4 // Copyright (c) 2000 - 2005, Intel Corporation
5 // All rights reserved.
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
12 // * Redistributions of source code must retain the above copyright
13 // notice, this list of conditions and the following disclaimer.
15 // * Redistributions in binary form must reproduce the above copyright
16 // notice, this list of conditions and the following disclaimer in the
17 // documentation and/or other materials provided with the distribution.
19 // * The name of Intel Corporation may not be used to endorse or promote
20 // products derived from this software without specific prior written
23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
28 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
29 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
30 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
31 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
32 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 // Intel Corporation is the author of this code, and requests that all
36 // problem reports or change requests be submitted to it directly at
37 // http://www.intel.com/software/products/opensource/libraries/num.htm.
40 //==============================================================
41 // 03/01/00 Initial version
42 // 08/15/00 Bundle added after call to __libm_error_support to properly
43 // set [the previously overwritten] GR_Parameter_RESULT.
44 // 01/10/01 Improved speed, fixed flags for neg denormals
45 // 05/20/02 Cleaned up namespace and sf0 syntax
46 // 05/23/02 Modified algorithm. Now only one polynomial is used
47 // for |x-1| >= 1/256 and for |x-1| < 1/256
48 // 02/10/03 Reordered header: .section, .global, .proc, .align
49 // 03/31/05 Reformatted delimiters between data tables
52 //==============================================================
54 // float log10f(float)
57 // Overview of operation
58 //==============================================================
62 // This algorithm is based on fact that
63 // log(a b) = log(a) + log(b).
65 // In our case we have x = 2^N f, where 1 <= f < 2.
67 // log(x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
69 // To calculate log(f) we do following
70 // log(f) = log(f * frcpa(f) / frcpa(f)) =
71 // = log(f * frcpa(f)) + log(1/frcpa(f))
73 // According to definition of IA-64's frcpa instruction it's a
74 // floating point that approximates 1/f using a lookup on the
75 // top of 8 bits of the input number's significand with relative
76 // error < 2^(-8.886). So we have following
78 // |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
82 // log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
85 // The first value can be computed by polynomial P(r) approximating
86 // log(1 + r) on |r| < 1/256 and the second is precomputed tabular
87 // value defined by top 8 bit of f.
89 // Finally we have that log(x) ~ (N*log(2) + T) + P(r)
91 // Note that if input argument is close to 1.0 (in our case it means
92 // that |1 - x| < 1/256) we can use just polynomial approximation
93 // because x = 2^0 * f = f = 1 + r and
94 // log(x) = log(1 + r) ~ P(r)
97 // To compute log10(x) we just use identity:
99 // log10(x) = log(x)/log(10)
103 // log10(x) = (N*log(2) + T + log(1+r)) / log(10) =
104 // = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10)
109 // It can be seen that formulas for log and log10 differ from one another
110 // only by coefficients and tabular values. Namely as log as log10 are
111 // calculated as (N*L1 + T) + L2*Series(r) where in case of log
113 // T = log(1/frcpa(x))
115 // and in case of log10
116 // L1 = log(2)/log(10)
117 // T = log(1/frcpa(x))/log(10)
120 // So common code with two different entry points those set pointers
121 // to the base address of coresponding data sets containing values
122 // of L2,T and prepare integer representation of L1 needed for following
123 // setf instruction can be used.
125 // Note that both log and log10 use common approximation polynomial
126 // it means we need only one set of coefficients of approximation.
128 // 1. Computation of log(x) for |x-1| >= 1/256
131 // P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
132 // A4,A3,A2 are created with setf inctruction.
133 // We use Taylor series and so A4 = 1/4, A3 = 1/3,
134 // A2 = 1/2 rounded to double.
136 // N = float(n) where n is true unbiased exponent of x
138 // T is tabular value of log(1/frcpa(x)) calculated in quad precision
139 // and rounded to double. To T we get bits from 55 to 62 of register
140 // format significand of x and calculate address
141 // ad_T = table_base_addr + 8 * index
143 // L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad
144 // precision and rounded to double; it's loaded from memory
146 // L1 (log(2) or log10(2) depending on function) is calculated in quad
147 // precision and rounded to double; it's created with setf.
149 // And final result = P2(r)*(r*L2) + (T + N*L1)
152 // 2. Computation of log(x) for |x-1| < 1/256
154 // P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
155 // A4,A3,A2 are the same as in case |x-1| >= 1/256
157 // And final result = P2(r)*(r*L2)
159 // 3. How we define is input argument such that |x-1| < 1/256 or not.
161 // To do it we analyze biased exponent and significand of input argument.
163 // a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e.
164 // we test is 0.5 <= x < 2). This comparison can be performed using
165 // unsigned version of cmp instruction in such a way
166 // biased_exponent_of_x - 0xFFFE < 2
169 // b) Second (in case when result of a) is true) we need to compare x
170 // with 1-1/256 and 1+1/256 or in register format representation with
171 // 0xFFFEFF00000000000000 and 0xFFFF8080000000000000 correspondingly.
172 // As far as biased exponent of x here can be equal only to 0xFFFE or
173 // 0xFFFF we need to test only last bit of it. Also signifigand always
174 // has implicit bit set to 1 that can be exluded from comparison.
175 // Thus it's quite enough to generate 64-bit integer bits of that are
176 // ix[63] = biased_exponent_of_x[0] and ix[62-0] = significand_of_x[62-0]
177 // and compare it with 0x7F00000000000000 and 0x80800000000000000 (those
178 // obtained like ix from register representatinos of 255/256 and
179 // 257/256). This comparison can be made like in a), using unsigned
180 // version of cmp i.e. ix - 0x7F00000000000000 < 0x0180000000000000.
181 // 0x0180000000000000 is difference between 0x80800000000000000 and
182 // 0x7F00000000000000.
184 // Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
185 // filtered and processed on special branches.
189 //==============================================================
194 // logf(+qnan) = +qnan
195 // logf(-qnan) = -qnan
196 // logf(+snan) = +qnan
197 // logf(-snan) = -qnan
199 // logf(-n) = QNAN Indefinite
200 // logf(-inf) = QNAN Indefinite
205 //==============================================================
206 // Floating Point registers used:
208 // f12 -> f14, f33 -> f39
210 // General registers used:
214 // Predicate registers used:
219 //==============================================================
244 GR_Parameter_RESULT = r39
245 GR_Parameter_TAG = r40
270 //==============================================================
273 LOCAL_OBJECT_START(logf_data)
274 data8 0x3FF0000000000000 // 1.0
276 // ln(1/frcpa(1+i/256)), i=0...255
277 data8 0x3F60040155D5889E // 0
278 data8 0x3F78121214586B54 // 1
279 data8 0x3F841929F96832F0 // 2
280 data8 0x3F8C317384C75F06 // 3
281 data8 0x3F91A6B91AC73386 // 4
282 data8 0x3F95BA9A5D9AC039 // 5
283 data8 0x3F99D2A8074325F4 // 6
284 data8 0x3F9D6B2725979802 // 7
285 data8 0x3FA0C58FA19DFAAA // 8
286 data8 0x3FA2954C78CBCE1B // 9
287 data8 0x3FA4A94D2DA96C56 // 10
288 data8 0x3FA67C94F2D4BB58 // 11
289 data8 0x3FA85188B630F068 // 12
290 data8 0x3FAA6B8ABE73AF4C // 13
291 data8 0x3FAC441E06F72A9E // 14
292 data8 0x3FAE1E6713606D07 // 15
293 data8 0x3FAFFA6911AB9301 // 16
294 data8 0x3FB0EC139C5DA601 // 17
295 data8 0x3FB1DBD2643D190B // 18
296 data8 0x3FB2CC7284FE5F1C // 19
297 data8 0x3FB3BDF5A7D1EE64 // 20
298 data8 0x3FB4B05D7AA012E0 // 21
299 data8 0x3FB580DB7CEB5702 // 22
300 data8 0x3FB674F089365A7A // 23
301 data8 0x3FB769EF2C6B568D // 24
302 data8 0x3FB85FD927506A48 // 25
303 data8 0x3FB9335E5D594989 // 26
304 data8 0x3FBA2B0220C8E5F5 // 27
305 data8 0x3FBB0004AC1A86AC // 28
306 data8 0x3FBBF968769FCA11 // 29
307 data8 0x3FBCCFEDBFEE13A8 // 30
308 data8 0x3FBDA727638446A2 // 31
309 data8 0x3FBEA3257FE10F7A // 32
310 data8 0x3FBF7BE9FEDBFDE6 // 33
311 data8 0x3FC02AB352FF25F4 // 34
312 data8 0x3FC097CE579D204D // 35
313 data8 0x3FC1178E8227E47C // 36
314 data8 0x3FC185747DBECF34 // 37
315 data8 0x3FC1F3B925F25D41 // 38
316 data8 0x3FC2625D1E6DDF57 // 39
317 data8 0x3FC2D1610C86813A // 40
318 data8 0x3FC340C59741142E // 41
319 data8 0x3FC3B08B6757F2A9 // 42
320 data8 0x3FC40DFB08378003 // 43
321 data8 0x3FC47E74E8CA5F7C // 44
322 data8 0x3FC4EF51F6466DE4 // 45
323 data8 0x3FC56092E02BA516 // 46
324 data8 0x3FC5D23857CD74D5 // 47
325 data8 0x3FC6313A37335D76 // 48
326 data8 0x3FC6A399DABBD383 // 49
327 data8 0x3FC70337DD3CE41B // 50
328 data8 0x3FC77654128F6127 // 51
329 data8 0x3FC7E9D82A0B022D // 52
330 data8 0x3FC84A6B759F512F // 53
331 data8 0x3FC8AB47D5F5A310 // 54
332 data8 0x3FC91FE49096581B // 55
333 data8 0x3FC981634011AA75 // 56
334 data8 0x3FC9F6C407089664 // 57
335 data8 0x3FCA58E729348F43 // 58
336 data8 0x3FCABB55C31693AD // 59
337 data8 0x3FCB1E104919EFD0 // 60
338 data8 0x3FCB94EE93E367CB // 61
339 data8 0x3FCBF851C067555F // 62
340 data8 0x3FCC5C0254BF23A6 // 63
341 data8 0x3FCCC000C9DB3C52 // 64
342 data8 0x3FCD244D99C85674 // 65
343 data8 0x3FCD88E93FB2F450 // 66
344 data8 0x3FCDEDD437EAEF01 // 67
345 data8 0x3FCE530EFFE71012 // 68
346 data8 0x3FCEB89A1648B971 // 69
347 data8 0x3FCF1E75FADF9BDE // 70
348 data8 0x3FCF84A32EAD7C35 // 71
349 data8 0x3FCFEB2233EA07CD // 72
350 data8 0x3FD028F9C7035C1C // 73
351 data8 0x3FD05C8BE0D9635A // 74
352 data8 0x3FD085EB8F8AE797 // 75
353 data8 0x3FD0B9C8E32D1911 // 76
354 data8 0x3FD0EDD060B78081 // 77
355 data8 0x3FD122024CF0063F // 78
356 data8 0x3FD14BE2927AECD4 // 79
357 data8 0x3FD180618EF18ADF // 80
358 data8 0x3FD1B50BBE2FC63B // 81
359 data8 0x3FD1DF4CC7CF242D // 82
360 data8 0x3FD214456D0EB8D4 // 83
361 data8 0x3FD23EC5991EBA49 // 84
362 data8 0x3FD2740D9F870AFB // 85
363 data8 0x3FD29ECDABCDFA04 // 86
364 data8 0x3FD2D46602ADCCEE // 87
365 data8 0x3FD2FF66B04EA9D4 // 88
366 data8 0x3FD335504B355A37 // 89
367 data8 0x3FD360925EC44F5D // 90
368 data8 0x3FD38BF1C3337E75 // 91
369 data8 0x3FD3C25277333184 // 92
370 data8 0x3FD3EDF463C1683E // 93
371 data8 0x3FD419B423D5E8C7 // 94
372 data8 0x3FD44591E0539F49 // 95
373 data8 0x3FD47C9175B6F0AD // 96
374 data8 0x3FD4A8B341552B09 // 97
375 data8 0x3FD4D4F3908901A0 // 98
376 data8 0x3FD501528DA1F968 // 99
377 data8 0x3FD52DD06347D4F6 // 100
378 data8 0x3FD55A6D3C7B8A8A // 101
379 data8 0x3FD5925D2B112A59 // 102
380 data8 0x3FD5BF406B543DB2 // 103
381 data8 0x3FD5EC433D5C35AE // 104
382 data8 0x3FD61965CDB02C1F // 105
383 data8 0x3FD646A84935B2A2 // 106
384 data8 0x3FD6740ADD31DE94 // 107
385 data8 0x3FD6A18DB74A58C5 // 108
386 data8 0x3FD6CF31058670EC // 109
387 data8 0x3FD6F180E852F0BA // 110
388 data8 0x3FD71F5D71B894F0 // 111
389 data8 0x3FD74D5AEFD66D5C // 112
390 data8 0x3FD77B79922BD37E // 113
391 data8 0x3FD7A9B9889F19E2 // 114
392 data8 0x3FD7D81B037EB6A6 // 115
393 data8 0x3FD8069E33827231 // 116
394 data8 0x3FD82996D3EF8BCB // 117
395 data8 0x3FD85855776DCBFB // 118
396 data8 0x3FD8873658327CCF // 119
397 data8 0x3FD8AA75973AB8CF // 120
398 data8 0x3FD8D992DC8824E5 // 121
399 data8 0x3FD908D2EA7D9512 // 122
400 data8 0x3FD92C59E79C0E56 // 123
401 data8 0x3FD95BD750EE3ED3 // 124
402 data8 0x3FD98B7811A3EE5B // 125
403 data8 0x3FD9AF47F33D406C // 126
404 data8 0x3FD9DF270C1914A8 // 127
405 data8 0x3FDA0325ED14FDA4 // 128
406 data8 0x3FDA33440224FA79 // 129
407 data8 0x3FDA57725E80C383 // 130
408 data8 0x3FDA87D0165DD199 // 131
409 data8 0x3FDAAC2E6C03F896 // 132
410 data8 0x3FDADCCC6FDF6A81 // 133
411 data8 0x3FDB015B3EB1E790 // 134
412 data8 0x3FDB323A3A635948 // 135
413 data8 0x3FDB56FA04462909 // 136
414 data8 0x3FDB881AA659BC93 // 137
415 data8 0x3FDBAD0BEF3DB165 // 138
416 data8 0x3FDBD21297781C2F // 139
417 data8 0x3FDC039236F08819 // 140
418 data8 0x3FDC28CB1E4D32FD // 141
419 data8 0x3FDC4E19B84723C2 // 142
420 data8 0x3FDC7FF9C74554C9 // 143
421 data8 0x3FDCA57B64E9DB05 // 144
422 data8 0x3FDCCB130A5CEBB0 // 145
423 data8 0x3FDCF0C0D18F326F // 146
424 data8 0x3FDD232075B5A201 // 147
425 data8 0x3FDD490246DEFA6B // 148
426 data8 0x3FDD6EFA918D25CD // 149
427 data8 0x3FDD9509707AE52F // 150
428 data8 0x3FDDBB2EFE92C554 // 151
429 data8 0x3FDDEE2F3445E4AF // 152
430 data8 0x3FDE148A1A2726CE // 153
431 data8 0x3FDE3AFC0A49FF40 // 154
432 data8 0x3FDE6185206D516E // 155
433 data8 0x3FDE882578823D52 // 156
434 data8 0x3FDEAEDD2EAC990C // 157
435 data8 0x3FDED5AC5F436BE3 // 158
436 data8 0x3FDEFC9326D16AB9 // 159
437 data8 0x3FDF2391A2157600 // 160
438 data8 0x3FDF4AA7EE03192D // 161
439 data8 0x3FDF71D627C30BB0 // 162
440 data8 0x3FDF991C6CB3B379 // 163
441 data8 0x3FDFC07ADA69A910 // 164
442 data8 0x3FDFE7F18EB03D3E // 165
443 data8 0x3FE007C053C5002E // 166
444 data8 0x3FE01B942198A5A1 // 167
445 data8 0x3FE02F74400C64EB // 168
446 data8 0x3FE04360BE7603AD // 169
447 data8 0x3FE05759AC47FE34 // 170
448 data8 0x3FE06B5F1911CF52 // 171
449 data8 0x3FE078BF0533C568 // 172
450 data8 0x3FE08CD9687E7B0E // 173
451 data8 0x3FE0A10074CF9019 // 174
452 data8 0x3FE0B5343A234477 // 175
453 data8 0x3FE0C974C89431CE // 176
454 data8 0x3FE0DDC2305B9886 // 177
455 data8 0x3FE0EB524BAFC918 // 178
456 data8 0x3FE0FFB54213A476 // 179
457 data8 0x3FE114253DA97D9F // 180
458 data8 0x3FE128A24F1D9AFF // 181
459 data8 0x3FE1365252BF0865 // 182
460 data8 0x3FE14AE558B4A92D // 183
461 data8 0x3FE15F85A19C765B // 184
462 data8 0x3FE16D4D38C119FA // 185
463 data8 0x3FE18203C20DD133 // 186
464 data8 0x3FE196C7BC4B1F3B // 187
465 data8 0x3FE1A4A738B7A33C // 188
466 data8 0x3FE1B981C0C9653D // 189
467 data8 0x3FE1CE69E8BB106B // 190
468 data8 0x3FE1DC619DE06944 // 191
469 data8 0x3FE1F160A2AD0DA4 // 192
470 data8 0x3FE2066D7740737E // 193
471 data8 0x3FE2147DBA47A394 // 194
472 data8 0x3FE229A1BC5EBAC3 // 195
473 data8 0x3FE237C1841A502E // 196
474 data8 0x3FE24CFCE6F80D9A // 197
475 data8 0x3FE25B2C55CD5762 // 198
476 data8 0x3FE2707F4D5F7C41 // 199
477 data8 0x3FE285E0842CA384 // 200
478 data8 0x3FE294294708B773 // 201
479 data8 0x3FE2A9A2670AFF0C // 202
480 data8 0x3FE2B7FB2C8D1CC1 // 203
481 data8 0x3FE2C65A6395F5F5 // 204
482 data8 0x3FE2DBF557B0DF43 // 205
483 data8 0x3FE2EA64C3F97655 // 206
484 data8 0x3FE3001823684D73 // 207
485 data8 0x3FE30E97E9A8B5CD // 208
486 data8 0x3FE32463EBDD34EA // 209
487 data8 0x3FE332F4314AD796 // 210
488 data8 0x3FE348D90E7464D0 // 211
489 data8 0x3FE35779F8C43D6E // 212
490 data8 0x3FE36621961A6A99 // 213
491 data8 0x3FE37C299F3C366A // 214
492 data8 0x3FE38AE2171976E7 // 215
493 data8 0x3FE399A157A603E7 // 216
494 data8 0x3FE3AFCCFE77B9D1 // 217
495 data8 0x3FE3BE9D503533B5 // 218
496 data8 0x3FE3CD7480B4A8A3 // 219
497 data8 0x3FE3E3C43918F76C // 220
498 data8 0x3FE3F2ACB27ED6C7 // 221
499 data8 0x3FE4019C2125CA93 // 222
500 data8 0x3FE4181061389722 // 223
501 data8 0x3FE42711518DF545 // 224
502 data8 0x3FE436194E12B6BF // 225
503 data8 0x3FE445285D68EA69 // 226
504 data8 0x3FE45BCC464C893A // 227
505 data8 0x3FE46AED21F117FC // 228
506 data8 0x3FE47A1527E8A2D3 // 229
507 data8 0x3FE489445EFFFCCC // 230
508 data8 0x3FE4A018BCB69835 // 231
509 data8 0x3FE4AF5A0C9D65D7 // 232
510 data8 0x3FE4BEA2A5BDBE87 // 233
511 data8 0x3FE4CDF28F10AC46 // 234
512 data8 0x3FE4DD49CF994058 // 235
513 data8 0x3FE4ECA86E64A684 // 236
514 data8 0x3FE503C43CD8EB68 // 237
515 data8 0x3FE513356667FC57 // 238
516 data8 0x3FE522AE0738A3D8 // 239
517 data8 0x3FE5322E26867857 // 240
518 data8 0x3FE541B5CB979809 // 241
519 data8 0x3FE55144FDBCBD62 // 242
520 data8 0x3FE560DBC45153C7 // 243
521 data8 0x3FE5707A26BB8C66 // 244
522 data8 0x3FE587F60ED5B900 // 245
523 data8 0x3FE597A7977C8F31 // 246
524 data8 0x3FE5A760D634BB8B // 247
525 data8 0x3FE5B721D295F10F // 248
526 data8 0x3FE5C6EA94431EF9 // 249
527 data8 0x3FE5D6BB22EA86F6 // 250
528 data8 0x3FE5E6938645D390 // 251
529 data8 0x3FE5F673C61A2ED2 // 252
530 data8 0x3FE6065BEA385926 // 253
531 data8 0x3FE6164BFA7CC06B // 254
532 data8 0x3FE62643FECF9743 // 255
533 LOCAL_OBJECT_END(logf_data)
535 LOCAL_OBJECT_START(log10f_data)
536 data8 0x3FDBCB7B1526E50E // 1/ln(10)
538 // ln(1/frcpa(1+i/256))/ln(10), i=0...255
539 data8 0x3F4BD27045BFD025 // 0
540 data8 0x3F64E84E793A474A // 1
541 data8 0x3F7175085AB85FF0 // 2
542 data8 0x3F787CFF9D9147A5 // 3
543 data8 0x3F7EA9D372B89FC8 // 4
544 data8 0x3F82DF9D95DA961C // 5
545 data8 0x3F866DF172D6372C // 6
546 data8 0x3F898D79EF5EEDF0 // 7
547 data8 0x3F8D22ADF3F9579D // 8
548 data8 0x3F9024231D30C398 // 9
549 data8 0x3F91F23A98897D4A // 10
550 data8 0x3F93881A7B818F9E // 11
551 data8 0x3F951F6E1E759E35 // 12
552 data8 0x3F96F2BCE7ADC5B4 // 13
553 data8 0x3F988D362CDF359E // 14
554 data8 0x3F9A292BAF010982 // 15
555 data8 0x3F9BC6A03117EB97 // 16
556 data8 0x3F9D65967DE3AB09 // 17
557 data8 0x3F9F061167FC31E8 // 18
558 data8 0x3FA05409E4F7819C // 19
559 data8 0x3FA125D0432EA20E // 20
560 data8 0x3FA1F85D440D299B // 21
561 data8 0x3FA2AD755749617D // 22
562 data8 0x3FA381772A00E604 // 23
563 data8 0x3FA45643E165A70B // 24
564 data8 0x3FA52BDD034475B8 // 25
565 data8 0x3FA5E3966B7E9295 // 26
566 data8 0x3FA6BAAF47C5B245 // 27
567 data8 0x3FA773B3E8C4F3C8 // 28
568 data8 0x3FA84C51EBEE8D15 // 29
569 data8 0x3FA906A6786FC1CB // 30
570 data8 0x3FA9C197ABF00DD7 // 31
571 data8 0x3FAA9C78712191F7 // 32
572 data8 0x3FAB58C09C8D637C // 33
573 data8 0x3FAC15A8BCDD7B7E // 34
574 data8 0x3FACD331E2C2967C // 35
575 data8 0x3FADB11ED766ABF4 // 36
576 data8 0x3FAE70089346A9E6 // 37
577 data8 0x3FAF2F96C6754AEE // 38
578 data8 0x3FAFEFCA8D451FD6 // 39
579 data8 0x3FB0585283764178 // 40
580 data8 0x3FB0B913AAC7D3A7 // 41
581 data8 0x3FB11A294F2569F6 // 42
582 data8 0x3FB16B51A2696891 // 43
583 data8 0x3FB1CD03ADACC8BE // 44
584 data8 0x3FB22F0BDD7745F5 // 45
585 data8 0x3FB2916ACA38D1E8 // 46
586 data8 0x3FB2F4210DF7663D // 47
587 data8 0x3FB346A6C3C49066 // 48
588 data8 0x3FB3A9FEBC60540A // 49
589 data8 0x3FB3FD0C10A3AA54 // 50
590 data8 0x3FB46107D3540A82 // 51
591 data8 0x3FB4C55DD16967FE // 52
592 data8 0x3FB51940330C000B // 53
593 data8 0x3FB56D620EE7115E // 54
594 data8 0x3FB5D2ABCF26178E // 55
595 data8 0x3FB6275AA5DEBF81 // 56
596 data8 0x3FB68D4EAF26D7EE // 57
597 data8 0x3FB6E28C5C54A28D // 58
598 data8 0x3FB7380B9665B7C8 // 59
599 data8 0x3FB78DCCC278E85B // 60
600 data8 0x3FB7F50C2CF2557A // 61
601 data8 0x3FB84B5FD5EAEFD8 // 62
602 data8 0x3FB8A1F6BAB2B226 // 63
603 data8 0x3FB8F8D144557BDF // 64
604 data8 0x3FB94FEFDCD61D92 // 65
605 data8 0x3FB9A752EF316149 // 66
606 data8 0x3FB9FEFAE7611EE0 // 67
607 data8 0x3FBA56E8325F5C87 // 68
608 data8 0x3FBAAF1B3E297BB4 // 69
609 data8 0x3FBB079479C372AD // 70
610 data8 0x3FBB6054553B12F7 // 71
611 data8 0x3FBBB95B41AB5CE6 // 72
612 data8 0x3FBC12A9B13FE079 // 73
613 data8 0x3FBC6C4017382BEA // 74
614 data8 0x3FBCB41FBA42686D // 75
615 data8 0x3FBD0E38CE73393F // 76
616 data8 0x3FBD689B2193F133 // 77
617 data8 0x3FBDC3472B1D2860 // 78
618 data8 0x3FBE0C06300D528B // 79
619 data8 0x3FBE6738190E394C // 80
620 data8 0x3FBEC2B50D208D9B // 81
621 data8 0x3FBF0C1C2B936828 // 82
622 data8 0x3FBF68216C9CC727 // 83
623 data8 0x3FBFB1F6381856F4 // 84
624 data8 0x3FC00742AF4CE5F8 // 85
625 data8 0x3FC02C64906512D2 // 86
626 data8 0x3FC05AF1E63E03B4 // 87
627 data8 0x3FC0804BEA723AA9 // 88
628 data8 0x3FC0AF1FD6711527 // 89
629 data8 0x3FC0D4B2A8805A00 // 90
630 data8 0x3FC0FA5EF136A06C // 91
631 data8 0x3FC1299A4FB3E306 // 92
632 data8 0x3FC14F806253C3ED // 93
633 data8 0x3FC175805D1587C1 // 94
634 data8 0x3FC19B9A637CA295 // 95
635 data8 0x3FC1CB5FC26EDE17 // 96
636 data8 0x3FC1F1B4E65F2590 // 97
637 data8 0x3FC218248B5DC3E5 // 98
638 data8 0x3FC23EAED62ADC76 // 99
639 data8 0x3FC26553EBD337BD // 100
640 data8 0x3FC28C13F1B11900 // 101
641 data8 0x3FC2BCAA14381386 // 102
642 data8 0x3FC2E3A740B7800F // 103
643 data8 0x3FC30ABFD8F333B6 // 104
644 data8 0x3FC331F403985097 // 105
645 data8 0x3FC35943E7A60690 // 106
646 data8 0x3FC380AFAC6E7C07 // 107
647 data8 0x3FC3A8377997B9E6 // 108
648 data8 0x3FC3CFDB771C9ADB // 109
649 data8 0x3FC3EDA90D39A5DF // 110
650 data8 0x3FC4157EC09505CD // 111
651 data8 0x3FC43D7113FB04C1 // 112
652 data8 0x3FC4658030AD1CCF // 113
653 data8 0x3FC48DAC404638F6 // 114
654 data8 0x3FC4B5F56CBBB869 // 115
655 data8 0x3FC4DE5BE05E7583 // 116
656 data8 0x3FC4FCBC0776FD85 // 117
657 data8 0x3FC525561E9256EE // 118
658 data8 0x3FC54E0DF3198865 // 119
659 data8 0x3FC56CAB7112BDE2 // 120
660 data8 0x3FC59597BA735B15 // 121
661 data8 0x3FC5BEA23A506FDA // 122
662 data8 0x3FC5DD7E08DE382F // 123
663 data8 0x3FC606BDD3F92355 // 124
664 data8 0x3FC6301C518A501F // 125
665 data8 0x3FC64F3770618916 // 126
666 data8 0x3FC678CC14C1E2D8 // 127
667 data8 0x3FC6981005ED2947 // 128
668 data8 0x3FC6C1DB5F9BB336 // 129
669 data8 0x3FC6E1488ECD2881 // 130
670 data8 0x3FC70B4B2E7E41B9 // 131
671 data8 0x3FC72AE209146BF9 // 132
672 data8 0x3FC7551C81BD8DCF // 133
673 data8 0x3FC774DD76CC43BE // 134
674 data8 0x3FC79F505DB00E88 // 135
675 data8 0x3FC7BF3BDE099F30 // 136
676 data8 0x3FC7E9E7CAC437F9 // 137
677 data8 0x3FC809FE4902D00D // 138
678 data8 0x3FC82A2757995CBE // 139
679 data8 0x3FC85525C625E098 // 140
680 data8 0x3FC8757A79831887 // 141
681 data8 0x3FC895E2058D8E03 // 142
682 data8 0x3FC8C13437695532 // 143
683 data8 0x3FC8E1C812EF32BE // 144
684 data8 0x3FC9026F112197E8 // 145
685 data8 0x3FC923294888880B // 146
686 data8 0x3FC94EEA4B8334F3 // 147
687 data8 0x3FC96FD1B639FC09 // 148
688 data8 0x3FC990CCA66229AC // 149
689 data8 0x3FC9B1DB33334843 // 150
690 data8 0x3FC9D2FD740E6607 // 151
691 data8 0x3FC9FF49EEDCB553 // 152
692 data8 0x3FCA209A84FBCFF8 // 153
693 data8 0x3FCA41FF1E43F02B // 154
694 data8 0x3FCA6377D2CE9378 // 155
695 data8 0x3FCA8504BAE0D9F6 // 156
696 data8 0x3FCAA6A5EEEBEFE3 // 157
697 data8 0x3FCAC85B878D7879 // 158
698 data8 0x3FCAEA259D8FFA0B // 159
699 data8 0x3FCB0C0449EB4B6B // 160
700 data8 0x3FCB2DF7A5C50299 // 161
701 data8 0x3FCB4FFFCA70E4D1 // 162
702 data8 0x3FCB721CD17157E3 // 163
703 data8 0x3FCB944ED477D4ED // 164
704 data8 0x3FCBB695ED655C7D // 165
705 data8 0x3FCBD8F2364AEC0F // 166
706 data8 0x3FCBFB63C969F4FF // 167
707 data8 0x3FCC1DEAC134D4E9 // 168
708 data8 0x3FCC4087384F4F80 // 169
709 data8 0x3FCC6339498F09E2 // 170
710 data8 0x3FCC86010FFC076C // 171
711 data8 0x3FCC9D3D065C5B42 // 172
712 data8 0x3FCCC029375BA07A // 173
713 data8 0x3FCCE32B66978BA4 // 174
714 data8 0x3FCD0643AFD51404 // 175
715 data8 0x3FCD29722F0DEA45 // 176
716 data8 0x3FCD4CB70070FE44 // 177
717 data8 0x3FCD6446AB3F8C96 // 178
718 data8 0x3FCD87B0EF71DB45 // 179
719 data8 0x3FCDAB31D1FE99A7 // 180
720 data8 0x3FCDCEC96FDC888F // 181
721 data8 0x3FCDE6908876357A // 182
722 data8 0x3FCE0A4E4A25C200 // 183
723 data8 0x3FCE2E2315755E33 // 184
724 data8 0x3FCE461322D1648A // 185
725 data8 0x3FCE6A0E95C7787B // 186
726 data8 0x3FCE8E216243DD60 // 187
727 data8 0x3FCEA63AF26E007C // 188
728 data8 0x3FCECA74ED15E0B7 // 189
729 data8 0x3FCEEEC692CCD25A // 190
730 data8 0x3FCF070A36B8D9C1 // 191
731 data8 0x3FCF2B8393E34A2D // 192
732 data8 0x3FCF5014EF538A5B // 193
733 data8 0x3FCF68833AF1B180 // 194
734 data8 0x3FCF8D3CD9F3F04F // 195
735 data8 0x3FCFA5C61ADD93E9 // 196
736 data8 0x3FCFCAA8567EBA7A // 197
737 data8 0x3FCFE34CC8743DD8 // 198
738 data8 0x3FD0042BFD74F519 // 199
739 data8 0x3FD016BDF6A18017 // 200
740 data8 0x3FD023262F907322 // 201
741 data8 0x3FD035CCED8D32A1 // 202
742 data8 0x3FD042430E869FFC // 203
743 data8 0x3FD04EBEC842B2E0 // 204
744 data8 0x3FD06182E84FD4AC // 205
745 data8 0x3FD06E0CB609D383 // 206
746 data8 0x3FD080E60BEC8F12 // 207
747 data8 0x3FD08D7E0D894735 // 208
748 data8 0x3FD0A06CC96A2056 // 209
749 data8 0x3FD0AD131F3B3C55 // 210
750 data8 0x3FD0C01771E775FB // 211
751 data8 0x3FD0CCCC3CAD6F4B // 212
752 data8 0x3FD0D986D91A34A9 // 213
753 data8 0x3FD0ECA9B8861A2D // 214
754 data8 0x3FD0F972F87FF3D6 // 215
755 data8 0x3FD106421CF0E5F7 // 216
756 data8 0x3FD11983EBE28A9D // 217
757 data8 0x3FD12661E35B785A // 218
758 data8 0x3FD13345D2779D3B // 219
759 data8 0x3FD146A6F597283A // 220
760 data8 0x3FD15399E81EA83D // 221
761 data8 0x3FD16092E5D3A9A6 // 222
762 data8 0x3FD17413C3B7AB5E // 223
763 data8 0x3FD1811BF629D6FB // 224
764 data8 0x3FD18E2A47B46686 // 225
765 data8 0x3FD19B3EBE1A4418 // 226
766 data8 0x3FD1AEE9017CB450 // 227
767 data8 0x3FD1BC0CED7134E2 // 228
768 data8 0x3FD1C93712ABC7FF // 229
769 data8 0x3FD1D66777147D3F // 230
770 data8 0x3FD1EA3BD1286E1C // 231
771 data8 0x3FD1F77BED932C4C // 232
772 data8 0x3FD204C25E1B031F // 233
773 data8 0x3FD2120F28CE69B1 // 234
774 data8 0x3FD21F6253C48D01 // 235
775 data8 0x3FD22CBBE51D60AA // 236
776 data8 0x3FD240CE4C975444 // 237
777 data8 0x3FD24E37F8ECDAE8 // 238
778 data8 0x3FD25BA8215AF7FC // 239
779 data8 0x3FD2691ECC29F042 // 240
780 data8 0x3FD2769BFFAB2E00 // 241
781 data8 0x3FD2841FC23952C9 // 242
782 data8 0x3FD291AA1A384978 // 243
783 data8 0x3FD29F3B0E15584B // 244
784 data8 0x3FD2B3A0EE479DF7 // 245
785 data8 0x3FD2C142842C09E6 // 246
786 data8 0x3FD2CEEACCB7BD6D // 247
787 data8 0x3FD2DC99CE82FF21 // 248
788 data8 0x3FD2EA4F902FD7DA // 249
789 data8 0x3FD2F80C186A25FD // 250
790 data8 0x3FD305CF6DE7B0F7 // 251
791 data8 0x3FD3139997683CE7 // 252
792 data8 0x3FD3216A9BB59E7C // 253
793 data8 0x3FD32F4281A3CEFF // 254
794 data8 0x3FD33D2150110092 // 255
795 LOCAL_OBJECT_END(log10f_data)
799 //==============================================================
802 // logf has p13 true, p14 false
803 // log10f has p14 true, p13 false
805 GLOBAL_IEEE754_ENTRY(log10f)
807 getf.exp GR_Exp = f8 // if x is unorm then must recompute
808 frcpa.s1 FR_RcpX,p0 = f1,f8
809 mov GR_05 = 0xFFFE // biased exponent of A2=0.5
812 addl GR_ad_T = @ltoff(log10f_data),gp
813 movl GR_A3 = 0x3FD5555555555555 // double precision memory
814 // representation of A3
817 getf.sig GR_Sig = f8 // if x is unorm then must recompute
818 fclass.m p8,p0 = f8,9 // is x positive unorm?
819 sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25
822 ld8 GR_ad_T = [GR_ad_T]
823 movl GR_Ln2 = 0x3FD34413509F79FF // double precision memory
828 setf.d FR_A3 = GR_A3 // create A3
829 fcmp.eq.s1 p14,p13 = f0,f0 // set p14 to 1 for log10f
830 dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number
832 // GR_xorg[63] = last bit of biased
833 // exponent of 255/256
834 // GR_xorg[62-0] = bits from 62 to 0
835 // of significand of 255/256
838 setf.exp FR_A2 = GR_05 // create A2
839 sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE
840 // needed for comparison with 0.5 and 2.0
841 br.cond.sptk logf_log10f_common
843 GLOBAL_IEEE754_END(log10f)
844 libm_alias_float_other (__log10, log10)
846 GLOBAL_IEEE754_ENTRY(logf)
848 getf.exp GR_Exp = f8 // if x is unorm then must recompute
849 frcpa.s1 FR_RcpX,p0 = f1,f8
850 mov GR_05 = 0xFFFE // biased exponent of A2=-0.5
853 addl GR_ad_T = @ltoff(logf_data),gp
854 movl GR_A3 = 0x3FD5555555555555 // double precision memory
855 // representation of A3
858 getf.sig GR_Sig = f8 // if x is unorm then must recompute
859 fclass.m p8,p0 = f8,9 // is x positive unorm?
860 dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number
862 // GR_xorg[63] = last bit of biased
863 // exponent of 255/256
864 // GR_xorg[62-0] = bits from 62 to 0
865 // of significand of 255/256
868 ld8 GR_ad_T = [GR_ad_T]
870 sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25
873 setf.d FR_A3 = GR_A3 // create A3
874 fcmp.eq.s1 p13,p14 = f0,f0 // p13 - true for logf
875 sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE
876 // needed for comparison with 0.5 and 2.0
879 setf.exp FR_A2 = GR_05 // create A2
880 movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory
881 // representation of log(2)
885 setf.exp FR_A4 = GR_025 // create A4=0.25
886 fclass.m p9,p0 = f8,0x3A // is x < 0 (including negateve unnormals)?
887 dep GR_x = GR_Exp,GR_Sig,63,1 // produce integer that bits are
888 // GR_x[63] = GR_Exp[0]
889 // GR_x[62-0] = GR_Sig[62-0]
892 sub GR_N = GR_Exp,GR_05,1 // unbiased exponent of x
893 cmp.gtu p6,p7 = 2,GR_de // is 0.5 <= x < 2.0?
894 (p8) br.cond.spnt logf_positive_unorm
898 setf.sig FR_N = GR_N // copy unbiased exponent of x to the
899 // significand field of FR_N
900 fclass.m p10,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
901 dep.z GR_dx = GR_05,54,3 // 0x0180000000000000 - difference
902 // between our integer representations
903 // of 257/256 and 255/256
908 sub GR_x = GR_x,GR_xorg // difference between representations
912 ldfd FR_InvLn10 = [GR_ad_T],8
913 fcmp.eq.s1 p11,p0 = f8,f1 // is x equal to 1.0?
914 extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
917 setf.d FR_Ln2 = GR_Ln2 // create log(2) or log10(2)
918 (p6) cmp.gtu p6,p7 = GR_dx,GR_x // set p6 if 255/256 <= x < 257/256
919 (p9) br.cond.spnt logf_negatives // jump if input argument is negative number
921 // p6 is true if |x-1| < 1/256
922 // p7 is true if |x-1| >= 1/256
923 .pred.rel "mutex",p6,p7
925 shladd GR_ad_T = GR_Ind,3,GR_ad_T // calculate address of T
926 (p7) fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256
927 extr.u GR_Exp = GR_Exp,0,17 // exponent without sign
931 (p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256
932 (p10) br.cond.spnt logf_nan_nat_pinf // exit for NaN, NaT or +Inf
935 ldfd FR_T = [GR_ad_T] // load T
936 (p11) fma.s.s0 f8 = f0,f0,f0
937 (p11) br.ret.spnt b0 // exit for x = 1.0
941 cmp.eq p12,p0 = r0,GR_Exp // is x +/-0? (here it's quite enough
942 // only to compare exponent with 0
943 // because all unnormals already
944 // have been filtered)
945 (p12) br.cond.spnt logf_zeroes // Branch if input argument is +/-0
949 fnma.s1 FR_A2 = FR_A2,FR_r,f1 // A2*r+1
954 fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
959 fcvt.xf FR_N = FR_N // convert integer N in significand of FR_N
960 // to floating-point representation
965 fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3
970 fma.s1 FR_r = FR_r,FR_InvLn10,f0 // For log10f we have r/log(10)
980 fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1)
985 fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T // N*Ln2+T
988 .pred.rel "mutex",p6,p7
991 (p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result for |x-1|>=1/256
996 (p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result for |x-1|<1/256
1001 logf_positive_unorm:
1004 (p8) fma.s0 f8 = f8,f1,f0 // Normalize & set D-flag
1008 getf.exp GR_Exp = f8 // recompute biased exponent
1010 cmp.ne p6,p7 = r0,r0 // p6 <- 0, p7 <- 1 because
1011 // in case of unorm we are out
1012 // interval [255/256; 257/256]
1015 getf.sig GR_Sig = f8 // recompute significand
1020 sub GR_N = GR_Exp,GR_05,1 // unbiased exponent N
1022 br.cond.sptk logf_core // return into main path
1029 fma.s.s0 f8 = f8,f1,f0 // set V-flag
1035 br.ret.sptk b0 // exit for NaN, NaT or +Inf
1042 fmerge.s FR_X = f8,f8 // keep input argument for subsequent
1043 // call of __libm_error_support#
1047 (p13) mov GR_TAG = 4 // set libm error in case of logf
1048 fms.s1 FR_tmp = f0,f0,f1 // -1.0
1053 frcpa.s0 f8,p0 = FR_tmp,f0 // log(+/-0) should be equal to -INF.
1054 // We can get it using frcpa because it
1055 // sets result to the IEEE-754 mandated
1056 // quotient of FR_tmp/f0.
1057 // As far as FR_tmp is -1 it'll be -INF
1061 (p14) mov GR_TAG = 10 // set libm error in case of log10f
1063 br.cond.sptk logf_libm_err
1069 (p13) mov GR_TAG = 5 // set libm error in case of logf
1070 fmerge.s FR_X = f8,f8 // keep input argument for subsequent
1071 // call of __libm_error_support#
1075 (p14) mov GR_TAG = 11 // set libm error in case of log10f
1076 frcpa.s0 f8,p0 = f0,f0 // log(negatives) should be equal to NaN.
1077 // We can get it using frcpa because it
1078 // sets result to the IEEE-754 mandated
1079 // quotient of f0/f0 i.e. NaN.
1086 alloc r32 = ar.pfs,1,4,4,0
1087 mov GR_Parameter_TAG = GR_TAG
1090 GLOBAL_IEEE754_END(logf)
1091 libm_alias_float_other (__log, log)
1093 .symver logf,logf@@GLIBC_2.27
1095 .set __logf_compat,__logf
1096 .symver __logf_compat,logf@GLIBC_2.2
1100 // Stack operations when calling error support.
1101 // (1) (2) (3) (call) (4)
1102 // sp -> + psp -> + psp -> + sp -> +
1104 // | | <- GR_Y R3 ->| <- GR_RESULT | -> f8
1106 // | <-GR_Y Y2->| Y2 ->| <- GR_Y |
1108 // | | <- GR_X X1 ->| |
1110 // sp-64 -> + sp -> + sp -> + +
1111 // save ar.pfs save b0 restore gp
1112 // save gp restore ar.pfs
1114 LOCAL_LIBM_ENTRY(__libm_error_region)
1117 add GR_Parameter_Y=-32,sp // Parameter 2 value
1119 .save ar.pfs,GR_SAVE_PFS
1120 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1124 add sp=-64,sp // Create new stack
1126 mov GR_SAVE_GP=gp // Save gp
1129 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
1130 add GR_Parameter_X = 16,sp // Parameter 1 address
1131 .save b0, GR_SAVE_B0
1132 mov GR_SAVE_B0=b0 // Save b0
1136 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
1137 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1141 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
1142 add GR_Parameter_Y = -16,GR_Parameter_Y
1143 br.call.sptk b0=__libm_error_support# // Call error handling function
1148 add GR_Parameter_RESULT = 48,sp
1151 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
1153 add sp = 64,sp // Restore stack pointer
1154 mov b0 = GR_SAVE_B0 // Restore return address
1157 mov gp = GR_SAVE_GP // Restore gp
1158 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1159 br.ret.sptk b0 // Return
1162 LOCAL_LIBM_END(__libm_error_region)
1164 .type __libm_error_support#,@function
1165 .global __libm_error_support#
projects / glibc.git / blob