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49721058 JM |
1 | /* Software floating-point emulation. |
2 | Basic one-word fraction declaration and manipulation. | |
fa1e55b0 | 3 | Copyright (C) 1997-2013 Free Software Foundation, Inc. |
49721058 JM |
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 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. | |
14 | ||
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 | ||
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 | |
27 | Lesser General Public License for more details. | |
28 | ||
29 | You should have received a copy of the GNU Lesser General Public | |
b7633ee3 KT |
30 | License along with the GNU C Library; if not, see |
31 | <http://www.gnu.org/licenses/>. */ | |
49721058 JM |
32 | |
33 | #define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f | |
34 | #define _FP_FRAC_COPY_1(D,S) (D##_f = S##_f) | |
35 | #define _FP_FRAC_SET_1(X,I) (X##_f = I) | |
36 | #define _FP_FRAC_HIGH_1(X) (X##_f) | |
37 | #define _FP_FRAC_LOW_1(X) (X##_f) | |
38 | #define _FP_FRAC_WORD_1(X,w) (X##_f) | |
39 | ||
40 | #define _FP_FRAC_ADDI_1(X,I) (X##_f += I) | |
41 | #define _FP_FRAC_SLL_1(X,N) \ | |
42 | do { \ | |
43 | if (__builtin_constant_p(N) && (N) == 1) \ | |
44 | X##_f += X##_f; \ | |
45 | else \ | |
46 | X##_f <<= (N); \ | |
47 | } while (0) | |
48 | #define _FP_FRAC_SRL_1(X,N) (X##_f >>= N) | |
49 | ||
50 | /* Right shift with sticky-lsb. */ | |
51 | #define _FP_FRAC_SRST_1(X,S,N,sz) __FP_FRAC_SRST_1(X##_f, S, N, sz) | |
52 | #define _FP_FRAC_SRS_1(X,N,sz) __FP_FRAC_SRS_1(X##_f, N, sz) | |
53 | ||
54 | #define __FP_FRAC_SRST_1(X,S,N,sz) \ | |
55 | do { \ | |
56 | S = (__builtin_constant_p(N) && (N) == 1 \ | |
57 | ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0); \ | |
58 | X = X >> (N); \ | |
59 | } while (0) | |
60 | ||
61 | #define __FP_FRAC_SRS_1(X,N,sz) \ | |
62 | (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1 \ | |
63 | ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0))) | |
64 | ||
65 | #define _FP_FRAC_ADD_1(R,X,Y) (R##_f = X##_f + Y##_f) | |
66 | #define _FP_FRAC_SUB_1(R,X,Y) (R##_f = X##_f - Y##_f) | |
67 | #define _FP_FRAC_DEC_1(X,Y) (X##_f -= Y##_f) | |
68 | #define _FP_FRAC_CLZ_1(z, X) __FP_CLZ(z, X##_f) | |
69 | ||
70 | /* Predicates */ | |
71 | #define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE)X##_f < 0) | |
72 | #define _FP_FRAC_ZEROP_1(X) (X##_f == 0) | |
73 | #define _FP_FRAC_OVERP_1(fs,X) (X##_f & _FP_OVERFLOW_##fs) | |
74 | #define _FP_FRAC_CLEAR_OVERP_1(fs,X) (X##_f &= ~_FP_OVERFLOW_##fs) | |
75 | #define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f) | |
76 | #define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f) | |
77 | #define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f) | |
78 | ||
79 | #define _FP_ZEROFRAC_1 0 | |
80 | #define _FP_MINFRAC_1 1 | |
81 | #define _FP_MAXFRAC_1 (~(_FP_WS_TYPE)0) | |
82 | ||
83 | /* | |
84 | * Unpack the raw bits of a native fp value. Do not classify or | |
85 | * normalize the data. | |
86 | */ | |
87 | ||
88 | #define _FP_UNPACK_RAW_1(fs, X, val) \ | |
89 | do { \ | |
90 | union _FP_UNION_##fs _flo; _flo.flt = (val); \ | |
91 | \ | |
92 | X##_f = _flo.bits.frac; \ | |
93 | X##_e = _flo.bits.exp; \ | |
94 | X##_s = _flo.bits.sign; \ | |
95 | } while (0) | |
96 | ||
97 | #define _FP_UNPACK_RAW_1_P(fs, X, val) \ | |
98 | do { \ | |
99 | union _FP_UNION_##fs *_flo = \ | |
100 | (union _FP_UNION_##fs *)(val); \ | |
101 | \ | |
102 | X##_f = _flo->bits.frac; \ | |
103 | X##_e = _flo->bits.exp; \ | |
104 | X##_s = _flo->bits.sign; \ | |
105 | } while (0) | |
106 | ||
107 | /* | |
108 | * Repack the raw bits of a native fp value. | |
109 | */ | |
110 | ||
111 | #define _FP_PACK_RAW_1(fs, val, X) \ | |
112 | do { \ | |
113 | union _FP_UNION_##fs _flo; \ | |
114 | \ | |
115 | _flo.bits.frac = X##_f; \ | |
116 | _flo.bits.exp = X##_e; \ | |
117 | _flo.bits.sign = X##_s; \ | |
118 | \ | |
119 | (val) = _flo.flt; \ | |
120 | } while (0) | |
121 | ||
122 | #define _FP_PACK_RAW_1_P(fs, val, X) \ | |
123 | do { \ | |
124 | union _FP_UNION_##fs *_flo = \ | |
125 | (union _FP_UNION_##fs *)(val); \ | |
126 | \ | |
127 | _flo->bits.frac = X##_f; \ | |
128 | _flo->bits.exp = X##_e; \ | |
129 | _flo->bits.sign = X##_s; \ | |
130 | } while (0) | |
131 | ||
132 | ||
133 | /* | |
134 | * Multiplication algorithms: | |
135 | */ | |
136 | ||
137 | /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the | |
138 | multiplication immediately. */ | |
139 | ||
140 | #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \ | |
141 | do { \ | |
142 | R##_f = X##_f * Y##_f; \ | |
143 | /* Normalize since we know where the msb of the multiplicands \ | |
144 | were (bit B), we know that the msb of the of the product is \ | |
145 | at either 2B or 2B-1. */ \ | |
146 | _FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits); \ | |
147 | } while (0) | |
148 | ||
149 | /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ | |
150 | ||
151 | #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \ | |
152 | do { \ | |
153 | _FP_W_TYPE _Z_f0, _Z_f1; \ | |
154 | doit(_Z_f1, _Z_f0, X##_f, Y##_f); \ | |
155 | /* Normalize since we know where the msb of the multiplicands \ | |
156 | were (bit B), we know that the msb of the of the product is \ | |
157 | at either 2B or 2B-1. */ \ | |
158 | _FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits); \ | |
159 | R##_f = _Z_f0; \ | |
160 | } while (0) | |
161 | ||
162 | /* Finally, a simple widening multiply algorithm. What fun! */ | |
163 | ||
164 | #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \ | |
165 | do { \ | |
166 | _FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1; \ | |
167 | \ | |
168 | /* split the words in half */ \ | |
169 | _xh = X##_f >> (_FP_W_TYPE_SIZE/2); \ | |
170 | _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \ | |
171 | _yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \ | |
172 | _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \ | |
173 | \ | |
174 | /* multiply the pieces */ \ | |
175 | _z_f0 = _xl * _yl; \ | |
176 | _a_f0 = _xh * _yl; \ | |
177 | _a_f1 = _xl * _yh; \ | |
178 | _z_f1 = _xh * _yh; \ | |
179 | \ | |
180 | /* reassemble into two full words */ \ | |
181 | if ((_a_f0 += _a_f1) < _a_f1) \ | |
182 | _z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2); \ | |
183 | _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2); \ | |
184 | _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2); \ | |
185 | _FP_FRAC_ADD_2(_z, _z, _a); \ | |
186 | \ | |
187 | /* normalize */ \ | |
188 | _FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits); \ | |
189 | R##_f = _z_f0; \ | |
190 | } while (0) | |
191 | ||
192 | ||
193 | /* | |
194 | * Division algorithms: | |
195 | */ | |
196 | ||
197 | /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the | |
198 | division immediately. Give this macro either _FP_DIV_HELP_imm for | |
199 | C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you | |
200 | choose will depend on what the compiler does with divrem4. */ | |
201 | ||
202 | #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \ | |
203 | do { \ | |
204 | _FP_W_TYPE _q, _r; \ | |
205 | X##_f <<= (X##_f < Y##_f \ | |
206 | ? R##_e--, _FP_WFRACBITS_##fs \ | |
207 | : _FP_WFRACBITS_##fs - 1); \ | |
208 | doit(_q, _r, X##_f, Y##_f); \ | |
209 | R##_f = _q | (_r != 0); \ | |
210 | } while (0) | |
211 | ||
212 | /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd | |
213 | that may be useful in this situation. This first is for a primitive | |
214 | that requires normalization, the second for one that does not. Look | |
215 | for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */ | |
216 | ||
217 | #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \ | |
218 | do { \ | |
219 | _FP_W_TYPE _nh, _nl, _q, _r, _y; \ | |
220 | \ | |
221 | /* Normalize Y -- i.e. make the most significant bit set. */ \ | |
222 | _y = Y##_f << _FP_WFRACXBITS_##fs; \ | |
223 | \ | |
224 | /* Shift X op correspondingly high, that is, up one full word. */ \ | |
225 | if (X##_f < Y##_f) \ | |
226 | { \ | |
227 | R##_e--; \ | |
228 | _nl = 0; \ | |
229 | _nh = X##_f; \ | |
230 | } \ | |
231 | else \ | |
232 | { \ | |
233 | _nl = X##_f << (_FP_W_TYPE_SIZE - 1); \ | |
234 | _nh = X##_f >> 1; \ | |
235 | } \ | |
fa1e55b0 | 236 | \ |
49721058 JM |
237 | udiv_qrnnd(_q, _r, _nh, _nl, _y); \ |
238 | R##_f = _q | (_r != 0); \ | |
239 | } while (0) | |
240 | ||
241 | #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \ | |
242 | do { \ | |
243 | _FP_W_TYPE _nh, _nl, _q, _r; \ | |
244 | if (X##_f < Y##_f) \ | |
245 | { \ | |
246 | R##_e--; \ | |
247 | _nl = X##_f << _FP_WFRACBITS_##fs; \ | |
248 | _nh = X##_f >> _FP_WFRACXBITS_##fs; \ | |
249 | } \ | |
250 | else \ | |
251 | { \ | |
252 | _nl = X##_f << (_FP_WFRACBITS_##fs - 1); \ | |
253 | _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \ | |
254 | } \ | |
255 | udiv_qrnnd(_q, _r, _nh, _nl, Y##_f); \ | |
256 | R##_f = _q | (_r != 0); \ | |
257 | } while (0) | |
fa1e55b0 JM |
258 | |
259 | ||
49721058 JM |
260 | /* |
261 | * Square root algorithms: | |
262 | * We have just one right now, maybe Newton approximation | |
263 | * should be added for those machines where division is fast. | |
264 | */ | |
fa1e55b0 | 265 | |
49721058 JM |
266 | #define _FP_SQRT_MEAT_1(R, S, T, X, q) \ |
267 | do { \ | |
268 | while (q != _FP_WORK_ROUND) \ | |
269 | { \ | |
270 | T##_f = S##_f + q; \ | |
271 | if (T##_f <= X##_f) \ | |
272 | { \ | |
273 | S##_f = T##_f + q; \ | |
274 | X##_f -= T##_f; \ | |
275 | R##_f += q; \ | |
276 | } \ | |
277 | _FP_FRAC_SLL_1(X, 1); \ | |
278 | q >>= 1; \ | |
279 | } \ | |
280 | if (X##_f) \ | |
281 | { \ | |
282 | if (S##_f < X##_f) \ | |
283 | R##_f |= _FP_WORK_ROUND; \ | |
284 | R##_f |= _FP_WORK_STICKY; \ | |
285 | } \ | |
286 | } while (0) | |
287 | ||
288 | /* | |
fa1e55b0 | 289 | * Assembly/disassembly for converting to/from integral types. |
49721058 JM |
290 | * No shifting or overflow handled here. |
291 | */ | |
292 | ||
293 | #define _FP_FRAC_ASSEMBLE_1(r, X, rsize) (r = X##_f) | |
294 | #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = r) | |
295 | ||
296 | ||
297 | /* | |
298 | * Convert FP values between word sizes | |
299 | */ | |
300 | ||
301 | #define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f) |