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d5efd131
MF		 1.file "acoshf.s"
2
3
4// Copyright (c) 2000 - 2003, 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// 03/28/01 Initial version
43// 04/19/01 Improved speed of the paths #1,2,3,4,5
44// 05/20/02 Cleaned up namespace and sf0 syntax
45// 02/06/03 Reordered header: .section, .global, .proc, .align
46// 05/14/03 Improved performance, set denormal flag for unorms >= 1.0
47//
48// API
49// ==============================================================
50// float acoshf(float)
51//
52// Overview of operation
53// ==============================================================
54//
55// There are 7 paths:
56// 1. x = 1.0
57// Return acoshf(x) = 0.0
58// 2. 1.0 < x < 1.000499725341796875(0x3FF0020C00000000)
59// Return acoshf(x) = sqrt(x-1) * Pol4(x),
60// where Pol4(x) = (x*C2 + C1)*(x-1) + C0
61//
62// 3. 1.000499725341796875(0x3FF0020C00000000) <= x < 2^51
63// Return acoshf(x) = log(x + sqrt(x^2 -1.0))
64// To compute x + sqrt(x^2 -1.0) modified Newton Raphson method is used
65// (2 iterations)
66// Algorithm description for log function see below.
67//
68// 4. 2^51 <= x < +INF
69// Return acoshf(x) = log(2*x)
70// Algorithm description for log function see below.
71//
72// 5. x = +INF
73// Return acoshf(x) = +INF
74//
75// 6. x = [S,Q]NaN
76// Return acoshf(x) = QNaN
77//
78// 7. x < 1.0
79// It's domain error. Error handler with tag = 137 is called
80//
81//==============================================================
82// Algorithm Description for log(x) function
83// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
84// true for this acosh implementation
85//
86// Consider x = 2^N 1.f1 f2 f3 f4...f63
87// Log(x) = log(frcpa(x) x/frcpa(x))
88// = log(1/frcpa(x)) + log(frcpa(x) x)
89// = -log(frcpa(x)) + log(frcpa(x) x)
90//
91// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
92//
93// -log(frcpa(x)) = -log(C)
94// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
95//
96// -log(frcpa(x)) = -log(C)
97// = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
98//
99// -log(frcpa(x)) = -log(C)
100// = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
101//
102// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
103//
104// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
105// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
106// Log(x) = +Nlog2 + T + log(frcpa(x) x)
107//
108// Log(x) = +Nlog2 + T + log(C x)
109//
110// Cx = 1 + r
111//
112// Log(x) = +Nlog2 + T + log(1+r)
113// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
114//
115// 1.f1 f2 ... f8 has 256 entries.
116// They are 1 + k/2^8, k = 0 ... 255
117// These 256 values are the table entries.
118//
119// Implementation
120//==============================================================
121// C = frcpa(x)
122// r = C * x - 1
123//
124// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
125//
126// x = f * 2*n where f is 1.f_1f_2f_3....f_63
127// Nfloat = float(n) where n is the true unbiased exponent
128// pre-index = f_1f_2....f_8
129// index = pre_index * 8
130// get the dxt table entry at index + offset = T
131//
132// result = (T + Nfloat * log(2)) + rseries
133//
134// The T table is calculated as follows
135// Form x_k = 1 + k/2^8 where k goes from 0... 255
136// y_k = frcpa(x_k)
137// log(1/y_k) in quad and round to double
138//
139
140// Registers used
141//==============================================================
142// Floating Point registers used:
143// f8, input
144// f9 -> f15, f32 -> f62
145//
146// General registers used:
147// r14 -> r27, r32 -> r39
148//
149// Predicate registers used:
150// p6 -> p15
151//
152// p6 to filter out case when x = [Q,S]NaN
153// p7,p8 to filter out case when x < 1.0
154//
155// p10 to select path #1
156// p11 to filter out case when x = +INF
157// p12 used in the frcpa
158// p13 to select path #4
159// p14,p15 to select path #2
160
161// Assembly macros
162//==============================================================
163log_GR_exp_17_ones = r14
164log_GR_signexp_f8 = r15
165log_table_address2 = r16
166log_GR_exp_16_ones = r17
167log_GR_exp_f8 = r18
168log_GR_true_exp_f8 = r19
169log_GR_significand_f8 = r20
170log_GR_index = r21
171log_GR_comp2 = r22
172acosh_GR_f8 = r23
173log_GR_comp = r24
174acosh_GR_f8_sig = r25
175log_table_address3 = r26
176NR_table_address = r27
177
178GR_SAVE_B0 = r33
179GR_SAVE_GP = r34
180GR_SAVE_PFS = r35
181
182GR_Parameter_X = r36
183GR_Parameter_Y = r37
184GR_Parameter_RESULT = r38
185acosh_GR_tag = r39
186
187//==============================================================
188log_y = f9
189NR1 = f10
190NR2 = f11
191log_y_rs = f12
192log_y_rs_iter = f13
193log_y_rs_iter1 = f14
194log_NORM_f8 = f15
195log_w = f32
196acosh_comp = f34
197acosh_comp2 = f33
198log_P3 = f35
199log_P2 = f36
200log_P1 = f37
201log2 = f38
202log_C0 = f39
203log_C1 = f40
204log_C2 = f41
205acosh_w_rs = f42
206log_C = f43
207log_arg = f44
208acosh_w_iter1 = f45
209acosh_w_iter2 = f46
210log_int_Nfloat = f47
211log_r = f48
212log_rsq = f49
213log_rp_p4 = f50
214log_rp_p32 = f51
215log_rcube = f52
216log_rp_p10 = f53
217log_rp_p2 = f54
218log_Nfloat = f55
219log_T = f56
220log_r2P_r = f57
221log_T_plus_Nlog2 = f58
222acosh_w_sqrt = f59
223acosh_w_1 = f60
224log_arg_early = f61
225log_y_rs_iter2 = f62
226
227
228// Data tables
229//==============================================================
230
231RODATA
232.align 16
233
234LOCAL_OBJECT_START(log_table_1)
235data8 0xbfd0001008f39d59 // p3
236data8 0x3fd5556073e0c45a // p2
237data8 0xbfdffffffffaea15 // p1
238data8 0x3FE62E42FEFA39EF // log2
239LOCAL_OBJECT_END(log_table_1)
240
241LOCAL_OBJECT_START(log_table_2)
242
243data8 0x3FE0000000000000 // 0.5
244data8 0x4008000000000000 // 3.0
245data8 0xD92CBAD213719F11, 0x00003FF9 // C2 3FF9D92CBAD213719F11
246data8 0x93D38EBF2EC9B073, 0x0000BFFC // C1 BFFC93D38EBF2EC9B073
247data8 0xB504F333F9DA0E32, 0x00003FFF // C0 3FFFB504F333F9DA0E32
248LOCAL_OBJECT_END(log_table_2)
249
250LOCAL_OBJECT_START(log_table_3)
251data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)
252data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)
253data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)
254data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)
255data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)
256data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)
257data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)
258data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)
259data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)
260data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)
261data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)
262data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)
263data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)
264data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)
265data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)
266data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)
267data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)
268data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)
269data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)
270data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)
271data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)
272data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)
273data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)
274data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)
275data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)
276data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)
277data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)
278data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)
279data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)
280data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)
281data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)
282data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)
283data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)
284data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)
285data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)
286data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)
287data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)
288data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)
289data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)
290data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)
291data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)
292data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)
293data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)
294data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)
295data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)
296data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)
297data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)
298data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)
299data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)
300data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)
301data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)
302data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)
303data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)
304data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)
305data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)
306data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)
307data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)
308data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)
309data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)
310data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)
311data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)
312data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)
313data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)
314data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)
315data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)
316data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)
317data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)
318data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)
319data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)
320data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)
321data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)
322data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)
323data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)
324data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)
325data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)
326data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)
327data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)
328data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)
329data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)
330data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)
331data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)
332data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)
333data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)
334data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)
335data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)
336data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)
337data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)
338data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)
339data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)
340data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)
341data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)
342data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)
343data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)
344data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)
345data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)
346data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)
347data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)
348data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)
349data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)
350data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)
351data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)
352data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)
353data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)
354data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)
355data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)
356data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)
357data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)
358data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)
359data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)
360data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)
361data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)
362data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)
363data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)
364data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)
365data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)
366data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)
367data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)
368data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)
369data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)
370data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)
371data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)
372data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)
373data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)
374data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)
375data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)
376data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)
377data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)
378data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)
379data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)
380data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)
381data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)
382data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)
383data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)
384data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)
385data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)
386data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)
387data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)
388data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)
389data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)
390data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)
391data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)
392data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)
393data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)
394data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)
395data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)
396data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)
397data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)
398data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)
399data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)
400data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)
401data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)
402data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)
403data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)
404data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)
405data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)
406data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)
407data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)
408data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)
409data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)
410data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)
411data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)
412data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)
413data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)
414data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)
415data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)
416data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)
417data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)
418data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)
419data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)
420data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)
421data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)
422data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)
423data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)
424data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)
425data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)
426data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)
427data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)
428data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)
429data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)
430data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)
431data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)
432data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)
433data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)
434data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)
435data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)
436data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)
437data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)
438data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)
439data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)
440data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)
441data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)
442data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)
443data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)
444data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)
445data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)
446data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)
447data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)
448data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)
449data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)
450data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)
451data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)
452data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)
453data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)
454data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)
455data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)
456data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)
457data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)
458data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)
459data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)
460data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)
461data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)
462data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)
463data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)
464data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)
465data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)
466data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)
467data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)
468data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)
469data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)
470data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)
471data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)
472data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)
473data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)
474data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)
475data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)
476data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)
477data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)
478data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)
479data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)
480data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)
481data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)
482data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)
483data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)
484data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)
485data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)
486data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)
487data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)
488data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)
489data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)
490data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)
491data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)
492data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)
493data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)
494data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)
495data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)
496data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)
497data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)
498data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)
499data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)
500data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)
501data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)
502data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)
503data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)
504data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)
505data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)
506data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
507LOCAL_OBJECT_END(log_table_3)
508
509
510.section .text
511GLOBAL_LIBM_ENTRY(acoshf)
512
513{ .mfi
514 getf.exp acosh_GR_f8 = f8
515 fclass.m p6,p0 = f8, 0xc3 // Test for x = NaN
516 mov log_GR_comp2 = 0x10032
517}
518{ .mfi
519 addl NR_table_address = @ltoff(log_table_1), gp
520 fms.s1 log_y = f8, f8, f1 // y = x^2-1
521 nop.i 0
522}
523;;
524
525{ .mfi
526 getf.sig acosh_GR_f8_sig = f8
527 fclass.m p11,p0 = f8, 0x21 // Test for x=+inf
528 mov log_GR_exp_17_ones = 0x1ffff
529}
530{ .mfi
531 ld8 NR_table_address = [NR_table_address]
532 fms.s1 log_w = f8,f1,f1 // w = x - 1
533 nop.i 0
534}
535;;
536
537{ .mfi
538 nop.m 0
539 fcmp.lt.s1 p7,p8 = f8, f1 // Test for x<1.0
540 addl log_GR_comp = 0x10020C,r0 // Upper 21 bits of signif of 1.0005
541}
542{ .mfb
543 mov log_GR_exp_16_ones = 0xffff //BIAS
544(p6) fma.s.s0 f8 = f8,f1,f0 // quietize nan result if x=nan
545(p6) br.ret.spnt b0 // Exit for x=nan
546}
547;;
548
549{ .mfb
550 //get second table address
551 adds log_table_address2 = 0x20, NR_table_address
552 fcmp.eq.s1 p10,p0 = f8, f1 // Test for x=+1.0
553(p11) br.ret.spnt b0 // Exit for x=+inf
554}
555;;
556
557{ .mfi
558 ldfpd NR1,NR2 = [log_table_address2],16
559 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
560 nop.i 0
561}
562{ .mfb
563 nop.m 0
564 fma.s1 log_arg = f8,f1,f8
565(p7) br.cond.spnt ACOSH_LESS_ONE // Branch if path 7, x < 1.0
566}
567;;
568
569{ .mfi
570 ldfe log_C2 = [log_table_address2],16
571(p8) fcmp.eq.s0 p6,p0 = f8, f0 // Dummy op sets denorm flag if unorm>=1.0
572 nop.i 0
573}
574{ .mfb
575(p8) cmp.le.unc p13,p0 = log_GR_comp2,acosh_GR_f8
576 nop.f 0
577(p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, x >= 2^51
578}
579;;
580
581{ .mfi
582 ldfe log_C1 = [log_table_address2],16
583(p10) fmerge.s f8 = f0, f0 // Return 0 if x=1.0
584 shr.u acosh_GR_f8_sig = acosh_GR_f8_sig,43
585}
586{ .mib
587 cmp.eq p14,p0 = log_GR_exp_16_ones,acosh_GR_f8
588 nop.i 0
589(p10) br.ret.spnt b0 // Exit for x=1.0
590}
591;;
592
593{ .mfi
594 ldfe log_C0 = [log_table_address2],16
595 frsqrta.s1 acosh_w_rs,p0 = log_w // t=1/sqrt(w)
596 nop.i 0
597}
598{ .mfb
599(p14) cmp.lt.unc p15,p0 = acosh_GR_f8_sig,log_GR_comp
600 nop.f 0
601(p15) br.cond.spnt ACOSH_NEAR_ONE // Branch if path 2, 1.0 < x < 1.0005
602}
603;;
604
605// Here is main path, 1.0005 <= x < 2^51
606/////////////// The first iteration //////////////////////////////////
607{ .mfi
608 ldfpd log_P3,log_P2 = [NR_table_address],16
609 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
610 nop.i 0
611}
612;;
613
614{ .mfi
615 ldfpd log_P1,log2 = [NR_table_address],16
616 fnma.s1 log_y_rs_iter2 = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
617 nop.i 0
618}
619{ .mfi
620 nop.m 0
621 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
622 nop.i 0
623}
624;;
625
626{ .mfi
627 nop.m 0
628 // (0.5*z)*(3-(y*z)*z)
629 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter2,f0
630 nop.i 0
631}
632{ .mfi
633 nop.m 0
634 // (0.5*z)*(3-(y*z)*z)
635 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs_iter2,f0
636 nop.i 0
637}
638;;
639
640/////////////////////////// The second iteration /////////////////////////////
641{ .mfi
642 nop.m 0
643 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
644 nop.i 0
645}
646{ .mfi
647 nop.m 0
648 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
649 nop.i 0
650}
651;;
652
653{ .mfi
654 nop.m 0
655 fma.s1 log_arg_early = log_arg_early,log_y,f8
656 nop.i 0
657}
658;;
659
660{ .mfi
661 nop.m 0
662 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
663 nop.i 0
664}
665{ .mfi
666 nop.m 0
667 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
668 nop.i 0
669}
670;;
671
672{ .mfi
673 nop.m 0
674 frcpa.s1 log_C,p0 = f1,log_arg_early
675 nop.i 0
676}
677;;
678
679{ .mfi
680 getf.exp log_GR_signexp_f8 = log_arg_early
681 nop.f 0
682 nop.i 0
683}
684;;
685
686{ .mfi
687 getf.sig log_GR_significand_f8 = log_arg_early
688 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,f8 // (0.5*z)*(3-(y*z)*z)
689 adds log_table_address3 = 0x40, NR_table_address
690}
691;;
692
693///////////////////////////////// The end NR iterations /////////////////////
694
695{ .mmi
696 //significant bit destruction
697 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
698;;
699 //BIAS subtraction
700 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
701 nop.i 0
702}
703;;
704
705{ .mfi
706 setf.sig log_int_Nfloat = log_GR_true_exp_f8
707 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
708 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
709}
710;;
711
712{ .mmi
713 //pre-index*8 + index
714 shladd log_table_address3 = log_GR_index,3,log_table_address3
715;;
716 ldfd log_T = [log_table_address3]
717 nop.i 0
718}
719;;
720
721{ .mfi
722 nop.m 0
723 fma.s1 log_rsq = log_r, log_r, f0 //r^2
724 nop.i 0
725}
726{ .mfi
727 nop.m 0
728 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
729 nop.i 0
730}
731;;
732
733{ .mfi
734 nop.m 0
735 fma.s1 log_rp_p10 = log_P1, log_r, f1 //P1*r + 1.0
736 nop.i 0
737}
738;;
739
740{ .mfi
741 nop.m 0
742 //convert N to the floating-point format log_Nfloat
743 fcvt.xf log_Nfloat = log_int_Nfloat
744 nop.i 0
745}
746;;
747
748{ .mfi
749 nop.m 0
750 //(P3*r + P2)*r^2 + P1*r + 1.0
751 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
752 nop.i 0
753}
754;;
755
756{ .mfi
757 nop.m 0
758 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
759 nop.i 0
760}
761;;
762
763{ .mfb
764 nop.m 0
765 fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
766 br.ret.sptk b0 // Exit main path, path 3: 1.0005 <= x < 2^51
767}
768;;
769
770// Here if path 2, 1.0 < x < 1.0005
771ACOSH_NEAR_ONE:
772// The first NR iteration
773{ .mfi
774 nop.m 0
775 fma.s1 acosh_w_iter1 = acosh_w_rs,log_w,f0 //t*w
776 nop.i 0
777}
778{ .mfi
779 nop.m 0
780 fma.s1 acosh_w_1 = f8,log_C2,log_C1 //x*C2 + C1
781 nop.i 0
782}
783;;
784
785{ .mfi
786 nop.m 0
787 fma.s1 acosh_w_iter2 = acosh_w_rs,NR1,f0 //t*0.5
788 nop.i 0
789}
790{ .mfi
791 nop.m 0
792 fnma.s1 acosh_w_iter1 = acosh_w_iter1,acosh_w_rs,NR2 //3-t*t*w
793 nop.i 0
794}
795;;
796
797{ .mfi
798 nop.m 0
799 //(3-t*t*w)*t*0.5
800 fma.s1 acosh_w_iter2 = acosh_w_iter2,acosh_w_iter1,f0
801 nop.i 0
802}
803{ .mfi
804 nop.m 0
805 fma.s1 acosh_w_1 = acosh_w_1,log_w,log_C0 //(x*C2 + C1)*(x-1) + C0
806 nop.i 0
807}
808;;
809
810// The second NR iteration
811{ .mfi
812 nop.m 0
813 fma.s1 acosh_w_rs = acosh_w_iter2,log_w,f0 //t*w
814 nop.i 0
815}
816;;
817
818{ .mfi
819 nop.m 0
820 fnma.s1 acosh_w_iter1 = acosh_w_iter2,acosh_w_rs,NR2
821 nop.i 0
822}
823{ .mfi
824 nop.m 0
825 fma.s1 acosh_w_iter2 = acosh_w_iter2,NR1,f0
826 nop.i 0
827}
828;;
829
830{ .mfi
831 nop.m 0
832 fma.s1 acosh_w_iter2 = acosh_w_iter2,acosh_w_iter1,f0
833 nop.i 0
834}
835;;
836
837{ .mfi
838 nop.m 0
839 fma.s1 acosh_w_sqrt = acosh_w_iter2,log_w,f0
840 nop.i 0
841}
842;;
843
844{ .mfb
845 nop.m 0
846 fma.s.s0 f8 = acosh_w_1,acosh_w_sqrt,f0
847 br.ret.sptk b0 // Exit path 2, 1.0 < x < 1.0005
848}
849;;
850
851// Here if path 4, x >= 2^51
852LOG_COMMON1:
853{ .mfi
854 ldfpd log_P3,log_P2 = [NR_table_address],16
855 frcpa.s1 log_C,p0 = f1,log_arg
856 nop.i 0
857}
858;;
859
860{ .mmi
861 getf.exp log_GR_signexp_f8 = log_arg
862 ldfpd log_P1,log2 = [NR_table_address],16
863 nop.i 0
864}
865;;
866
867{ .mmi
868 getf.sig log_GR_significand_f8 = log_arg
869 nop.m 0
870 nop.i 0
871}
872;;
873
874{ .mfi
875 adds log_table_address3 = 0x40, NR_table_address
876 nop.f 0
877 //significant bit destruction
878 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
879}
880;;
881
882{ .mmf
883 nop.m 0
884 //BIAS subtraction
885 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
886 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
887}
888;;
889
890{ .mfi
891 setf.sig log_int_Nfloat = log_GR_true_exp_f8
892 nop.f 0
893 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
894}
895;;
896
897{ .mmi
898 //pre-index*8 + index
899 shladd log_table_address3 = log_GR_index,3,log_table_address3
900;;
901 ldfd log_T = [log_table_address3]
902 nop.i 0
903}
904;;
905
906{ .mfi
907 nop.m 0
908 fma.s1 log_rsq = log_r, log_r, f0 //r^2
909 nop.i 0
910}
911{ .mfi
912 nop.m 0
913 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
914 nop.i 0
915}
916;;
917
918{ .mfi
919 nop.m 0
920 fma.s1 log_rp_p10 = log_P1, log_r, f1 //P1*r + 1.0
921 nop.i 0
922}
923;;
924
925{ .mfi
926 nop.m 0
927 //convert N to the floating-point format log_Nfloat
928 fcvt.xf log_Nfloat = log_int_Nfloat
929 nop.i 0
930}
931{ .mfi
932 nop.m 0
933 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
934 nop.i 0
935}
936;;
937
938{ .mfi
939 nop.m 0
940 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
941 nop.i 0
942}
943;;
944
945{ .mfb
946 nop.m 0
947 fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
948 br.ret.sptk b0 // Exit path 4, x >= 2^51
949}
950;;
951
952// Here if path 7, x < 1.0
953ACOSH_LESS_ONE:
954{ .mfi
955 alloc r32 = ar.pfs,1,3,4,0
956 fmerge.s f10 = f8,f8
957 nop.i 0
958}
959;;
960
961{ .mfb
962 mov acosh_GR_tag = 137
963 frcpa.s0 f8,p0 = f0,f0
964 br.cond.sptk __libm_error_region
965}
966;;
967
968GLOBAL_LIBM_END(acoshf)
aa1142c5 969libm_alias_float_other (acosh, acosh)
d5efd131
MF		 970
971
972LOCAL_LIBM_ENTRY(__libm_error_region)
973.prologue
974
975{ .mfi
976 add GR_Parameter_Y=-32,sp // Parameter 2 value
977 nop.f 0
978.save ar.pfs,GR_SAVE_PFS
979 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
980}
981{ .mfi
982.fframe 64
983 add sp=-64,sp // Create new stack
984 nop.f 0
985 mov GR_SAVE_GP=gp // Save gp
986};;
987
988{ .mmi
989 stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
990 add GR_Parameter_X = 16,sp // Parameter 1 address
991.save b0, GR_SAVE_B0
992 mov GR_SAVE_B0=b0 // Save b0
993};;
994
995.body
996{ .mib
997 stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
998 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
999 nop.b 0
1000}
1001{ .mib
1002 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
1003 add GR_Parameter_Y = -16,GR_Parameter_Y
1004 br.call.sptk b0=__libm_error_support# // Call error handling function
1005};;
1006
1007{ .mmi
1008 add GR_Parameter_RESULT = 48,sp
1009 nop.m 0
1010 nop.i 0
1011};;
1012
1013{ .mmi
1014 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
1015.restore sp
1016 add sp = 64,sp // Restore stack pointer
1017 mov b0 = GR_SAVE_B0 // Restore return address
1018};;
1019
1020{ .mib
1021 mov gp = GR_SAVE_GP // Restore gp
1022 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1023 br.ret.sptk b0 // Return
1024};;
1025
1026LOCAL_LIBM_END(__libm_error_region)
1027
1028
1029.type __libm_error_support#,@function
1030.global __libm_error_support#
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