| blob | a9ef4e1143e592483c8897a510b246e72460fe9e |
1 .file "asinh.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 // ==============================================================
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 //
50 // API
51 // ==============================================================
52 // double asinh(double)
53 //
54 // Overview of operation
55 // ==============================================================
56 //
57 // There are 7 paths:
58 // 1. x = 0.0
59 // Return asinh(x) = 0.0
60 //
61 // 2. 0.0 <|x| < 2^(-3)
62 // Return asinh(x) = POL13(x),
63 // where POL13(x) = (x^2*C13 + ...)*x^2 + C5)*x^2 + C3)*x^3 + x
64 //
65 // 3. 2^(-3) <= |x| < 2^63
66 // Return asinh(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
67 // To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
68 // (3 iterations)
69 // Algorithm description for log function see below.
70 //
71 // 4. 2^63 <= |x| < +INF
72 // Return asinh(x) = sign(x)*log(2*|x|)
73 // Algorithm description for log function see below.
74 //
75 // 5. x = INF
76 // Return asinh(x) = INF
77 //
78 // 6. x = [S,Q]NaN
79 // Return asinh(x) = QNaN
80 //
81 // 7. x = denormal
82 // Return asinh(x) = x correctly rounded
83 //
84 //==============================================================
85 // Algorithm Description for log(x) function
86 // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
87 // true for this asinh implementation
88 //
89 // Consider x = 2^N 1.f1 f2 f3 f4...f63
90 // Log(x) = log(frcpa(x) x/frcpa(x))
91 // = log(1/frcpa(x)) + log(frcpa(x) x)
92 // = -log(frcpa(x)) + log(frcpa(x) x)
93 //
94 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
95 //
96 // -log(frcpa(x)) = -log(C)
97 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
98 //
99 // -log(frcpa(x)) = -log(C)
100 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
101 //
102 // -log(frcpa(x)) = -log(C)
103 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
104 //
105 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
106 //
107 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
108 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
109 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
110 //
111 // Log(x) = +Nlog2 + T + log(C x)
112 //
113 // Cx = 1 + r
114 //
115 // Log(x) = +Nlog2 + T + log(1+r)
116 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
117 //
118 // 1.f1 f2 ... f8 has 256 entries.
119 // They are 1 + k/2^8, k = 0 ... 255
120 // These 256 values are the table entries.
121 //
122 // Implementation
123 //==============================================================
124 // C = frcpa(x)
125 // r = C * x - 1
126 //
127 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
128 //
129 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
130 // Nfloat = float(n) where n is the true unbiased exponent
131 // pre-index = f_1f_2....f_8
132 // index = pre_index * 16
133 // get the dxt table entry at index + offset = T
134 //
135 // result = (T + Nfloat * log(2)) + rseries
136 //
137 // The T table is calculated as follows
138 // Form x_k = 1 + k/2^8 where k goes from 0... 255
139 // y_k = frcpa(x_k)
140 // log(1/y_k) in quad and round to double-extended
141 //
142 //
143 // Registers used
144 //==============================================================
145 // Floating Point registers used:
146 // f8, input
147 // f9 -> f15, f32 -> f68
149 // General registers used:
150 // r14 -> r27
152 // Predicate registers used:
153 // p6 -> p14
155 // p6 to filter out case when x = [Q,S]NaN or INF or zero
156 // p7 to filter out case when x < 0.0
157 // p8 to select path #2
158 // p9 used in the frcpa from path #3
159 // p11 to filter out case when x >= 0
160 // p12 to filter out case when x = unorm
161 // p13 to select path #4
162 // Assembly macros
163 //==============================================================
164 log_GR_exp_17_ones = r14
165 log_GR_signexp_f8 = r15
166 log_table_address2 = r16
167 log_GR_exp_16_ones = r17
168 log_GR_exp_f8 = r18
169 log_GR_true_exp_f8 = r19
170 log_GR_significand_f8 = r20
171 log_GR_index = r21
172 log_GR_comp2 = r22
173 asinh_GR_f8 = r23
174 asinh_GR_comp = r24
175 asinh_GR_f8 = r25
176 log_table_address3 = r26
177 NR_table_address = r27
179 //==============================================================
180 log_y = f9
181 NR1 = f10
182 NR2 = f11
183 log_y_rs = f12
184 log_y_rs_iter = f13
185 log_y_rs_iter1 = f14
186 fNormX = f15
187 asinh_w_sq = f32
188 log_C13 = f33
189 log_C11 = f34
190 log_P3 = f35
191 log_P2 = f36
192 log_P1 = f37
193 log_P5 = f38
194 log_P4 = f39
195 log_C3 = f40
196 log_C5 = f41
197 log_C7 = f42
198 log2 = f43
199 asinh_f8 = f44
200 log_C = f45
201 log_arg = f46
202 log_C9 = f47
203 asinh_w_four = f48
204 log_int_Nfloat = f49
205 log_r = f50
206 log_rsq = f51
207 log_rp_p4 = f52
208 log_rp_p32 = f53
209 log_rcube = f54
210 log_rp_p10 = f55
211 log_rp_p2 = f56
212 log_Nfloat = f57
213 log_T = f58
214 log_r2P_r = f59
215 log_T_plus_Nlog2 = f60
216 asinh_w_3 = f61
217 asinh_w_5 = f62
218 asinh_w_cube = f63
219 asinh_w_7 = f64
220 log_arg_early = f65
221 asinh_w_9 = f66
222 asinh_w_13 = f67
223 asinh_w_seven = f68
225 // Data tables
226 //==============================================================
228 RODATA
229 .align 16
231 LOCAL_OBJECT_START(log_table_1)
232 data8 0xBFC5555DA7212371 // P5
233 data8 0x3FC999A19EEF5826 // P4
234 data8 0xBFCFFFFFFFFEF009 // P3
235 data8 0x3FD555555554ECB2 // P2
236 data8 0xBFE0000000000000 // P1 = -0.5
237 data8 0x0000000000000000 // pad
238 data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
239 LOCAL_OBJECT_END(log_table_1)
241 LOCAL_OBJECT_START(log_table_2)
242 data8 0x3FE0000000000000 // 0.5
243 data8 0x4008000000000000 // 3.0
244 //
245 data8 0x8824BE4D74BC4F00, 0x00003FF9 // C13
246 data8 0xB725A2CD9556CC57, 0x0000BFF9 // C11
247 data8 0xF8E339127FBFF49D, 0x00003FF9 // C9
248 data8 0xB6DB6D7DCE17CB78, 0x0000BFFA // C7
249 data8 0x999999998802CCEF, 0x00003FFB // C5
250 data8 0xAAAAAAAAAAA8DC40, 0x0000BFFC // C3
251 LOCAL_OBJECT_END(log_table_2)
254 LOCAL_OBJECT_START(log_table_3)
255 data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
256 //
257 data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
258 data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
259 data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
260 data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
261 data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
262 //
263 data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
264 data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
265 data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
266 data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
267 data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
268 //
269 data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
270 data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
271 data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
272 data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
273 data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
274 //
275 data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
276 data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
277 data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
278 data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
279 data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
280 //
281 data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
282 data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
283 data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
284 data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
285 data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
286 //
287 data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
288 data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
289 data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
290 data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
291 data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
292 //
293 data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
294 data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
295 data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
296 data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
297 data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
298 //
299 data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
300 data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
301 data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
302 data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
303 data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
304 //
305 data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
306 data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
307 data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
308 data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
309 data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
310 //
311 data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
312 data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
313 data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
314 data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
315 data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
316 //
317 data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
318 data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
319 data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
320 data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
321 data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
322 //
323 data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
324 data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
325 data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
326 data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
327 data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
328 //
329 data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
330 data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
331 data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
332 data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
333 data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
334 //
335 data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
336 data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
337 data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
338 data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
339 data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
340 //
341 data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
342 data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
343 data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
344 data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
345 data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
346 //
347 data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
348 data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
349 data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
350 data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
351 data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
352 //
353 data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
354 data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
355 data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
356 data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
357 data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
358 //
359 data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
360 data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
361 data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
362 data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
363 data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
364 //
365 data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
366 data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
367 data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
368 data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
369 data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
370 //
371 data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
372 data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
373 data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
374 data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
375 data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
376 //
377 data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
378 data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
379 data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
380 data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
381 data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
382 //
383 data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
384 data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
385 data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
386 data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
387 data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
388 //
389 data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
390 data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
391 data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
392 data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
393 data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
394 //
395 data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
396 data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
397 data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
398 data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
399 data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
400 //
401 data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
402 data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
403 data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
404 data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
405 data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
406 //
407 data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
408 data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
409 data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
410 data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
411 data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
412 //
413 data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
414 data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
415 data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
416 data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
417 data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
418 //
419 data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
420 data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
421 data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
422 data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
423 data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
424 //
425 data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
426 data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
427 data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
428 data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
429 data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
430 //
431 data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
432 data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
433 data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
434 data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
435 data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
436 //
437 data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
438 data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
439 data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
440 data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
441 data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
442 //
443 data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
444 data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
445 data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
446 data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
447 data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
448 //
449 data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
450 data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
451 data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
452 data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
453 data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
454 //
455 data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
456 data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
457 data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
458 data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
459 data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
460 //
461 data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
462 data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
463 data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
464 data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
465 data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
466 //
467 data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
468 data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
469 data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
470 data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
471 data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
472 //
473 data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
474 data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
475 data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
476 data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
477 data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
478 //
479 data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
480 data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
481 data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
482 data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
483 data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
484 //
485 data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
486 data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
487 data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
488 data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
489 data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
490 //
491 data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
492 data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
493 data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
494 data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
495 data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
496 //
497 data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
498 data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
499 data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
500 data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
501 data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
502 //
503 data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
504 data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
505 data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
506 data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
507 data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
508 //
509 data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
510 data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
511 data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
512 data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
513 data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
514 //
515 data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
516 data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
517 data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
518 data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
519 data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
520 //
521 data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
522 data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
523 data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
524 data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
525 data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
526 //
527 data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
528 data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
529 data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
530 data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
531 data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
532 //
533 data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
534 data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
535 data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
536 data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
537 data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
538 //
539 data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
540 data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
541 data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
542 data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
543 data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
544 //
545 data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
546 data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
547 data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
548 data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
549 data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
550 //
551 data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
552 data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
553 data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
554 data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
555 data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
556 //
557 data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
558 data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
559 data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
560 data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
561 data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
562 LOCAL_OBJECT_END(log_table_3)
565 .section .text
566 GLOBAL_LIBM_ENTRY(asinh)
568 { .mfi
569 getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
570 fclass.m p12,p0 = f8, 0x0b // Test x unorm
571 mov log_GR_exp_17_ones = 0x1ffff
572 }
573 { .mfi
574 addl NR_table_address = @ltoff(log_table_1), gp
575 fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
576 mov asinh_GR_comp = 0xfffc
577 }
578 ;;
580 { .mfi
581 mov log_GR_exp_16_ones = 0xffff //BIAS
582 fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
583 mov log_GR_comp2 = 0x1003e
584 }
585 { .mfi
586 ld8 NR_table_address = [NR_table_address]
587 fma.s1 asinh_w_sq = f8,f8,f0 // x^2
588 nop.i 0
589 }
590 ;;
592 { .mfi
593 nop.m 0
594 fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
595 nop.i 0
596 }
597 { .mfb
598 nop.m 0
599 fnorm.s1 fNormX = f8 // Normalize x
600 (p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
601 }
602 ;;
604 ASINH_COMMON:
605 // Return here if x=unorm and not denorm
606 { .mfi
607 //to get second table address
608 adds log_table_address2 = 0x40, NR_table_address
609 fma.s1 log_arg = f8,f1,f8
610 nop.i 0
611 }
612 { .mfb
613 nop.m 0
614 (p6) fma.d.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
615 (p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
616 }
617 ;;
619 { .mfi
620 ldfpd NR1,NR2 = [log_table_address2],16
621 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
622 nop.i 0
623 }
624 ;;
626 { .mfi
627 ldfe log_C13 = [log_table_address2],16
628 nop.f 0
629 and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
630 }
631 ;;
633 { .mib
634 ldfe log_C11 = [log_table_address2],16
635 cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
636 (p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, |x| >= 2^63
637 }
638 ;;
640 { .mfi
641 nop.m 0
642 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
643 nop.i 0
644 }
645 ;;
647 .pred.rel "mutex",p7,p11
648 { .mfi
649 nop.m 0
650 (p11) mov asinh_f8 = fNormX
651 nop.i 0
652 }
653 { .mfb
654 cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
655 (p7) fnma.s1 asinh_f8 = fNormX,f1,f0
656 (p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2, 0 < |x| < 2^-3
657 }
658 ;;
660 // Here if main path, 2^-3 <= |x| < 2^63
661 ///////////////////////////////// The first iteration /////////////////////////
662 { .mfi
663 ldfpd log_P5,log_P4 = [NR_table_address],16
664 fnma.s1 log_y_rs_iter = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
665 nop.i 0
666 }
667 { .mfi
668 nop.m 0
669 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
670 nop.i 0
671 }
672 ;;
674 { .mfi
675 ldfpd log_P3,log_P2 = [NR_table_address],16
676 // (0.5*z)*(3-(y*z)*z)
677 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter,f0
678 nop.i 0
679 }
680 ;;
682 /////////////////////////// The second iteration /////////////////////////////
683 { .mfi
684 ldfd log_P1 = [NR_table_address],16
685 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
686 nop.i 0
687 }
688 ;;
690 { .mfi
691 nop.m 0
692 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
693 nop.i 0
694 }
695 { .mfi
696 nop.m 0
697 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
698 nop.i 0
699 }
700 ;;
702 { .mfi
703 ldfe log2 = [NR_table_address],16
704 // (0.5*z)*(3-(y*z)*z)
705 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs,f0
706 nop.i 0
707 }
708 { .mfi
709 nop.m 0
710 // (0.5*z)*(3-(y*z)*z)
711 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs,f0
712 nop.i 0
713 }
714 ;;
716 ////////////////////////////////// The third iteration ////////////////////////
717 { .mfi
718 nop.m 0
719 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
720 nop.i 0
721 }
722 { .mfi
723 nop.m 0
724 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
725 nop.i 0
726 }
727 ;;
729 { .mfi
730 nop.m 0
731 fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
732 nop.i 0
733 }
734 ;;
736 { .mfi
737 nop.m 0
738 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
739 nop.i 0
740 }
741 { .mfi
742 nop.m 0
743 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
744 nop.i 0
745 }
746 ;;
748 { .mfi
749 nop.m 0
750 frcpa.s1 log_C,p0 = f1,log_arg_early
751 nop.i 0
752 }
753 ;;
755 { .mfi
756 getf.exp log_GR_signexp_f8 = log_arg_early
757 nop.f 0
758 nop.i 0
759 }
760 ;;
762 { .mfi
763 getf.sig log_GR_significand_f8 = log_arg_early
764 // (0.5*z)*(3-(y*z)*z)*y + |x|
765 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
766 //to get third table address
767 adds log_table_address3 = 0x70, NR_table_address
768 }
769 ;;
771 ///////////////////////////////// The end NR iterations /////////////////////
772 { .mfi
773 nop.m 0
774 nop.f 0
775 //significant bit destruction
776 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
777 }
778 ;;
780 { .mfi
781 //BIAS subtraction
782 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
783 (p7) fnma.s1 log2 = log2,f1,f0
784 nop.i 0
785 }
786 ;;
788 { .mfi
789 setf.sig log_int_Nfloat = log_GR_true_exp_f8
790 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
791 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
792 }
793 ;;
795 { .mmi
796 //pre-index*16 + index
797 shladd log_table_address3 = log_GR_index,4,log_table_address3
798 ;;
799 ldfe log_T = [log_table_address3]
800 nop.i 0
801 }
802 ;;
804 { .mfi
805 nop.m 0
806 fma.s1 log_rsq = log_r, log_r, f0 //r^2
807 nop.i 0
808 }
809 { .mfi
810 nop.m 0
811 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
812 nop.i 0
813 }
814 ;;
816 { .mfi
817 nop.m 0
818 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
819 nop.i 0
820 }
821 ;;
823 { .mfi
824 nop.m 0
825 //convert N to the floating-point format
826 fcvt.xf log_Nfloat = log_int_Nfloat
827 nop.i 0
828 }
829 ;;
831 { .mfi
832 nop.m 0
833 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
834 nop.i 0
835 }
836 { .mfi
837 nop.m 0
838 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
839 nop.i 0
840 }
841 ;;
843 { .mfi
844 nop.m 0
845 //(P5*r + P4)*r^2 + P3*r + P2
846 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
847 nop.i 0
848 }
849 ;;
851 .pred.rel "mutex",p7,p11
852 { .mfi
853 nop.m 0
854 (p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
855 nop.i 0
856 }
857 { .mfi
858 nop.m 0
859 (p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
860 nop.i 0
861 }
862 ;;
864 { .mfi
865 nop.m 0
866 //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
867 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
868 nop.i 0
869 }
870 ;;
872 { .mfi
873 nop.m 0
874 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
875 (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
876 nop.i 0
877 }
878 { .mfb
879 nop.m 0
880 // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
881 (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
882 br.ret.sptk b0 // Exit main path, path 3: 2^-3 <= |x| < 2^63
883 }
884 ;;
886 // Here if path 4, |x| >= 2^63
887 LOG_COMMON1:
888 { .mfi
889 ldfpd log_P5,log_P4 = [NR_table_address],16
890 nop.f 0
891 nop.i 0
892 }
893 ;;
895 { .mfi
896 ldfpd log_P3,log_P2 = [NR_table_address],16
897 frcpa.s1 log_C,p0 = f1,log_arg
898 nop.i 0
899 }
900 ;;
902 { .mmi
903 getf.exp log_GR_signexp_f8 = log_arg
904 ldfd log_P1 = [NR_table_address],16
905 nop.i 0
906 }
907 ;;
909 { .mmi
910 getf.sig log_GR_significand_f8 = log_arg
911 ldfe log2 = [NR_table_address],16
912 nop.i 0
913 }
914 ;;
916 { .mfi
917 adds log_table_address3 = 0x70, NR_table_address
918 nop.f 0
919 //significant bit destruction
920 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
921 }
922 ;;
924 { .mmf
925 nop.m 0
926 //BIAS subtraction
927 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
928 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
929 }
930 ;;
932 { .mfi
933 setf.sig log_int_Nfloat = log_GR_true_exp_f8
934 nop.f 0
935 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
936 }
937 ;;
939 { .mmi
940 //pre-index*16 + index
941 shladd log_table_address3 = log_GR_index,4,log_table_address3
942 ;;
943 ldfe log_T = [log_table_address3]
944 nop.i 0
946 }
947 ;;
949 { .mfi
950 nop.m 0
951 fma.s1 log_rsq = log_r, log_r, f0 //r^2
952 nop.i 0
953 }
954 { .mfi
955 nop.m 0
956 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
957 nop.i 0
958 }
959 ;;
961 { .mfi
962 nop.m 0
963 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
964 nop.i 0
965 }
966 { .mfi
967 nop.m 0
968 (p7) fnma.s1 log2 = log2,f1,f0
969 nop.i 0
970 }
971 ;;
973 { .mfi
974 nop.m 0
975 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
976 nop.i 0
977 }
978 { .mfi
979 nop.m 0
980 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
981 nop.i 0
982 }
983 ;;
985 { .mfi
986 nop.m 0
987 //convert N to the floating-point format
988 fcvt.xf log_Nfloat = log_int_Nfloat
989 nop.i 0
990 }
991 { .mfi
992 nop.m 0
993 //(P5*r + P4)*r^2 + P3*r + P2
994 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
995 nop.i 0
996 }
997 ;;
999 { .mfi
1000 nop.m 0
1001 (p7) fnma.s1 log_T = log_T,f1,f0
1002 nop.i 0
1003 }
1004 ;;
1006 { .mfi
1007 nop.m 0
1008 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
1009 nop.i 0
1010 }
1011 { .mfi
1012 nop.m 0
1013 //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
1014 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
1015 nop.i 0
1016 }
1017 ;;
1019 .pred.rel "mutex",p7,p11
1020 { .mfi
1021 nop.m 0
1022 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
1023 (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
1024 nop.i 0
1025 }
1026 { .mfb
1027 nop.m 0
1028 // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
1029 (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
1030 br.ret.sptk b0 // Exit path 4, |x| >= 2^63
1031 }
1032 ;;
1034 // Here is path 2, 0 < |x| < 2^-3
1035 ASINH_NEAR_ZERO:
1036 { .mfi
1037 ldfe log_C9 = [log_table_address2],16
1038 fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
1039 nop.i 0
1040 }
1041 ;;
1043 { .mfi
1044 ldfe log_C7 = [log_table_address2],16
1045 fma.s1 asinh_w_four = asinh_w_sq,asinh_w_sq,f0
1046 nop.i 0
1047 }
1048 ;;
1050 { .mfi
1051 ldfe log_C5 = [log_table_address2],16
1052 nop.f 0
1053 nop.i 0
1054 }
1055 ;;
1057 { .mfi
1058 ldfe log_C3 = [log_table_address2],16
1059 nop.f 0
1060 nop.i 0
1061 }
1062 ;;
1064 { .mfi
1065 nop.m 0
1066 fma.s1 asinh_w_13 = log_C13,asinh_w_sq,log_C11
1067 nop.i 0
1068 }
1069 { .mfi
1070 nop.m 0
1071 fma.s1 asinh_w_9 = log_C9,asinh_w_sq,log_C7
1072 nop.i 0
1073 }
1074 ;;
1076 { .mfi
1077 nop.m 0
1078 fma.s1 asinh_w_3 = log_C5,asinh_w_sq,log_C3
1079 nop.i 0
1080 }
1081 { .mfi
1082 nop.m 0
1083 fma.s1 asinh_w_seven = asinh_w_four,asinh_w_cube,f0
1084 nop.i 0
1085 }
1086 ;;
1088 { .mfi
1089 nop.m 0
1090 fma.s1 asinh_w_7 = asinh_w_13,asinh_w_four,asinh_w_9
1091 nop.i 0
1092 }
1093 { .mfi
1094 nop.m 0
1095 fma.s1 asinh_w_5 = asinh_w_3,asinh_w_cube,fNormX
1096 nop.i 0
1097 }
1098 ;;
1100 { .mfb
1101 nop.m 0
1102 fma.d.s0 f8 = asinh_w_7,asinh_w_seven,asinh_w_5
1103 br.ret.sptk b0 // Exit path 2 (0.0 <|x| < 2^(-3))
1104 }
1105 ;;
1107 ASINH_UNORM:
1108 // Here if x=unorm
1109 { .mfi
1110 getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
1111 fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
1112 nop.i 0
1113 }
1114 ;;
1116 { .mfb
1117 nop.m 0
1118 fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
1119 (p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
1120 }
1121 ;;
1123 .pred.rel "mutex",p7,p11
1124 { .mfi
1125 nop.m 0
1126 (p7) fma.d.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
1127 nop.i 0
1128 }
1129 { .mfb
1130 nop.m 0
1131 (p11) fnma.d.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
1132 br.ret.spnt b0 // Exit if denorm
1133 }
1134 ;;
1136 GLOBAL_LIBM_END(asinh)