| blob | fb25fa00537f7831b7e42690ff288db559fba1e9 |
1 .file "acosh.s"
4 // Copyright (c) 2000 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // ==============================================================
41 // History
42 // ==============================================================
43 // 03/23/01 Initial version
44 // 04/19/01 Improved speed of the paths #1,2,3,4,5
45 // 05/20/02 Cleaned up namespace and sf0 syntax
46 // 02/06/03 Reordered header: .section, .global, .proc, .align
47 // 05/14/03 Improved performance, set denormal flag for unorms >= 1.0
48 // 03/31/05 Reformatted delimiters between data tables
49 //
50 // API
51 // ==============================================================
52 // double acosh(double)
53 //
54 // Overview of operation
55 // ==============================================================
56 //
57 // There are 7 paths:
58 // 1. x = 1.0
59 // Return acosh(x) = 0.0
60 // 2. 1.0 < x < 1.000499725341796875(0x3FF0020C00000000)
61 // Return acosh(x) = sqrt(x-1) * Pol4(x), where Pol4(x) =
62 // (((x*C4 + C3)*(x-1) + C2)*(x-1) + C1)*(x-1) + C0
64 // 3. 1.000499725341796875(0x3FF0020C00000000) <= x < 2^63
65 // Return acosh(x) = log(x + sqrt(x^2 -1.0))
66 // To compute x + sqrt(x^2 -1.0) modified Newton Raphson method is used
67 // (3 iterations)
68 // Algorithm description for log function see below.
69 //
70 // 4. 2^63 <= x < +INF
71 // Return acosh(x) = log(2*x)
72 // Algorithm description for log function see below.
73 //
74 // 5. x = +INF
75 // Return acosh(x) = +INF
76 //
77 // 6. x = [S,Q]NaN
78 // Return acosh(x) = QNaN
79 //
80 // 7. x < 1.0
81 // It's domain error. Error handler with tag = 136 is called
82 //
83 //==============================================================
84 // Algorithm Description for log(x) function
85 // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
86 // true for this acosh implementation
87 //
88 // Consider x = 2^N 1.f1 f2 f3 f4...f63
89 // Log(x) = log(frcpa(x) x/frcpa(x))
90 // = log(1/frcpa(x)) + log(frcpa(x) x)
91 // = -log(frcpa(x)) + log(frcpa(x) x)
92 //
93 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
94 //
95 // -log(frcpa(x)) = -log(C)
96 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
97 //
98 // -log(frcpa(x)) = -log(C)
99 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
100 //
101 // -log(frcpa(x)) = -log(C)
102 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
103 //
104 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
105 //
106 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
107 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
108 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
109 //
110 // Log(x) = +Nlog2 + T + log(C x)
111 //
112 // Cx = 1 + r
113 //
114 // Log(x) = +Nlog2 + T + log(1+r)
115 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
116 //
117 // 1.f1 f2 ... f8 has 256 entries.
118 // They are 1 + k/2^8, k = 0 ... 255
119 // These 256 values are the table entries.
120 //
121 // Implementation
122 //==============================================================
123 // C = frcpa(x)
124 // r = C * x - 1
125 //
126 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
127 //
128 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
129 // Nfloat = float(n) where n is the true unbiased exponent
130 // pre-index = f_1f_2....f_8
131 // index = pre_index * 16
132 // get the dxt table entry at index + offset = T
133 //
134 // result = (T + Nfloat * log(2)) + rseries
135 //
136 // The T table is calculated as follows
137 // Form x_k = 1 + k/2^8 where k goes from 0... 255
138 // y_k = frcpa(x_k)
139 // log(1/y_k) in quad and round to double-extended
140 //
142 // Registers used
143 //==============================================================
144 // Floating Point registers used:
145 // f8, input
146 // f9 -> f15, f32 -> f65
148 // General registers used:
149 // r14 -> r27, r32 -> r39
151 // Predicate registers used:
152 // p6 -> p15
154 // p6 to filter out case when x = [Q,S]NaN
155 // p7,p8 to filter out case when x < 1.0
156 // p10 to select path #1
157 // p11 to filter out case when x = +INF
158 // p12 used in the frcpa
159 // p13 to select path #4
160 // p14,p15 to select path #2
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 acosh_GR_f8 = r23
174 log_GR_comp = r24
175 acosh_GR_f8_sig = r25
176 log_table_address3 = r26
177 NR_table_address = r27
179 GR_SAVE_B0 = r33
180 GR_SAVE_GP = r34
181 GR_SAVE_PFS = r35
183 GR_Parameter_X = r36
184 GR_Parameter_Y = r37
185 GR_Parameter_RESULT = r38
186 acosh_GR_tag = r39
188 //==============================================================
189 log_y = f9
190 NR1 = f10
191 NR2 = f11
192 log_y_rs = f12
193 log_y_rs_iter = f13
194 log_y_rs_iter1 = f14
195 log_NORM_f8 = f15
196 acosh_comp = f32
197 log_w = f34
198 log_P5 = f35
199 log_P4 = f36
200 log_P3 = f37
201 log_P2 = f38
202 log_P1 = f39
203 log_C0 = f40
204 log_C1 = f41
205 log_C2 = f42
206 log2 = f43
207 acosh_w_rs = f44
208 log_C = f45
209 log_arg = f46
210 acosh_w_iter1 = f47
211 acosh_w_iter2 = f48
212 log_int_Nfloat = f49
213 log_r = f50
214 log_rsq = f51
215 log_rp_p4 = f52
216 log_rp_p32 = f53
217 log_rcube = f54
218 log_rp_p10 = f55
219 log_rp_p2 = f56
220 log_Nfloat = f57
221 log_T = f58
222 log_r2P_r = f59
223 log_T_plus_Nlog2 = f60
224 acosh_w_sqrt = f61
225 acosh_w_1 = f62
226 log_C3 = f63
227 log_C4 = f64
228 log_arg_early = f65
231 // Data tables
232 //==============================================================
234 RODATA
235 .align 16
237 LOCAL_OBJECT_START(log_table_1)
238 data8 0x3FF0020C49BA5E35 // 1.0005
239 data8 0xBFC5555DA7212371 // P5
240 data8 0x3FC999A19EEF5826 // P4
241 data8 0xBFCFFFFFFFFEF009 // P3
242 data8 0x3FD555555554ECB2 // P2
243 data8 0xBFE0000000000000 // P1 = -0.5
244 //
245 data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
246 LOCAL_OBJECT_END(log_table_1)
248 LOCAL_OBJECT_START(log_table_2)
249 data8 0x3FE0000000000000 // 0.5
250 data8 0x4008000000000000 // 3.0
251 //
252 data8 0xAFE8F9203939CCF8, 0x00003FF6 // C4 3FF6AFE8F9203939CCF8
253 data8 0xAD46EB6AE752D809, 0x0000BFF8 // C3 BFF8AD46EB6AE752D809
254 data8 0xD93923D7F53F3627, 0x00003FF9 // C2 3FF9D93923D7F53F3627
255 data8 0xF15BEEEFF7D32D36, 0x0000BFFB // C1 BFFBF15BEEEFF7D32D36
256 data8 0xB504F333F9DE6484, 0x00003FFF // C0 3FFFB504F333F9DE6484
257 LOCAL_OBJECT_END(log_table_2)
260 LOCAL_OBJECT_START(log_table_3)
261 data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
262 //
263 data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
264 data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
265 data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
266 data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
267 data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
268 //
269 data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
270 data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
271 data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
272 data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
273 data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
274 //
275 data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
276 data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
277 data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
278 data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
279 data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
280 //
281 data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
282 data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
283 data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
284 data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
285 data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
286 //
287 data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
288 data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
289 data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
290 data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
291 data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
292 //
293 data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
294 data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
295 data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
296 data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
297 data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
298 //
299 data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
300 data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
301 data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
302 data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
303 data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
304 //
305 data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
306 data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
307 data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
308 data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
309 data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
310 //
311 data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
312 data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
313 data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
314 data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
315 data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
316 //
317 data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
318 data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
319 data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
320 data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
321 data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
322 //
323 data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
324 data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
325 data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
326 data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
327 data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
328 //
329 data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
330 data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
331 data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
332 data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
333 data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
334 //
335 data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
336 data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
337 data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
338 data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
339 data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
340 //
341 data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
342 data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
343 data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
344 data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
345 data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
346 //
347 data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
348 data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
349 data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
350 data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
351 data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
352 //
353 data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
354 data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
355 data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
356 data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
357 data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
358 //
359 data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
360 data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
361 data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
362 data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
363 data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
364 //
365 data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
366 data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
367 data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
368 data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
369 data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
370 //
371 data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
372 data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
373 data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
374 data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
375 data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
376 //
377 data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
378 data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
379 data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
380 data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
381 data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
382 //
383 data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
384 data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
385 data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
386 data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
387 data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
388 //
389 data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
390 data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
391 data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
392 data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
393 data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
394 //
395 data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
396 data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
397 data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
398 data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
399 data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
400 //
401 data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
402 data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
403 data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
404 data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
405 data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
406 //
407 data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
408 data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
409 data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
410 data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
411 data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
412 //
413 data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
414 data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
415 data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
416 data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
417 data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
418 //
419 data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
420 data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
421 data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
422 data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
423 data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
424 //
425 data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
426 data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
427 data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
428 data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
429 data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
430 //
431 data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
432 data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
433 data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
434 data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
435 data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
436 //
437 data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
438 data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
439 data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
440 data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
441 data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
442 //
443 data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
444 data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
445 data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
446 data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
447 data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
448 //
449 data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
450 data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
451 data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
452 data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
453 data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
454 //
455 data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
456 data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
457 data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
458 data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
459 data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
460 //
461 data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
462 data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
463 data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
464 data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
465 data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
466 //
467 data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
468 data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
469 data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
470 data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
471 data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
472 //
473 data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
474 data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
475 data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
476 data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
477 data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
478 //
479 data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
480 data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
481 data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
482 data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
483 data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
484 //
485 data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
486 data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
487 data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
488 data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
489 data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
490 //
491 data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
492 data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
493 data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
494 data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
495 data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
496 //
497 data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
498 data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
499 data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
500 data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
501 data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
502 //
503 data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
504 data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
505 data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
506 data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
507 data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
508 //
509 data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
510 data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
511 data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
512 data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
513 data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
514 //
515 data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
516 data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
517 data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
518 data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
519 data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
520 //
521 data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
522 data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
523 data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
524 data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
525 data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
526 //
527 data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
528 data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
529 data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
530 data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
531 data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
532 //
533 data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
534 data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
535 data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
536 data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
537 data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
538 //
539 data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
540 data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
541 data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
542 data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
543 data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
544 //
545 data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
546 data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
547 data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
548 data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
549 data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
550 //
551 data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
552 data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
553 data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
554 data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
555 data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
556 //
557 data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
558 data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
559 data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
560 data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
561 data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
562 //
563 data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
564 data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
565 data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
566 data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
567 data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
568 LOCAL_OBJECT_END(log_table_3)
571 .section .text
572 GLOBAL_LIBM_ENTRY(acosh)
574 { .mfi
575 getf.exp acosh_GR_f8 = f8
576 fclass.m p6,p0 = f8, 0xc3 // Test for x = NaN
577 mov log_GR_comp2 = 0x1003e
578 }
579 { .mfi
580 addl NR_table_address = @ltoff(log_table_1), gp
581 fms.s1 log_y = f8, f8, f1 // y = x^2-1
582 nop.i 0
583 }
584 ;;
586 { .mfi
587 getf.sig acosh_GR_f8_sig = f8
588 fclass.m p11,p0 = f8, 0x21 // Test for x=+inf
589 mov log_GR_exp_17_ones = 0x1ffff
590 }
591 { .mfi
592 ld8 NR_table_address = [NR_table_address]
593 fms.s1 log_w = f8,f1,f1 // w = x - 1
594 nop.i 0
595 }
596 ;;
598 { .mfi
599 nop.m 0
600 fcmp.lt.s1 p7,p8 = f8, f1 // Test for x<1.0
601 addl log_GR_comp = 0x10020C,r0 // Upper 21 bits of signif of 1.0005
602 }
603 { .mfb
604 mov log_GR_exp_16_ones = 0xffff //BIAS
605 (p6) fma.d.s0 f8 = f8,f1,f0 // quietize nan result if x=nan
606 (p6) br.ret.spnt b0 // Exit for x=nan
607 }
608 ;;
610 { .mfb
611 //get second table address
612 adds log_table_address2 = 0x40, NR_table_address
613 fcmp.eq.s1 p10,p0 = f8, f1 // Test for x=+1.0
614 (p11) br.ret.spnt b0 // Exit for x=+inf
615 }
616 ;;
618 { .mfi
619 ldfpd NR1,NR2 = [log_table_address2],16
620 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
621 nop.i 0
622 }
623 { .mfb
624 nop.m 0
625 fma.s1 log_arg = f8,f1,f8
626 (p7) br.cond.spnt ACOSH_LESS_ONE // Branch if path 7, x < 1.0
627 }
628 ;;
630 { .mfi
631 ldfe log_C4 = [log_table_address2],16
632 (p8) fcmp.eq.s0 p6,p0 = f8, f0 // Dummy op sets denorm flag if unorm>=1.0
633 nop.i 0
634 }
635 { .mfb
636 (p8) cmp.le.unc p13,p0 = log_GR_comp2,acosh_GR_f8
637 nop.f 0
638 (p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, x >= 2^63
639 }
640 ;;
642 { .mfi
643 ldfe log_C3 = [log_table_address2],16
644 (p10) fmerge.s f8 = f0, f0 // Return 0 if x=1.0
645 shr.u acosh_GR_f8_sig = acosh_GR_f8_sig,43
646 }
647 { .mib
648 cmp.eq p14,p0 = log_GR_exp_16_ones,acosh_GR_f8
649 nop.i 0
650 (p10) br.ret.spnt b0 // Exit for x=1.0
651 }
652 ;;
654 { .mfi
655 ldfe log_C2 = [log_table_address2],16
656 frsqrta.s1 acosh_w_rs,p0 = log_w // t=1/sqrt(w)
657 nop.i 0
658 }
659 { .mfb
660 (p14) cmp.lt.unc p15,p0 = acosh_GR_f8_sig,log_GR_comp
661 nop.f 0
662 (p15) br.cond.spnt ACOSH_NEAR_ONE // Branch if path 2, 1.0 < x < 1.0005
663 }
664 ;;
666 // Here is main path, 1.0005 <= x < 2^63
667 /////////////// The first iteration //////////////////////////////////
668 { .mfi
669 ldfpd acosh_comp,log_P5 = [NR_table_address],16
670 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
671 nop.i 0
672 }
673 ;;
675 { .mfi
676 ldfpd log_P4,log_P3 = [NR_table_address],16
677 fnma.s1 log_y_rs_iter = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
678 nop.i 0
679 }
680 { .mfi
681 nop.m 0
682 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
683 nop.i 0
684 }
685 ;;
687 { .mfi
688 ldfpd log_P2,log_P1 = [NR_table_address],16
689 //(0.5*z)*(3-(y*z)*z)
690 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter,f0
691 nop.i 0
692 }
693 ;;
695 /////////////////////////// The second iteration /////////////////////////////
696 { .mfi
697 nop.m 0
698 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
699 nop.i 0
700 }
701 ;;
703 { .mfi
704 nop.m 0
705 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
706 nop.i 0
707 }
708 { .mfi
709 nop.m 0
710 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
711 nop.i 0
712 }
713 ;;
715 { .mfi
716 nop.m 0
717 //(0.5*z)*(3-(y*z)*z)
718 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs,f0
719 nop.i 0
720 }
721 { .mfi
722 nop.m 0
723 //(0.5*z)*(3-(y*z)*z)
724 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs,f0
725 nop.i 0
726 }
727 ;;
729 //////////////////////////////////////// The third iteration /////////////////
730 { .mfi
731 nop.m 0
732 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
733 nop.i 0
734 }
735 { .mfi
736 nop.m 0
737 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
738 nop.i 0
739 }
740 ;;
742 { .mfi
743 nop.m 0
744 fma.s1 log_arg_early = log_arg_early,log_y,f8
745 nop.i 0
746 }
747 ;;
749 { .mfi
750 nop.m 0
751 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
752 nop.i 0
753 }
754 { .mfi
755 nop.m 0
756 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
757 nop.i 0
758 }
759 ;;
761 { .mfi
762 nop.m 0
763 frcpa.s1 log_C,p0 = f1,log_arg_early
764 nop.i 0
765 }
766 ;;
768 { .mfi
769 getf.exp log_GR_signexp_f8 = log_arg_early
770 nop.f 0
771 nop.i 0
772 }
773 ;;
775 { .mfi
776 getf.sig log_GR_significand_f8 = log_arg_early
777 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,f8 // (0.5*z)*(3-(y*z)*z)
778 adds log_table_address3 = 0x70, NR_table_address
779 }
780 ;;
782 ///////////////////////////////// The end NR iterations /////////////////////
783 { .mfi
784 ldfe log2 = [NR_table_address],16
785 nop.f 0
786 nop.i 0
787 }
788 ;;
790 { .mmi
791 //significant bit destruction
792 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
793 ;;
794 //BIAS subtraction
795 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
796 nop.i 0
797 }
798 ;;
800 { .mfi
801 setf.sig log_int_Nfloat = log_GR_true_exp_f8
802 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
803 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
804 }
805 ;;
807 { .mmi
808 //pre-index*16 + index
809 shladd log_table_address3 = log_GR_index,4,log_table_address3
810 ;;
811 ldfe log_T = [log_table_address3]
812 nop.i 0
813 }
814 ;;
816 { .mfi
817 nop.m 0
818 fma.s1 log_rsq = log_r, log_r, f0 //r^2
819 nop.i 0
820 }
821 { .mfi
822 nop.m 0
823 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
824 nop.i 0
825 }
826 ;;
828 { .mfi
829 nop.m 0
830 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
831 nop.i 0
832 }
833 ;;
835 { .mfi
836 nop.m 0
837 //convert N to the floating-point format log_Nfloat
838 fcvt.xf log_Nfloat = log_int_Nfloat
839 nop.i 0
840 }
841 ;;
843 { .mfi
844 nop.m 0
845 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
846 nop.i 0
847 }
848 { .mfi
849 nop.m 0
850 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
851 nop.i 0
852 }
853 ;;
855 { .mfi
856 nop.m 0
857 //(P5*r + P4)*r^2 + P3*r + P2
858 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
859 nop.i 0
860 }
861 ;;
863 { .mfi
864 nop.m 0
865 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
866 nop.i 0
867 }
868 { .mfi
869 nop.m 0
870 //((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
871 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
872 nop.i 0
873 }
874 ;;
876 { .mfb
877 nop.m 0
878 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
879 fadd.d.s0 f8 = log_T_plus_Nlog2, log_r2P_r
880 br.ret.sptk b0 // Exit main path, path 3: 1.0005 <= x < 2^63
881 }
882 ;;
884 // Here if path 2, 1.0 < x < 1.0005
885 ACOSH_NEAR_ONE:
886 // The first NR iteration
887 { .mfi
888 ldfe log_C1 = [log_table_address2],16
889 fma.s1 acosh_w_iter1 = acosh_w_rs,log_w,f0 //t*w
890 nop.i 0
891 }
892 { .mfi
893 nop.m 0
894 fma.s1 acosh_w_1 = f8,log_C4,log_C3 //x*C4 + C3
895 nop.i 0
896 }
897 ;;
899 { .mfi
900 ldfe log_C0 = [log_table_address2],16
901 fma.s1 acosh_w_iter2 = acosh_w_rs,NR1,f0 //t*0.5
902 nop.i 0
903 }
904 { .mfi
905 nop.m 0
906 fnma.s1 acosh_w_iter1 = acosh_w_iter1,acosh_w_rs,NR2 //3-t*t*w
907 nop.i 0
908 }
909 ;;
911 { .mfi
912 nop.m 0
913 //(3-t*t*w)*t*0.5
914 fma.s1 acosh_w_iter2 = acosh_w_iter2,acosh_w_iter1,f0
915 nop.i 0
916 }
917 { .mfi
918 nop.m 0
919 fma.s1 acosh_w_1 = acosh_w_1,log_w,log_C2 //(x*C4 + C3)*(x-1) + C2
920 nop.i 0
921 }
922 ;;
924 // The second NR iteration
925 { .mfi
926 nop.m 0
927 fma.s1 acosh_w_rs = acosh_w_iter2,log_w,f0 //t*w
928 nop.i 0
929 }
930 { .mfi
931 nop.m 0
932 //((x*C4 + C3)*(x-1) + C2)*(x-1) + C1
933 fma.s1 acosh_w_1 = acosh_w_1,log_w,log_C1
934 nop.i 0
935 }
936 ;;
938 { .mfi
939 nop.m 0
940 fnma.s1 acosh_w_iter1 = acosh_w_iter2,acosh_w_rs,NR2
941 nop.i 0
942 }
943 { .mfi
944 nop.m 0
945 fma.s1 acosh_w_iter2 = acosh_w_iter2,NR1,f0
946 nop.i 0
947 }
948 ;;
950 { .mfi
951 nop.m 0
952 fma.s1 acosh_w_iter2 = acosh_w_iter2,acosh_w_iter1,f0
953 nop.i 0
954 }
955 { .mfi
956 nop.m 0
957 //(((x*C4 + C3)*(x-1) + C2)*(x-1) + C1)*(x-1) + C0
958 fma.s1 acosh_w_1 = acosh_w_1,log_w,log_C0
959 nop.i 0
960 }
961 ;;
963 //The third NR iteration
964 { .mfi
965 nop.m 0
966 fma.s1 acosh_w_rs = acosh_w_iter2,log_w,f0 //t*w
967 nop.i 0
968 }
969 ;;
971 { .mfi
972 nop.m 0
973 fnma.s1 acosh_w_iter1 = acosh_w_iter2,acosh_w_rs,NR2
974 nop.i 0
975 }
976 { .mfi
977 nop.m 0
978 fma.s1 acosh_w_iter2 = acosh_w_iter2,NR1,f0
979 nop.i 0
980 }
981 ;;
983 { .mfi
984 nop.m 0
985 fma.s1 acosh_w_iter2 = acosh_w_iter2,acosh_w_iter1,f0
986 nop.i 0
987 }
988 ;;
990 { .mfi
991 nop.m 0
992 fma.s1 acosh_w_sqrt = acosh_w_iter2,log_w,f0
993 nop.i 0
994 }
995 ;;
997 { .mfb
998 nop.m 0
999 fma.d.s0 f8 = acosh_w_1,acosh_w_sqrt,f0
1000 br.ret.sptk b0 // Exit path 2, 1.0 < x < 1.0005
1001 }
1002 ;;
1004 // Here if path 4, x >= 2^63
1005 LOG_COMMON1:
1006 { .mfi
1007 ldfpd acosh_comp,log_P5 = [NR_table_address],16
1008 frcpa.s1 log_C,p0 = f1,log_arg
1009 nop.i 0
1010 }
1011 ;;
1013 { .mmi
1014 getf.exp log_GR_signexp_f8 = log_arg
1015 ldfpd log_P4,log_P3 = [NR_table_address],16
1016 nop.i 0
1017 }
1018 ;;
1020 { .mmi
1021 getf.sig log_GR_significand_f8 = log_arg
1022 ldfpd log_P2,log_P1 = [NR_table_address],16
1023 nop.i 0
1024 }
1025 ;;
1027 { .mfi
1028 adds log_table_address3 = 0x70, NR_table_address
1029 nop.f 0
1030 //significant bit destruction
1031 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
1032 }
1033 ;;
1035 { .mmf
1036 ldfe log2 = [NR_table_address],16
1037 //BIAS subtraction
1038 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
1039 fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
1040 }
1041 ;;
1043 { .mfi
1044 setf.sig log_int_Nfloat = log_GR_true_exp_f8
1045 nop.f 0
1046 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
1047 }
1048 ;;
1050 { .mmi
1051 //pre-index*16 + index
1052 shladd log_table_address3 = log_GR_index,4,log_table_address3
1053 ;;
1054 ldfe log_T = [log_table_address3]
1055 nop.i 0
1056 }
1057 ;;
1059 { .mfi
1060 nop.m 0
1061 fma.s1 log_rsq = log_r, log_r, f0 //r^2
1062 nop.i 0
1063 }
1064 { .mfi
1065 nop.m 0
1066 fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
1067 nop.i 0
1068 }
1069 ;;
1071 { .mfi
1072 nop.m 0
1073 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
1074 nop.i 0
1075 }
1076 ;;
1078 { .mfi
1079 nop.m 0
1080 fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
1081 nop.i 0
1082 }
1083 { .mfi
1084 nop.m 0
1085 fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
1086 nop.i 0
1087 }
1088 ;;
1090 { .mfi
1091 nop.m 0
1092 //convert N to the floating-point format log_Nfloat
1093 fcvt.xf log_Nfloat = log_int_Nfloat
1094 nop.i 0
1095 }
1096 { .mfi
1097 nop.m 0
1098 //(P5*r + P4)*r^2 + P3*r + P2
1099 fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
1100 nop.i 0
1101 }
1102 ;;
1104 { .mfi
1105 nop.m 0
1106 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
1107 nop.i 0
1108 }
1109 { .mfi
1110 nop.m 0
1111 //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
1112 fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
1113 nop.i 0
1114 }
1115 ;;
1117 { .mfb
1118 nop.m 0
1119 // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
1120 fadd.d.s0 f8 = log_T_plus_Nlog2, log_r2P_r
1121 br.ret.sptk b0 // Exit path 4, x >= 2^63
1122 }
1123 ;;
1125 // Here if path 7, x < 1.0
1126 ACOSH_LESS_ONE:
1127 { .mfi
1128 alloc r32 = ar.pfs,1,3,4,0
1129 fmerge.s f10 = f8,f8
1130 nop.i 0
1131 }
1132 ;;
1134 { .mfb
1135 mov acosh_GR_tag = 136
1136 frcpa.s0 f8,p0 = f0,f0
1137 br.cond.sptk __libm_error_region
1138 }
1139 ;;
1141 GLOBAL_LIBM_END(acosh)
1144 LOCAL_LIBM_ENTRY(__libm_error_region)
1145 .prologue
1147 { .mfi
1148 add GR_Parameter_Y=-32,sp // Parameter 2 value
1149 nop.f 0
1150 .save ar.pfs,GR_SAVE_PFS
1151 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1152 }
1153 { .mfi
1154 .fframe 64
1155 add sp=-64,sp // Create new stack
1156 nop.f 0
1157 mov GR_SAVE_GP=gp // Save gp
1158 };;
1160 { .mmi
1161 stfd [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
1162 add GR_Parameter_X = 16,sp // Parameter 1 address
1163 .save b0, GR_SAVE_B0
1164 mov GR_SAVE_B0=b0 // Save b0
1165 };;
1167 .body
1168 { .mib
1169 stfd [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
1170 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1171 nop.b 0
1172 }
1173 { .mib
1174 stfd [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
1175 add GR_Parameter_Y = -16,GR_Parameter_Y
1176 br.call.sptk b0=__libm_error_support# // Call error handling function
1177 };;
1179 { .mmi
1180 add GR_Parameter_RESULT = 48,sp
1181 nop.m 0
1182 nop.i 0
1183 };;
1185 { .mmi
1186 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
1187 .restore sp
1188 add sp = 64,sp // Restore stack pointer
1189 mov b0 = GR_SAVE_B0 // Restore return address
1190 };;
1192 { .mib
1193 mov gp = GR_SAVE_GP // Restore gp
1194 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1195 br.ret.sptk b0 // Return
1196 };;
1198 LOCAL_LIBM_END(__libm_error_region)
1201 .type __libm_error_support#,@function
1202 .global __libm_error_support#