| blob | 9ad1e5fe560c7b71d9d20558c21def785105388b |
1 .file "log.s"
3 // Copyright (C) 2000, 2001, Intel Corporation
4 // All rights reserved.
5 //
6 // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
7 // and Ping Tak Peter Tang of the Computational Software Lab, 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 //
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://developer.intel.com/opensource.
39 //
40 // History
41 //==============================================================
42 // 2/02/00 Initial version
43 // 4/04/00 Unwind support added
44 // 6/16/00 Updated table to be rounded correctly
45 // 8/15/00 Bundle added after call to __libm_error_support to properly
46 // set [the previously overwritten] GR_Parameter_RESULT.
47 // 8/17/00 Improved speed of main path by 5 cycles
48 // Shortened path for x=1.0
49 // 1/09/01 Improved speed, fixed flags for neg denormals
50 //
51 //
52 // API
53 //==============================================================
54 // double log(double)
55 // double log10(double)
56 //
57 // Overview of operation
58 //==============================================================
59 // Background
60 //
61 // Consider x = 2^N 1.f1 f2 f3 f4...f63
62 // Log(x) = log(frcpa(x) x/frcpa(x))
63 // = log(1/frcpa(x)) + log(frcpa(x) x)
64 // = -log(frcpa(x)) + log(frcpa(x) x)
65 //
66 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
67 //
68 // -log(frcpa(x)) = -log(C)
69 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
70 //
71 // -log(frcpa(x)) = -log(C)
72 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
73 //
74 // -log(frcpa(x)) = -log(C)
75 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
76 //
77 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
79 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
80 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
81 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
82 //
83 // Log(x) = +Nlog2 + T + log(C x)
84 //
85 // Cx = 1 + r
86 //
87 // Log(x) = +Nlog2 + T + log(1+r)
88 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
89 //
90 // 1.f1 f2 ... f8 has 256 entries.
91 // They are 1 + k/2^8, k = 0 ... 255
92 // These 256 values are the table entries.
93 //
94 // Implementation
95 //===============
96 // CASE 1: |x-1| >= 2^-6
97 // C = frcpa(x)
98 // r = C * x - 1
99 //
100 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
101 //
102 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
103 // Nfloat = float(n) where n is the true unbiased exponent
104 // pre-index = f_1f_2....f_8
105 // index = pre_index * 16
106 // get the dxt table entry at index + offset = T
107 //
108 // result = (T + Nfloat * log(2)) + rseries
109 //
110 // The T table is calculated as follows
111 // Form x_k = 1 + k/2^8 where k goes from 0... 255
112 // y_k = frcpa(x_k)
113 // log(1/y_k) in quad and round to double-extended
115 // CASE 2: |x-1| < 2^-6
116 // w = x - 1
117 //
118 // Form wseries = w + Q1*w^2 + Q2*w^3 + ... + Q7*w^8 + Q8*w^9
119 //
120 // result = wseries
122 // Special values
123 //==============================================================
126 // log(+0) = -inf
127 // log(-0) = -inf
129 // log(+qnan) = +qnan
130 // log(-qnan) = -qnan
131 // log(+snan) = +qnan
132 // log(-snan) = -qnan
134 // log(-n) = QNAN Indefinite
135 // log(-inf) = QNAN Indefinite
137 // log(+inf) = +inf
139 // Registers used
140 //==============================================================
141 // Floating Point registers used:
142 // f8, input
143 // f9 -> f15, f32 -> f68
145 // General registers used:
146 // r32 -> r51
148 // Predicate registers used:
149 // p6 -> p15
151 // p8 log base e
152 // p6 log base e special
153 // p9 used in the frcpa
154 // p13 log base e large W
155 // p14 log base e small w
157 // p7 log base 10
158 // p10 log base 10 large W
159 // p11 log base 10 small w
160 // p12 log base 10 special
162 #include "libm_support.h"
164 // Assembly macros
165 //==============================================================
167 log_int_Nfloat = f9
168 log_Nfloat = f10
170 log_P5 = f11
171 log_P4 = f12
172 log_P3 = f13
173 log_P2 = f14
174 log_half = f15
176 log_log2 = f32
177 log_T = f33
179 log_rp_p4 = f34
180 log_rp_p32 = f35
181 log_rp_p2 = f36
182 log_w6 = f37
183 log_rp_p10 = f38
184 log_rcube = f39
185 log_rsq = f40
187 log_T_plus_Nlog2 = f41
188 log_w3 = f42
190 log_r = f43
191 log_C = f44
193 log_w = f45
194 log_Q8 = f46
195 log_Q7 = f47
196 log_Q4 = f48
197 log_Q3 = f49
198 log_Q6 = f50
199 log_Q5 = f51
200 log_Q2 = f52
201 log_Q1 = f53
202 log_P1 = f53
204 log_rp_q7 = f54
205 log_rp_q65 = f55
206 log_Qlo = f56
208 log_rp_q3 = f57
209 log_rp_q21 = f58
210 log_Qhi = f59
212 log_wsq = f60
213 log_w4 = f61
214 log_Q = f62
216 log_inv_ln10 = f63
217 log_log10_hi = f64
218 log_log10_lo = f65
219 log_rp_q10 = f66
220 log_NORM_f8 = f67
221 log_r2P_r = f68
223 // ===================================
225 log_GR_exp_17_ones = r33
226 log_GR_exp_16_ones = r34
227 log_GR_exp_f8 = r35
228 log_GR_signexp_f8 = r36
229 log_GR_true_exp_f8 = r37
230 log_GR_significand_f8 = r38
231 log_GR_half_exp = r39
232 log_GR_index = r39
233 log_AD_1 = r40
234 log_GR_signexp_w = r41
235 log_GR_fff9 = r42
236 log_AD_2 = r43
237 log_GR_exp_w = r44
239 GR_SAVE_B0 = r45
240 GR_SAVE_GP = r46
241 GR_SAVE_PFS = r47
243 GR_Parameter_X = r48
244 GR_Parameter_Y = r49
245 GR_Parameter_RESULT = r50
246 log_GR_tag = r51
249 // Data tables
250 //==============================================================
252 #ifdef _LIBC
253 .rodata
254 #else
255 .data
256 #endif
258 .align 16
260 log_table_1:
261 ASM_TYPE_DIRECTIVE(log_table_1,@object)
262 data8 0xBFC5555DA7212371 // P5
263 data8 0x3FC999A19EEF5826 // P4
264 data8 0x3FBC756AC654273B // Q8
265 data8 0xBFC001A42489AB4D // Q7
266 data8 0x3FC99999999A169B // Q4
267 data8 0xBFD00000000019AC // Q3
268 ASM_SIZE_DIRECTIVE(log_table_1)
269 log_table_2:
270 ASM_TYPE_DIRECTIVE(log_table_2,@object)
271 data8 0xBFCFFFFFFFFEF009 // P3
272 data8 0x3FD555555554ECB2 // P2
273 data8 0x3FC2492479AA0DF8 // Q6
274 data8 0xBFC5555544986F52 // Q5
275 data8 0x3FD5555555555555 // Q2
276 data8 0xBFE0000000000000 // Q1, P1 = -0.5
279 data8 0xde5bd8a937287195, 0x00003ffd // double-extended 1/ln(10)
280 data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
281 // b17217f7d1cf79ab c9e3b39803f2f6a
284 data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
286 data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
287 data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
288 data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
289 data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
290 data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
292 data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
293 data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
294 data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
295 data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
296 data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
298 data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
299 data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
300 data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
301 data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
302 data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
304 data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
305 data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
306 data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
307 data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
308 data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
310 data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
311 data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
312 data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
313 data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
314 data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
316 data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
317 data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
318 data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
319 data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
320 data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
322 data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
323 data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
324 data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
325 data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
326 data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
328 data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
329 data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
330 data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
331 data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
332 data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
334 data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
335 data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
336 data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
337 data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
338 data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
340 data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
341 data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
342 data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
343 data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
344 data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
346 data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
347 data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
348 data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
349 data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
350 data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
352 data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
353 data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
354 data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
355 data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
356 data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
358 data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
359 data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
360 data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
361 data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
362 data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
364 data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
365 data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
366 data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
367 data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
368 data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
370 data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
371 data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
372 data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
373 data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
374 data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
376 data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
377 data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
378 data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
379 data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
380 data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
382 data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
383 data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
384 data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
385 data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
386 data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
388 data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
389 data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
390 data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
391 data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
392 data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
394 data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
395 data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
396 data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
397 data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
398 data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
400 data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
401 data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
402 data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
403 data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
404 data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
406 data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
407 data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
408 data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
409 data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
410 data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
412 data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
413 data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
414 data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
415 data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
416 data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
418 data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
419 data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
420 data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
421 data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
422 data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
424 data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
425 data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
426 data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
427 data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
428 data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
430 data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
431 data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
432 data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
433 data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
434 data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
436 data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
437 data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
438 data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
439 data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
440 data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
442 data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
443 data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
444 data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
445 data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
446 data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
448 data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
449 data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
450 data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
451 data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
452 data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
454 data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
455 data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
456 data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
457 data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
458 data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
460 data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
461 data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
462 data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
463 data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
464 data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
466 data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
467 data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
468 data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
469 data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
470 data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
472 data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
473 data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
474 data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
475 data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
476 data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
478 data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
479 data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
480 data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
481 data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
482 data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
484 data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
485 data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
486 data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
487 data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
488 data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
490 data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
491 data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
492 data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
493 data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
494 data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
496 data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
497 data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
498 data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
499 data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
500 data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
502 data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
503 data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
504 data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
505 data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
506 data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
508 data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
509 data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
510 data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
511 data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
512 data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
514 data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
515 data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
516 data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
517 data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
518 data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
520 data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
521 data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
522 data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
523 data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
524 data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
526 data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
527 data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
528 data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
529 data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
530 data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
532 data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
533 data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
534 data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
535 data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
536 data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
538 data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
539 data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
540 data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
541 data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
542 data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
544 data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
545 data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
546 data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
547 data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
548 data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
550 data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
551 data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
552 data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
553 data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
554 data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
556 data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
557 data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
558 data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
559 data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
560 data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
562 data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
563 data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
564 data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
565 data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
566 data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
568 data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
569 data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
570 data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
571 data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
572 data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
574 data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
575 data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
576 data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
577 data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
578 data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
580 data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
581 data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
582 data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
583 data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
584 data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
586 data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
587 data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
588 data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
589 data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
590 data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
591 ASM_SIZE_DIRECTIVE(log_table_2)
594 .align 32
595 .global log#
596 .global log10#
598 // log10 has p7 true, p8 false
599 // log has p8 true, p7 false
601 .section .text
602 .proc log10#
603 .align 32
605 log10:
606 #ifdef _LIBC
607 .global __ieee754_log10
608 .type __ieee754_log10,@function
609 __ieee754_log10:
610 #endif
611 { .mfi
612 alloc r32=ar.pfs,1,15,4,0
613 frcpa.s1 log_C,p9 = f1,f8
614 cmp.eq.unc p7,p8 = r0, r0
615 }
616 { .mfb
617 addl log_AD_1 = @ltoff(log_table_1), gp
618 fnorm.s1 log_NORM_f8 = f8
619 br.sptk L(LOG_LOG10_X)
620 }
621 ;;
623 .endp log10
624 ASM_SIZE_DIRECTIVE(log10)
625 ASM_SIZE_DIRECTIVE(__ieee754_log10)
628 .section .text
629 .proc log#
630 .align 32
631 log:
632 #ifdef _LIBC
633 .global __ieee754_log
634 .type __ieee754_log,@function
635 __ieee754_log:
636 #endif
638 { .mfi
639 alloc r32=ar.pfs,1,15,4,0
640 frcpa.s1 log_C,p9 = f1,f8
641 cmp.eq.unc p8,p7 = r0, r0
642 }
643 { .mfi
644 addl log_AD_1 = @ltoff(log_table_1), gp
645 fnorm.s1 log_NORM_f8 = f8
646 nop.i 999
647 }
648 ;;
650 L(LOG_LOG10_X):
652 { .mfi
653 ld8 log_AD_1 = [log_AD_1]
654 fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm
655 mov log_GR_fff9 = 0xfff9
656 }
657 { .mfi
658 mov log_GR_half_exp = 0x0fffe
659 fms.s1 log_w = f8,f1,f1
660 mov log_GR_exp_17_ones = 0x1ffff
661 }
662 ;;
664 { .mmi
665 getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute
666 setf.exp log_half = log_GR_half_exp // Form 0.5 = -Q1
667 nop.i 999
668 }
669 ;;
671 { .mmb
672 adds log_AD_2 = 0x30, log_AD_1
673 mov log_GR_exp_16_ones = 0xffff
674 (p15) br.cond.spnt L(LOG_DENORM)
675 }
676 ;;
678 L(LOG_COMMON):
679 {.mfi
680 ldfpd log_P5,log_P4 = [log_AD_1],16
681 fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan
682 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
683 }
684 {.mfi
685 ldfpd log_P3,log_P2 = [log_AD_2],16
686 nop.f 999
687 nop.i 999
688 }
689 ;;
691 { .mfi
692 ldfpd log_Q8,log_Q7 = [log_AD_1],16
693 fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf
694 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
695 }
696 { .mfi
697 ldfpd log_Q6,log_Q5 = [log_AD_2],16
698 nop.f 999
699 nop.i 999
700 }
701 ;;
704 { .mfi
705 ldfpd log_Q4,log_Q3 = [log_AD_1],16
706 fma.s1 log_wsq = log_w, log_w, f0
707 nop.i 999
708 }
709 { .mfb
710 ldfpd log_Q2,log_Q1 = [log_AD_2],16
711 (p6) fma.d.s0 f8 = f8,f1,f0 // quietize nan result if x=nan
712 (p6) br.ret.spnt b0 // Exit for x=nan
713 }
714 ;;
717 { .mfi
718 setf.sig log_int_Nfloat = log_GR_true_exp_f8
719 fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0
720 nop.i 999
721 }
722 { .mfb
723 nop.m 999
724 fms.s1 log_r = log_C,f8,f1
725 (p11) br.ret.spnt b0 // Exit for x=+inf
726 }
727 ;;
730 { .mmf
731 getf.sig log_GR_significand_f8 = log_NORM_f8
732 ldfe log_inv_ln10 = [log_AD_2],16
733 fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0
734 }
735 ;;
738 { .mfb
739 nop.m 999
740 (p10) fmerge.s f8 = f0, f0
741 (p10) br.ret.spnt b0 // Exit for x=1.0
742 ;;
743 }
745 { .mfi
746 getf.exp log_GR_signexp_w = log_w
747 fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf
748 shl log_GR_index = log_GR_significand_f8,1
749 }
750 ;;
752 { .mfi
753 ldfe log_log2 = [log_AD_2],16
754 fnma.s1 log_rp_q10 = log_half, log_wsq, log_w
755 shr.u log_GR_index = log_GR_index,56
756 }
757 { .mfb
758 nop.m 999
759 fma.s1 log_w3 = log_wsq, log_w, f0
760 (p6) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x=0
761 ;;
762 }
765 { .mfi
766 and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w
767 fma.s1 log_w4 = log_wsq, log_wsq, f0
768 nop.i 999
769 }
770 { .mfb
771 shladd log_AD_2 = log_GR_index,4,log_AD_2
772 fma.s1 log_rsq = log_r, log_r, f0
773 (p12) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x<0
774 ;;
775 }
777 { .mfi
778 ldfe log_T = [log_AD_2]
779 fma.s1 log_rp_p4 = log_P5, log_r, log_P4
780 nop.i 999
781 }
782 { .mfi
783 nop.m 999
784 fma.s1 log_rp_p32 = log_P3, log_r, log_P2
785 nop.i 999
786 ;;
787 }
790 { .mfi
791 nop.m 999
792 fma.s1 log_rp_q7 = log_Q8, log_w, log_Q7
793 nop.i 999
794 }
795 { .mfi
796 nop.m 999
797 fma.s1 log_rp_q65 = log_Q6, log_w, log_Q5
798 nop.i 999
799 ;;
800 }
802 // p13 <== large w log
803 // p14 <== small w log
804 { .mfi
805 (p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff9
806 fma.s1 log_rp_q3 = log_Q4, log_w, log_Q3
807 nop.i 999
808 ;;
809 }
811 // p10 <== large w log10
812 // p11 <== small w log10
813 { .mfi
814 (p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff9
815 fcvt.xf log_Nfloat = log_int_Nfloat
816 nop.i 999
817 }
819 { .mfi
820 nop.m 999
821 fma.s1 log_rp_q21 = log_Q2, log_w3, log_rp_q10
822 nop.i 999 ;;
823 }
825 { .mfi
826 nop.m 999
827 fma.s1 log_rcube = log_rsq, log_r, f0
828 nop.i 999
829 }
830 { .mfi
831 nop.m 999
832 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r
833 nop.i 999
834 ;;
835 }
837 { .mfi
838 nop.m 999
839 fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input
840 nop.i 999
841 }
842 { .mfi
843 nop.m 999
844 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
845 nop.i 999
846 ;;
847 }
850 { .mfi
851 nop.m 999
852 fma.s1 log_w6 = log_w3, log_w3, f0
853 nop.i 999
854 }
855 { .mfi
856 nop.m 999
857 fma.s1 log_Qlo = log_rp_q7, log_wsq, log_rp_q65
858 nop.i 999
859 }
860 ;;
862 { .mfi
863 nop.m 999
864 fma.s1 log_Qhi = log_rp_q3, log_w4, log_rp_q21
865 nop.i 999 ;;
866 }
869 { .mfi
870 nop.m 999
871 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T
872 nop.i 999 ;;
873 }
875 { .mfi
876 nop.m 999
877 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
878 nop.i 999 ;;
879 }
882 // small w, log <== p14
883 { .mfi
884 nop.m 999
885 (p14) fma.d f8 = log_Qlo, log_w6, log_Qhi
886 nop.i 999
887 }
888 { .mfi
889 nop.m 999
890 fma.s1 log_Q = log_Qlo, log_w6, log_Qhi
891 nop.i 999 ;;
892 }
895 { .mfi
896 nop.m 999
897 (p10) fma.s1 log_log10_hi = log_T_plus_Nlog2, log_inv_ln10,f0
898 nop.i 999 ;;
899 }
901 // large w, log <== p13
902 .pred.rel "mutex",p13,p10
903 { .mfi
904 nop.m 999
905 (p13) fadd.d f8 = log_T_plus_Nlog2, log_r2P_r
906 nop.i 999
907 }
908 { .mfi
909 nop.m 999
910 (p10) fma.s1 log_log10_lo = log_inv_ln10, log_r2P_r,f0
911 nop.i 999 ;;
912 }
915 // small w, log10 <== p11
916 { .mfi
917 nop.m 999
918 (p11) fma.d f8 = log_inv_ln10,log_Q,f0
919 nop.i 999 ;;
920 }
922 // large w, log10 <== p10
923 { .mfb
924 nop.m 999
925 (p10) fma.d f8 = log_log10_hi, f1, log_log10_lo
926 br.ret.sptk b0
927 ;;
928 }
930 L(LOG_DENORM):
931 { .mfb
932 getf.exp log_GR_signexp_f8 = log_NORM_f8
933 nop.f 999
934 br.cond.sptk L(LOG_COMMON)
935 }
936 ;;
938 L(LOG_ZERO_NEG):
940 // qnan snan inf norm unorm 0 -+
941 // 0 0 0 0 0 1 11 0x7
942 // 0 0 1 1 1 0 10 0x3a
944 // Save x (f8) in f10
945 { .mfi
946 nop.m 999
947 fmerge.s f10 = f8,f8
948 nop.i 999 ;;
949 }
951 // p8 p9 means ln(+-0) = -inf
952 // p7 p10 means log(+-0) = -inf
954 // p13 means ln(-)
955 // p14 means log(-)
958 { .mfi
959 nop.m 999
960 fmerge.ns f6 = f1,f1 // Form -1.0
961 nop.i 999 ;;
962 }
964 // p9 means ln(+-0) = -inf
965 // p10 means log(+-0) = -inf
966 // Log(+-0) = -inf
968 { .mfi
969 nop.m 999
970 (p8) fclass.m.unc p9,p0 = f10, 0x07
971 nop.i 999
972 }
973 { .mfi
974 nop.m 999
975 (p7) fclass.m.unc p10,p0 = f10, 0x07
976 nop.i 999 ;;
977 }
980 // p13 ln(-)
981 // p14 log(-)
983 // Log(-inf, -normal, -unnormal) = QNAN indefinite
984 { .mfi
985 nop.m 999
986 (p8) fclass.m.unc p13,p0 = f10, 0x3a
987 nop.i 999
988 }
989 { .mfi
990 nop.m 999
991 (p7) fclass.m.unc p14,p0 = f10, 0x3a
992 nop.i 999 ;;
993 }
996 .pred.rel "mutex",p9,p10
997 { .mfi
998 (p9) mov log_GR_tag = 2
999 (p9) frcpa f8,p11 = f6,f0
1000 nop.i 999
1001 }
1002 { .mfi
1003 (p10) mov log_GR_tag = 8
1004 (p10) frcpa f8,p12 = f6,f0
1005 nop.i 999 ;;
1006 }
1008 .pred.rel "mutex",p13,p14
1009 { .mfi
1010 (p13) mov log_GR_tag = 3
1011 (p13) frcpa f8,p11 = f0,f0
1012 nop.i 999
1013 }
1014 { .mfb
1015 (p14) mov log_GR_tag = 9
1016 (p14) frcpa f8,p12 = f0,f0
1017 br.cond.sptk __libm_error_region ;;
1018 }
1019 .endp log
1020 ASM_SIZE_DIRECTIVE(log)
1021 ASM_SIZE_DIRECTIVE(__ieee754_log)
1024 // Stack operations when calling error support.
1025 // (1) (2) (3) (call) (4)
1026 // sp -> + psp -> + psp -> + sp -> +
1027 // | | | |
1028 // | | <- GR_Y R3 ->| <- GR_RESULT | -> f8
1029 // | | | |
1030 // | <-GR_Y Y2->| Y2 ->| <- GR_Y |
1031 // | | | |
1032 // | | <- GR_X X1 ->| |
1033 // | | | |
1034 // sp-64 -> + sp -> + sp -> + +
1035 // save ar.pfs save b0 restore gp
1036 // save gp restore ar.pfs
1040 .proc __libm_error_region
1041 __libm_error_region:
1042 .prologue
1044 // (1)
1045 { .mfi
1046 add GR_Parameter_Y=-32,sp // Parameter 2 value
1047 nop.f 0
1048 .save ar.pfs,GR_SAVE_PFS
1049 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1050 }
1051 { .mfi
1052 .fframe 64
1053 add sp=-64,sp // Create new stack
1054 nop.f 0
1055 mov GR_SAVE_GP=gp // Save gp
1056 };;
1059 // (2)
1060 { .mmi
1061 stfd [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
1062 add GR_Parameter_X = 16,sp // Parameter 1 address
1063 .save b0, GR_SAVE_B0
1064 mov GR_SAVE_B0=b0 // Save b0
1065 };;
1067 .body
1068 // (3)
1069 { .mib
1070 stfd [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
1071 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1072 nop.b 0
1073 }
1074 { .mib
1075 stfd [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
1076 add GR_Parameter_Y = -16,GR_Parameter_Y
1077 br.call.sptk b0=__libm_error_support# // Call error handling function
1078 };;
1080 { .mmi
1081 nop.m 0
1082 nop.m 0
1083 add GR_Parameter_RESULT = 48,sp
1084 };;
1086 // (4)
1087 { .mmi
1088 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
1089 .restore sp
1090 add sp = 64,sp // Restore stack pointer
1091 mov b0 = GR_SAVE_B0 // Restore return address
1092 };;
1093 { .mib
1094 mov gp = GR_SAVE_GP // Restore gp
1095 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1096 br.ret.sptk b0 // Return
1097 };;
1099 .endp __libm_error_region
1100 ASM_SIZE_DIRECTIVE(__libm_error_region)
1103 .type __libm_error_support#,@function
1104 .global __libm_error_support#