| blob | 7eba39eb40b0058ba5e10b4840aa7ab34a48eb9d |
1 .file "asinh.s"
4 // Copyright (c) 2000 - 2005, 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 // ==============================================================
41 // History
42 // ==============================================================
43 // 04/02/01 Initial version
44 // 04/19/01 Improved speed of the paths #1,2,3,4,5
45 // 10/18/01 Improved accuracy
46 // 05/20/02 Cleaned up namespace and sf0 syntax
47 // 02/06/03 Reordered header: .section, .global, .proc, .align
48 // 05/21/03 Improved performance, fixed to handle unorms
49 // 03/31/05 Reformatted delimiters between data tables
50 //
51 // API
52 // ==============================================================
53 // double asinh(double)
54 //
55 // Overview of operation
56 // ==============================================================
57 //
58 // There are 7 paths:
59 // 1. x = 0.0
60 // Return asinh(x) = 0.0
61 //
62 // 2. 0.0 <|x| < 2^(-3)
63 // Return asinh(x) = POL13(x),
64 // where POL13(x) = (x^2*C13 + ...)*x^2 + C5)*x^2 + C3)*x^3 + x
65 //
66 // 3. 2^(-3) <= |x| < 2^63
67 // Return asinh(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
68 // To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
69 // (3 iterations)
70 // Algorithm description for log function see below.
71 //
72 // 4. 2^63 <= |x| < +INF
73 // Return asinh(x) = sign(x)*log(2*|x|)
74 // Algorithm description for log function see below.
75 //
76 // 5. x = INF
77 // Return asinh(x) = INF
78 //
79 // 6. x = [S,Q]NaN
80 // Return asinh(x) = QNaN
81 //
82 // 7. x = denormal
83 // Return asinh(x) = x correctly rounded
84 //
85 //==============================================================
86 // Algorithm Description for log(x) function
87 // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
88 // true for this asinh implementation
89 //
90 // Consider x = 2^N 1.f1 f2 f3 f4...f63
91 // Log(x) = log(frcpa(x) x/frcpa(x))
92 // = log(1/frcpa(x)) + log(frcpa(x) x)
93 // = -log(frcpa(x)) + log(frcpa(x) x)
94 //
95 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
96 //
97 // -log(frcpa(x)) = -log(C)
98 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
99 //
100 // -log(frcpa(x)) = -log(C)
101 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
102 //
103 // -log(frcpa(x)) = -log(C)
104 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
105 //
106 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
107 //
108 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
109 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
110 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
111 //
112 // Log(x) = +Nlog2 + T + log(C x)
113 //
114 // Cx = 1 + r
115 //
116 // Log(x) = +Nlog2 + T + log(1+r)
117 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
118 //
119 // 1.f1 f2 ... f8 has 256 entries.
120 // They are 1 + k/2^8, k = 0 ... 255
121 // These 256 values are the table entries.
122 //
123 // Implementation
124 //==============================================================
125 // C = frcpa(x)
126 // r = C * x - 1
127 //
128 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
129 //
130 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
131 // Nfloat = float(n) where n is the true unbiased exponent
132 // pre-index = f_1f_2....f_8
133 // index = pre_index * 16
134 // get the dxt table entry at index + offset = T
135 //
136 // result = (T + Nfloat * log(2)) + rseries
137 //
138 // The T table is calculated as follows
139 // Form x_k = 1 + k/2^8 where k goes from 0... 255
140 // y_k = frcpa(x_k)
141 // log(1/y_k) in quad and round to double-extended
142 //
143 //
144 // Registers used
145 //==============================================================
146 // Floating Point registers used:
147 // f8, input
148 // f9 -> f15, f32 -> f68
150 // General registers used:
151 // r14 -> r27
153 // Predicate registers used:
154 // p6 -> p14
156 // p6 to filter out case when x = [Q,S]NaN or INF or zero
157 // p7 to filter out case when x < 0.0
158 // p8 to select path #2
159 // p9 used in the frcpa from path #3
160 // p11 to filter out case when x >= 0
161 // p12 to filter out case when x = unorm
162 // p13 to select path #4
163 // Assembly macros
164 //==============================================================
165 log_GR_exp_17_ones = r14
166 log_GR_signexp_f8 = r15
167 log_table_address2 = r16
168 log_GR_exp_16_ones = r17
169 log_GR_exp_f8 = r18
170 log_GR_true_exp_f8 = r19
171 log_GR_significand_f8 = r20
172 log_GR_index = r21
173 log_GR_comp2 = r22
174 asinh_GR_f8 = r23
175 asinh_GR_comp = r24
176 asinh_GR_f8 = r25
177 log_table_address3 = r26
178 NR_table_address = r27
180 //==============================================================
181 log_y = f9
182 NR1 = f10
183 NR2 = f11
184 log_y_rs = f12
185 log_y_rs_iter = f13
186 log_y_rs_iter1 = f14
187 fNormX = f15
188 asinh_w_sq = f32
189 log_C13 = f33
190 log_C11 = f34
191 log_P3 = f35
192 log_P2 = f36
193 log_P1 = f37
194 log_P5 = f38
195 log_P4 = f39
196 log_C3 = f40
197 log_C5 = f41
198 log_C7 = f42
199 log2 = f43
200 asinh_f8 = f44
201 log_C = f45
202 log_arg = f46
203 log_C9 = f47
204 asinh_w_four = f48
205 log_int_Nfloat = f49
206 log_r = f50
207 log_rsq = f51
208 log_rp_p4 = f52
209 log_rp_p32 = f53
210 log_rcube = f54
211 log_rp_p10 = f55
212 log_rp_p2 = f56
213 log_Nfloat = f57
214 log_T = f58
215 log_r2P_r = f59
216 log_T_plus_Nlog2 = f60
217 asinh_w_3 = f61
218 asinh_w_5 = f62
219 asinh_w_cube = f63
220 asinh_w_7 = f64
221 log_arg_early = f65
222 asinh_w_9 = f66
223 asinh_w_13 = f67
224 asinh_w_seven = f68
226 // Data tables
227 //==============================================================
229 RODATA
230 .align 16
232 LOCAL_OBJECT_START(log_table_1)
233 data8 0xBFC5555DA7212371 // P5
234 data8 0x3FC999A19EEF5826 // P4
235 data8 0xBFCFFFFFFFFEF009 // P3
236 data8 0x3FD555555554ECB2 // P2
237 data8 0xBFE0000000000000 // P1 = -0.5
238 data8 0x0000000000000000 // pad
239 data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
240 LOCAL_OBJECT_END(log_table_1)
242 LOCAL_OBJECT_START(log_table_2)
243 data8 0x3FE0000000000000 // 0.5
244 data8 0x4008000000000000 // 3.0
245 //
246 data8 0x8824BE4D74BC4F00, 0x00003FF9 // C13
247 data8 0xB725A2CD9556CC57, 0x0000BFF9 // C11
248 data8 0xF8E339127FBFF49D, 0x00003FF9 // C9
249 data8 0xB6DB6D7DCE17CB78, 0x0000BFFA // C7
250 data8 0x999999998802CCEF, 0x00003FFB // C5
251 data8 0xAAAAAAAAAAA8DC40, 0x0000BFFC // C3
252 LOCAL_OBJECT_END(log_table_2)
255 LOCAL_OBJECT_START(log_table_3)
256 data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
257 //
258 data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
259 data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
260 data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
261 data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
262 data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
263 //
264 data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
265 data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
266 data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
267 data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
268 data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
269 //
270 data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
271 data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
272 data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
273 data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
274 data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
275 //
276 data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
277 data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
278 data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
279 data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
280 data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
281 //
282 data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
283 data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
284 data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
285 data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
286 data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
287 //
288 data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
289 data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
290 data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
291 data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
292 data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
293 //
294 data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
295 data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
296 data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
297 data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
298 data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
299 //
300 data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
301 data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
302 data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
303 data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
304 data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
305 //
306 data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
307 data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
308 data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
309 data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
310 data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
311 //
312 data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
313 data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
314 data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
315 data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
316 data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
317 //
318 data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
319 data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
320 data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
321 data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
322 data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
323 //
324 data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
325 data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
326 data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
327 data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
328 data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
329 //
330 data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
331 data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
332 data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
333 data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
334 data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
335 //
336 data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
337 data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
338 data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
339 data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
340 data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
341 //
342 data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
343 data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
344 data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
345 data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
346 data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
347 //
348 data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
349 data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
350 data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
351 data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
352 data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
353 //
354 data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
355 data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
356 data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
357 data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
358 data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
359 //
360 data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
361 data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
362 data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
363 data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
364 data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
365 //
366 data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
367 data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
368 data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
369 data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
370 data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
371 //
372 data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
373 data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
374 data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
375 data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
376 data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
377 //
378 data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
379 data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
380 data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
381 data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
382 data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
383 //
384 data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
385 data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
386 data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
387 data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
388 data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
389 //
390 data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
391 data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
392 data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
393 data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
394 data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
395 //
396 data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
397 data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
398 data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
399 data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
400 data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
401 //
402 data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
403 data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
404 data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
405 data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
406 data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
407 //
408 data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
409 data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
410 data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
411 data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
412 data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
413 //
414 data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
415 data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
416 data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
417 data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
418 data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
419 //
420 data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
421 data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
422 data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
423 data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
424 data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
425 //
426 data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
427 data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
428 data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
429 data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
430 data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
431 //
432 data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
433 data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
434 data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
435 data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
436 data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
437 //
438 data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
439 data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
440 data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
441 data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
442 data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
443 //
444 data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
445 data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
446 data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
447 data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
448 data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
449 //
450 data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
451 data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
452 data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
453 data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
454 data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
455 //
456 data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
457 data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
458 data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
459 data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
460 data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
461 //
462 data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
463 data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
464 data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
465 data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
466 data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
467 //
468 data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
469 data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
470 data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
471 data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
472 data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
473 //
474 data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
475 data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
476 data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
477 data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
478 data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
479 //
480 data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
481 data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
482 data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
483 data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
484 data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
485 //
486 data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
487 data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
488 data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
489 data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
490 data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
491 //
492 data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
493 data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
494 data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
495 data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
496 data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
497 //
498 data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
499 data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
500 data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
501 data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
502 data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
503 //
504 data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
505 data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
506 data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
507 data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
508 data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
509 //
510 data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
511 data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
512 data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
513 data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
514 data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
515 //
516 data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
517 data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
518 data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
519 data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
520 data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
521 //
522 data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
523 data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
524 data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
525 data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
526 data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
527 //
528 data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
529 data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
530 data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
531 data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
532 data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
533 //
534 data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
535 data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
536 data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
537 data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
538 data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
539 //
540 data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
541 data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
542 data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
543 data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
544 data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
545 //
546 data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
547 data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
548 data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
549 data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
550 data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
551 //
552 data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
553 data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
554 data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
555 data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
556 data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
557 //
558 data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
559 data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
560 data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
561 data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
562 data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
563 LOCAL_OBJECT_END(log_table_3)
566 .section .text
567 GLOBAL_LIBM_ENTRY(asinh)
569 { .mfi
570 getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
571 fclass.m p12,p0 = f8, 0x0b // Test x unorm
572 mov log_GR_exp_17_ones = 0x1ffff
573 }
574 { .mfi
575 addl NR_table_address = @ltoff(log_table_1), gp
576 fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
577 mov asinh_GR_comp = 0xfffc
578 }
579 ;;
581 { .mfi
582 mov log_GR_exp_16_ones = 0xffff //BIAS
583 fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
584 mov log_GR_comp2 = 0x1003e
585 }
586 { .mfi
587 ld8 NR_table_address = [NR_table_address]
588 fma.s1 asinh_w_sq = f8,f8,f0 // x^2
589 nop.i 0
590 }
591 ;;
593 { .mfi
594 nop.m 0
595 fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
596 nop.i 0
597 }
598 { .mfb
599 nop.m 0
600 fnorm.s1 fNormX = f8 // Normalize x
601 (p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
602 }
603 ;;
605 ASINH_COMMON:
606 // Return here if x=unorm and not denorm
607 { .mfi
608 //to get second table address
609 adds log_table_address2 = 0x40, NR_table_address
610 fma.s1 log_arg = f8,f1,f8
611 nop.i 0
612 }
613 { .mfb
614 nop.m 0
615 (p6) fma.d.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
616 (p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
617 }
618 ;;
620 { .mfi
621 ldfpd NR1,NR2 = [log_table_address2],16
622 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
623 nop.i 0
624 }
625 ;;
627 { .mfi
628 ldfe log_C13 = [log_table_address2],16
629 nop.f 0
630 and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
631 }
632 ;;
634 { .mib
635 ldfe log_C11 = [log_table_address2],16
636 cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
637 (p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, |x| >= 2^63
638 }
639 ;;
641 { .mfi
642 nop.m 0
643 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
644 nop.i 0
645 }
646 ;;
648 .pred.rel "mutex",p7,p11
649 { .mfi
650 nop.m 0
651 (p11) mov asinh_f8 = fNormX
652 nop.i 0
653 }
654 { .mfb
655 cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
656 (p7) fnma.s1 asinh_f8 = fNormX,f1,f0
657 (p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2, 0 < |x| < 2^-3
658 }
659 ;;
661 // Here if main path, 2^-3 <= |x| < 2^63
662 ///////////////////////////////// The first iteration /////////////////////////
663 { .mfi
664 ldfpd log_P5,log_P4 = [NR_table_address],16
665 fnma.s1 log_y_rs_iter = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
666 nop.i 0
667 }
668 { .mfi
669 nop.m 0
670 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
671 nop.i 0
672 }
673 ;;
675 { .mfi
676 ldfpd log_P3,log_P2 = [NR_table_address],16
677 // (0.5*z)*(3-(y*z)*z)
678 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter,f0
679 nop.i 0
680 }
681 ;;
683 /////////////////////////// The second iteration /////////////////////////////
684 { .mfi
685 ldfd log_P1 = [NR_table_address],16
686 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
687 nop.i 0
688 }
689 ;;
691 { .mfi
692 nop.m 0
693 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
694 nop.i 0
695 }
696 { .mfi
697 nop.m 0
698 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
699 nop.i 0
700 }
701 ;;
703 { .mfi
704 ldfe log2 = [NR_table_address],16
705 // (0.5*z)*(3-(y*z)*z)
706 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs,f0
707 nop.i 0
708 }
709 { .mfi
710 nop.m 0
711 // (0.5*z)*(3-(y*z)*z)
712 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs,f0
713 nop.i 0
714 }
715 ;;
717 ////////////////////////////////// The third iteration ////////////////////////
718 { .mfi
719 nop.m 0
720 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
721 nop.i 0
722 }
723 { .mfi
724 nop.m 0
725 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
726 nop.i 0
727 }
728 ;;
730 { .mfi
731 nop.m 0
732 fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
733 nop.i 0
734 }
735 ;;
737 { .mfi
738 nop.m 0
739 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
740 nop.i 0
741 }
742 { .mfi
743 nop.m 0
744 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
745 nop.i 0
746 }
747 ;;
749 { .mfi
750 nop.m 0
751 frcpa.s1 log_C,p0 = f1,log_arg_early
752 nop.i 0
753 }
754 ;;
756 { .mfi
757 getf.exp log_GR_signexp_f8 = log_arg_early
758 nop.f 0
759 nop.i 0
760 }
761 ;;
763 { .mfi
764 getf.sig log_GR_significand_f8 = log_arg_early
765 // (0.5*z)*(3-(y*z)*z)*y + |x|
766 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
767 //to get third table address
768 adds log_table_address3 = 0x70, NR_table_address
769 }
770 ;;
772 ///////////////////////////////// The end NR iterations /////////////////////
773 { .mfi
774 nop.m 0
775 nop.f 0
776 //significant bit destruction
777 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
778 }
779 ;;
781 { .mfi
782 //BIAS subtraction
783 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
784 (p7) fnma.s1 log2 = log2,f1,f0
785 nop.i 0
786 }
787 ;;
789 { .mfi
790 setf.sig log_int_Nfloat = log_GR_true_exp_f8
791 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
792 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
793 }
794 ;;
796 { .mmi
797 //pre-index*16 + index
798 shladd log_table_address3 = log_GR_index,4,log_table_address3
799 ;;
800 ldfe log_T = [log_table_address3]
801 nop.i 0
802 }
803 ;;
805 { .mfi
806 nop.m 0
807 fma.s1 log_rsq = log_r, log_r, f0 //r^2
808 nop.i 0
809 }
810 { .mfi
811 nop.m 0
812 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
813 nop.i 0
814 }
815 ;;
817 { .mfi
818 nop.m 0
819 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
820 nop.i 0
821 }
822 ;;
824 { .mfi
825 nop.m 0
826 //convert N to the floating-point format
827 fcvt.xf log_Nfloat = log_int_Nfloat
828 nop.i 0
829 }
830 ;;
832 { .mfi
833 nop.m 0
834 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
835 nop.i 0
836 }
837 { .mfi
838 nop.m 0
839 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
840 nop.i 0
841 }
842 ;;
844 { .mfi
845 nop.m 0
846 //(P5*r + P4)*r^2 + P3*r + P2
847 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
848 nop.i 0
849 }
850 ;;
852 .pred.rel "mutex",p7,p11
853 { .mfi
854 nop.m 0
855 (p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
856 nop.i 0
857 }
858 { .mfi
859 nop.m 0
860 (p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
861 nop.i 0
862 }
863 ;;
865 { .mfi
866 nop.m 0
867 //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
868 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
869 nop.i 0
870 }
871 ;;
873 { .mfi
874 nop.m 0
875 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
876 (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
877 nop.i 0
878 }
879 { .mfb
880 nop.m 0
881 // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
882 (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
883 br.ret.sptk b0 // Exit main path, path 3: 2^-3 <= |x| < 2^63
884 }
885 ;;
887 // Here if path 4, |x| >= 2^63
888 LOG_COMMON1:
889 { .mfi
890 ldfpd log_P5,log_P4 = [NR_table_address],16
891 nop.f 0
892 nop.i 0
893 }
894 ;;
896 { .mfi
897 ldfpd log_P3,log_P2 = [NR_table_address],16
898 frcpa.s1 log_C,p0 = f1,log_arg
899 nop.i 0
900 }
901 ;;
903 { .mmi
904 getf.exp log_GR_signexp_f8 = log_arg
905 ldfd log_P1 = [NR_table_address],16
906 nop.i 0
907 }
908 ;;
910 { .mmi
911 getf.sig log_GR_significand_f8 = log_arg
912 ldfe log2 = [NR_table_address],16
913 nop.i 0
914 }
915 ;;
917 { .mfi
918 adds log_table_address3 = 0x70, NR_table_address
919 nop.f 0
920 //significant bit destruction
921 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
922 }
923 ;;
925 { .mmf
926 nop.m 0
927 //BIAS subtraction
928 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
929 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
930 }
931 ;;
933 { .mfi
934 setf.sig log_int_Nfloat = log_GR_true_exp_f8
935 nop.f 0
936 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
937 }
938 ;;
940 { .mmi
941 //pre-index*16 + index
942 shladd log_table_address3 = log_GR_index,4,log_table_address3
943 ;;
944 ldfe log_T = [log_table_address3]
945 nop.i 0
947 }
948 ;;
950 { .mfi
951 nop.m 0
952 fma.s1 log_rsq = log_r, log_r, f0 //r^2
953 nop.i 0
954 }
955 { .mfi
956 nop.m 0
957 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
958 nop.i 0
959 }
960 ;;
962 { .mfi
963 nop.m 0
964 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
965 nop.i 0
966 }
967 { .mfi
968 nop.m 0
969 (p7) fnma.s1 log2 = log2,f1,f0
970 nop.i 0
971 }
972 ;;
974 { .mfi
975 nop.m 0
976 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
977 nop.i 0
978 }
979 { .mfi
980 nop.m 0
981 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
982 nop.i 0
983 }
984 ;;
986 { .mfi
987 nop.m 0
988 //convert N to the floating-point format
989 fcvt.xf log_Nfloat = log_int_Nfloat
990 nop.i 0
991 }
992 { .mfi
993 nop.m 0
994 //(P5*r + P4)*r^2 + P3*r + P2
995 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
996 nop.i 0
997 }
998 ;;
1000 { .mfi
1001 nop.m 0
1002 (p7) fnma.s1 log_T = log_T,f1,f0
1003 nop.i 0
1004 }
1005 ;;
1007 { .mfi
1008 nop.m 0
1009 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
1010 nop.i 0
1011 }
1012 { .mfi
1013 nop.m 0
1014 //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
1015 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
1016 nop.i 0
1017 }
1018 ;;
1020 .pred.rel "mutex",p7,p11
1021 { .mfi
1022 nop.m 0
1023 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
1024 (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
1025 nop.i 0
1026 }
1027 { .mfb
1028 nop.m 0
1029 // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
1030 (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
1031 br.ret.sptk b0 // Exit path 4, |x| >= 2^63
1032 }
1033 ;;
1035 // Here is path 2, 0 < |x| < 2^-3
1036 ASINH_NEAR_ZERO:
1037 { .mfi
1038 ldfe log_C9 = [log_table_address2],16
1039 fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
1040 nop.i 0
1041 }
1042 ;;
1044 { .mfi
1045 ldfe log_C7 = [log_table_address2],16
1046 fma.s1 asinh_w_four = asinh_w_sq,asinh_w_sq,f0
1047 nop.i 0
1048 }
1049 ;;
1051 { .mfi
1052 ldfe log_C5 = [log_table_address2],16
1053 nop.f 0
1054 nop.i 0
1055 }
1056 ;;
1058 { .mfi
1059 ldfe log_C3 = [log_table_address2],16
1060 nop.f 0
1061 nop.i 0
1062 }
1063 ;;
1065 { .mfi
1066 nop.m 0
1067 fma.s1 asinh_w_13 = log_C13,asinh_w_sq,log_C11
1068 nop.i 0
1069 }
1070 { .mfi
1071 nop.m 0
1072 fma.s1 asinh_w_9 = log_C9,asinh_w_sq,log_C7
1073 nop.i 0
1074 }
1075 ;;
1077 { .mfi
1078 nop.m 0
1079 fma.s1 asinh_w_3 = log_C5,asinh_w_sq,log_C3
1080 nop.i 0
1081 }
1082 { .mfi
1083 nop.m 0
1084 fma.s1 asinh_w_seven = asinh_w_four,asinh_w_cube,f0
1085 nop.i 0
1086 }
1087 ;;
1089 { .mfi
1090 nop.m 0
1091 fma.s1 asinh_w_7 = asinh_w_13,asinh_w_four,asinh_w_9
1092 nop.i 0
1093 }
1094 { .mfi
1095 nop.m 0
1096 fma.s1 asinh_w_5 = asinh_w_3,asinh_w_cube,fNormX
1097 nop.i 0
1098 }
1099 ;;
1101 { .mfb
1102 nop.m 0
1103 fma.d.s0 f8 = asinh_w_7,asinh_w_seven,asinh_w_5
1104 br.ret.sptk b0 // Exit path 2 (0.0 <|x| < 2^(-3))
1105 }
1106 ;;
1108 ASINH_UNORM:
1109 // Here if x=unorm
1110 { .mfi
1111 getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
1112 fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
1113 nop.i 0
1114 }
1115 ;;
1117 { .mfb
1118 nop.m 0
1119 fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
1120 (p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
1121 }
1122 ;;
1124 .pred.rel "mutex",p7,p11
1125 { .mfi
1126 nop.m 0
1127 (p7) fma.d.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
1128 nop.i 0
1129 }
1130 { .mfb
1131 nop.m 0
1132 (p11) fnma.d.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
1133 br.ret.spnt b0 // Exit if denorm
1134 }
1135 ;;
1137 GLOBAL_LIBM_END(asinh)