]>
Commit | Line | Data |
---|---|---|
d5efd131 MF |
1 | .file "log2.s" |
2 | ||
3 | ||
4 | // Copyright (c) 2000 - 2003, Intel Corporation | |
5 | // All rights reserved. | |
6 | // | |
7 | // Contributed 2000 by the Intel Numerics Group, Intel Corporation | |
8 | // | |
9 | // Redistribution and use in source and binary forms, with or without | |
10 | // modification, are permitted provided that the following conditions are | |
11 | // met: | |
12 | // | |
13 | // * Redistributions of source code must retain the above copyright | |
14 | // notice, this list of conditions and the following disclaimer. | |
15 | // | |
16 | // * Redistributions in binary form must reproduce the above copyright | |
17 | // notice, this list of conditions and the following disclaimer in the | |
18 | // documentation and/or other materials provided with the distribution. | |
19 | // | |
20 | // * The name of Intel Corporation may not be used to endorse or promote | |
21 | // products derived from this software without specific prior written | |
22 | // permission. | |
23 | ||
0347518d MF |
24 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
25 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
d5efd131 | 26 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
0347518d | 27 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
d5efd131 | 28 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
0347518d MF |
29 | // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
30 | // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
31 | // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY | |
d5efd131 | 32 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
0347518d MF |
33 | // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
34 | // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
35 | // | |
d5efd131 | 36 | // Intel Corporation is the author of this code, and requests that all |
0347518d | 37 | // problem reports or change requests be submitted to it directly at |
d5efd131 MF |
38 | // http://www.intel.com/software/products/opensource/libraries/num.htm. |
39 | // | |
40 | // History | |
41 | //================================================================= | |
0347518d | 42 | // 09/11/00 Initial version |
d5efd131 MF |
43 | // 03/19/01 Added one polynomial coefficient, to improve accuracy |
44 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
45 | // 02/10/03 Reordered header: .section, .global, .proc, .align | |
46 | // 04/18/03 Reformatted T[255] | |
47 | // | |
48 | // API | |
49 | //================================================================= | |
50 | // double log2(double) | |
51 | // | |
52 | // Overview of operation | |
53 | //================================================================= | |
54 | // Background | |
55 | // | |
56 | // Implementation | |
57 | // | |
58 | // Let x = 2^l * m, where m=1.b1 b2 ... b8 b9 ... b52 | |
59 | // y=frcpa(m), r=m*y-1, f=b1 b2 .. b8 (table index) | |
60 | // j=0 if f<128; j=1 if f>=128 | |
61 | // T is a table that stores log2(1/y) (in entries 1..255) rounded to | |
62 | // double extended precision; f is used as an index; T[255]=0 | |
0347518d | 63 | // |
d5efd131 | 64 | // If f=0 and b9=0, r is set to 2^{-8}* 0.b9 b10 ... b52 = m-1 (fractional part of m), |
0347518d | 65 | // and 0 is used instead of T[0] |
d5efd131 MF |
66 | // (polynomial evaluation only, for m=1+r, 0<=r<2^{-9}) |
67 | // If f=255, r is set to (m-2)/2 (T[255]=0, and only polynomial evaluation is used | |
68 | // for m=2(1-r'), 0<=r'<2^{-9}) | |
69 | // | |
70 | // log2(x) is approximated as | |
71 | // (l-j) + T[f] + (c1*r+c2*r^2+...+c7*r^7), if f>0 | |
0347518d | 72 | // |
d5efd131 MF |
73 | |
74 | ||
0347518d | 75 | // Special values |
d5efd131 MF |
76 | //================================================================= |
77 | // log2(0)=-inf, raises Divide by Zero | |
78 | // log2(+inf)=inf | |
79 | // log2(x)=NaN, raises Invalid if x<0 | |
80 | // | |
81 | ||
82 | ||
83 | // Registers used | |
84 | //============================================================== | |
85 | // f6-f15, f32-f33 | |
86 | // r2-r3, r23-r30 | |
87 | // p6,p7,p8,p12 | |
88 | // | |
89 | ||
90 | ||
91 | GR_SAVE_B0 = r33 | |
92 | GR_SAVE_PFS = r34 | |
0347518d | 93 | GR_SAVE_GP = r35 // This reg. can safely be used |
d5efd131 MF |
94 | GR_SAVE_SP = r36 |
95 | ||
96 | GR_Parameter_X = r37 | |
97 | GR_Parameter_Y = r38 | |
98 | GR_Parameter_RESULT = r39 | |
99 | GR_Parameter_TAG = r40 | |
100 | ||
101 | FR_X = f10 | |
102 | FR_Y = f1 | |
103 | FR_RESULT = f8 | |
104 | ||
105 | ||
106 | ||
107 | ||
108 | // Data tables | |
109 | //============================================================== | |
110 | ||
111 | RODATA | |
112 | ||
113 | .align 16 | |
114 | ||
115 | LOCAL_OBJECT_START(poly_coeffs) | |
116 | ||
117 | data8 0xbfd0000000000000, 0x3fc999999999999a //C_4, C_5 | |
118 | data8 0xbfc5555555555555, 0x3fc2492492492492 //C_6, C_7 | |
119 | data8 0xb8aa3b295c17f0bc, 0x00003fff // C_1 | |
120 | data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // C_3=1/3 | |
121 | LOCAL_OBJECT_END(poly_coeffs) | |
122 | ||
123 | ||
124 | LOCAL_OBJECT_START(T_table) | |
125 | ||
126 | data8 0xb8d8752172fed131, 0x00003ff6 | |
127 | data8 0x8ae7f475764180a3, 0x00003ff8 | |
128 | data8 0xe7f73862e72ee35d, 0x00003ff8 | |
129 | data8 0xa2b25310c941a2f2, 0x00003ff9 | |
130 | data8 0xcbb91d671abb2e85, 0x00003ff9 | |
131 | data8 0xfac91e34daa50483, 0x00003ff9 | |
132 | data8 0x9504a5042eb495c5, 0x00003ffa | |
133 | data8 0xa9c4a0bbb580ee02, 0x00003ffa | |
134 | data8 0xc19264dc8a5e3bf9, 0x00003ffa | |
135 | data8 0xd67aa6703ebf4a77, 0x00003ffa | |
136 | data8 0xee76cac6d6e08ce7, 0x00003ffa | |
137 | data8 0x81c3f7de5434ed04, 0x00003ffb | |
138 | data8 0x8c563033a3ce01e4, 0x00003ffb | |
139 | data8 0x9876e9f09a98661c, 0x00003ffb | |
140 | data8 0xa31e0ac9b2326ce2, 0x00003ffb | |
141 | data8 0xadcf09e1fd10e4a5, 0x00003ffb | |
142 | data8 0xb889f992cf03cdb6, 0x00003ffb | |
143 | data8 0xc34eec68d901a714, 0x00003ffb | |
144 | data8 0xce1df524e9909ed9, 0x00003ffb | |
145 | data8 0xd8f726bcb0b80ad0, 0x00003ffb | |
146 | data8 0xe3da945b878e27d1, 0x00003ffb | |
147 | data8 0xeec851633b76a320, 0x00003ffb | |
148 | data8 0xf82ea4bb6101421a, 0x00003ffb | |
149 | data8 0x8197ddd7736b2864, 0x00003ffc | |
150 | data8 0x871dad4f994253f0, 0x00003ffc | |
151 | data8 0x8ca8cae3e892d549, 0x00003ffc | |
152 | data8 0x916d6e1559a4b697, 0x00003ffc | |
153 | data8 0x97028118efabeb7d, 0x00003ffc | |
154 | data8 0x9bcfbce1592ad5d5, 0x00003ffc | |
155 | data8 0xa16ee95d0da54a91, 0x00003ffc | |
156 | data8 0xa644dcf3403fa5d0, 0x00003ffc | |
157 | data8 0xab1ee14ffd659064, 0x00003ffc | |
158 | data8 0xb0cd12faebcc6757, 0x00003ffc | |
159 | data8 0xb5affdf9b3b221e0, 0x00003ffc | |
160 | data8 0xba970fb307c6ade1, 0x00003ffc | |
161 | data8 0xbf824f3a9f3e7561, 0x00003ffc | |
162 | data8 0xc544c055fde99333, 0x00003ffc | |
163 | data8 0xca39266532bdf26c, 0x00003ffc | |
164 | data8 0xcf31d124b8fa2f56, 0x00003ffc | |
165 | data8 0xd42ec7f59017b6ab, 0x00003ffc | |
166 | data8 0xd930124bea9a2c67, 0x00003ffc | |
167 | data8 0xde35b7af70e4dab3, 0x00003ffc | |
168 | data8 0xe33fbfbb8533ef03, 0x00003ffc | |
169 | data8 0xe77625911a7dcef3, 0x00003ffc | |
170 | data8 0xec884bd689cc12e3, 0x00003ffc | |
171 | data8 0xf19eeabf9e99a40a, 0x00003ffc | |
172 | data8 0xf6ba0a35e3d88051, 0x00003ffc | |
173 | data8 0xfbd9b237f7b4192b, 0x00003ffc | |
174 | data8 0x80111d4a1ee0c79e, 0x00003ffd | |
175 | data8 0x82a523a5f875bbfc, 0x00003ffd | |
176 | data8 0x84ccecdc92cd0815, 0x00003ffd | |
177 | data8 0x87653369d92c057a, 0x00003ffd | |
178 | data8 0x89ffd1742da3aa21, 0x00003ffd | |
179 | data8 0x8c2d2227d053d9b6, 0x00003ffd | |
180 | data8 0x8e5c189793f7f798, 0x00003ffd | |
181 | data8 0x90fd0a20e72f3c96, 0x00003ffd | |
182 | data8 0x932fa937301e59ae, 0x00003ffd | |
183 | data8 0x95d5061a5f0f5f7f, 0x00003ffd | |
184 | data8 0x980b5a2ef10e7023, 0x00003ffd | |
185 | data8 0x9a4361c5514d3c27, 0x00003ffd | |
186 | data8 0x9c7d1f7d541313fd, 0x00003ffd | |
187 | data8 0x9f2b16040b500d04, 0x00003ffd | |
188 | data8 0xa168a0fa9db22c98, 0x00003ffd | |
189 | data8 0xa3a7eaa1f9116293, 0x00003ffd | |
190 | data8 0xa5e8f5b4072a3d44, 0x00003ffd | |
191 | data8 0xa82bc4f11a5e88aa, 0x00003ffd | |
192 | data8 0xaa705b2001db8317, 0x00003ffd | |
193 | data8 0xacb6bb0e1e0f8005, 0x00003ffd | |
194 | data8 0xaefee78f75707221, 0x00003ffd | |
195 | data8 0xb148e37ec994dd99, 0x00003ffd | |
196 | data8 0xb394b1bdaca0bc17, 0x00003ffd | |
197 | data8 0xb5e255349707e496, 0x00003ffd | |
198 | data8 0xb831d0d2fda791cc, 0x00003ffd | |
199 | data8 0xba83278f6838ab20, 0x00003ffd | |
200 | data8 0xbcd65c67881c7d47, 0x00003ffd | |
201 | data8 0xbeb3e0f21d72dc92, 0x00003ffd | |
202 | data8 0xc10a7a03457d35dc, 0x00003ffd | |
203 | data8 0xc362f9b6f51eddd3, 0x00003ffd | |
204 | data8 0xc5bd6326ebfce656, 0x00003ffd | |
205 | data8 0xc7a0b3d0637c8f97, 0x00003ffd | |
206 | data8 0xc9fe96af0df8e4b5, 0x00003ffd | |
207 | data8 0xcc5e6c214b4a2cd7, 0x00003ffd | |
208 | data8 0xce46199f374d29cf, 0x00003ffd | |
209 | data8 0xd0a978a14c0d9ebe, 0x00003ffd | |
210 | data8 0xd293fecafec7f9b5, 0x00003ffd | |
211 | data8 0xd4faf1f6f5cf32e6, 0x00003ffd | |
212 | data8 0xd6e8595abaad34d1, 0x00003ffd | |
213 | data8 0xd952eb7a8ffc1593, 0x00003ffd | |
214 | data8 0xdb433ccd805f171e, 0x00003ffd | |
215 | data8 0xddb178dc43e6bd84, 0x00003ffd | |
216 | data8 0xdfa4bcfb333342a4, 0x00003ffd | |
217 | data8 0xe19953741ccea015, 0x00003ffd | |
218 | data8 0xe40cee16a2ff21c5, 0x00003ffd | |
219 | data8 0xe6048470cdbde8ea, 0x00003ffd | |
220 | data8 0xe7fd7308d6895b14, 0x00003ffd | |
221 | data8 0xe9f7bbb6a1ff9f87, 0x00003ffd | |
222 | data8 0xec7280138809433d, 0x00003ffd | |
223 | data8 0xee6fda4365cd051f, 0x00003ffd | |
224 | data8 0xf06e94a122ff1f12, 0x00003ffd | |
225 | data8 0xf26eb1151441fce5, 0x00003ffd | |
226 | data8 0xf470318b88a77e2f, 0x00003ffd | |
227 | data8 0xf67317f4d4c8aa58, 0x00003ffd | |
228 | data8 0xf8f8b250a9c4cde6, 0x00003ffd | |
229 | data8 0xfafec54831f1a484, 0x00003ffd | |
230 | data8 0xfd06449bf3eaea1e, 0x00003ffd | |
231 | data8 0xff0f324ddb19ab67, 0x00003ffd | |
232 | data8 0x808cc8320a9acf15, 0x00003ffe | |
233 | data8 0x8192b0748f2cef06, 0x00003ffe | |
234 | data8 0x829952f5e6a24ee5, 0x00003ffe | |
235 | data8 0x83a0b0bfafe1424e, 0x00003ffe | |
236 | data8 0x8466b29f9c41caea, 0x00003ffe | |
237 | data8 0x856f5aae0881d857, 0x00003ffe | |
238 | data8 0x8678c0eae8ee8190, 0x00003ffe | |
239 | data8 0x8782e6685676b9d7, 0x00003ffe | |
240 | data8 0x888dcc3abc4554ec, 0x00003ffe | |
241 | data8 0x89997378de7b98b8, 0x00003ffe | |
242 | data8 0x8aa5dd3be1044279, 0x00003ffe | |
243 | data8 0x8b6facdfd0360ab8, 0x00003ffe | |
244 | data8 0x8c7d6db7169e0cdb, 0x00003ffe | |
245 | data8 0x8d8bf424d6e130b2, 0x00003ffe | |
246 | data8 0x8e575b506f409fa6, 0x00003ffe | |
247 | data8 0x8f673e418776492c, 0x00003ffe | |
248 | data8 0x9077e9ed700ef9ba, 0x00003ffe | |
249 | data8 0x9144ef1baec80b20, 0x00003ffe | |
250 | data8 0x9256fcdb537f035f, 0x00003ffe | |
251 | data8 0x9369d68d75e7e1d6, 0x00003ffe | |
252 | data8 0x943880613b8f9f1e, 0x00003ffe | |
253 | data8 0x954cc1d9e0d94206, 0x00003ffe | |
254 | data8 0xd3c70a37bdf7a294, 0x0000bffd | |
255 | data8 0xd19bb053fb0284ec, 0x0000bffd | |
256 | data8 0xcffa1a3b7dafb8bf, 0x0000bffd | |
257 | data8 0xcdcbe1e2776479ee, 0x0000bffd | |
258 | data8 0xcc282218b8bfdda2, 0x0000bffd | |
259 | data8 0xc9f703a9afcb38ac, 0x0000bffd | |
260 | data8 0xc851146ab89593c6, 0x0000bffd | |
261 | data8 0xc61d08265927a860, 0x0000bffd | |
262 | data8 0xc474e39705912d26, 0x0000bffd | |
263 | data8 0xc23de19ec30c6e3e, 0x0000bffd | |
264 | data8 0xc09381cc45db45b4, 0x0000bffd | |
265 | data8 0xbee82b4e025ff90c, 0x0000bffd | |
266 | data8 0xbcace101149788ec, 0x0000bffd | |
267 | data8 0xbaff46962ea47964, 0x0000bffd | |
268 | data8 0xb950b1be5e0c14a2, 0x0000bffd | |
269 | data8 0xb7110e6ce866f2bc, 0x0000bffd | |
270 | data8 0xb5602ccc2a81db52, 0x0000bffd | |
271 | data8 0xb3ae4ce740fc8ef1, 0x0000bffd | |
272 | data8 0xb1fb6d92c8240ccc, 0x0000bffd | |
273 | data8 0xafb609c09b244abc, 0x0000bffd | |
274 | data8 0xae00d1cfdeb43cfd, 0x0000bffd | |
275 | data8 0xac4a967a8c8c9bd0, 0x0000bffd | |
276 | data8 0xaa93568c249e6c52, 0x0000bffd | |
277 | data8 0xa8db10cdff375343, 0x0000bffd | |
278 | data8 0xa68e6fc5a42376e3, 0x0000bffd | |
279 | data8 0xa4d3c25e68dc57f2, 0x0000bffd | |
280 | data8 0xa3180b0c192a3816, 0x0000bffd | |
281 | data8 0xa15b488e7aa329a0, 0x0000bffd | |
282 | data8 0x9f9d79a30f0e1d5f, 0x0000bffd | |
283 | data8 0x9dde9d050ee7d4ac, 0x0000bffd | |
284 | data8 0x9c1eb16d63d7356c, 0x0000bffd | |
285 | data8 0x9a5db592a310c36a, 0x0000bffd | |
286 | data8 0x989ba82907a9016f, 0x0000bffd | |
287 | data8 0x96d887e26cd57b79, 0x0000bffd | |
288 | data8 0x9514536e481c3a4f, 0x0000bffd | |
289 | data8 0x934f0979a3715fc9, 0x0000bffd | |
290 | data8 0x9188a8af1742a9d5, 0x0000bffd | |
291 | data8 0x8fc12fb6c470995f, 0x0000bffd | |
292 | data8 0x8df89d364e34f8f1, 0x0000bffd | |
293 | data8 0x8c2eefd0d3f67dd6, 0x0000bffd | |
294 | data8 0x8a642626eb093d54, 0x0000bffd | |
295 | data8 0x88983ed6985bae58, 0x0000bffd | |
296 | data8 0x86cb387b4a0feec6, 0x0000bffd | |
297 | data8 0x84fd11add101024b, 0x0000bffd | |
298 | data8 0x83c856dd81804b78, 0x0000bffd | |
299 | data8 0x81f84c2c62afd6f1, 0x0000bffd | |
300 | data8 0x80271d3e4be5ea5a, 0x0000bffd | |
301 | data8 0xfca991447e7b485d, 0x0000bffc | |
302 | data8 0xf90299c904793a3c, 0x0000bffc | |
303 | data8 0xf559511d2dc1ed69, 0x0000bffc | |
304 | data8 0xf2e72afee9bd2aee, 0x0000bffc | |
305 | data8 0xef39ff1d8a40770e, 0x0000bffc | |
306 | data8 0xeb8a7a2311c935dc, 0x0000bffc | |
307 | data8 0xe7d8990dc620012f, 0x0000bffc | |
308 | data8 0xe560b1e3b86e44b6, 0x0000bffc | |
309 | data8 0xe1aadb38caee80c4, 0x0000bffc | |
310 | data8 0xddf2a051f81b76a4, 0x0000bffc | |
311 | data8 0xdb7678bafcaf4b5f, 0x0000bffc | |
312 | data8 0xd7ba3a8f0df19bfc, 0x0000bffc | |
313 | data8 0xd3fb8fdbdd5cebdb, 0x0000bffc | |
314 | data8 0xd17b191905c35652, 0x0000bffc | |
315 | data8 0xcdb85d29cefd7121, 0x0000bffc | |
316 | data8 0xc9f32c3c88221ef6, 0x0000bffc | |
317 | data8 0xc76e5741a95b5dae, 0x0000bffc | |
318 | data8 0xc3a506d80d38c718, 0x0000bffc | |
319 | data8 0xbfd938ccef8b68c1, 0x0000bffc | |
320 | data8 0xbd4ff63e82eef78c, 0x0000bffc | |
321 | data8 0xb97ffa2b563865bd, 0x0000bffc | |
322 | data8 0xb6f3eb3011eddcea, 0x0000bffc | |
323 | data8 0xb31fb7d64898b3e6, 0x0000bffc | |
324 | data8 0xb090d63a409e7880, 0x0000bffc | |
325 | data8 0xacb8623c7ffa4f39, 0x0000bffc | |
326 | data8 0xa8dd5c83d2e45246, 0x0000bffc | |
327 | data8 0xa649e998a8d91f2e, 0x0000bffc | |
328 | data8 0xa26a93fed6faa94f, 0x0000bffc | |
329 | data8 0x9fd43df079d0db1f, 0x0000bffc | |
330 | data8 0x9d3cbe69aecac4c2, 0x0000bffc | |
331 | data8 0x99574f13c570d0fb, 0x0000bffc | |
332 | data8 0x96bce349bf7ee6c7, 0x0000bffc | |
333 | data8 0x92d30c9b86cee18e, 0x0000bffc | |
334 | data8 0x9035adef17c5bd5c, 0x0000bffc | |
335 | data8 0x8c4765e8e8b5f251, 0x0000bffc | |
336 | data8 0x89a70da448316ffa, 0x0000bffc | |
337 | data8 0x85b44a24474af78a, 0x0000bffc | |
338 | data8 0x8310f17aab5adf70, 0x0000bffc | |
339 | data8 0x806c6388d0965f29, 0x0000bffc | |
340 | data8 0xf8e69092bf0c5ead, 0x0000bffb | |
341 | data8 0xf397608bfd2d90e6, 0x0000bffb | |
342 | data8 0xee45be24d0eedbc4, 0x0000bffb | |
343 | data8 0xe646af233db881e9, 0x0000bffb | |
344 | data8 0xe0eee4e1ce3d06fb, 0x0000bffb | |
345 | data8 0xdb94a049e6e87a4f, 0x0000bffb | |
346 | data8 0xd3888ef9a4249f5a, 0x0000bffb | |
347 | data8 0xce280e6fbac39194, 0x0000bffb | |
348 | data8 0xc8c50b72319ad574, 0x0000bffb | |
349 | data8 0xc0abcd39f41e329b, 0x0000bffb | |
350 | data8 0xbb4279cfa7f9667b, 0x0000bffb | |
351 | data8 0xb5d69bac77ec398a, 0x0000bffb | |
352 | data8 0xb068306bf20d6233, 0x0000bffb | |
353 | data8 0xa83dc1b019ddb6a8, 0x0000bffb | |
354 | data8 0xa2c8eb1886c2d024, 0x0000bffb | |
355 | data8 0x9d517ee93f8e16c0, 0x0000bffb | |
356 | data8 0x97d77aae659b92fb, 0x0000bffb | |
357 | data8 0x8f9b91da5736d415, 0x0000bffb | |
358 | data8 0x8a1b06b09b7fd1d1, 0x0000bffb | |
359 | data8 0x8497daca0a2e077a, 0x0000bffb | |
360 | data8 0xfe241745a453f10c, 0x0000bffa | |
361 | data8 0xf3132d6708d723c5, 0x0000bffa | |
362 | data8 0xe7fcf2e21a0e7d77, 0x0000bffa | |
363 | data8 0xd75198b04afb8da9, 0x0000bffa | |
364 | data8 0xcc2dfe1a4a8ca305, 0x0000bffa | |
365 | data8 0xc10500d63aa65882, 0x0000bffa | |
366 | data8 0xb5d69bac77ec398a, 0x0000bffa | |
367 | data8 0xaaa2c95dc66abcde, 0x0000bffa | |
368 | data8 0x9f6984a342d13101, 0x0000bffa | |
369 | data8 0x942ac82e5387ac51, 0x0000bffa | |
370 | data8 0x88e68ea899a0976c, 0x0000bffa | |
371 | data8 0xefebc4409ccf872e, 0x0000bff9 | |
372 | data8 0xd947b0c6642ef69e, 0x0000bff9 | |
373 | data8 0xc2987d51e043d407, 0x0000bff9 | |
374 | data8 0xabde1eeee6bfd257, 0x0000bff9 | |
375 | data8 0x95188a9917cf2e01, 0x0000bff9 | |
376 | data8 0xfc8f6a777c1b7f1e, 0x0000bff8 | |
377 | data8 0xced727635c59725c, 0x0000bff8 | |
378 | data8 0xa108358a4c904615, 0x0000bff8 | |
379 | data8 0xe644fcbeb3ac9c90, 0x0000bff7 | |
380 | data8 0x8a4bd667bf08e7de, 0x0000bff7 | |
381 | data8 0x0000000000000000 // T[255] Low | |
382 | data8 0x0000000000000000 // T[255] High | |
383 | LOCAL_OBJECT_END(T_table) | |
384 | ||
385 | ||
386 | ||
387 | .section .text | |
718d6542 | 388 | WEAK_LIBM_ENTRY(log2) |
d5efd131 MF |
389 | |
390 | { .mfi | |
0347518d MF |
391 | alloc r32=ar.pfs,1,4,4,0 |
392 | // y=frcpa(x) | |
d5efd131 | 393 | frcpa.s1 f6,p0=f1,f8 |
0347518d | 394 | // will form significand of 1.5 (to test whether the index is 128 or above) |
d5efd131 MF |
395 | mov r24=0xc |
396 | } | |
397 | {.mfi | |
398 | nop.m 0 | |
0347518d | 399 | // normalize x |
d5efd131 MF |
400 | fma.s1 f7=f8,f1,f0 |
401 | // r2 = pointer to C_1...C_6 followed by T_table | |
402 | addl r2 = @ltoff(poly_coeffs), gp;; | |
403 | } | |
404 | {.mfi | |
405 | // get significand | |
406 | getf.sig r25=f8 | |
407 | // f8 denormal ? | |
408 | fclass.m p8,p10=f8,0x9 | |
0347518d | 409 | // will form significand of 1.5 (to test whether the index is 128 or above) |
d5efd131 MF |
410 | shl r24=r24,60 |
411 | } | |
412 | {.mfi | |
413 | mov r26=0x804 | |
414 | nop.f 0 | |
415 | // r23=bias-1 | |
416 | mov r23=0xfffe;; | |
417 | } | |
418 | ||
419 | {.mmf | |
420 | getf.exp r29=f8 | |
421 | // load start address for C_1...C_6 followed by T_table | |
422 | ld8 r2=[r2] | |
0347518d | 423 | // will continue only for positive normal/denormal numbers |
d5efd131 MF |
424 | fclass.nm.unc p12,p7 = f8, 0x19 ;; |
425 | } | |
426 | ||
427 | .pred.rel "mutex",p8,p10 | |
428 | {.mfi | |
429 | // denormal input, repeat get significand (after normalization) | |
430 | (p8) getf.sig r25=f7 | |
431 | // x=1 ? | |
432 | fcmp.eq.s0 p6,p0=f8,f1 | |
433 | // get T_index | |
434 | (p10) shr.u r28=r25,63-8 | |
435 | } | |
436 | {.mfi | |
437 | // f32=0.5 | |
438 | setf.exp f32=r23 | |
439 | nop.f 0 | |
440 | // r27=bias | |
441 | mov r27=0xffff;; | |
442 | } | |
443 | ||
444 | {.mmi | |
445 | // denormal input, repeat get exponent (after normalization) | |
446 | (p8) getf.exp r29=f7 | |
447 | mov r23=0xff | |
448 | // r26=0x80400...0 (threshold for using polynomial approximation) | |
449 | shl r26=r26,64-12;; | |
450 | } | |
451 | ||
452 | {.mfb | |
453 | add r3=48,r2 | |
454 | // r=1-x*y | |
455 | fms.s1 f6=f6,f8,f1 | |
456 | (p12) br.cond.spnt SPECIAL_LOG2 | |
457 | } | |
458 | {.mfi | |
459 | // load C_4, C_5 | |
460 | ldfpd f10,f11=[r2],16 | |
461 | nop.f 0 | |
462 | cmp.geu p12,p0=r25,r24;; | |
463 | } | |
464 | ||
465 | {.mmi | |
466 | // load C_6, C_7 | |
467 | ldfpd f12,f13=[r2],16 | |
0347518d | 468 | // r27=bias-1 (if index >=128, will add exponent+1) |
d5efd131 MF |
469 | (p12) mov r27=0xfffe |
470 | (p8) shr.u r28=r25,63-8;; | |
471 | } | |
472 | ||
473 | ||
474 | {.mfi | |
475 | // load C_1 | |
476 | ldfe f14=[r2],32 | |
477 | fmerge.se f7=f1,f7 | |
478 | // if first 9 bits after leading 1 are all zero, then p8=1 | |
479 | cmp.ltu p8,p12=r25,r26 | |
480 | } | |
481 | {.mfi | |
482 | // load C_3 | |
483 | ldfe f15=[r3] | |
484 | nop.f 0 | |
485 | // get T_index | |
486 | and r28=r28,r23;; | |
487 | } | |
488 | {.mfi | |
489 | // r29=exponent-bias | |
490 | sub r29=r29,r27 | |
491 | // x=1, return 0 | |
492 | (p6) fma.d.s0 f8=f0,f0,f0 | |
493 | // get T address | |
494 | shladd r2=r28,4,r2 | |
495 | } | |
496 | {.mfb | |
497 | // first 8 bits after leading 1 are all ones ? | |
498 | cmp.eq p10,p0=r23,r28 | |
499 | // if first 8 bits after leading bit are 0, use polynomial approx. only | |
500 | (p8) fms.s1 f6=f7,f1,f1 | |
501 | // x=1, return | |
502 | (p6) br.ret.spnt b0;; | |
503 | } | |
504 | {.mfi | |
505 | // r26=1 | |
506 | mov r26=1 | |
507 | // if first 8 bits after leading 1 are all ones, use polynomial approx. only | |
508 | (p10) fms.s1 f6=f7,f32,f1 | |
509 | nop.i 0;; | |
510 | } | |
511 | ||
512 | .pred.rel "mutex",p8,p12 | |
513 | {.mmf | |
514 | // load T (unless first 9 bits after leading 1 are 0) | |
515 | (p12) ldfe f33=[r2] | |
0347518d | 516 | // f8=expon - bias |
d5efd131 MF |
517 | setf.sig f8=r29 |
518 | // set T=0 (if first 9 bits after leading 1 are 0) | |
519 | (p8) fma.s1 f33=f0,f0,f0;; | |
520 | } | |
521 | ||
522 | {.mfi | |
523 | nop.m 0 | |
524 | // P12=1-0.5*r | |
525 | fnma.s1 f32=f32,f6,f1 | |
526 | // r26=2^{63} | |
527 | shl r26=r26,63 | |
528 | } | |
529 | {.mfi | |
530 | nop.m 0 | |
531 | // r2=r*r | |
532 | fma.s1 f7=f6,f6,f0 | |
533 | nop.i 0;; | |
534 | } | |
535 | {.mfi | |
536 | // significand(x)=1 ? | |
537 | cmp.eq p0,p6=r26,r25 | |
538 | // P67=C_6+C_7*r | |
539 | fma.s1 f13=f13,f6,f12 | |
540 | nop.i 0 | |
541 | } | |
542 | {.mfi | |
543 | nop.m 0 | |
544 | // P45=C_4+C_5*r | |
545 | fma.s1 f10=f11,f6,f10 | |
546 | nop.i 0;; | |
547 | } | |
548 | ||
549 | {.mfi | |
550 | nop.m 0 | |
551 | // C_1*r | |
552 | (p6) fma.s1 f14=f14,f6,f0 | |
553 | nop.i 0;; | |
554 | } | |
555 | {.mfi | |
556 | nop.m 0 | |
557 | // normalize additive term (l=exponent of x) | |
558 | fcvt.xf f8=f8 | |
559 | nop.i 0 | |
560 | } | |
561 | {.mfi | |
562 | nop.m 0 | |
563 | // P13=1-0.5*r+C_3*r^2 | |
564 | (p6) fma.s1 f15=f15,f7,f32 | |
565 | nop.i 0;; | |
566 | } | |
567 | ||
568 | {.mfi | |
569 | nop.m 0 | |
570 | // P47=P45+r2*P67 | |
571 | (p6) fma.s1 f13=f13,f7,f10 | |
572 | // if significand(x)=1, return exponent (l) | |
573 | nop.i 0 | |
574 | } | |
575 | {.mfi | |
576 | nop.m 0 | |
577 | // r3=r^3 | |
578 | (p6) fma.s1 f7=f7,f6,f0 | |
579 | nop.i 0;; | |
580 | } | |
581 | ||
582 | {.mfi | |
583 | nop.m 0 | |
584 | // add T+l | |
585 | (p6) fma.s1 f8=f8,f1,f33 | |
586 | nop.i 0 | |
587 | } | |
588 | {.mfi | |
589 | nop.m 0 | |
590 | // P17=P13+r3*P47 | |
591 | (p6) fma.s1 f13=f13,f7,f15 | |
592 | nop.i 0;; | |
593 | } | |
594 | ||
595 | {.mfb | |
596 | nop.m 0 | |
597 | // result=T+l+(C_1*r)*P16 | |
598 | (p6) fma.d.s0 f8=f13,f14,f8 | |
599 | // return | |
600 | br.ret.sptk b0;; | |
601 | } | |
602 | ||
603 | ||
604 | SPECIAL_LOG2: | |
0347518d | 605 | {.mfi |
d5efd131 MF |
606 | nop.m 0 |
607 | // x=+Infinity ? | |
608 | fclass.m p7,p0=f8,0x21 | |
609 | nop.i 0;; | |
610 | } | |
611 | {.mfi | |
612 | nop.m 0 | |
613 | // x=+/-Zero ? | |
614 | fclass.m p8,p0=f8,0x7 | |
615 | nop.i 0;; | |
616 | } | |
617 | {.mfi | |
618 | nop.m 0 | |
619 | // x=-Infinity, -normal, -denormal ? | |
620 | fclass.m p6,p0=f8,0x3a | |
621 | nop.i 0;; | |
622 | } | |
623 | {.mfb | |
624 | nop.m 0 | |
625 | // log2(+Infinity)=+Infinity | |
626 | nop.f 0 | |
627 | (p7) br.ret.spnt b0;; | |
628 | } | |
629 | {.mfi | |
0347518d | 630 | (p8) mov GR_Parameter_TAG = 170 |
d5efd131 MF |
631 | // log2(+/-0)=-infinity, raises Divide by Zero |
632 | // set f8=-0 | |
633 | (p8) fmerge.ns f8=f0,f8 | |
634 | nop.i 0;; | |
635 | } | |
636 | {.mfb | |
637 | nop.m 0 | |
638 | (p8) frcpa.s0 f8,p0=f1,f8 | |
639 | (p8) br.cond.sptk __libm_error_region;; | |
640 | } | |
641 | {.mfb | |
0347518d | 642 | (p6) mov GR_Parameter_TAG = 171 |
d5efd131 MF |
643 | // x<0: return NaN, raise Invalid |
644 | (p6) frcpa.s0 f8,p0=f0,f0 | |
645 | (p6) br.cond.sptk __libm_error_region;; | |
0347518d MF |
646 | } |
647 | ||
d5efd131 MF |
648 | |
649 | {.mfb | |
650 | nop.m 0 | |
651 | // Remaining cases: NaNs | |
652 | fma.d.s0 f8=f8,f1,f0 | |
653 | br.ret.sptk b0;; | |
654 | } | |
655 | ||
718d6542 SN |
656 | WEAK_LIBM_END(log2) |
657 | libm_alias_double_other (__log2, log2) | |
658 | #ifdef SHARED | |
659 | .symver log2,log2@@GLIBC_2.29 | |
660 | .weak __log2_compat | |
661 | .set __log2_compat,__log2 | |
662 | .symver __log2_compat,log2@GLIBC_2.2 | |
663 | #endif | |
d5efd131 MF |
664 | |
665 | ||
666 | LOCAL_LIBM_ENTRY(__libm_error_region) | |
667 | .prologue | |
668 | { .mfi | |
669 | add GR_Parameter_Y=-32,sp // Parameter 2 value | |
670 | nop.f 0 | |
671 | .save ar.pfs,GR_SAVE_PFS | |
0347518d | 672 | mov GR_SAVE_PFS=ar.pfs // Save ar.pfs |
d5efd131 MF |
673 | } |
674 | { .mfi | |
0347518d | 675 | .fframe 64 |
d5efd131 MF |
676 | add sp=-64,sp // Create new stack |
677 | nop.f 0 | |
678 | mov GR_SAVE_GP=gp // Save gp | |
679 | };; | |
680 | { .mmi | |
681 | stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack | |
682 | add GR_Parameter_X = 16,sp // Parameter 1 address | |
0347518d MF |
683 | .save b0, GR_SAVE_B0 |
684 | mov GR_SAVE_B0=b0 // Save b0 | |
d5efd131 MF |
685 | };; |
686 | .body | |
687 | { .mib | |
0347518d MF |
688 | stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack |
689 | add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address | |
690 | nop.b 0 | |
d5efd131 MF |
691 | } |
692 | { .mib | |
693 | stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack | |
0347518d | 694 | add GR_Parameter_Y = -16,GR_Parameter_Y |
d5efd131 MF |
695 | br.call.sptk b0=__libm_error_support# // Call error handling function |
696 | };; | |
697 | { .mmi | |
698 | nop.m 0 | |
699 | nop.m 0 | |
700 | add GR_Parameter_RESULT = 48,sp | |
701 | };; | |
702 | { .mmi | |
703 | ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack | |
704 | .restore sp | |
705 | add sp = 64,sp // Restore stack pointer | |
706 | mov b0 = GR_SAVE_B0 // Restore return address | |
707 | };; | |
708 | { .mib | |
0347518d | 709 | mov gp = GR_SAVE_GP // Restore gp |
d5efd131 MF |
710 | mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs |
711 | br.ret.sptk b0 // Return | |
0347518d | 712 | };; |
d5efd131 MF |
713 | |
714 | LOCAL_LIBM_END(__libm_error_region) | |
715 | .type __libm_error_support#,@function | |
716 | .global __libm_error_support# |