370 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0); \ | |
51ca9e29 | 371 | __FP_FRAC_ADD_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \ |
3a6e9887 JM |
372 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \ |
373 | _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, \ | |
51ca9e29 | 374 | _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2)); \ |
1e145589 JM |
375 | } \ |
376 | while (0) | |
77f01ab5 JM |
377 | |
378 | #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ | |
1e145589 JM |
379 | do \ |
380 | { \ | |
3a6e9887 | 381 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_3mul_z); \ |
d876f532 | 382 | \ |
5c0508a3 | 383 | _FP_MUL_MEAT_DW_2_wide_3mul ((wfracbits), \ |
3a6e9887 JM |
384 | _FP_MUL_MEAT_2_wide_3mul_z, \ |
385 | X, Y, doit); \ | |
d876f532 | 386 | \ |
1e145589 JM |
387 | /* Normalize since we know where the msb of the multiplicands \ |
388 | were (bit B), we know that the msb of the of the product is \ | |
389 | at either 2B or 2B-1. */ \ | |
3a6e9887 | 390 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_3mul_z, \ |
5c0508a3 | 391 | (wfracbits)-1, 2*(wfracbits)); \ |
3a6e9887 JM |
392 | R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 0); \ |
393 | R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 1); \ | |
1e145589 JM |
394 | } \ |
395 | while (0) | |
396 | ||
397 | #define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \ | |
398 | do \ | |
399 | { \ | |
3a6e9887 JM |
400 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_x[2]; \ |
401 | _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_y[2]; \ | |
402 | _FP_MUL_MEAT_DW_2_gmp_x[0] = X##_f0; \ | |
403 | _FP_MUL_MEAT_DW_2_gmp_x[1] = X##_f1; \ | |
404 | _FP_MUL_MEAT_DW_2_gmp_y[0] = Y##_f0; \ | |
405 | _FP_MUL_MEAT_DW_2_gmp_y[1] = Y##_f1; \ | |
1e145589 | 406 | \ |
3a6e9887 JM |
407 | mpn_mul_n (R##_f, _FP_MUL_MEAT_DW_2_gmp_x, \ |
408 | _FP_MUL_MEAT_DW_2_gmp_y, 2); \ | |
1e145589 JM |
409 | } \ |
410 | while (0) | |
77f01ab5 JM |
411 | |
412 | #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ | |
1e145589 JM |
413 | do \ |
414 | { \ | |
3a6e9887 | 415 | _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_gmp_z); \ |
77f01ab5 | 416 | \ |
5c0508a3 | 417 | _FP_MUL_MEAT_DW_2_gmp ((wfracbits), _FP_MUL_MEAT_2_gmp_z, X, Y); \ |
d876f532 | 418 | \ |
1e145589 JM |
419 | /* Normalize since we know where the msb of the multiplicands \ |
420 | were (bit B), we know that the msb of the of the product is \ | |
421 | at either 2B or 2B-1. */ \ | |
5c0508a3 JM |
422 | _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_gmp_z, (wfracbits)-1, \ |
423 | 2*(wfracbits)); \ | |
3a6e9887 JM |
424 | R##_f0 = _FP_MUL_MEAT_2_gmp_z_f[0]; \ |
425 | R##_f1 = _FP_MUL_MEAT_2_gmp_z_f[1]; \ | |
1e145589 JM |
426 | } \ |
427 | while (0) | |
d876f532 UD |
428 | |
429 | /* Do at most 120x120=240 bits multiplication using double floating | |
430 | point multiplication. This is useful if floating point | |
431 | multiplication has much bigger throughput than integer multiply. | |
432 | It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits | |
9c84384c | 433 | between 106 and 120 only. |
d876f532 UD |
434 | Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. |
435 | SETFETZ is a macro which will disable all FPU exceptions and set rounding | |
436 | towards zero, RESETFE should optionally reset it back. */ | |
437 | ||
1e145589 JM |
438 | #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ |
439 | do \ | |
440 | { \ | |
441 | static const double _const[] = \ | |
442 | { \ | |
443 | /* 2^-24 */ 5.9604644775390625e-08, \ | |
444 | /* 2^-48 */ 3.5527136788005009e-15, \ | |
445 | /* 2^-72 */ 2.1175823681357508e-22, \ | |
446 | /* 2^-96 */ 1.2621774483536189e-29, \ | |
447 | /* 2^28 */ 2.68435456e+08, \ | |
448 | /* 2^4 */ 1.600000e+01, \ | |
449 | /* 2^-20 */ 9.5367431640625e-07, \ | |
450 | /* 2^-44 */ 5.6843418860808015e-14, \ | |
451 | /* 2^-68 */ 3.3881317890172014e-21, \ | |
452 | /* 2^-92 */ 2.0194839173657902e-28, \ | |
453 | /* 2^-116 */ 1.2037062152420224e-35 \ | |
454 | }; \ | |
455 | double _a240, _b240, _c240, _d240, _e240, _f240, \ | |
456 | _g240, _h240, _i240, _j240, _k240; \ | |
457 | union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ | |
458 | _p240, _q240, _r240, _s240; \ | |
459 | UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ | |
460 | \ | |
7d67a196 JM |
461 | _FP_STATIC_ASSERT ((wfracbits) >= 106 && (wfracbits) <= 120, \ |
462 | "wfracbits out of range"); \ | |
1e145589 JM |
463 | \ |
464 | setfetz; \ | |
465 | \ | |
51ca9e29 JM |
466 | _e240 = (double) (long) (X##_f0 & 0xffffff); \ |
467 | _j240 = (double) (long) (Y##_f0 & 0xffffff); \ | |
468 | _d240 = (double) (long) ((X##_f0 >> 24) & 0xffffff); \ | |
469 | _i240 = (double) (long) ((Y##_f0 >> 24) & 0xffffff); \ | |
470 | _c240 = (double) (long) (((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ | |
471 | _h240 = (double) (long) (((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ | |
472 | _b240 = (double) (long) ((X##_f1 >> 8) & 0xffffff); \ | |
473 | _g240 = (double) (long) ((Y##_f1 >> 8) & 0xffffff); \ | |
474 | _a240 = (double) (long) (X##_f1 >> 32); \ | |
475 | _f240 = (double) (long) (Y##_f1 >> 32); \ | |
1e145589 JM |
476 | _e240 *= _const[3]; \ |
477 | _j240 *= _const[3]; \ | |
478 | _d240 *= _const[2]; \ | |
479 | _i240 *= _const[2]; \ | |
480 | _c240 *= _const[1]; \ | |
481 | _h240 *= _const[1]; \ | |
482 | _b240 *= _const[0]; \ | |
483 | _g240 *= _const[0]; \ | |
484 | _s240.d = _e240*_j240; \ | |
485 | _r240.d = _d240*_j240 + _e240*_i240; \ | |
486 | _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240; \ | |
487 | _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \ | |
488 | _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \ | |
489 | _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ | |
490 | _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ | |
491 | _l240.d = _a240*_g240 + _b240*_f240; \ | |
492 | _k240 = _a240*_f240; \ | |
493 | _r240.d += _s240.d; \ | |
494 | _q240.d += _r240.d; \ | |
495 | _p240.d += _q240.d; \ | |
496 | _o240.d += _p240.d; \ | |
497 | _n240.d += _o240.d; \ | |
498 | _m240.d += _n240.d; \ | |
499 | _l240.d += _m240.d; \ | |
500 | _k240 += _l240.d; \ | |
501 | _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ | |
502 | _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ | |
503 | _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ | |
504 | _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ | |
505 | _o240.d += _const[7]; \ | |
506 | _n240.d += _const[6]; \ | |
507 | _m240.d += _const[5]; \ | |
508 | _l240.d += _const[4]; \ | |
509 | if (_s240.d != 0.0) \ | |
510 | _y240 = 1; \ | |
511 | if (_r240.d != 0.0) \ | |
512 | _y240 = 1; \ | |
513 | if (_q240.d != 0.0) \ | |
514 | _y240 = 1; \ | |
515 | if (_p240.d != 0.0) \ | |
516 | _y240 = 1; \ | |
51ca9e29 | 517 | _t240 = (DItype) _k240; \ |
1e145589 JM |
518 | _u240 = _l240.i; \ |
519 | _v240 = _m240.i; \ | |
520 | _w240 = _n240.i; \ | |
521 | _x240 = _o240.i; \ | |
522 | R##_f1 = ((_t240 << (128 - (wfracbits - 1))) \ | |
523 | | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104))); \ | |
524 | R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ | |
525 | | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ | |
526 | | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ | |
527 | | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ | |
528 | | _y240); \ | |
529 | resetfe; \ | |
530 | } \ | |
531 | while (0) | |
d876f532 | 532 | |
c4fe3ea7 | 533 | /* Division algorithms: */ |
d876f532 UD |
534 | |
535 | #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ | |
1e145589 JM |
536 | do \ |
537 | { \ | |
3a6e9887 JM |
538 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f2; \ |
539 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f1; \ | |
540 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f0; \ | |
541 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f1; \ | |
542 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f0; \ | |
543 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f1; \ | |
544 | _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f0; \ | |
51ca9e29 | 545 | if (_FP_FRAC_GE_2 (X, Y)) \ |
1e145589 | 546 | { \ |
3a6e9887 JM |
547 | _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1 >> 1; \ |
548 | _FP_DIV_MEAT_2_udiv_n_f1 \ | |
549 | = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ | |
550 | _FP_DIV_MEAT_2_udiv_n_f0 \ | |
551 | = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ | |
1e145589 JM |
552 | } \ |
553 | else \ | |
554 | { \ | |
555 | R##_e--; \ | |
3a6e9887 JM |
556 | _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1; \ |
557 | _FP_DIV_MEAT_2_udiv_n_f1 = X##_f0; \ | |
558 | _FP_DIV_MEAT_2_udiv_n_f0 = 0; \ | |
1e145589 | 559 | } \ |
d876f532 | 560 | \ |
1e145589 | 561 | /* Normalize, i.e. make the most significant bit of the \ |
c4fe3ea7 | 562 | denominator set. */ \ |
51ca9e29 | 563 | _FP_FRAC_SLL_2 (Y, _FP_WFRACXBITS_##fs); \ |
d876f532 | 564 | \ |
3a6e9887 JM |
565 | udiv_qrnnd (R##_f1, _FP_DIV_MEAT_2_udiv_r_f1, \ |
566 | _FP_DIV_MEAT_2_udiv_n_f2, _FP_DIV_MEAT_2_udiv_n_f1, \ | |
567 | Y##_f1); \ | |
568 | umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, _FP_DIV_MEAT_2_udiv_m_f0, \ | |
569 | R##_f1, Y##_f0); \ | |
570 | _FP_DIV_MEAT_2_udiv_r_f0 = _FP_DIV_MEAT_2_udiv_n_f0; \ | |
571 | if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, _FP_DIV_MEAT_2_udiv_r)) \ | |
1e145589 JM |
572 | { \ |
573 | R##_f1--; \ | |
3a6e9887 JM |
574 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
575 | _FP_DIV_MEAT_2_udiv_r); \ | |
576 | if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ | |
577 | && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ | |
578 | _FP_DIV_MEAT_2_udiv_r)) \ | |
1e145589 JM |
579 | { \ |
580 | R##_f1--; \ | |
3a6e9887 JM |
581 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
582 | _FP_DIV_MEAT_2_udiv_r); \ | |
1e145589 JM |
583 | } \ |
584 | } \ | |
3a6e9887 | 585 | _FP_FRAC_DEC_2 (_FP_DIV_MEAT_2_udiv_r, _FP_DIV_MEAT_2_udiv_m); \ |
d876f532 | 586 | \ |
3a6e9887 | 587 | if (_FP_DIV_MEAT_2_udiv_r_f1 == Y##_f1) \ |
1e145589 JM |
588 | { \ |
589 | /* This is a special case, not an optimization \ | |
3a6e9887 JM |
590 | (_FP_DIV_MEAT_2_udiv_r/Y##_f1 would not fit into UWtype). \ |
591 | As _FP_DIV_MEAT_2_udiv_r is guaranteed to be < Y, \ | |
592 | R##_f0 can be either (UWtype)-1 or (UWtype)-2. But as we \ | |
593 | know what kind of bits it is (sticky, guard, round), \ | |
594 | we don't care. We also don't care what the reminder is, \ | |
595 | because the guard bit will be set anyway. -jj */ \ | |
1e145589 JM |
596 | R##_f0 = -1; \ |
597 | } \ | |
598 | else \ | |
599 | { \ | |
3a6e9887 JM |
600 | udiv_qrnnd (R##_f0, _FP_DIV_MEAT_2_udiv_r_f1, \ |
601 | _FP_DIV_MEAT_2_udiv_r_f1, \ | |
602 | _FP_DIV_MEAT_2_udiv_r_f0, Y##_f1); \ | |
603 | umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, \ | |
604 | _FP_DIV_MEAT_2_udiv_m_f0, R##_f0, Y##_f0); \ | |
605 | _FP_DIV_MEAT_2_udiv_r_f0 = 0; \ | |
606 | if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ | |
607 | _FP_DIV_MEAT_2_udiv_r)) \ | |
1e145589 JM |
608 | { \ |
609 | R##_f0--; \ | |
3a6e9887 JM |
610 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
611 | _FP_DIV_MEAT_2_udiv_r); \ | |
612 | if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \ | |
613 | && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \ | |
614 | _FP_DIV_MEAT_2_udiv_r)) \ | |
1e145589 JM |
615 | { \ |
616 | R##_f0--; \ | |
3a6e9887 JM |
617 | _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \ |
618 | _FP_DIV_MEAT_2_udiv_r); \ | |
1e145589 JM |
619 | } \ |
620 | } \ | |
3a6e9887 JM |
621 | if (!_FP_FRAC_EQ_2 (_FP_DIV_MEAT_2_udiv_r, \ |
622 | _FP_DIV_MEAT_2_udiv_m)) \ | |
1e145589 JM |
623 | R##_f0 |= _FP_WORK_STICKY; \ |
624 | } \ | |
625 | } \ | |
626 | while (0) | |
d876f532 UD |
627 | |
628 | ||
c4fe3ea7 JM |
629 | /* Square root algorithms: |
630 | We have just one right now, maybe Newton approximation | |
631 | should be added for those machines where division is fast. */ | |
9c84384c | 632 | |
1e145589 JM |
633 | #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ |
634 | do \ | |
635 | { \ | |
636 | while (q) \ | |
637 | { \ | |
5c0508a3 | 638 | T##_f1 = S##_f1 + (q); \ |
1e145589 JM |
639 | if (T##_f1 <= X##_f1) \ |
640 | { \ | |
5c0508a3 | 641 | S##_f1 = T##_f1 + (q); \ |
1e145589 | 642 | X##_f1 -= T##_f1; \ |
5c0508a3 | 643 | R##_f1 += (q); \ |
1e145589 | 644 | } \ |
51ca9e29 | 645 | _FP_FRAC_SLL_2 (X, 1); \ |
5c0508a3 | 646 | (q) >>= 1; \ |
1e145589 | 647 | } \ |
5c0508a3 JM |
648 | (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \ |
649 | while ((q) != _FP_WORK_ROUND) \ | |
1e145589 | 650 | { \ |
5c0508a3 | 651 | T##_f0 = S##_f0 + (q); \ |
1e145589 JM |
652 | T##_f1 = S##_f1; \ |
653 | if (T##_f1 < X##_f1 \ | |
654 | || (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ | |
655 | { \ | |
5c0508a3 | 656 | S##_f0 = T##_f0 + (q); \ |
1e145589 | 657 | S##_f1 += (T##_f0 > S##_f0); \ |
51ca9e29 | 658 | _FP_FRAC_DEC_2 (X, T); \ |
5c0508a3 | 659 | R##_f0 += (q); \ |
1e145589 | 660 | } \ |
51ca9e29 | 661 | _FP_FRAC_SLL_2 (X, 1); \ |
5c0508a3 | 662 | (q) >>= 1; \ |
1e145589 JM |
663 | } \ |
664 | if (X##_f0 | X##_f1) \ | |
665 | { \ | |
666 | if (S##_f1 < X##_f1 \ | |
667 | || (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ | |
668 | R##_f0 |= _FP_WORK_ROUND; \ | |
669 | R##_f0 |= _FP_WORK_STICKY; \ | |
670 | } \ | |
671 | } \ | |
672 | while (0) | |
d876f532 UD |
673 | |
674 | ||
c4fe3ea7 JM |
675 | /* Assembly/disassembly for converting to/from integral types. |
676 | No shifting or overflow handled here. */ | |
d876f532 UD |
677 | |
678 | #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ | |
5c0508a3 JM |
679 | (void) (((rsize) <= _FP_W_TYPE_SIZE) \ |
680 | ? ({ (r) = X##_f0; }) \ | |
51ca9e29 | 681 | : ({ \ |
5c0508a3 JM |
682 | (r) = X##_f1; \ |
683 | (r) <<= _FP_W_TYPE_SIZE; \ | |
684 | (r) += X##_f0; \ | |
51ca9e29 | 685 | })) |
d876f532 | 686 | |
5c0508a3 JM |
687 | #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ |
688 | do \ | |
689 | { \ | |
690 | X##_f0 = (r); \ | |
691 | X##_f1 = ((rsize) <= _FP_W_TYPE_SIZE \ | |
692 | ? 0 \ | |
693 | : (r) >> _FP_W_TYPE_SIZE); \ | |
694 | } \ | |
1e145589 | 695 | while (0) |
d876f532 | 696 | |
c4fe3ea7 | 697 | /* Convert FP values between word sizes. */ |
d876f532 | 698 | |
fe0b1e85 | 699 | #define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0) |
d876f532 | 700 | |
fe0b1e85 | 701 | #define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0)) |
37002cbc | 702 | |
51ca9e29 | 703 | #define _FP_FRAC_COPY_2_2(D, S) _FP_FRAC_COPY_2 (D, S) |
a2f8be9c JM |
704 | |
705 | #endif /* !SOFT_FP_OP_2_H */ |