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1.file "asinh.s"
2
3
4// Copyright (c) 2000 - 2005, Intel Corporation
5// All rights reserved.
6//
d5efd131
MF
7//
8// Redistribution and use in source and binary forms, with or without
9// modification, are permitted provided that the following conditions are
10// met:
11//
12// * Redistributions of source code must retain the above copyright
13// notice, this list of conditions and the following disclaimer.
14//
15// * Redistributions in binary form must reproduce the above copyright
16// notice, this list of conditions and the following disclaimer in the
17// documentation and/or other materials provided with the distribution.
18//
19// * The name of Intel Corporation may not be used to endorse or promote
20// products derived from this software without specific prior written
21// permission.
22
23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34//
35// Intel Corporation is the author of this code, and requests that all
36// problem reports or change requests be submitted to it directly at
37// http://www.intel.com/software/products/opensource/libraries/num.htm.
38//
39// ==============================================================
40// History
41// ==============================================================
42// 04/02/01 Initial version
43// 04/19/01 Improved speed of the paths #1,2,3,4,5
44// 10/18/01 Improved accuracy
45// 05/20/02 Cleaned up namespace and sf0 syntax
46// 02/06/03 Reordered header: .section, .global, .proc, .align
47// 05/21/03 Improved performance, fixed to handle unorms
48// 03/31/05 Reformatted delimiters between data tables
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
148
149// General registers used:
150// r14 -> r27
151
152// Predicate registers used:
153// p6 -> p14
154
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//==============================================================
164log_GR_exp_17_ones = r14
165log_GR_signexp_f8 = r15
166log_table_address2 = r16
167log_GR_exp_16_ones = r17
168log_GR_exp_f8 = r18
169log_GR_true_exp_f8 = r19
170log_GR_significand_f8 = r20
171log_GR_index = r21
172log_GR_comp2 = r22
173asinh_GR_f8 = r23
174asinh_GR_comp = r24
175asinh_GR_f8 = r25
176log_table_address3 = r26
177NR_table_address = r27
178
179//==============================================================
180log_y = f9
181NR1 = f10
182NR2 = f11
183log_y_rs = f12
184log_y_rs_iter = f13
185log_y_rs_iter1 = f14
186fNormX = f15
187asinh_w_sq = f32
188log_C13 = f33
189log_C11 = f34
190log_P3 = f35
191log_P2 = f36
192log_P1 = f37
193log_P5 = f38
194log_P4 = f39
195log_C3 = f40
196log_C5 = f41
197log_C7 = f42
198log2 = f43
199asinh_f8 = f44
200log_C = f45
201log_arg = f46
202log_C9 = f47
203asinh_w_four = f48
204log_int_Nfloat = f49
205log_r = f50
206log_rsq = f51
207log_rp_p4 = f52
208log_rp_p32 = f53
209log_rcube = f54
210log_rp_p10 = f55
211log_rp_p2 = f56
212log_Nfloat = f57
213log_T = f58
214log_r2P_r = f59
215log_T_plus_Nlog2 = f60
216asinh_w_3 = f61
217asinh_w_5 = f62
218asinh_w_cube = f63
219asinh_w_7 = f64
220log_arg_early = f65
221asinh_w_9 = f66
222asinh_w_13 = f67
223asinh_w_seven = f68
224
225// Data tables
226//==============================================================
227
228RODATA
229.align 16
230
231LOCAL_OBJECT_START(log_table_1)
232data8 0xBFC5555DA7212371 // P5
233data8 0x3FC999A19EEF5826 // P4
234data8 0xBFCFFFFFFFFEF009 // P3
235data8 0x3FD555555554ECB2 // P2
236data8 0xBFE0000000000000 // P1 = -0.5
237data8 0x0000000000000000 // pad
238data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
239LOCAL_OBJECT_END(log_table_1)
240
241LOCAL_OBJECT_START(log_table_2)
242data8 0x3FE0000000000000 // 0.5
243data8 0x4008000000000000 // 3.0
244//
245data8 0x8824BE4D74BC4F00, 0x00003FF9 // C13
246data8 0xB725A2CD9556CC57, 0x0000BFF9 // C11
247data8 0xF8E339127FBFF49D, 0x00003FF9 // C9
248data8 0xB6DB6D7DCE17CB78, 0x0000BFFA // C7
249data8 0x999999998802CCEF, 0x00003FFB // C5
250data8 0xAAAAAAAAAAA8DC40, 0x0000BFFC // C3
251LOCAL_OBJECT_END(log_table_2)
252
253
254LOCAL_OBJECT_START(log_table_3)
255data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
256//
257data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
258data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
259data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
260data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
261data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
262//
263data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
264data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
265data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
266data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
267data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
268//
269data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
270data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
271data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
272data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
273data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
274//
275data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
276data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
277data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
278data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
279data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
280//
281data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
282data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
283data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
284data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
285data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
286//
287data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
288data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
289data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
290data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
291data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
292//
293data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
294data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
295data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
296data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
297data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
298//
299data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
300data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
301data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
302data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
303data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
304//
305data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
306data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
307data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
308data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
309data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
310//
311data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
312data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
313data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
314data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
315data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
316//
317data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
318data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
319data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
320data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
321data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
322//
323data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
324data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
325data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
326data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
327data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
328//
329data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
330data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
331data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
332data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
333data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
334//
335data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
336data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
337data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
338data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
339data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
340//
341data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
342data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
343data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
344data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
345data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
346//
347data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
348data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
349data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
350data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
351data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
352//
353data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
354data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
355data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
356data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
357data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
358//
359data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
360data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
361data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
362data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
363data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
364//
365data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
366data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
367data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
368data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
369data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
370//
371data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
372data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
373data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
374data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
375data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
376//
377data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
378data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
379data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
380data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
381data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
382//
383data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
384data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
385data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
386data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
387data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
388//
389data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
390data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
391data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
392data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
393data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
394//
395data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
396data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
397data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
398data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
399data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
400//
401data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
402data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
403data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
404data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
405data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
406//
407data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
408data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
409data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
410data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
411data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
412//
413data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
414data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
415data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
416data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
417data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
418//
419data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
420data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
421data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
422data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
423data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
424//
425data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
426data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
427data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
428data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
429data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
430//
431data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
432data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
433data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
434data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
435data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
436//
437data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
438data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
439data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
440data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
441data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
442//
443data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
444data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
445data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
446data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
447data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
448//
449data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
450data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
451data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
452data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
453data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
454//
455data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
456data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
457data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
458data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
459data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
460//
461data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
462data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
463data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
464data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
465data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
466//
467data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
468data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
469data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
470data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
471data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
472//
473data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
474data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
475data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
476data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
477data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
478//
479data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
480data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
481data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
482data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
483data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
484//
485data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
486data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
487data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
488data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
489data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
490//
491data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
492data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
493data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
494data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
495data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
496//
497data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
498data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
499data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
500data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
501data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
502//
503data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
504data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
505data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
506data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
507data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
508//
509data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
510data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
511data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
512data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
513data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
514//
515data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
516data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
517data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
518data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
519data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
520//
521data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
522data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
523data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
524data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
525data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
526//
527data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
528data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
529data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
530data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
531data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
532//
533data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
534data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
535data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
536data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
537data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
538//
539data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
540data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
541data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
542data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
543data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
544//
545data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
546data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
547data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
548data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
549data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
550//
551data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
552data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
553data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
554data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
555data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
556//
557data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
558data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
559data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
560data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
561data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
562LOCAL_OBJECT_END(log_table_3)
563
564
565.section .text
566GLOBAL_LIBM_ENTRY(asinh)
567
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;;
579
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;;
591
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;;
603
604ASINH_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;;
618
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;;
625
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;;
632
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;;
639
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;;
646
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;;
659
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;;
673
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;;
681
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;;
689
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;;
701
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;;
715
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;;
728
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;;
735
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;;
747
748{ .mfi
749 nop.m 0
750 frcpa.s1 log_C,p0 = f1,log_arg_early
751 nop.i 0
752}
753;;
754
755{ .mfi
756 getf.exp log_GR_signexp_f8 = log_arg_early
757 nop.f 0
758 nop.i 0
759}
760;;
761
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;;
770
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;;
779
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;;
787
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;;
794
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;;
803
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;;
815
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;;
822
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;;
830
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;;
842
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;;
850
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;;
863
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;;
871
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;;
885
886// Here if path 4, |x| >= 2^63
887LOG_COMMON1:
888{ .mfi
889 ldfpd log_P5,log_P4 = [NR_table_address],16
890 nop.f 0
891 nop.i 0
892}
893;;
894
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;;
901
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;;
908
909{ .mmi
910 getf.sig log_GR_significand_f8 = log_arg
911 ldfe log2 = [NR_table_address],16
912 nop.i 0
913}
914;;
915
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;;
923
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;;
931
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;;
938
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
945
946}
947;;
948
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;;
960
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;;
972
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;;
984
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;;
998
999{ .mfi
1000 nop.m 0
1001(p7) fnma.s1 log_T = log_T,f1,f0
1002 nop.i 0
1003}
1004;;
1005
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;;
1018
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;;
1033
1034// Here is path 2, 0 < |x| < 2^-3
1035ASINH_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;;
1042
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;;
1049
1050{ .mfi
1051 ldfe log_C5 = [log_table_address2],16
1052 nop.f 0
1053 nop.i 0
1054}
1055;;
1056
1057{ .mfi
1058 ldfe log_C3 = [log_table_address2],16
1059 nop.f 0
1060 nop.i 0
1061}
1062;;
1063
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;;
1075
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;;
1087
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;;
1099
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;;
1106
1107ASINH_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;;
1115
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;;
1122
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;;
1135
1136GLOBAL_LIBM_END(asinh)
0609ec0a 1137libm_alias_double_other (asinh, asinh)