| blob | cd3551984a796e842199a90fbcc0c16e084c6c39 |
1 .file "log1p.s"
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.
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://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 02/02/00 Initial version
43 // 04/04/00 Unwind support added
44 // 08/15/00 Bundle added after call to __libm_error_support to properly
45 // set [the previously overwritten] GR_Parameter_RESULT.
46 // 06/29/01 Improved speed of all paths
47 // 05/20/02 Cleaned up namespace and sf0 syntax
48 // 10/02/02 Improved performance by basing on log algorithm
49 // 02/10/03 Reordered header: .section, .global, .proc, .align
50 // 04/18/03 Eliminate possible WAW dependency warning
51 //
52 // API
53 //==============================================================
54 // double log1p(double)
55 //
56 // log1p(x) = log(x+1)
57 //
58 // Overview of operation
59 //==============================================================
60 // Background
61 // ----------
62 //
63 // This algorithm is based on fact that
64 // log1p(x) = log(1+x) and
65 // log(a b) = log(a) + log(b).
66 // In our case we have 1+x = 2^N f, where 1 <= f < 2.
67 // So
68 // log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
69 //
70 // To calculate log(f) we do following
71 // log(f) = log(f * frcpa(f) / frcpa(f)) =
72 // = log(f * frcpa(f)) + log(1/frcpa(f))
73 //
74 // According to definition of IA-64's frcpa instruction it's a
75 // floating point that approximates 1/f using a lookup on the
76 // top of 8 bits of the input number's + 1 significand with relative
77 // error < 2^(-8.886). So we have following
78 //
79 // |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
80 //
81 // and
82 //
83 // log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
84 // = log(1 + r) + T
85 //
86 // The first value can be computed by polynomial P(r) approximating
87 // log(1 + r) on |r| < 1/256 and the second is precomputed tabular
88 // value defined by top 8 bit of f.
89 //
90 // Finally we have that log(1+x) ~ (N*log(2) + T) + P(r)
91 //
92 // Note that if input argument is close to 0.0 (in our case it means
93 // that |x| < 1/256) we can use just polynomial approximation
94 // because 1+x = 2^0 * f = f = 1 + r and
95 // log(1+x) = log(1 + r) ~ P(r)
96 //
97 //
98 // Implementation
99 // --------------
100 //
101 // 1. |x| >= 2^(-8), and x > -1
102 // InvX = frcpa(x+1)
103 // r = InvX*(x+1) - 1
104 // P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
105 // all coefficients are calcutated in quad and rounded to double
106 // precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2
107 // created with setf.
108 //
109 // N = float(n) where n is true unbiased exponent of x
110 //
111 // T is tabular value of log(1/frcpa(x)) calculated in quad precision
112 // and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo.
113 // To load Thi,Tlo we get bits from 55 to 62 of register format significand
114 // as index and calculate two addresses
115 // ad_Thi = Thi_table_base_addr + 8 * index
116 // ad_Tlo = Tlo_table_base_addr + 4 * index
117 //
118 // L1 (log(2)) is calculated in quad
119 // precision and represented by two floating-point 64-bit numbers L1hi,L1lo
120 // stored in memory.
121 //
122 // And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + P(r)
123 //
124 //
125 // 2. 2^(-80) <= |x| < 2^(-8)
126 // r = x
127 // P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
128 // A7,A6,A5,A4,A3,A2 are the same as in case |x| >= 1/256
129 //
130 // And final results
131 // log(1+x) = P(r)
132 //
133 // 3. 0 < |x| < 2^(-80)
134 // Although log1p(x) is basically x, we would like to preserve the inexactness
135 // nature as well as consistent behavior under different rounding modes.
136 // We can do this by computing the result as
137 //
138 // log1p(x) = x - x*x
139 //
140 //
141 // Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
142 // filtered and processed on special branches.
143 //
145 //
146 // Special values
147 //==============================================================
148 //
149 // log1p(-1) = -inf // Call error support
150 //
151 // log1p(+qnan) = +qnan
152 // log1p(-qnan) = -qnan
153 // log1p(+snan) = +qnan
154 // log1p(-snan) = -qnan
155 //
156 // log1p(x),x<-1= QNAN Indefinite // Call error support
157 // log1p(-inf) = QNAN Indefinite
158 // log1p(+inf) = +inf
159 // log1p(+/-0) = +/-0
160 //
161 //
162 // Registers used
163 //==============================================================
164 // Floating Point registers used:
165 // f8, input
166 // f7 -> f15, f32 -> f40
167 //
168 // General registers used:
169 // r8 -> r11
170 // r14 -> r20
171 //
172 // Predicate registers used:
173 // p6 -> p12
175 // Assembly macros
176 //==============================================================
177 GR_TAG = r8
178 GR_ad_1 = r8
179 GR_ad_2 = r9
180 GR_Exp = r10
181 GR_N = r11
183 GR_signexp_x = r14
184 GR_exp_mask = r15
185 GR_exp_bias = r16
186 GR_05 = r17
187 GR_A3 = r18
188 GR_Sig = r19
189 GR_Ind = r19
190 GR_exp_x = r20
193 GR_SAVE_B0 = r33
194 GR_SAVE_PFS = r34
195 GR_SAVE_GP = r35
196 GR_SAVE_SP = r36
198 GR_Parameter_X = r37
199 GR_Parameter_Y = r38
200 GR_Parameter_RESULT = r39
201 GR_Parameter_TAG = r40
205 FR_NormX = f7
206 FR_RcpX = f9
207 FR_r = f10
208 FR_r2 = f11
209 FR_r4 = f12
210 FR_N = f13
211 FR_Ln2hi = f14
212 FR_Ln2lo = f15
214 FR_A7 = f32
215 FR_A6 = f33
216 FR_A5 = f34
217 FR_A4 = f35
218 FR_A3 = f36
219 FR_A2 = f37
221 FR_Thi = f38
222 FR_NxLn2hipThi = f38
223 FR_NxLn2pT = f38
224 FR_Tlo = f39
225 FR_NxLn2lopTlo = f39
227 FR_Xp1 = f40
230 FR_Y = f1
231 FR_X = f10
232 FR_RESULT = f8
235 // Data
236 //==============================================================
237 RODATA
238 .align 16
240 LOCAL_OBJECT_START(log_data)
241 // coefficients of polynomial approximation
242 data8 0x3FC2494104381A8E // A7
243 data8 0xBFC5556D556BBB69 // A6
244 data8 0x3FC999999988B5E9 // A5
245 data8 0xBFCFFFFFFFF6FFF5 // A4
246 //
247 // hi parts of ln(1/frcpa(1+i/256)), i=0...255
248 data8 0x3F60040155D5889D // 0
249 data8 0x3F78121214586B54 // 1
250 data8 0x3F841929F96832EF // 2
251 data8 0x3F8C317384C75F06 // 3
252 data8 0x3F91A6B91AC73386 // 4
253 data8 0x3F95BA9A5D9AC039 // 5
254 data8 0x3F99D2A8074325F3 // 6
255 data8 0x3F9D6B2725979802 // 7
256 data8 0x3FA0C58FA19DFAA9 // 8
257 data8 0x3FA2954C78CBCE1A // 9
258 data8 0x3FA4A94D2DA96C56 // 10
259 data8 0x3FA67C94F2D4BB58 // 11
260 data8 0x3FA85188B630F068 // 12
261 data8 0x3FAA6B8ABE73AF4C // 13
262 data8 0x3FAC441E06F72A9E // 14
263 data8 0x3FAE1E6713606D06 // 15
264 data8 0x3FAFFA6911AB9300 // 16
265 data8 0x3FB0EC139C5DA600 // 17
266 data8 0x3FB1DBD2643D190B // 18
267 data8 0x3FB2CC7284FE5F1C // 19
268 data8 0x3FB3BDF5A7D1EE64 // 20
269 data8 0x3FB4B05D7AA012E0 // 21
270 data8 0x3FB580DB7CEB5701 // 22
271 data8 0x3FB674F089365A79 // 23
272 data8 0x3FB769EF2C6B568D // 24
273 data8 0x3FB85FD927506A47 // 25
274 data8 0x3FB9335E5D594988 // 26
275 data8 0x3FBA2B0220C8E5F4 // 27
276 data8 0x3FBB0004AC1A86AB // 28
277 data8 0x3FBBF968769FCA10 // 29
278 data8 0x3FBCCFEDBFEE13A8 // 30
279 data8 0x3FBDA727638446A2 // 31
280 data8 0x3FBEA3257FE10F79 // 32
281 data8 0x3FBF7BE9FEDBFDE5 // 33
282 data8 0x3FC02AB352FF25F3 // 34
283 data8 0x3FC097CE579D204C // 35
284 data8 0x3FC1178E8227E47B // 36
285 data8 0x3FC185747DBECF33 // 37
286 data8 0x3FC1F3B925F25D41 // 38
287 data8 0x3FC2625D1E6DDF56 // 39
288 data8 0x3FC2D1610C868139 // 40
289 data8 0x3FC340C59741142E // 41
290 data8 0x3FC3B08B6757F2A9 // 42
291 data8 0x3FC40DFB08378003 // 43
292 data8 0x3FC47E74E8CA5F7C // 44
293 data8 0x3FC4EF51F6466DE4 // 45
294 data8 0x3FC56092E02BA516 // 46
295 data8 0x3FC5D23857CD74D4 // 47
296 data8 0x3FC6313A37335D76 // 48
297 data8 0x3FC6A399DABBD383 // 49
298 data8 0x3FC70337DD3CE41A // 50
299 data8 0x3FC77654128F6127 // 51
300 data8 0x3FC7E9D82A0B022D // 52
301 data8 0x3FC84A6B759F512E // 53
302 data8 0x3FC8AB47D5F5A30F // 54
303 data8 0x3FC91FE49096581B // 55
304 data8 0x3FC981634011AA75 // 56
305 data8 0x3FC9F6C407089664 // 57
306 data8 0x3FCA58E729348F43 // 58
307 data8 0x3FCABB55C31693AC // 59
308 data8 0x3FCB1E104919EFD0 // 60
309 data8 0x3FCB94EE93E367CA // 61
310 data8 0x3FCBF851C067555E // 62
311 data8 0x3FCC5C0254BF23A5 // 63
312 data8 0x3FCCC000C9DB3C52 // 64
313 data8 0x3FCD244D99C85673 // 65
314 data8 0x3FCD88E93FB2F450 // 66
315 data8 0x3FCDEDD437EAEF00 // 67
316 data8 0x3FCE530EFFE71012 // 68
317 data8 0x3FCEB89A1648B971 // 69
318 data8 0x3FCF1E75FADF9BDE // 70
319 data8 0x3FCF84A32EAD7C35 // 71
320 data8 0x3FCFEB2233EA07CD // 72
321 data8 0x3FD028F9C7035C1C // 73
322 data8 0x3FD05C8BE0D9635A // 74
323 data8 0x3FD085EB8F8AE797 // 75
324 data8 0x3FD0B9C8E32D1911 // 76
325 data8 0x3FD0EDD060B78080 // 77
326 data8 0x3FD122024CF0063F // 78
327 data8 0x3FD14BE2927AECD4 // 79
328 data8 0x3FD180618EF18ADF // 80
329 data8 0x3FD1B50BBE2FC63B // 81
330 data8 0x3FD1DF4CC7CF242D // 82
331 data8 0x3FD214456D0EB8D4 // 83
332 data8 0x3FD23EC5991EBA49 // 84
333 data8 0x3FD2740D9F870AFB // 85
334 data8 0x3FD29ECDABCDFA03 // 86
335 data8 0x3FD2D46602ADCCEE // 87
336 data8 0x3FD2FF66B04EA9D4 // 88
337 data8 0x3FD335504B355A37 // 89
338 data8 0x3FD360925EC44F5C // 90
339 data8 0x3FD38BF1C3337E74 // 91
340 data8 0x3FD3C25277333183 // 92
341 data8 0x3FD3EDF463C1683E // 93
342 data8 0x3FD419B423D5E8C7 // 94
343 data8 0x3FD44591E0539F48 // 95
344 data8 0x3FD47C9175B6F0AD // 96
345 data8 0x3FD4A8B341552B09 // 97
346 data8 0x3FD4D4F39089019F // 98
347 data8 0x3FD501528DA1F967 // 99
348 data8 0x3FD52DD06347D4F6 // 100
349 data8 0x3FD55A6D3C7B8A89 // 101
350 data8 0x3FD5925D2B112A59 // 102
351 data8 0x3FD5BF406B543DB1 // 103
352 data8 0x3FD5EC433D5C35AD // 104
353 data8 0x3FD61965CDB02C1E // 105
354 data8 0x3FD646A84935B2A1 // 106
355 data8 0x3FD6740ADD31DE94 // 107
356 data8 0x3FD6A18DB74A58C5 // 108
357 data8 0x3FD6CF31058670EC // 109
358 data8 0x3FD6F180E852F0B9 // 110
359 data8 0x3FD71F5D71B894EF // 111
360 data8 0x3FD74D5AEFD66D5C // 112
361 data8 0x3FD77B79922BD37D // 113
362 data8 0x3FD7A9B9889F19E2 // 114
363 data8 0x3FD7D81B037EB6A6 // 115
364 data8 0x3FD8069E33827230 // 116
365 data8 0x3FD82996D3EF8BCA // 117
366 data8 0x3FD85855776DCBFA // 118
367 data8 0x3FD8873658327CCE // 119
368 data8 0x3FD8AA75973AB8CE // 120
369 data8 0x3FD8D992DC8824E4 // 121
370 data8 0x3FD908D2EA7D9511 // 122
371 data8 0x3FD92C59E79C0E56 // 123
372 data8 0x3FD95BD750EE3ED2 // 124
373 data8 0x3FD98B7811A3EE5B // 125
374 data8 0x3FD9AF47F33D406B // 126
375 data8 0x3FD9DF270C1914A7 // 127
376 data8 0x3FDA0325ED14FDA4 // 128
377 data8 0x3FDA33440224FA78 // 129
378 data8 0x3FDA57725E80C382 // 130
379 data8 0x3FDA87D0165DD199 // 131
380 data8 0x3FDAAC2E6C03F895 // 132
381 data8 0x3FDADCCC6FDF6A81 // 133
382 data8 0x3FDB015B3EB1E790 // 134
383 data8 0x3FDB323A3A635948 // 135
384 data8 0x3FDB56FA04462909 // 136
385 data8 0x3FDB881AA659BC93 // 137
386 data8 0x3FDBAD0BEF3DB164 // 138
387 data8 0x3FDBD21297781C2F // 139
388 data8 0x3FDC039236F08818 // 140
389 data8 0x3FDC28CB1E4D32FC // 141
390 data8 0x3FDC4E19B84723C1 // 142
391 data8 0x3FDC7FF9C74554C9 // 143
392 data8 0x3FDCA57B64E9DB05 // 144
393 data8 0x3FDCCB130A5CEBAF // 145
394 data8 0x3FDCF0C0D18F326F // 146
395 data8 0x3FDD232075B5A201 // 147
396 data8 0x3FDD490246DEFA6B // 148
397 data8 0x3FDD6EFA918D25CD // 149
398 data8 0x3FDD9509707AE52F // 150
399 data8 0x3FDDBB2EFE92C554 // 151
400 data8 0x3FDDEE2F3445E4AE // 152
401 data8 0x3FDE148A1A2726CD // 153
402 data8 0x3FDE3AFC0A49FF3F // 154
403 data8 0x3FDE6185206D516D // 155
404 data8 0x3FDE882578823D51 // 156
405 data8 0x3FDEAEDD2EAC990C // 157
406 data8 0x3FDED5AC5F436BE2 // 158
407 data8 0x3FDEFC9326D16AB8 // 159
408 data8 0x3FDF2391A21575FF // 160
409 data8 0x3FDF4AA7EE03192C // 161
410 data8 0x3FDF71D627C30BB0 // 162
411 data8 0x3FDF991C6CB3B379 // 163
412 data8 0x3FDFC07ADA69A90F // 164
413 data8 0x3FDFE7F18EB03D3E // 165
414 data8 0x3FE007C053C5002E // 166
415 data8 0x3FE01B942198A5A0 // 167
416 data8 0x3FE02F74400C64EA // 168
417 data8 0x3FE04360BE7603AC // 169
418 data8 0x3FE05759AC47FE33 // 170
419 data8 0x3FE06B5F1911CF51 // 171
420 data8 0x3FE078BF0533C568 // 172
421 data8 0x3FE08CD9687E7B0E // 173
422 data8 0x3FE0A10074CF9019 // 174
423 data8 0x3FE0B5343A234476 // 175
424 data8 0x3FE0C974C89431CD // 176
425 data8 0x3FE0DDC2305B9886 // 177
426 data8 0x3FE0EB524BAFC918 // 178
427 data8 0x3FE0FFB54213A475 // 179
428 data8 0x3FE114253DA97D9F // 180
429 data8 0x3FE128A24F1D9AFF // 181
430 data8 0x3FE1365252BF0864 // 182
431 data8 0x3FE14AE558B4A92D // 183
432 data8 0x3FE15F85A19C765B // 184
433 data8 0x3FE16D4D38C119FA // 185
434 data8 0x3FE18203C20DD133 // 186
435 data8 0x3FE196C7BC4B1F3A // 187
436 data8 0x3FE1A4A738B7A33C // 188
437 data8 0x3FE1B981C0C9653C // 189
438 data8 0x3FE1CE69E8BB106A // 190
439 data8 0x3FE1DC619DE06944 // 191
440 data8 0x3FE1F160A2AD0DA3 // 192
441 data8 0x3FE2066D7740737E // 193
442 data8 0x3FE2147DBA47A393 // 194
443 data8 0x3FE229A1BC5EBAC3 // 195
444 data8 0x3FE237C1841A502E // 196
445 data8 0x3FE24CFCE6F80D9A // 197
446 data8 0x3FE25B2C55CD5762 // 198
447 data8 0x3FE2707F4D5F7C40 // 199
448 data8 0x3FE285E0842CA383 // 200
449 data8 0x3FE294294708B773 // 201
450 data8 0x3FE2A9A2670AFF0C // 202
451 data8 0x3FE2B7FB2C8D1CC0 // 203
452 data8 0x3FE2C65A6395F5F5 // 204
453 data8 0x3FE2DBF557B0DF42 // 205
454 data8 0x3FE2EA64C3F97654 // 206
455 data8 0x3FE3001823684D73 // 207
456 data8 0x3FE30E97E9A8B5CC // 208
457 data8 0x3FE32463EBDD34E9 // 209
458 data8 0x3FE332F4314AD795 // 210
459 data8 0x3FE348D90E7464CF // 211
460 data8 0x3FE35779F8C43D6D // 212
461 data8 0x3FE36621961A6A99 // 213
462 data8 0x3FE37C299F3C366A // 214
463 data8 0x3FE38AE2171976E7 // 215
464 data8 0x3FE399A157A603E7 // 216
465 data8 0x3FE3AFCCFE77B9D1 // 217
466 data8 0x3FE3BE9D503533B5 // 218
467 data8 0x3FE3CD7480B4A8A2 // 219
468 data8 0x3FE3E3C43918F76C // 220
469 data8 0x3FE3F2ACB27ED6C6 // 221
470 data8 0x3FE4019C2125CA93 // 222
471 data8 0x3FE4181061389722 // 223
472 data8 0x3FE42711518DF545 // 224
473 data8 0x3FE436194E12B6BF // 225
474 data8 0x3FE445285D68EA69 // 226
475 data8 0x3FE45BCC464C893A // 227
476 data8 0x3FE46AED21F117FC // 228
477 data8 0x3FE47A1527E8A2D3 // 229
478 data8 0x3FE489445EFFFCCB // 230
479 data8 0x3FE4A018BCB69835 // 231
480 data8 0x3FE4AF5A0C9D65D7 // 232
481 data8 0x3FE4BEA2A5BDBE87 // 233
482 data8 0x3FE4CDF28F10AC46 // 234
483 data8 0x3FE4DD49CF994058 // 235
484 data8 0x3FE4ECA86E64A683 // 236
485 data8 0x3FE503C43CD8EB68 // 237
486 data8 0x3FE513356667FC57 // 238
487 data8 0x3FE522AE0738A3D7 // 239
488 data8 0x3FE5322E26867857 // 240
489 data8 0x3FE541B5CB979809 // 241
490 data8 0x3FE55144FDBCBD62 // 242
491 data8 0x3FE560DBC45153C6 // 243
492 data8 0x3FE5707A26BB8C66 // 244
493 data8 0x3FE587F60ED5B8FF // 245
494 data8 0x3FE597A7977C8F31 // 246
495 data8 0x3FE5A760D634BB8A // 247
496 data8 0x3FE5B721D295F10E // 248
497 data8 0x3FE5C6EA94431EF9 // 249
498 data8 0x3FE5D6BB22EA86F5 // 250
499 data8 0x3FE5E6938645D38F // 251
500 data8 0x3FE5F673C61A2ED1 // 252
501 data8 0x3FE6065BEA385926 // 253
502 data8 0x3FE6164BFA7CC06B // 254
503 data8 0x3FE62643FECF9742 // 255
504 //
505 // two parts of ln(2)
506 data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED
507 //
508 // lo parts of ln(1/frcpa(1+i/256)), i=0...255
509 data4 0x20E70672 // 0
510 data4 0x1F60A5D0 // 1
511 data4 0x218EABA0 // 2
512 data4 0x21403104 // 3
513 data4 0x20E9B54E // 4
514 data4 0x21EE1382 // 5
515 data4 0x226014E3 // 6
516 data4 0x2095E5C9 // 7
517 data4 0x228BA9D4 // 8
518 data4 0x22932B86 // 9
519 data4 0x22608A57 // 10
520 data4 0x220209F3 // 11
521 data4 0x212882CC // 12
522 data4 0x220D46E2 // 13
523 data4 0x21FA4C28 // 14
524 data4 0x229E5BD9 // 15
525 data4 0x228C9838 // 16
526 data4 0x2311F954 // 17
527 data4 0x221365DF // 18
528 data4 0x22BD0CB3 // 19
529 data4 0x223D4BB7 // 20
530 data4 0x22A71BBE // 21
531 data4 0x237DB2FA // 22
532 data4 0x23194C9D // 23
533 data4 0x22EC639E // 24
534 data4 0x2367E669 // 25
535 data4 0x232E1D5F // 26
536 data4 0x234A639B // 27
537 data4 0x2365C0E0 // 28
538 data4 0x234646C1 // 29
539 data4 0x220CBF9C // 30
540 data4 0x22A00FD4 // 31
541 data4 0x2306A3F2 // 32
542 data4 0x23745A9B // 33
543 data4 0x2398D756 // 34
544 data4 0x23DD0B6A // 35
545 data4 0x23DE338B // 36
546 data4 0x23A222DF // 37
547 data4 0x223164F8 // 38
548 data4 0x23B4E87B // 39
549 data4 0x23D6CCB8 // 40
550 data4 0x220C2099 // 41
551 data4 0x21B86B67 // 42
552 data4 0x236D14F1 // 43
553 data4 0x225A923F // 44
554 data4 0x22748723 // 45
555 data4 0x22200D13 // 46
556 data4 0x23C296EA // 47
557 data4 0x2302AC38 // 48
558 data4 0x234B1996 // 49
559 data4 0x2385E298 // 50
560 data4 0x23175BE5 // 51
561 data4 0x2193F482 // 52
562 data4 0x23BFEA90 // 53
563 data4 0x23D70A0C // 54
564 data4 0x231CF30A // 55
565 data4 0x235D9E90 // 56
566 data4 0x221AD0CB // 57
567 data4 0x22FAA08B // 58
568 data4 0x23D29A87 // 59
569 data4 0x20C4B2FE // 60
570 data4 0x2381B8B7 // 61
571 data4 0x23F8D9FC // 62
572 data4 0x23EAAE7B // 63
573 data4 0x2329E8AA // 64
574 data4 0x23EC0322 // 65
575 data4 0x2357FDCB // 66
576 data4 0x2392A9AD // 67
577 data4 0x22113B02 // 68
578 data4 0x22DEE901 // 69
579 data4 0x236A6D14 // 70
580 data4 0x2371D33E // 71
581 data4 0x2146F005 // 72
582 data4 0x23230B06 // 73
583 data4 0x22F1C77D // 74
584 data4 0x23A89FA3 // 75
585 data4 0x231D1241 // 76
586 data4 0x244DA96C // 77
587 data4 0x23ECBB7D // 78
588 data4 0x223E42B4 // 79
589 data4 0x23801BC9 // 80
590 data4 0x23573263 // 81
591 data4 0x227C1158 // 82
592 data4 0x237BD749 // 83
593 data4 0x21DDBAE9 // 84
594 data4 0x23401735 // 85
595 data4 0x241D9DEE // 86
596 data4 0x23BC88CB // 87
597 data4 0x2396D5F1 // 88
598 data4 0x23FC89CF // 89
599 data4 0x2414F9A2 // 90
600 data4 0x2474A0F5 // 91
601 data4 0x24354B60 // 92
602 data4 0x23C1EB40 // 93
603 data4 0x2306DD92 // 94
604 data4 0x24353B6B // 95
605 data4 0x23CD1701 // 96
606 data4 0x237C7A1C // 97
607 data4 0x245793AA // 98
608 data4 0x24563695 // 99
609 data4 0x23C51467 // 100
610 data4 0x24476B68 // 101
611 data4 0x212585A9 // 102
612 data4 0x247B8293 // 103
613 data4 0x2446848A // 104
614 data4 0x246A53F8 // 105
615 data4 0x246E496D // 106
616 data4 0x23ED1D36 // 107
617 data4 0x2314C258 // 108
618 data4 0x233244A7 // 109
619 data4 0x245B7AF0 // 110
620 data4 0x24247130 // 111
621 data4 0x22D67B38 // 112
622 data4 0x2449F620 // 113
623 data4 0x23BBC8B8 // 114
624 data4 0x237D3BA0 // 115
625 data4 0x245E8F13 // 116
626 data4 0x2435573F // 117
627 data4 0x242DE666 // 118
628 data4 0x2463BC10 // 119
629 data4 0x2466587D // 120
630 data4 0x2408144B // 121
631 data4 0x2405F0E5 // 122
632 data4 0x22381CFF // 123
633 data4 0x24154F9B // 124
634 data4 0x23A4E96E // 125
635 data4 0x24052967 // 126
636 data4 0x2406963F // 127
637 data4 0x23F7D3CB // 128
638 data4 0x2448AFF4 // 129
639 data4 0x24657A21 // 130
640 data4 0x22FBC230 // 131
641 data4 0x243C8DEA // 132
642 data4 0x225DC4B7 // 133
643 data4 0x23496EBF // 134
644 data4 0x237C2B2B // 135
645 data4 0x23A4A5B1 // 136
646 data4 0x2394E9D1 // 137
647 data4 0x244BC950 // 138
648 data4 0x23C7448F // 139
649 data4 0x2404A1AD // 140
650 data4 0x246511D5 // 141
651 data4 0x24246526 // 142
652 data4 0x23111F57 // 143
653 data4 0x22868951 // 144
654 data4 0x243EB77F // 145
655 data4 0x239F3DFF // 146
656 data4 0x23089666 // 147
657 data4 0x23EBFA6A // 148
658 data4 0x23C51312 // 149
659 data4 0x23E1DD5E // 150
660 data4 0x232C0944 // 151
661 data4 0x246A741F // 152
662 data4 0x2414DF8D // 153
663 data4 0x247B5546 // 154
664 data4 0x2415C980 // 155
665 data4 0x24324ABD // 156
666 data4 0x234EB5E5 // 157
667 data4 0x2465E43E // 158
668 data4 0x242840D1 // 159
669 data4 0x24444057 // 160
670 data4 0x245E56F0 // 161
671 data4 0x21AE30F8 // 162
672 data4 0x23FB3283 // 163
673 data4 0x247A4D07 // 164
674 data4 0x22AE314D // 165
675 data4 0x246B7727 // 166
676 data4 0x24EAD526 // 167
677 data4 0x24B41DC9 // 168
678 data4 0x24EE8062 // 169
679 data4 0x24A0C7C4 // 170
680 data4 0x24E8DA67 // 171
681 data4 0x231120F7 // 172
682 data4 0x24401FFB // 173
683 data4 0x2412DD09 // 174
684 data4 0x248C131A // 175
685 data4 0x24C0A7CE // 176
686 data4 0x243DD4C8 // 177
687 data4 0x24457FEB // 178
688 data4 0x24DEEFBB // 179
689 data4 0x243C70AE // 180
690 data4 0x23E7A6FA // 181
691 data4 0x24C2D311 // 182
692 data4 0x23026255 // 183
693 data4 0x2437C9B9 // 184
694 data4 0x246BA847 // 185
695 data4 0x2420B448 // 186
696 data4 0x24C4CF5A // 187
697 data4 0x242C4981 // 188
698 data4 0x24DE1525 // 189
699 data4 0x24F5CC33 // 190
700 data4 0x235A85DA // 191
701 data4 0x24A0B64F // 192
702 data4 0x244BA0A4 // 193
703 data4 0x24AAF30A // 194
704 data4 0x244C86F9 // 195
705 data4 0x246D5B82 // 196
706 data4 0x24529347 // 197
707 data4 0x240DD008 // 198
708 data4 0x24E98790 // 199
709 data4 0x2489B0CE // 200
710 data4 0x22BC29AC // 201
711 data4 0x23F37C7A // 202
712 data4 0x24987FE8 // 203
713 data4 0x22AFE20B // 204
714 data4 0x24C8D7C2 // 205
715 data4 0x24B28B7D // 206
716 data4 0x23B6B271 // 207
717 data4 0x24C77CB6 // 208
718 data4 0x24EF1DCA // 209
719 data4 0x24A4F0AC // 210
720 data4 0x24CF113E // 211
721 data4 0x2496BBAB // 212
722 data4 0x23C7CC8A // 213
723 data4 0x23AE3961 // 214
724 data4 0x2410A895 // 215
725 data4 0x23CE3114 // 216
726 data4 0x2308247D // 217
727 data4 0x240045E9 // 218
728 data4 0x24974F60 // 219
729 data4 0x242CB39F // 220
730 data4 0x24AB8D69 // 221
731 data4 0x23436788 // 222
732 data4 0x24305E9E // 223
733 data4 0x243E71A9 // 224
734 data4 0x23C2A6B3 // 225
735 data4 0x23FFE6CF // 226
736 data4 0x2322D801 // 227
737 data4 0x24515F21 // 228
738 data4 0x2412A0D6 // 229
739 data4 0x24E60D44 // 230
740 data4 0x240D9251 // 231
741 data4 0x247076E2 // 232
742 data4 0x229B101B // 233
743 data4 0x247B12DE // 234
744 data4 0x244B9127 // 235
745 data4 0x2499EC42 // 236
746 data4 0x21FC3963 // 237
747 data4 0x23E53266 // 238
748 data4 0x24CE102D // 239
749 data4 0x23CC45D2 // 240
750 data4 0x2333171D // 241
751 data4 0x246B3533 // 242
752 data4 0x24931129 // 243
753 data4 0x24405FFA // 244
754 data4 0x24CF464D // 245
755 data4 0x237095CD // 246
756 data4 0x24F86CBD // 247
757 data4 0x24E2D84B // 248
758 data4 0x21ACBB44 // 249
759 data4 0x24F43A8C // 250
760 data4 0x249DB931 // 251
761 data4 0x24A385EF // 252
762 data4 0x238B1279 // 253
763 data4 0x2436213E // 254
764 data4 0x24F18A3B // 255
765 LOCAL_OBJECT_END(log_data)
768 // Code
769 //==============================================================
771 .section .text
772 GLOBAL_IEEE754_ENTRY(log1p)
773 { .mfi
774 getf.exp GR_signexp_x = f8 // if x is unorm then must recompute
775 fadd.s1 FR_Xp1 = f8, f1 // Form 1+x
776 mov GR_05 = 0xfffe
777 }
778 { .mlx
779 addl GR_ad_1 = @ltoff(log_data),gp
780 movl GR_A3 = 0x3fd5555555555557 // double precision memory
781 // representation of A3
782 }
783 ;;
785 { .mfi
786 ld8 GR_ad_1 = [GR_ad_1]
787 fclass.m p8,p0 = f8,0xb // Is x unorm?
788 mov GR_exp_mask = 0x1ffff
789 }
790 { .mfi
791 nop.m 0
792 fnorm.s1 FR_NormX = f8 // Normalize x
793 mov GR_exp_bias = 0xffff
794 }
795 ;;
797 { .mfi
798 setf.exp FR_A2 = GR_05 // create A2 = 0.5
799 fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
800 nop.i 0
801 }
802 { .mib
803 setf.d FR_A3 = GR_A3 // create A3
804 add GR_ad_2 = 16,GR_ad_1 // address of A5,A4
805 (p8) br.cond.spnt log1p_unorm // Branch if x=unorm
806 }
807 ;;
809 log1p_common:
810 { .mfi
811 nop.m 0
812 frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1
813 nop.i 0
814 }
815 { .mfb
816 nop.m 0
817 (p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag
818 (p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
819 }
820 ;;
822 { .mfi
823 getf.exp GR_Exp = FR_Xp1 // signexp of x+1
824 fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
825 and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
826 }
827 { .mfi
828 ldfpd FR_A7,FR_A6 = [GR_ad_1]
829 nop.f 0
830 nop.i 0
831 }
832 ;;
834 { .mfi
835 getf.sig GR_Sig = FR_Xp1 // get significand to calculate index
836 // for Thi,Tlo if |x| >= 2^-8
837 fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0?
838 sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
839 }
840 ;;
842 { .mfi
843 sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
844 fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1?
845 cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8
846 }
847 { .mfb
848 ldfpd FR_A5,FR_A4 = [GR_ad_2],16
849 nop.f 0
850 (p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1
851 }
852 ;;
854 // p6 is true if |x| < 1/256
855 // p7 is true if |x| >= 1/256
856 .pred.rel "mutex",p6,p7
857 { .mfi
858 (p7) add GR_ad_1 = 0x820,GR_ad_1 // address of log(2) parts
859 (p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256
860 (p6) cmp.gt.unc p10,p0 = -80, GR_exp_x // Is |x| < 2^-80
861 }
862 { .mfb
863 (p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the
864 // significand field of FR_N
865 (p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
866 (p12) br.ret.spnt b0 // exit for x=0, return x
867 }
868 ;;
870 { .mib
871 (p7) ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16
872 (p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
873 (p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1
874 }
875 ;;
877 { .mmf
878 (p7) shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi
879 (p7) shladd GR_ad_1 = GR_Ind,2,GR_ad_1 // address of Tlo
880 (p10) fnma.d.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x
881 }
882 ;;
884 { .mmb
885 (p7) ldfd FR_Thi = [GR_ad_2]
886 (p7) ldfs FR_Tlo = [GR_ad_1]
887 (p10) br.ret.spnt b0 // Exit if |x| < 2^(-80)
888 }
889 ;;
891 { .mfi
892 nop.m 0
893 fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
894 nop.i 0
895 }
896 { .mfi
897 nop.m 0
898 fms.s1 FR_A2 = FR_A3,FR_r,FR_A2 // A3*r+A2
899 nop.i 0
900 }
901 ;;
903 { .mfi
904 nop.m 0
905 fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6
906 nop.i 0
907 }
908 { .mfi
909 nop.m 0
910 fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4
911 nop.i 0
912 }
913 ;;
915 { .mfi
916 nop.m 0
917 (p7) fcvt.xf FR_N = FR_N
918 nop.i 0
919 }
920 ;;
922 { .mfi
923 nop.m 0
924 fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4
925 nop.i 0
926 }
927 { .mfi
928 nop.m 0
929 // (A3*r+A2)*r^2+r
930 fma.s1 FR_A2 = FR_A2,FR_r2,FR_r
931 nop.i 0
932 }
933 ;;
935 { .mfi
936 nop.m 0
937 // (A7*r+A6)*r^2+(A5*r+A4)
938 fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4
939 nop.i 0
940 }
941 ;;
943 { .mfi
944 nop.m 0
945 // N*Ln2hi+Thi
946 (p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi
947 nop.i 0
948 }
949 { .mfi
950 nop.m 0
951 // N*Ln2lo+Tlo
952 (p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo
953 nop.i 0
954 }
955 ;;
957 { .mfi
958 nop.m 0
959 (p7) fma.s1 f8 = FR_A4,FR_r4,FR_A2 // P(r) if |x| >= 1/256
960 nop.i 0
961 }
962 { .mfi
963 nop.m 0
964 // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo)
965 (p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo
966 nop.i 0
967 }
968 ;;
970 .pred.rel "mutex",p6,p7
971 { .mfi
972 nop.m 0
973 (p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A2 // result if 2^(-80) <= |x| < 1/256
974 nop.i 0
975 }
976 { .mfb
977 nop.m 0
978 (p7) fma.d.s0 f8 = f8,f1,FR_NxLn2pT // result if |x| >= 1/256
979 br.ret.sptk b0 // Exit if |x| >= 2^(-80)
980 }
981 ;;
983 .align 32
984 log1p_unorm:
985 // Here if x=unorm
986 { .mfb
987 getf.exp GR_signexp_x = FR_NormX // recompute biased exponent
988 nop.f 0
989 br.cond.sptk log1p_common
990 }
991 ;;
993 .align 32
994 log1p_eq_minus_1:
995 // Here if x=-1
996 { .mfi
997 nop.m 0
998 fmerge.s FR_X = f8,f8 // keep input argument for subsequent
999 // call of __libm_error_support#
1000 nop.i 0
1001 }
1002 ;;
1004 { .mfi
1005 mov GR_TAG = 140 // set libm error in case of log1p(-1).
1006 frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
1007 // We can get it using frcpa because it
1008 // sets result to the IEEE-754 mandated
1009 // quotient of f8/f0.
1010 nop.i 0
1011 }
1012 { .mib
1013 nop.m 0
1014 nop.i 0
1015 br.cond.sptk log_libm_err
1016 }
1017 ;;
1019 .align 32
1020 log1p_lt_minus_1:
1021 // Here if x < -1
1022 { .mfi
1023 nop.m 0
1024 fmerge.s FR_X = f8,f8
1025 nop.i 0
1026 }
1027 ;;
1029 { .mfi
1030 mov GR_TAG = 141 // set libm error in case of x < -1.
1031 frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN.
1032 // We can get it using frcpa because it
1033 // sets result to the IEEE-754 mandated
1034 // quotient of f0/f0 i.e. NaN.
1035 nop.i 0
1036 }
1037 ;;
1039 .align 32
1040 log_libm_err:
1041 { .mmi
1042 alloc r32 = ar.pfs,1,4,4,0
1043 mov GR_Parameter_TAG = GR_TAG
1044 nop.i 0
1045 }
1046 ;;
1048 GLOBAL_IEEE754_END(log1p)
1050 LOCAL_LIBM_ENTRY(__libm_error_region)
1051 .prologue
1052 { .mfi
1053 add GR_Parameter_Y = -32,sp // Parameter 2 value
1054 nop.f 0
1055 .save ar.pfs,GR_SAVE_PFS
1056 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs
1057 }
1058 { .mfi
1059 .fframe 64
1060 add sp = -64,sp // Create new stack
1061 nop.f 0
1062 mov GR_SAVE_GP = gp // Save gp
1063 };;
1064 { .mmi
1065 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
1066 add GR_Parameter_X = 16,sp // Parameter 1 address
1067 .save b0, GR_SAVE_B0
1068 mov GR_SAVE_B0 = b0 // Save b0
1069 };;
1070 .body
1071 { .mib
1072 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
1073 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1074 nop.b 0
1075 }
1076 { .mib
1077 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
1078 add GR_Parameter_Y = -16,GR_Parameter_Y
1079 br.call.sptk b0=__libm_error_support# // Call error handling function
1080 };;
1081 { .mmi
1082 add GR_Parameter_RESULT = 48,sp
1083 nop.m 0
1084 nop.i 0
1085 };;
1086 { .mmi
1087 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
1088 .restore sp
1089 add sp = 64,sp // Restore stack pointer
1090 mov b0 = GR_SAVE_B0 // Restore return address
1091 };;
1092 { .mib
1093 mov gp = GR_SAVE_GP // Restore gp
1094 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1095 br.ret.sptk b0 // Return
1096 };;
1097 LOCAL_LIBM_END(__libm_error_region)
1099 .type __libm_error_support#,@function
1100 .global __libm_error_support#