| blob | 1799e4c1c2800856918bad82caf4ed80fb639130 |
1 .file "logf.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 // WARRANTY DISCLAIMER
10 //
11 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
12 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
13 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
14 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
15 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
16 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
17 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
18 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
19 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
20 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
21 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
22 //
23 // Intel Corporation is the author of this code, and requests that all
24 // problem reports or change requests be submitted to it directly at
25 // http://developer.intel.com/opensource.
26 //
27 // History
28 //==============================================================
29 // 3/01/00 Initial version
30 // 8/15/00 Bundle added after call to __libm_error_support to properly
31 // set [the previously overwritten] GR_Parameter_RESULT.
32 // 1/10/01 Improved speed, fixed flags for neg denormals
33 //
34 //
35 // API
36 //==============================================================
37 // float logf(float)
38 // float log10f(float)
39 //
40 // Overview of operation
41 //==============================================================
42 // Background
43 //
44 // Consider x = 2^N 1.f1 f2 f3 f4...f63
45 // Log(x) = log(frcpa(x) x/frcpa(x))
46 // = log(1/frcpa(x)) + log(frcpa(x) x)
47 // = -log(frcpa(x)) + log(frcpa(x) x)
48 //
49 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
50 //
51 // -log(frcpa(x)) = -log(C)
52 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
53 //
54 // -log(frcpa(x)) = -log(C)
55 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
56 //
57 // -log(frcpa(x)) = -log(C)
58 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
59 //
60 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
62 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
63 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
64 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
65 //
66 // Log(x) = +Nlog2 + T + log(C x)
67 //
68 // Cx = 1 + r
69 //
70 // Log(x) = +Nlog2 + T + log(1+r)
71 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
72 //
73 // 1.f1 f2 ... f8 has 256 entries.
74 // They are 1 + k/2^8, k = 0 ... 255
75 // These 256 values are the table entries.
76 //
77 // Implementation
78 //===============
79 // CASE 1: |x-1| >= 2^-8
80 // C = frcpa(x)
81 // r = C * x - 1
82 //
83 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
84 //
85 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
86 // Nfloat = float(n) where n is the true unbiased exponent
87 // pre-index = f_1f_2....f_8
88 // index = pre_index * 16
89 // get the dxt table entry at index + offset = T
90 //
91 // result = (T + Nfloat * log(2)) + rseries
92 //
93 // The T table is calculated as follows
94 // Form x_k = 1 + k/2^8 where k goes from 0... 255
95 // y_k = frcpa(x_k)
96 // log(1/y_k) in quad and round to double
98 // CASE 2: |x-1| < 2^-6
99 // w = x - 1
100 //
101 // Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4
102 //
103 // result = wseries
105 // Special values
106 //==============================================================
109 // log(+0) = -inf
110 // log(-0) = -inf
112 // log(+qnan) = +qnan
113 // log(-qnan) = -qnan
114 // log(+snan) = +qnan
115 // log(-snan) = -qnan
117 // log(-n) = QNAN Indefinite
118 // log(-inf) = QNAN Indefinite
120 // log(+inf) = +inf
122 // Registers used
123 //==============================================================
124 // Floating Point registers used:
125 // f8, input
126 // f9 -> f15, f32 -> f47
128 // General registers used:
129 // r32 -> r51
131 // Predicate registers used:
132 // p6 -> p15
134 // p8 log base e
135 // p6 log base e special
136 // p9 used in the frcpa
137 // p13 log base e large W
138 // p14 log base e small w
140 // p7 log base 10
141 // p10 log base 10 large W
142 // p11 log base 10 small w
143 // p12 log base 10 special
145 #include "libm_support.h"
147 // Assembly macros
148 //==============================================================
150 log_int_Nfloat = f9
151 log_Nfloat = f10
153 log_P3 = f11
154 log_P2 = f12
155 log_P1 = f13
156 log_inv_ln10 = f14
157 log_log2 = f15
159 log_w = f32
160 log_T = f33
161 log_rp_p32 = f34
162 log_rp_p2 = f35
163 log_rp_p10 = f36
164 log_rsq = f37
165 log_T_plus_Nlog2 = f38
166 log_r = f39
167 log_C = f40
168 log_rp_q32 = f41
169 log_rp_q2 = f42
170 log_rp_q10 = f43
171 log_wsq = f44
172 log_Q = f45
173 log_inv_ln10 = f46
174 log_NORM_f8 = f47
176 // ===================================
178 log_GR_exp_17_ones = r33
179 log_GR_exp_16_ones = r34
180 log_GR_exp_f8 = r35
181 log_GR_signexp_f8 = r36
182 log_GR_true_exp_f8 = r37
183 log_GR_significand_f8 = r38
184 log_GR_index = r39
185 log_AD_1 = r40
186 log_GR_signexp_w = r41
187 log_GR_fff7 = r42
188 log_AD_2 = r43
189 log_GR_exp_w = r44
191 GR_SAVE_B0 = r45
192 GR_SAVE_GP = r46
193 GR_SAVE_PFS = r47
195 GR_Parameter_X = r48
196 GR_Parameter_Y = r49
197 GR_Parameter_RESULT = r50
198 log_GR_tag = r51
201 // Data tables
202 //==============================================================
204 #ifdef _LIBC
205 .rodata
206 #else
207 .data
208 #endif
210 .align 16
212 log_table_1:
213 ASM_TYPE_DIRECTIVE(log_table_1,@object)
214 data8 0xbfd0001008f39d59 // p3
215 data8 0x3fd5556073e0c45a // p2
216 ASM_SIZE_DIRECTIVE(log_table_1)
218 log_table_2:
219 ASM_TYPE_DIRECTIVE(log_table_2,@object)
220 data8 0xbfdffffffffaea15 // p1
221 data8 0x3fdbcb7b1526e50e // 1/ln10
222 data8 0x3fe62e42fefa39ef // Log(2)
223 data8 0x0 // pad
225 data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)
226 data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)
227 data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)
228 data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)
229 data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)
230 data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)
231 data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)
232 data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)
233 data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)
234 data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)
235 data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)
236 data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)
237 data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)
238 data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)
239 data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)
240 data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)
241 data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)
242 data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)
243 data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)
244 data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)
245 data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)
246 data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)
247 data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)
248 data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)
249 data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)
250 data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)
251 data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)
252 data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)
253 data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)
254 data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)
255 data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)
256 data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)
257 data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)
258 data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)
259 data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)
260 data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)
261 data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)
262 data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)
263 data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)
264 data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)
265 data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)
266 data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)
267 data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)
268 data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)
269 data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)
270 data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)
271 data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)
272 data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)
273 data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)
274 data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)
275 data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)
276 data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)
277 data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)
278 data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)
279 data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)
280 data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)
281 data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)
282 data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)
283 data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)
284 data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)
285 data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)
286 data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)
287 data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)
288 data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)
289 data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)
290 data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)
291 data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)
292 data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)
293 data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)
294 data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)
295 data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)
296 data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)
297 data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)
298 data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)
299 data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)
300 data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)
301 data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)
302 data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)
303 data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)
304 data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)
305 data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)
306 data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)
307 data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)
308 data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)
309 data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)
310 data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)
311 data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)
312 data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)
313 data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)
314 data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)
315 data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)
316 data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)
317 data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)
318 data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)
319 data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)
320 data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)
321 data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)
322 data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)
323 data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)
324 data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)
325 data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)
326 data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)
327 data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)
328 data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)
329 data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)
330 data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)
331 data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)
332 data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)
333 data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)
334 data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)
335 data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)
336 data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)
337 data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)
338 data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)
339 data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)
340 data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)
341 data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)
342 data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)
343 data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)
344 data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)
345 data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)
346 data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)
347 data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)
348 data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)
349 data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)
350 data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)
351 data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)
352 data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)
353 data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)
354 data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)
355 data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)
356 data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)
357 data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)
358 data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)
359 data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)
360 data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)
361 data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)
362 data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)
363 data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)
364 data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)
365 data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)
366 data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)
367 data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)
368 data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)
369 data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)
370 data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)
371 data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)
372 data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)
373 data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)
374 data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)
375 data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)
376 data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)
377 data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)
378 data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)
379 data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)
380 data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)
381 data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)
382 data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)
383 data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)
384 data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)
385 data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)
386 data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)
387 data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)
388 data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)
389 data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)
390 data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)
391 data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)
392 data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)
393 data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)
394 data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)
395 data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)
396 data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)
397 data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)
398 data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)
399 data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)
400 data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)
401 data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)
402 data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)
403 data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)
404 data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)
405 data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)
406 data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)
407 data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)
408 data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)
409 data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)
410 data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)
411 data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)
412 data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)
413 data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)
414 data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)
415 data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)
416 data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)
417 data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)
418 data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)
419 data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)
420 data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)
421 data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)
422 data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)
423 data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)
424 data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)
425 data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)
426 data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)
427 data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)
428 data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)
429 data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)
430 data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)
431 data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)
432 data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)
433 data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)
434 data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)
435 data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)
436 data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)
437 data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)
438 data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)
439 data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)
440 data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)
441 data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)
442 data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)
443 data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)
444 data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)
445 data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)
446 data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)
447 data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)
448 data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)
449 data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)
450 data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)
451 data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)
452 data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)
453 data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)
454 data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)
455 data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)
456 data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)
457 data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)
458 data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)
459 data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)
460 data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)
461 data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)
462 data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)
463 data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)
464 data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)
465 data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)
466 data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)
467 data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)
468 data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)
469 data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)
470 data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)
471 data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)
472 data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)
473 data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)
474 data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)
475 data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)
476 data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)
477 data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)
478 data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)
479 data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)
480 data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
481 ASM_SIZE_DIRECTIVE(log_table_2)
484 .align 32
485 .global logf#
486 .global log10f#
488 // log10 has p7 true, p8 false
489 // log has p8 true, p7 false
491 .section .text
492 .proc log10f#
493 .align 32
495 log10f:
496 #ifdef _LIBC
497 .global __ieee754_log10f
498 .type __ieee754_log10f,@function
499 __ieee754_log10f:
500 #endif
501 { .mfi
502 alloc r32=ar.pfs,1,15,4,0
503 frcpa.s1 log_C,p9 = f1,f8
504 cmp.eq.unc p7,p8 = r0, r0
505 }
506 { .mfb
507 addl log_AD_1 = @ltoff(log_table_1), gp
508 fnorm.s1 log_NORM_f8 = f8
509 br.sptk L(LOG_LOG10_X)
510 }
511 ;;
513 .endp log10f
514 ASM_SIZE_DIRECTIVE(log10f)
515 ASM_SIZE_DIRECTIVE(__ieee754_log10f)
519 .section .text
520 .proc logf#
521 .align 32
522 logf:
523 #ifdef _LIBC
524 .global __ieee754_logf
525 .type __ieee754_logf,@function
526 __ieee754_logf:
527 #endif
529 { .mfi
530 alloc r32=ar.pfs,1,15,4,0
531 frcpa.s1 log_C,p9 = f1,f8
532 cmp.eq.unc p8,p7 = r0, r0
533 }
534 { .mfi
535 addl log_AD_1 = @ltoff(log_table_1), gp
536 fnorm.s1 log_NORM_f8 = f8
537 nop.i 999
538 }
539 ;;
541 L(LOG_LOG10_X):
543 { .mfi
544 getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute
545 fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm
546 mov log_GR_fff7 = 0xfff7
547 }
548 { .mfi
549 ld8 log_AD_1 = [log_AD_1]
550 fms.s1 log_w = f8,f1,f1
551 mov log_GR_exp_17_ones = 0x1ffff
552 }
553 ;;
555 { .mmi
556 getf.sig log_GR_significand_f8 = f8 // If x unorm then must recompute
557 mov log_GR_exp_16_ones = 0xffff
558 nop.i 999
559 }
560 ;;
562 { .mmb
563 adds log_AD_2 = 0x10, log_AD_1
564 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
565 (p15) br.cond.spnt L(LOG_DENORM)
566 }
567 ;;
569 L(LOG_COMMON):
570 {.mfi
571 ldfpd log_P3,log_P2 = [log_AD_1],16
572 fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan
573 shl log_GR_index = log_GR_significand_f8,1
574 }
575 {.mfi
576 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
577 nop.f 999
578 nop.i 999
579 }
580 ;;
582 { .mfi
583 ldfpd log_P1,log_inv_ln10 = [log_AD_2],16
584 fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf
585 shr.u log_GR_index = log_GR_index,56
586 }
587 { .mfi
588 setf.sig log_int_Nfloat = log_GR_true_exp_f8
589 nop.f 999
590 nop.i 999
591 }
592 ;;
595 { .mfi
596 ldfd log_log2 = [log_AD_2],16
597 fma.s1 log_wsq = log_w, log_w, f0
598 nop.i 999
599 }
600 { .mfb
601 nop.m 999
602 (p6) fma.s.s0 f8 = f8,f1,f0 // quietize nan result if x=nan
603 (p6) br.ret.spnt b0 // Exit for x=nan
604 }
605 ;;
608 { .mfi
609 shladd log_AD_2 = log_GR_index,3,log_AD_2
610 fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0
611 nop.i 999
612 }
613 { .mfb
614 nop.m 999
615 fms.s1 log_r = log_C,f8,f1
616 (p11) br.ret.spnt b0 // Exit for x=+inf
617 }
618 ;;
621 { .mmf
622 nop.m 999
623 nop.m 999
624 fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0
625 }
626 ;;
629 { .mfb
630 ldfd log_T = [log_AD_2]
631 (p10) fmerge.s f8 = f0, f0
632 (p10) br.ret.spnt b0 // Exit for x=1.0
633 ;;
634 }
636 { .mfi
637 getf.exp log_GR_signexp_w = log_w
638 fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf
639 nop.i 999
640 }
641 ;;
643 { .mmb
644 nop.m 999
645 nop.m 999
646 (p6) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x=0
647 ;;
648 }
651 { .mfi
652 and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w
653 nop.f 999
654 nop.i 999
655 }
656 { .mfb
657 nop.m 999
658 fma.s1 log_rsq = log_r, log_r, f0
659 (p12) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x<0
660 ;;
661 }
663 { .mfi
664 nop.m 999
665 fma.s1 log_rp_p32 = log_P3, log_r, log_P2
666 nop.i 999
667 }
668 { .mfi
669 nop.m 999
670 fma.s1 log_rp_q32 = log_P3, log_w, log_P2
671 nop.i 999
672 ;;
673 }
675 { .mfi
676 nop.m 999
677 fcvt.xf log_Nfloat = log_int_Nfloat
678 nop.i 999 ;;
679 }
681 { .mfi
682 nop.m 999
683 fma.s1 log_rp_p10 = log_P1, log_r, f1
684 nop.i 999
685 }
686 { .mfi
687 nop.m 999
688 fma.s1 log_rp_q10 = log_P1, log_w, f1
689 nop.i 999
690 ;;
691 }
693 // p13 <== large w log
694 // p14 <== small w log
695 { .mfi
696 (p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff7
697 fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input
698 nop.i 999
699 ;;
700 }
702 // p10 <== large w log10
703 // p11 <== small w log10
704 { .mfi
705 (p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7
706 nop.f 999
707 nop.i 999 ;;
708 }
710 { .mfi
711 nop.m 999
712 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T
713 nop.i 999 ;;
714 }
717 { .mfi
718 nop.m 999
719 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
720 nop.i 999
721 }
722 { .mfi
723 nop.m 999
724 fma.s1 log_rp_q2 = log_rp_q32, log_wsq, log_rp_q10
725 nop.i 999
726 ;;
727 }
730 // small w, log <== p14
731 { .mfi
732 nop.m 999
733 (p14) fma.s f8 = log_rp_q2, log_w, f0
734 nop.i 999
735 }
736 { .mfi
737 nop.m 999
738 (p11) fma.s1 log_Q = log_rp_q2, log_w, f0
739 nop.i 999 ;;
740 }
743 // large w, log <== p13
744 .pred.rel "mutex",p13,p10
745 { .mfi
746 nop.m 999
747 (p13) fma.s f8 = log_rp_p2, log_r, log_T_plus_Nlog2
748 nop.i 999
749 }
750 { .mfi
751 nop.m 999
752 (p10) fma.s1 log_Q = log_rp_p2, log_r, log_T_plus_Nlog2
753 nop.i 999 ;;
754 }
757 // log10
758 { .mfb
759 nop.m 999
760 (p7) fma.s f8 = log_inv_ln10,log_Q,f0
761 br.ret.sptk b0
762 ;;
763 }
766 L(LOG_DENORM):
767 { .mmi
768 getf.exp log_GR_signexp_f8 = log_NORM_f8
769 nop.m 999
770 nop.i 999
771 }
772 ;;
773 { .mmb
774 getf.sig log_GR_significand_f8 = log_NORM_f8
775 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
776 br.cond.sptk L(LOG_COMMON)
777 }
778 ;;
780 L(LOG_ZERO_NEG):
782 // qnan snan inf norm unorm 0 -+
783 // 0 0 0 0 0 1 11 0x7
784 // 0 0 1 1 1 0 10 0x3a
786 // Save x (f8) in f10
787 { .mfi
788 nop.m 999
789 fmerge.s f10 = f8,f8
790 nop.i 999 ;;
791 }
793 // p8 p9 means ln(+-0) = -inf
794 // p7 p10 means log(+-0) = -inf
796 // p13 means ln(-)
797 // p14 means log(-)
800 { .mfi
801 nop.m 999
802 fmerge.ns f6 = f1,f1 // Form -1.0
803 nop.i 999 ;;
804 }
806 // p9 means ln(+-0) = -inf
807 // p10 means log(+-0) = -inf
808 // Log(+-0) = -inf
810 { .mfi
811 nop.m 999
812 (p8) fclass.m.unc p9,p0 = f10, 0x07
813 nop.i 999
814 }
815 { .mfi
816 nop.m 999
817 (p7) fclass.m.unc p10,p0 = f10, 0x07
818 nop.i 999 ;;
819 }
822 // p13 ln(-)
823 // p14 log(-)
825 // Log(-inf, -normal, -unnormal) = QNAN indefinite
826 { .mfi
827 nop.m 999
828 (p8) fclass.m.unc p13,p0 = f10, 0x3a
829 nop.i 999
830 }
831 { .mfi
832 nop.m 999
833 (p7) fclass.m.unc p14,p0 = f10, 0x3a
834 nop.i 999 ;;
835 }
838 .pred.rel "mutex",p9,p10
839 { .mfi
840 (p9) mov log_GR_tag = 4
841 (p9) frcpa f8,p11 = f6,f0
842 nop.i 999
843 }
844 { .mfi
845 (p10) mov log_GR_tag = 10
846 (p10) frcpa f8,p12 = f6,f0
847 nop.i 999 ;;
848 }
850 .pred.rel "mutex",p13,p14
851 { .mfi
852 (p13) mov log_GR_tag = 5
853 (p13) frcpa f8,p11 = f0,f0
854 nop.i 999
855 }
856 { .mfb
857 (p14) mov log_GR_tag = 11
858 (p14) frcpa f8,p12 = f0,f0
859 br.cond.sptk __libm_error_region ;;
860 }
861 .endp logf
862 ASM_SIZE_DIRECTIVE(logf)
863 ASM_SIZE_DIRECTIVE(__ieee754_logf)
866 // Stack operations when calling error support.
867 // (1) (2) (3) (call) (4)
868 // sp -> + psp -> + psp -> + sp -> +
869 // | | | |
870 // | | <- GR_Y R3 ->| <- GR_RESULT | -> f8
871 // | | | |
872 // | <-GR_Y Y2->| Y2 ->| <- GR_Y |
873 // | | | |
874 // | | <- GR_X X1 ->| |
875 // | | | |
876 // sp-64 -> + sp -> + sp -> + +
877 // save ar.pfs save b0 restore gp
878 // save gp restore ar.pfs
882 .proc __libm_error_region
883 __libm_error_region:
884 .prologue
886 // (1)
887 { .mfi
888 add GR_Parameter_Y=-32,sp // Parameter 2 value
889 nop.f 0
890 .save ar.pfs,GR_SAVE_PFS
891 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
892 }
893 { .mfi
894 .fframe 64
895 add sp=-64,sp // Create new stack
896 nop.f 0
897 mov GR_SAVE_GP=gp // Save gp
898 };;
901 // (2)
902 { .mmi
903 stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
904 add GR_Parameter_X = 16,sp // Parameter 1 address
905 .save b0, GR_SAVE_B0
906 mov GR_SAVE_B0=b0 // Save b0
907 };;
909 .body
910 // (3)
911 { .mib
912 stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
913 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
914 nop.b 0
915 }
916 { .mib
917 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
918 add GR_Parameter_Y = -16,GR_Parameter_Y
919 br.call.sptk b0=__libm_error_support# // Call error handling function
920 };;
922 { .mmi
923 nop.m 0
924 nop.m 0
925 add GR_Parameter_RESULT = 48,sp
926 };;
928 // (4)
929 { .mmi
930 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
931 .restore sp
932 add sp = 64,sp // Restore stack pointer
933 mov b0 = GR_SAVE_B0 // Restore return address
934 };;
935 { .mib
936 mov gp = GR_SAVE_GP // Restore gp
937 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
938 br.ret.sptk b0 // Return
939 };;
941 .endp __libm_error_region
942 ASM_SIZE_DIRECTIVE(__libm_error_region)
945 .type __libm_error_support#,@function
946 .global __libm_error_support#