| blob | 4ae5ee69269e4b551c43409f63dfc704cadc571f |
1 .file "atanh.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 // 05/03/01 Initial version
44 // 05/20/02 Cleaned up namespace and sf0 syntax
45 // 02/06/03 Reordered header: .section, .global, .proc, .align
46 // 05/26/03 Improved performance, fixed to handle unorms
47 // 03/31/05 Reformatted delimiters between data tables
48 //
49 // API
50 // ==============================================================
51 // double atanh(double)
52 //
53 // Overview of operation
54 // ==============================================================
55 //
56 // There are 7 paths:
57 // 1. x = +/-0.0
58 // Return atanh(x) = +/-0.0
59 //
60 // 2. 0.0 < |x| < 1/4
61 // Return atanh(x) = Po2l(x),
62 // where Po2l(x) = (((((((((C9*x^2 + C8)*x^2 + C7)*x^2 + C6)*x^2 +
63 // C5)*x^2 + C4)*x^2 + C3)*x^2 + C2)*x^2 + C1)* x^2 + C0)*x^3 + x
64 // 3. 1/4 <= |x| < 1
65 // Return atanh(x) = sign(x) * log((1 + |x|)/(1 - |x|))
66 // To compute (1 + |x|)/(1 - |x|) modified Newton Raphson method is used
67 // (3 iterations)
68 // Algorithm description for log function see below.
69 //
70 // 4. |x| = 1
71 // Return atanh(x) = sign(x) * +INF
72 //
73 // 5. 1 < |x| <= +INF
74 // Return atanh(x) = QNaN
75 //
76 // 6. x = [S,Q]NaN
77 // Return atanh(x) = QNaN
78 //
79 // 7. x = denormal
80 // Return atanh(x) = x
81 //
82 //==============================================================
83 // Algorithm Description for log(x) function
84 // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always true
85 // for this atanh implementation
86 //
87 // Consider x = 2^N 1.f1 f2 f3 f4...f63
88 // Log(x) = log(x * frcpa(x) / frcpa(x))
89 // = log(x * frcpa(x)) + log(1/frcpa(x))
90 // = log(x * frcpa(x)) - log(frcpa(x))
91 //
92 // frcpa(x) = 2^-N * frcpa(1.f1 f2 ... f63)
93 //
94 // -log(frcpa(x)) = -log(C)
95 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
96 //
97 // -log(frcpa(x)) = -log(C)
98 // = N*log2 - log(frcpa(1.f1 f2 ... f63))
99 //
100 //
101 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
102 //
103 // Log(x) = N*log2 + log(1./frcpa(1.f1 f2 ... f63)) + log(x * frcpa(x))
104 // Log(x) = N*log2 + T + log(frcpa(x) x)
105 //
106 // Log(x) = N*log2 + T + log(C * x)
107 //
108 // C * x = 1 + r
109 //
110 // Log(x) = N*log2 + T + log(1 + r)
111 // Log(x) = N*log2 + T + Series(r - r^2/2 + r^3/3 - r^4/4 + ...)
112 //
113 // 1.f1 f2 ... f8 has 256 entries.
114 // They are 1 + k/2^8, k = 0 ... 255
115 // These 256 values are the table entries.
116 //
117 // Implementation
118 //==============================================================
119 // C = frcpa(x)
120 // r = C * x - 1
121 //
122 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
123 //
124 // x = f * 2*N where f is 1.f_1f_2f_3...f_63
125 // Nfloat = float(n) where n is the true unbiased exponent
126 // pre-index = f_1f_2....f_8
127 // index = pre_index * 16
128 // get the dxt table entry at index + offset = T
129 //
130 // result = (T + Nfloat * log(2)) + rseries
131 //
132 // The T table is calculated as follows
133 // Form x_k = 1 + k/2^8 where k goes from 0... 255
134 // y_k = frcpa(x_k)
135 // log(1/y_k) in quad and round to double-extended
136 //
137 //
138 // Registers used
139 //==============================================================
140 // Floating Point registers used:
141 // f8, input
142 // f32 -> f77
144 // General registers used:
145 // r14 -> r27, r33 -> r39
147 // Predicate registers used:
148 // p6 -> p14
150 // p10, p11 to indicate is argument positive or negative
151 // p12 to filter out case when x = [Q,S]NaN or +/-0
152 // p13 to filter out case when x = denormal
153 // p6, p7 to filter out case when |x| >= 1
154 // p8 to filter out case when |x| < 1/4
156 // Assembly macros
157 //==============================================================
158 Data2Ptr = r14
159 Data3Ptr = r15
160 RcpTablePtr = r16
161 rExpbMask = r17
162 rBias = r18
163 rNearZeroBound = r19
164 rArgSExpb = r20
165 rArgExpb = r21
166 rSExpb = r22
167 rExpb = r23
168 rSig = r24
169 rN = r25
170 rInd = r26
171 DataPtr = r27
173 GR_SAVE_B0 = r33
174 GR_SAVE_GP = r34
175 GR_SAVE_PFS = r35
177 GR_Parameter_X = r36
178 GR_Parameter_Y = r37
179 GR_Parameter_RESULT = r38
180 atanh_GR_tag = r39
182 //==============================================================
183 fAbsX = f32
184 fOneMx = f33
185 fOnePx = f34
186 fY = f35
187 fR = f36
188 fR2 = f37
189 fR3 = f38
190 fRcp = f39
191 fY4Rcp = f40
192 fRcp0 = f41
193 fRcp0n = f42
194 fRcp1 = f43
195 fRcp2 = f44
196 fRcp3 = f45
197 fN4Cvt = f46
198 fN = f47
199 fY2 = f48
200 fLog2 = f49
201 fLogT = f50
202 fLogT_N = f51
203 fX2 = f52
204 fX3 = f53
205 fX4 = f54
206 fX8 = f55
207 fP0 = f56
208 fP5 = f57
209 fP4 = f58
210 fP3 = f59
211 fP2 = f60
212 fP1 = f61
213 fNormX = f62
214 fC9 = f63
215 fC8 = f64
216 fC7 = f65
217 fC6 = f66
218 fC5 = f67
219 fC4 = f68
220 fC3 = f69
221 fC2 = f70
222 fC1 = f71
223 fC0 = f72
224 fP98 = f73
225 fP76 = f74
226 fP54 = f75
227 fP32 = f76
228 fP10 = f77
230 // Data tables
231 //==============================================================
232 RODATA
233 .align 16
235 LOCAL_OBJECT_START(atanh_data)
236 data8 0xBFC5555DA7212371 // P5
237 data8 0x3FC999A19EEF5826 // P4
238 data8 0xBFCFFFFFFFFEF009 // P3
239 data8 0x3FD555555554ECB2 // P2
240 data8 0xBFE0000000000000 // P1 = -0.5
241 data8 0x0000000000000000 // pad
242 data8 0xb17217f7d1cf79ac , 0x00003ffd // 0.5*log(2)
243 data8 0x0000000000000000 , 0x00000000 // pad to eliminate bank conflicts
244 LOCAL_OBJECT_END(atanh_data)
246 LOCAL_OBJECT_START(atanh_data_2)
247 data8 0x8649FB89D3AD51FB , 0x00003FFB // C9
248 data8 0xCC10AABEF160077A , 0x00003FFA // C8
249 data8 0xF1EDB99AC0819CE2 , 0x00003FFA // C7
250 data8 0x8881E53A809AD24D , 0x00003FFB // C6
251 data8 0x9D8A116EF212F271 , 0x00003FFB // C5
252 data8 0xBA2E8A6D1D756453 , 0x00003FFB // C4
253 data8 0xE38E38E7A0945692 , 0x00003FFB // C3
254 data8 0x924924924536891A , 0x00003FFC // C2
255 data8 0xCCCCCCCCCCD08D51 , 0x00003FFC // C1
256 data8 0xAAAAAAAAAAAAAA0C , 0x00003FFD // C0
257 LOCAL_OBJECT_END(atanh_data_2)
260 LOCAL_OBJECT_START(atanh_data_3)
261 data8 0x80200aaeac44ef38 , 0x00003ff5 // log(1/frcpa(1+0/2^-8))/2
262 //
263 data8 0xc09090a2c35aa070 , 0x00003ff6 // log(1/frcpa(1+1/2^-8))/2
264 data8 0xa0c94fcb41977c75 , 0x00003ff7 // log(1/frcpa(1+2/2^-8))/2
265 data8 0xe18b9c263af83301 , 0x00003ff7 // log(1/frcpa(1+3/2^-8))/2
266 data8 0x8d35c8d6399c30ea , 0x00003ff8 // log(1/frcpa(1+4/2^-8))/2
267 data8 0xadd4d2ecd601cbb8 , 0x00003ff8 // log(1/frcpa(1+5/2^-8))/2
268 //
269 data8 0xce95403a192f9f01 , 0x00003ff8 // log(1/frcpa(1+6/2^-8))/2
270 data8 0xeb59392cbcc01096 , 0x00003ff8 // log(1/frcpa(1+7/2^-8))/2
271 data8 0x862c7d0cefd54c5d , 0x00003ff9 // log(1/frcpa(1+8/2^-8))/2
272 data8 0x94aa63c65e70d499 , 0x00003ff9 // log(1/frcpa(1+9/2^-8))/2
273 data8 0xa54a696d4b62b382 , 0x00003ff9 // log(1/frcpa(1+10/2^-8))/2
274 //
275 data8 0xb3e4a796a5dac208 , 0x00003ff9 // log(1/frcpa(1+11/2^-8))/2
276 data8 0xc28c45b1878340a9 , 0x00003ff9 // log(1/frcpa(1+12/2^-8))/2
277 data8 0xd35c55f39d7a6235 , 0x00003ff9 // log(1/frcpa(1+13/2^-8))/2
278 data8 0xe220f037b954f1f5 , 0x00003ff9 // log(1/frcpa(1+14/2^-8))/2
279 data8 0xf0f3389b036834f3 , 0x00003ff9 // log(1/frcpa(1+15/2^-8))/2
280 //
281 data8 0xffd3488d5c980465 , 0x00003ff9 // log(1/frcpa(1+16/2^-8))/2
282 data8 0x87609ce2ed300490 , 0x00003ffa // log(1/frcpa(1+17/2^-8))/2
283 data8 0x8ede9321e8c85927 , 0x00003ffa // log(1/frcpa(1+18/2^-8))/2
284 data8 0x96639427f2f8e2f4 , 0x00003ffa // log(1/frcpa(1+19/2^-8))/2
285 data8 0x9defad3e8f73217b , 0x00003ffa // log(1/frcpa(1+20/2^-8))/2
286 //
287 data8 0xa582ebd50097029c , 0x00003ffa // log(1/frcpa(1+21/2^-8))/2
288 data8 0xac06dbe75ab80fee , 0x00003ffa // log(1/frcpa(1+22/2^-8))/2
289 data8 0xb3a78449b2d3ccca , 0x00003ffa // log(1/frcpa(1+23/2^-8))/2
290 data8 0xbb4f79635ab46bb2 , 0x00003ffa // log(1/frcpa(1+24/2^-8))/2
291 data8 0xc2fec93a83523f3f , 0x00003ffa // log(1/frcpa(1+25/2^-8))/2
292 //
293 data8 0xc99af2eaca4c4571 , 0x00003ffa // log(1/frcpa(1+26/2^-8))/2
294 data8 0xd1581106472fa653 , 0x00003ffa // log(1/frcpa(1+27/2^-8))/2
295 data8 0xd8002560d4355f2e , 0x00003ffa // log(1/frcpa(1+28/2^-8))/2
296 data8 0xdfcb43b4fe508632 , 0x00003ffa // log(1/frcpa(1+29/2^-8))/2
297 data8 0xe67f6dff709d4119 , 0x00003ffa // log(1/frcpa(1+30/2^-8))/2
298 //
299 data8 0xed393b1c22351280 , 0x00003ffa // log(1/frcpa(1+31/2^-8))/2
300 data8 0xf5192bff087bcc35 , 0x00003ffa // log(1/frcpa(1+32/2^-8))/2
301 data8 0xfbdf4ff6dfef2fa3 , 0x00003ffa // log(1/frcpa(1+33/2^-8))/2
302 data8 0x81559a97f92f9cc7 , 0x00003ffb // log(1/frcpa(1+34/2^-8))/2
303 data8 0x84be72bce90266e8 , 0x00003ffb // log(1/frcpa(1+35/2^-8))/2
304 //
305 data8 0x88bc74113f23def2 , 0x00003ffb // log(1/frcpa(1+36/2^-8))/2
306 data8 0x8c2ba3edf6799d11 , 0x00003ffb // log(1/frcpa(1+37/2^-8))/2
307 data8 0x8f9dc92f92ea08b1 , 0x00003ffb // log(1/frcpa(1+38/2^-8))/2
308 data8 0x9312e8f36efab5a7 , 0x00003ffb // log(1/frcpa(1+39/2^-8))/2
309 data8 0x968b08643409ceb6 , 0x00003ffb // log(1/frcpa(1+40/2^-8))/2
310 //
311 data8 0x9a062cba08a1708c , 0x00003ffb // log(1/frcpa(1+41/2^-8))/2
312 data8 0x9d845b3abf95485c , 0x00003ffb // log(1/frcpa(1+42/2^-8))/2
313 data8 0xa06fd841bc001bb4 , 0x00003ffb // log(1/frcpa(1+43/2^-8))/2
314 data8 0xa3f3a74652fbe0db , 0x00003ffb // log(1/frcpa(1+44/2^-8))/2
315 data8 0xa77a8fb2336f20f5 , 0x00003ffb // log(1/frcpa(1+45/2^-8))/2
316 //
317 data8 0xab0497015d28b0a0 , 0x00003ffb // log(1/frcpa(1+46/2^-8))/2
318 data8 0xae91c2be6ba6a615 , 0x00003ffb // log(1/frcpa(1+47/2^-8))/2
319 data8 0xb189d1b99aebb20b , 0x00003ffb // log(1/frcpa(1+48/2^-8))/2
320 data8 0xb51cced5de9c1b2c , 0x00003ffb // log(1/frcpa(1+49/2^-8))/2
321 data8 0xb819bee9e720d42f , 0x00003ffb // log(1/frcpa(1+50/2^-8))/2
322 //
323 data8 0xbbb2a0947b093a5d , 0x00003ffb // log(1/frcpa(1+51/2^-8))/2
324 data8 0xbf4ec1505811684a , 0x00003ffb // log(1/frcpa(1+52/2^-8))/2
325 data8 0xc2535bacfa8975ff , 0x00003ffb // log(1/frcpa(1+53/2^-8))/2
326 data8 0xc55a3eafad187eb8 , 0x00003ffb // log(1/frcpa(1+54/2^-8))/2
327 data8 0xc8ff2484b2c0da74 , 0x00003ffb // log(1/frcpa(1+55/2^-8))/2
328 //
329 data8 0xcc0b1a008d53ab76 , 0x00003ffb // log(1/frcpa(1+56/2^-8))/2
330 data8 0xcfb6203844b3209b , 0x00003ffb // log(1/frcpa(1+57/2^-8))/2
331 data8 0xd2c73949a47a19f5 , 0x00003ffb // log(1/frcpa(1+58/2^-8))/2
332 data8 0xd5daae18b49d6695 , 0x00003ffb // log(1/frcpa(1+59/2^-8))/2
333 data8 0xd8f08248cf7e8019 , 0x00003ffb // log(1/frcpa(1+60/2^-8))/2
334 //
335 data8 0xdca7749f1b3e540e , 0x00003ffb // log(1/frcpa(1+61/2^-8))/2
336 data8 0xdfc28e033aaaf7c7 , 0x00003ffb // log(1/frcpa(1+62/2^-8))/2
337 data8 0xe2e012a5f91d2f55 , 0x00003ffb // log(1/frcpa(1+63/2^-8))/2
338 data8 0xe600064ed9e292a8 , 0x00003ffb // log(1/frcpa(1+64/2^-8))/2
339 data8 0xe9226cce42b39f60 , 0x00003ffb // log(1/frcpa(1+65/2^-8))/2
340 //
341 data8 0xec4749fd97a28360 , 0x00003ffb // log(1/frcpa(1+66/2^-8))/2
342 data8 0xef6ea1bf57780495 , 0x00003ffb // log(1/frcpa(1+67/2^-8))/2
343 data8 0xf29877ff38809091 , 0x00003ffb // log(1/frcpa(1+68/2^-8))/2
344 data8 0xf5c4d0b245cb89be , 0x00003ffb // log(1/frcpa(1+69/2^-8))/2
345 data8 0xf8f3afd6fcdef3aa , 0x00003ffb // log(1/frcpa(1+70/2^-8))/2
346 //
347 data8 0xfc2519756be1abc7 , 0x00003ffb // log(1/frcpa(1+71/2^-8))/2
348 data8 0xff59119f503e6832 , 0x00003ffb // log(1/frcpa(1+72/2^-8))/2
349 data8 0x8147ce381ae0e146 , 0x00003ffc // log(1/frcpa(1+73/2^-8))/2
350 data8 0x82e45f06cb1ad0f2 , 0x00003ffc // log(1/frcpa(1+74/2^-8))/2
351 data8 0x842f5c7c573cbaa2 , 0x00003ffc // log(1/frcpa(1+75/2^-8))/2
352 //
353 data8 0x85ce471968c8893a , 0x00003ffc // log(1/frcpa(1+76/2^-8))/2
354 data8 0x876e8305bc04066d , 0x00003ffc // log(1/frcpa(1+77/2^-8))/2
355 data8 0x891012678031fbb3 , 0x00003ffc // log(1/frcpa(1+78/2^-8))/2
356 data8 0x8a5f1493d766a05f , 0x00003ffc // log(1/frcpa(1+79/2^-8))/2
357 data8 0x8c030c778c56fa00 , 0x00003ffc // log(1/frcpa(1+80/2^-8))/2
358 //
359 data8 0x8da85df17e31d9ae , 0x00003ffc // log(1/frcpa(1+81/2^-8))/2
360 data8 0x8efa663e7921687e , 0x00003ffc // log(1/frcpa(1+82/2^-8))/2
361 data8 0x90a22b6875c6a1f8 , 0x00003ffc // log(1/frcpa(1+83/2^-8))/2
362 data8 0x91f62cc8f5d24837 , 0x00003ffc // log(1/frcpa(1+84/2^-8))/2
363 data8 0x93a06cfc3857d980 , 0x00003ffc // log(1/frcpa(1+85/2^-8))/2
364 //
365 data8 0x94f66d5e6fd01ced , 0x00003ffc // log(1/frcpa(1+86/2^-8))/2
366 data8 0x96a330156e6772f2 , 0x00003ffc // log(1/frcpa(1+87/2^-8))/2
367 data8 0x97fb3582754ea25b , 0x00003ffc // log(1/frcpa(1+88/2^-8))/2
368 data8 0x99aa8259aad1bbf2 , 0x00003ffc // log(1/frcpa(1+89/2^-8))/2
369 data8 0x9b0492f6227ae4a8 , 0x00003ffc // log(1/frcpa(1+90/2^-8))/2
370 //
371 data8 0x9c5f8e199bf3a7a5 , 0x00003ffc // log(1/frcpa(1+91/2^-8))/2
372 data8 0x9e1293b9998c1daa , 0x00003ffc // log(1/frcpa(1+92/2^-8))/2
373 data8 0x9f6fa31e0b41f308 , 0x00003ffc // log(1/frcpa(1+93/2^-8))/2
374 data8 0xa0cda11eaf46390e , 0x00003ffc // log(1/frcpa(1+94/2^-8))/2
375 data8 0xa22c8f029cfa45aa , 0x00003ffc // log(1/frcpa(1+95/2^-8))/2
376 //
377 data8 0xa3e48badb7856b34 , 0x00003ffc // log(1/frcpa(1+96/2^-8))/2
378 data8 0xa5459a0aa95849f9 , 0x00003ffc // log(1/frcpa(1+97/2^-8))/2
379 data8 0xa6a79c84480cfebd , 0x00003ffc // log(1/frcpa(1+98/2^-8))/2
380 data8 0xa80a946d0fcb3eb2 , 0x00003ffc // log(1/frcpa(1+99/2^-8))/2
381 data8 0xa96e831a3ea7b314 , 0x00003ffc // log(1/frcpa(1+100/2^-8))/2
382 //
383 data8 0xaad369e3dc544e3b , 0x00003ffc // log(1/frcpa(1+101/2^-8))/2
384 data8 0xac92e9588952c815 , 0x00003ffc // log(1/frcpa(1+102/2^-8))/2
385 data8 0xadfa035aa1ed8fdc , 0x00003ffc // log(1/frcpa(1+103/2^-8))/2
386 data8 0xaf6219eae1ad6e34 , 0x00003ffc // log(1/frcpa(1+104/2^-8))/2
387 data8 0xb0cb2e6d8160f753 , 0x00003ffc // log(1/frcpa(1+105/2^-8))/2
388 //
389 data8 0xb2354249ad950f72 , 0x00003ffc // log(1/frcpa(1+106/2^-8))/2
390 data8 0xb3a056e98ef4a3b4 , 0x00003ffc // log(1/frcpa(1+107/2^-8))/2
391 data8 0xb50c6dba52c6292a , 0x00003ffc // log(1/frcpa(1+108/2^-8))/2
392 data8 0xb679882c33876165 , 0x00003ffc // log(1/frcpa(1+109/2^-8))/2
393 data8 0xb78c07429785cedc , 0x00003ffc // log(1/frcpa(1+110/2^-8))/2
394 //
395 data8 0xb8faeb8dc4a77d24 , 0x00003ffc // log(1/frcpa(1+111/2^-8))/2
396 data8 0xba6ad77eb36ae0d6 , 0x00003ffc // log(1/frcpa(1+112/2^-8))/2
397 data8 0xbbdbcc915e9bee50 , 0x00003ffc // log(1/frcpa(1+113/2^-8))/2
398 data8 0xbd4dcc44f8cf12ef , 0x00003ffc // log(1/frcpa(1+114/2^-8))/2
399 data8 0xbec0d81bf5b531fa , 0x00003ffc // log(1/frcpa(1+115/2^-8))/2
400 //
401 data8 0xc034f19c139186f4 , 0x00003ffc // log(1/frcpa(1+116/2^-8))/2
402 data8 0xc14cb69f7c5e55ab , 0x00003ffc // log(1/frcpa(1+117/2^-8))/2
403 data8 0xc2c2abbb6e5fd56f , 0x00003ffc // log(1/frcpa(1+118/2^-8))/2
404 data8 0xc439b2c193e6771e , 0x00003ffc // log(1/frcpa(1+119/2^-8))/2
405 data8 0xc553acb9d5c67733 , 0x00003ffc // log(1/frcpa(1+120/2^-8))/2
406 //
407 data8 0xc6cc96e441272441 , 0x00003ffc // log(1/frcpa(1+121/2^-8))/2
408 data8 0xc8469753eca88c30 , 0x00003ffc // log(1/frcpa(1+122/2^-8))/2
409 data8 0xc962cf3ce072b05c , 0x00003ffc // log(1/frcpa(1+123/2^-8))/2
410 data8 0xcadeba8771f694aa , 0x00003ffc // log(1/frcpa(1+124/2^-8))/2
411 data8 0xcc5bc08d1f72da94 , 0x00003ffc // log(1/frcpa(1+125/2^-8))/2
412 //
413 data8 0xcd7a3f99ea035c29 , 0x00003ffc // log(1/frcpa(1+126/2^-8))/2
414 data8 0xcef93860c8a53c35 , 0x00003ffc // log(1/frcpa(1+127/2^-8))/2
415 data8 0xd0192f68a7ed23df , 0x00003ffc // log(1/frcpa(1+128/2^-8))/2
416 data8 0xd19a201127d3c645 , 0x00003ffc // log(1/frcpa(1+129/2^-8))/2
417 data8 0xd2bb92f4061c172c , 0x00003ffc // log(1/frcpa(1+130/2^-8))/2
418 //
419 data8 0xd43e80b2ee8cc8fc , 0x00003ffc // log(1/frcpa(1+131/2^-8))/2
420 data8 0xd56173601fc4ade4 , 0x00003ffc // log(1/frcpa(1+132/2^-8))/2
421 data8 0xd6e6637efb54086f , 0x00003ffc // log(1/frcpa(1+133/2^-8))/2
422 data8 0xd80ad9f58f3c8193 , 0x00003ffc // log(1/frcpa(1+134/2^-8))/2
423 data8 0xd991d1d31aca41f8 , 0x00003ffc // log(1/frcpa(1+135/2^-8))/2
424 //
425 data8 0xdab7d02231484a93 , 0x00003ffc // log(1/frcpa(1+136/2^-8))/2
426 data8 0xdc40d532cde49a54 , 0x00003ffc // log(1/frcpa(1+137/2^-8))/2
427 data8 0xdd685f79ed8b265e , 0x00003ffc // log(1/frcpa(1+138/2^-8))/2
428 data8 0xde9094bbc0e17b1d , 0x00003ffc // log(1/frcpa(1+139/2^-8))/2
429 data8 0xe01c91b78440c425 , 0x00003ffc // log(1/frcpa(1+140/2^-8))/2
430 //
431 data8 0xe14658f26997e729 , 0x00003ffc // log(1/frcpa(1+141/2^-8))/2
432 data8 0xe270cdc2391e0d23 , 0x00003ffc // log(1/frcpa(1+142/2^-8))/2
433 data8 0xe3ffce3a2aa64922 , 0x00003ffc // log(1/frcpa(1+143/2^-8))/2
434 data8 0xe52bdb274ed82887 , 0x00003ffc // log(1/frcpa(1+144/2^-8))/2
435 data8 0xe6589852e75d7df6 , 0x00003ffc // log(1/frcpa(1+145/2^-8))/2
436 //
437 data8 0xe786068c79937a7d , 0x00003ffc // log(1/frcpa(1+146/2^-8))/2
438 data8 0xe91903adad100911 , 0x00003ffc // log(1/frcpa(1+147/2^-8))/2
439 data8 0xea481236f7d35bb0 , 0x00003ffc // log(1/frcpa(1+148/2^-8))/2
440 data8 0xeb77d48c692e6b14 , 0x00003ffc // log(1/frcpa(1+149/2^-8))/2
441 data8 0xeca84b83d7297b87 , 0x00003ffc // log(1/frcpa(1+150/2^-8))/2
442 //
443 data8 0xedd977f4962aa158 , 0x00003ffc // log(1/frcpa(1+151/2^-8))/2
444 data8 0xef7179a22f257754 , 0x00003ffc // log(1/frcpa(1+152/2^-8))/2
445 data8 0xf0a450d139366ca7 , 0x00003ffc // log(1/frcpa(1+153/2^-8))/2
446 data8 0xf1d7e0524ff9ffdb , 0x00003ffc // log(1/frcpa(1+154/2^-8))/2
447 data8 0xf30c29036a8b6cae , 0x00003ffc // log(1/frcpa(1+155/2^-8))/2
448 //
449 data8 0xf4412bc411ea8d92 , 0x00003ffc // log(1/frcpa(1+156/2^-8))/2
450 data8 0xf576e97564c8619d , 0x00003ffc // log(1/frcpa(1+157/2^-8))/2
451 data8 0xf6ad62fa1b5f172f , 0x00003ffc // log(1/frcpa(1+158/2^-8))/2
452 data8 0xf7e499368b55c542 , 0x00003ffc // log(1/frcpa(1+159/2^-8))/2
453 data8 0xf91c8d10abaffe22 , 0x00003ffc // log(1/frcpa(1+160/2^-8))/2
454 //
455 data8 0xfa553f7018c966f3 , 0x00003ffc // log(1/frcpa(1+161/2^-8))/2
456 data8 0xfb8eb13e185d802c , 0x00003ffc // log(1/frcpa(1+162/2^-8))/2
457 data8 0xfcc8e3659d9bcbed , 0x00003ffc // log(1/frcpa(1+163/2^-8))/2
458 data8 0xfe03d6d34d487fd2 , 0x00003ffc // log(1/frcpa(1+164/2^-8))/2
459 data8 0xff3f8c7581e9f0ae , 0x00003ffc // log(1/frcpa(1+165/2^-8))/2
460 //
461 data8 0x803e029e280173ae , 0x00003ffd // log(1/frcpa(1+166/2^-8))/2
462 data8 0x80dca10cc52d0757 , 0x00003ffd // log(1/frcpa(1+167/2^-8))/2
463 data8 0x817ba200632755a1 , 0x00003ffd // log(1/frcpa(1+168/2^-8))/2
464 data8 0x821b05f3b01d6774 , 0x00003ffd // log(1/frcpa(1+169/2^-8))/2
465 data8 0x82bacd623ff19d06 , 0x00003ffd // log(1/frcpa(1+170/2^-8))/2
466 //
467 data8 0x835af8c88e7a8f47 , 0x00003ffd // log(1/frcpa(1+171/2^-8))/2
468 data8 0x83c5f8299e2b4091 , 0x00003ffd // log(1/frcpa(1+172/2^-8))/2
469 data8 0x8466cb43f3d87300 , 0x00003ffd // log(1/frcpa(1+173/2^-8))/2
470 data8 0x850803a67c80ca4b , 0x00003ffd // log(1/frcpa(1+174/2^-8))/2
471 data8 0x85a9a1d11a23b461 , 0x00003ffd // log(1/frcpa(1+175/2^-8))/2
472 //
473 data8 0x864ba644a18e6e05 , 0x00003ffd // log(1/frcpa(1+176/2^-8))/2
474 data8 0x86ee1182dcc432f7 , 0x00003ffd // log(1/frcpa(1+177/2^-8))/2
475 data8 0x875a925d7e48c316 , 0x00003ffd // log(1/frcpa(1+178/2^-8))/2
476 data8 0x87fdaa109d23aef7 , 0x00003ffd // log(1/frcpa(1+179/2^-8))/2
477 data8 0x88a129ed4becfaf2 , 0x00003ffd // log(1/frcpa(1+180/2^-8))/2
478 //
479 data8 0x89451278ecd7f9cf , 0x00003ffd // log(1/frcpa(1+181/2^-8))/2
480 data8 0x89b29295f8432617 , 0x00003ffd // log(1/frcpa(1+182/2^-8))/2
481 data8 0x8a572ac5a5496882 , 0x00003ffd // log(1/frcpa(1+183/2^-8))/2
482 data8 0x8afc2d0ce3b2dadf , 0x00003ffd // log(1/frcpa(1+184/2^-8))/2
483 data8 0x8b6a69c608cfd3af , 0x00003ffd // log(1/frcpa(1+185/2^-8))/2
484 //
485 data8 0x8c101e106e899a83 , 0x00003ffd // log(1/frcpa(1+186/2^-8))/2
486 data8 0x8cb63de258f9d626 , 0x00003ffd // log(1/frcpa(1+187/2^-8))/2
487 data8 0x8d2539c5bd19e2b1 , 0x00003ffd // log(1/frcpa(1+188/2^-8))/2
488 data8 0x8dcc0e064b29e6f1 , 0x00003ffd // log(1/frcpa(1+189/2^-8))/2
489 data8 0x8e734f45d88357ae , 0x00003ffd // log(1/frcpa(1+190/2^-8))/2
490 //
491 data8 0x8ee30cef034a20db , 0x00003ffd // log(1/frcpa(1+191/2^-8))/2
492 data8 0x8f8b0515686d1d06 , 0x00003ffd // log(1/frcpa(1+192/2^-8))/2
493 data8 0x90336bba039bf32f , 0x00003ffd // log(1/frcpa(1+193/2^-8))/2
494 data8 0x90a3edd23d1c9d58 , 0x00003ffd // log(1/frcpa(1+194/2^-8))/2
495 data8 0x914d0de2f5d61b32 , 0x00003ffd // log(1/frcpa(1+195/2^-8))/2
496 //
497 data8 0x91be0c20d28173b5 , 0x00003ffd // log(1/frcpa(1+196/2^-8))/2
498 data8 0x9267e737c06cd34a , 0x00003ffd // log(1/frcpa(1+197/2^-8))/2
499 data8 0x92d962ae6abb1237 , 0x00003ffd // log(1/frcpa(1+198/2^-8))/2
500 data8 0x9383fa6afbe2074c , 0x00003ffd // log(1/frcpa(1+199/2^-8))/2
501 data8 0x942f0421651c1c4e , 0x00003ffd // log(1/frcpa(1+200/2^-8))/2
502 //
503 data8 0x94a14a3845bb985e , 0x00003ffd // log(1/frcpa(1+201/2^-8))/2
504 data8 0x954d133857f861e7 , 0x00003ffd // log(1/frcpa(1+202/2^-8))/2
505 data8 0x95bfd96468e604c4 , 0x00003ffd // log(1/frcpa(1+203/2^-8))/2
506 data8 0x9632d31cafafa858 , 0x00003ffd // log(1/frcpa(1+204/2^-8))/2
507 data8 0x96dfaabd86fa1647 , 0x00003ffd // log(1/frcpa(1+205/2^-8))/2
508 //
509 data8 0x9753261fcbb2a594 , 0x00003ffd // log(1/frcpa(1+206/2^-8))/2
510 data8 0x9800c11b426b996d , 0x00003ffd // log(1/frcpa(1+207/2^-8))/2
511 data8 0x9874bf4d45ae663c , 0x00003ffd // log(1/frcpa(1+208/2^-8))/2
512 data8 0x99231f5ee9a74f79 , 0x00003ffd // log(1/frcpa(1+209/2^-8))/2
513 data8 0x9997a18a56bcad28 , 0x00003ffd // log(1/frcpa(1+210/2^-8))/2
514 //
515 data8 0x9a46c873a3267e79 , 0x00003ffd // log(1/frcpa(1+211/2^-8))/2
516 data8 0x9abbcfc621eb6cb6 , 0x00003ffd // log(1/frcpa(1+212/2^-8))/2
517 data8 0x9b310cb0d354c990 , 0x00003ffd // log(1/frcpa(1+213/2^-8))/2
518 data8 0x9be14cf9e1b3515c , 0x00003ffd // log(1/frcpa(1+214/2^-8))/2
519 data8 0x9c5710b8cbb73a43 , 0x00003ffd // log(1/frcpa(1+215/2^-8))/2
520 //
521 data8 0x9ccd0abd301f399c , 0x00003ffd // log(1/frcpa(1+216/2^-8))/2
522 data8 0x9d7e67f3bdce8888 , 0x00003ffd // log(1/frcpa(1+217/2^-8))/2
523 data8 0x9df4ea81a99daa01 , 0x00003ffd // log(1/frcpa(1+218/2^-8))/2
524 data8 0x9e6ba405a54514ba , 0x00003ffd // log(1/frcpa(1+219/2^-8))/2
525 data8 0x9f1e21c8c7bb62b3 , 0x00003ffd // log(1/frcpa(1+220/2^-8))/2
526 //
527 data8 0x9f956593f6b6355c , 0x00003ffd // log(1/frcpa(1+221/2^-8))/2
528 data8 0xa00ce1092e5498c3 , 0x00003ffd // log(1/frcpa(1+222/2^-8))/2
529 data8 0xa0c08309c4b912c1 , 0x00003ffd // log(1/frcpa(1+223/2^-8))/2
530 data8 0xa1388a8c6faa2afa , 0x00003ffd // log(1/frcpa(1+224/2^-8))/2
531 data8 0xa1b0ca7095b5f985 , 0x00003ffd // log(1/frcpa(1+225/2^-8))/2
532 //
533 data8 0xa22942eb47534a00 , 0x00003ffd // log(1/frcpa(1+226/2^-8))/2
534 data8 0xa2de62326449d0a3 , 0x00003ffd // log(1/frcpa(1+227/2^-8))/2
535 data8 0xa357690f88bfe345 , 0x00003ffd // log(1/frcpa(1+228/2^-8))/2
536 data8 0xa3d0a93f45169a4b , 0x00003ffd // log(1/frcpa(1+229/2^-8))/2
537 data8 0xa44a22f7ffe65f30 , 0x00003ffd // log(1/frcpa(1+230/2^-8))/2
538 //
539 data8 0xa500c5e5b4c1aa36 , 0x00003ffd // log(1/frcpa(1+231/2^-8))/2
540 data8 0xa57ad064eb2ebbc2 , 0x00003ffd // log(1/frcpa(1+232/2^-8))/2
541 data8 0xa5f5152dedf4384e , 0x00003ffd // log(1/frcpa(1+233/2^-8))/2
542 data8 0xa66f9478856233ec , 0x00003ffd // log(1/frcpa(1+234/2^-8))/2
543 data8 0xa6ea4e7cca02c32e , 0x00003ffd // log(1/frcpa(1+235/2^-8))/2
544 //
545 data8 0xa765437325341ccf , 0x00003ffd // log(1/frcpa(1+236/2^-8))/2
546 data8 0xa81e21e6c75b4020 , 0x00003ffd // log(1/frcpa(1+237/2^-8))/2
547 data8 0xa899ab333fe2b9ca , 0x00003ffd // log(1/frcpa(1+238/2^-8))/2
548 data8 0xa9157039c51ebe71 , 0x00003ffd // log(1/frcpa(1+239/2^-8))/2
549 data8 0xa991713433c2b999 , 0x00003ffd // log(1/frcpa(1+240/2^-8))/2
550 //
551 data8 0xaa0dae5cbcc048b3 , 0x00003ffd // log(1/frcpa(1+241/2^-8))/2
552 data8 0xaa8a27ede5eb13ad , 0x00003ffd // log(1/frcpa(1+242/2^-8))/2
553 data8 0xab06de228a9e3499 , 0x00003ffd // log(1/frcpa(1+243/2^-8))/2
554 data8 0xab83d135dc633301 , 0x00003ffd // log(1/frcpa(1+244/2^-8))/2
555 data8 0xac3fb076adc7fe7a , 0x00003ffd // log(1/frcpa(1+245/2^-8))/2
556 //
557 data8 0xacbd3cbbe47988f1 , 0x00003ffd // log(1/frcpa(1+246/2^-8))/2
558 data8 0xad3b06b1a5dc57c3 , 0x00003ffd // log(1/frcpa(1+247/2^-8))/2
559 data8 0xadb90e94af887717 , 0x00003ffd // log(1/frcpa(1+248/2^-8))/2
560 data8 0xae3754a218f7c816 , 0x00003ffd // log(1/frcpa(1+249/2^-8))/2
561 data8 0xaeb5d9175437afa2 , 0x00003ffd // log(1/frcpa(1+250/2^-8))/2
562 //
563 data8 0xaf349c322e9c7cee , 0x00003ffd // log(1/frcpa(1+251/2^-8))/2
564 data8 0xafb39e30d1768d1c , 0x00003ffd // log(1/frcpa(1+252/2^-8))/2
565 data8 0xb032df51c2c93116 , 0x00003ffd // log(1/frcpa(1+253/2^-8))/2
566 data8 0xb0b25fd3e6035ad9 , 0x00003ffd // log(1/frcpa(1+254/2^-8))/2
567 data8 0xb1321ff67cba178c , 0x00003ffd // log(1/frcpa(1+255/2^-8))/2
568 LOCAL_OBJECT_END(atanh_data_3)
572 .section .text
573 GLOBAL_LIBM_ENTRY(atanh)
575 { .mfi
576 getf.exp rArgSExpb = f8 // Must recompute if x unorm
577 fclass.m p13,p0 = f8, 0x0b // is arg denormal ?
578 mov rExpbMask = 0x1ffff
579 }
580 { .mfi
581 addl DataPtr = @ltoff(atanh_data), gp
582 fnma.s1 fOneMx = f8, f1, f1 // fOneMx = 1 - x
583 mov rBias = 0xffff
584 }
585 ;;
587 { .mfi
588 mov rNearZeroBound = 0xfffd // biased exp of 1/4
589 fclass.m p12,p0 = f8, 0xc7 // is arg NaN or +/-0 ?
590 nop.i 0
591 }
592 { .mfi
593 ld8 DataPtr = [DataPtr]
594 fma.s1 fOnePx = f8, f1, f1 // fOnePx = 1 + x
595 nop.i 0
596 }
597 ;;
599 { .mfi
600 nop.m 0
601 fcmp.lt.s1 p10,p11 = f8,f0 // is x < 0 ?
602 nop.i 0
603 }
604 { .mfb
605 nop.m 0
606 fnorm.s1 fNormX = f8 // Normalize x
607 (p13) br.cond.spnt ATANH_UNORM // Branch if x=unorm
608 }
609 ;;
611 ATANH_COMMON:
612 // Return here if x=unorm and not denorm
613 { .mfi
614 adds Data2Ptr = 0x50, DataPtr
615 fma.s1 fX2 = f8, f8, f0 // x^2
616 nop.i 0
617 }
618 { .mfb
619 adds Data3Ptr = 0xC0, DataPtr
620 (p12) fma.d.s0 f8 = f8,f1,f8 // NaN or +/-0
621 (p12) br.ret.spnt b0 // Exit for x Nan or zero
622 }
623 ;;
625 { .mfi
626 ldfe fC9 = [Data2Ptr], 16
627 (p11) frcpa.s1 fRcp0, p0 = f1, fOneMx
628 nop.i 0
629 }
630 ;;
632 { .mfi
633 ldfe fC8 = [Data2Ptr], 16
634 (p10) frcpa.s1 fRcp0n, p0 = f1, fOnePx
635 and rArgExpb = rArgSExpb, rExpbMask // biased exponent
636 }
637 { .mfi
638 nop.m 0
639 (p10) fma.s1 fOneMx = fOnePx, f1, f0 // fOnePx = 1 - |x|
640 nop.i 0
641 }
642 ;;
644 { .mfi
645 ldfe fC7 = [Data2Ptr], 16
646 (p10) fnma.s1 fOnePx = fNormX, f1, f1 // fOnePx = 1 + |x|
647 cmp.ge p6,p0 = rArgExpb, rBias // is Expb(Arg) >= Expb(1) ?
648 }
649 { .mfb
650 nop.m 0
651 nop.f 0
652 (p6) br.cond.spnt atanh_ge_one // Branch if |x| >=1.0
653 }
654 ;;
656 { .mfi
657 ldfe fC6 = [Data2Ptr], 16
658 nop.f 0
659 nop.i 0
660 }
661 ;;
663 { .mfi
664 ldfe fC5 = [Data2Ptr], 16
665 fma.s1 fX4 = fX2, fX2, f0 // x^4
666 cmp.gt p8,p0 = rNearZeroBound, rArgExpb
667 }
668 { .mfb
669 ldfe fC2 = [Data3Ptr], 16
670 fma.s1 fX3 = fX2, fNormX, f0 // x^3
671 (p8) br.cond.spnt atanh_near_zero // Exit if 0 < |x| < 0.25
672 }
673 ;;
675 // Main path: 0.25 <= |x| < 1.0
676 // NR method: iteration #1
677 .pred.rel "mutex",p11,p10
678 { .mfi
679 ldfpd fP5, fP4 = [DataPtr], 16
680 (p11) fnma.s1 fRcp1 = fRcp0, fOneMx, f1 // t = 1 - r0*x
681 nop.i 0
682 }
683 { .mfi
684 nop.m 0
685 (p10) fnma.s1 fRcp1 = fRcp0n, fOneMx, f1 // t = 1 - r0*x
686 nop.i 0
687 }
688 ;;
690 { .mfi
691 ldfpd fP3, fP2 = [DataPtr], 16
692 // r1 = r0 + r0*t = r0 + r0*(1 - r0*x)
693 (p11) fma.s1 fRcp1 = fRcp0, fRcp1, fRcp0
694 nop.i 0
695 }
696 { .mfi
697 nop.m 0
698 // r1 = r0 + r0*t = r0 + r0*(1 - r0*x)
699 (p10) fma.s1 fRcp1 = fRcp0n, fRcp1, fRcp0n
700 nop.i 0
701 }
702 ;;
704 // NR method: iteration #2
705 { .mfi
706 ldfd fP1 = [DataPtr], 16
707 fnma.s1 fRcp2 = fRcp1, fOneMx, f1 // t = 1 - r1*x
708 nop.i 0
709 }
710 ;;
712 { .mfi
713 ldfe fLog2 = [DataPtr], 16
714 // r2 = r1 + r1*t = r1 + r1*(1 - r1*x)
715 fma.s1 fRcp2 = fRcp1, fRcp2, fRcp1
716 nop.i 0
717 }
718 ;;
720 // NR method: iteration #3
721 { .mfi
722 adds RcpTablePtr = 0xB0, DataPtr
723 fnma.s1 fRcp3 = fRcp2, fOneMx, f1 // t = 1 - r2*x
724 nop.i 0
725 }
726 { .mfi
727 nop.m 0
728 fma.s1 fY4Rcp = fRcp2, fOnePx, f0 // fY4Rcp = r2*(1 + x)
729 nop.i 0
730 }
731 ;;
733 // polynomial approximation & final reconstruction
734 { .mfi
735 nop.m 0
736 frcpa.s1 fRcp, p0 = f1, fY4Rcp
737 nop.i 0
738 }
739 { .mfi
740 nop.m 0
741 // y = r2 * (1 + x) + r2 * (1 + x) * t = (1 + x) * (r2 + r2*(1 - r2*x))
742 fma.s1 fY = fY4Rcp, fRcp3, fY4Rcp
743 nop.i 0
744 }
745 ;;
747 { .mmi
748 getf.exp rSExpb = fY4Rcp // biased exponent and sign
749 ;;
750 getf.sig rSig = fY4Rcp // significand
751 nop.i 0
752 }
753 ;;
755 { .mfi
756 nop.m 0
757 fms.s1 fR = fY, fRcp, f1 // fR = fY * fRcp - 1
758 nop.i 0
759 }
760 ;;
762 { .mmi
763 and rExpb = rSExpb, rExpbMask
764 ;;
765 sub rN = rExpb, rBias // exponent
766 extr.u rInd = rSig,55,8 // Extract 8 bits
767 }
768 ;;
770 { .mmi
771 setf.sig fN4Cvt = rN
772 shladd RcpTablePtr = rInd, 4, RcpTablePtr
773 nop.i 0
774 }
775 ;;
777 { .mfi
778 ldfe fLogT = [RcpTablePtr]
779 fma.s1 fR2 = fR, fR, f0 // r^2
780 nop.i 0
781 }
782 {
783 nop.m 0
784 fma.s1 fP54 = fP5, fR, fP4 // P5*r + P4
785 nop.i 0
786 }
787 ;;
789 { .mfi
790 nop.m 0
791 fma.s1 fP32 = fP3, fR, fP2 // P3*r + P2
792 nop.i 0
793 }
794 ;;
796 { .mfi
797 nop.m 0
798 fma.s1 fR3 = fR2, fR, f0 // r^3
799 nop.i 0
800 }
801 { .mfi
802 nop.m 0
803 fma.s1 fP10 = fP1, fR2, fR // P1*r^2 + r
804 nop.i 0
805 }
806 ;;
808 { .mfi
809 nop.m 0
810 fcvt.xf fN = fN4Cvt
811 nop.i 0
812 }
813 { .mfi
814 nop.m 0
815 fma.s1 fP54 = fP54, fR2, fP32 // (P5*r + P4)*r^2 + P3*r + P2
816 nop.i 0
817 }
818 ;;
820 { .mfi
821 nop.m 0
822 fma.s1 fLogT_N = fN, fLog2, fLogT // N*Log2 + LogT
823 nop.i 0
824 }
825 { .mfi
826 nop.m 0
827 // ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
828 fma.s1 fP54 = fP54, fR3, fP10
829 nop.i 0
830 }
831 ;;
833 .pred.rel "mutex",p11,p10
834 { .mfi
835 nop.m 0
836 // 0.5*(((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r) + 0.5*(N*Log2 + T)
837 (p11) fnma.d.s0 f8 = fP54, fP1, fLogT_N
838 nop.i 0
839 }
840 { .mfb
841 nop.m 0
842 // -0.5*(((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r) - 0.5*(N*Log2 + T)
843 (p10) fms.d.s0 f8 = fP54, fP1, fLogT_N
844 br.ret.sptk b0 // Exit for 0.25 <= |x| < 1.0
845 }
846 ;;
848 // Here if 0 < |x| < 0.25
849 atanh_near_zero:
850 { .mfi
851 ldfe fC4 = [Data2Ptr], 16
852 fma.s1 fP98 = fC9, fX2, fC8 // C9*x^2 + C8
853 nop.i 0
854 }
855 { .mfi
856 ldfe fC1 = [Data3Ptr], 16
857 fma.s1 fP76 = fC7, fX2, fC6 // C7*x^2 + C6
858 nop.i 0
859 }
860 ;;
862 { .mfi
863 ldfe fC3 = [Data2Ptr], 16
864 fma.s1 fX8 = fX4, fX4, f0 // x^8
865 nop.i 0
866 }
867 { .mfi
868 ldfe fC0 = [Data3Ptr], 16
869 nop.f 0
870 nop.i 0
871 }
872 ;;
874 { .mfi
875 nop.m 0
876 fma.s1 fP98 = fP98, fX4, fP76 // C9*x^6 + C8*x^4 + C7*x^2 + C6
877 nop.i 0
878 }
879 ;;
881 { .mfi
882 nop.m 0
883 fma.s1 fP54 = fC5, fX2, fC4 // C5*x^2 + C4
884 nop.i 0
885 }
886 ;;
888 { .mfi
889 nop.m 0
890 fma.s1 fP32 = fC3, fX2, fC2 // C3*x^2 + C2
891 nop.i 0
892 }
893 ;;
895 { .mfi
896 nop.m 0
897 fma.s1 fP10 = fC1, fX2, fC0 // C1*x^2 + C0
898 nop.i 0
899 }
900 ;;
902 { .mfi
903 nop.m 0
904 fma.s1 fP54 = fP54, fX4, fP32 // C5*x^6 + C4*x^4 + C3*x^2 + C2
905 nop.i 0
906 }
907 ;;
909 { .mfi
910 nop.m 0
911 // C9*x^14 + C8*x^12 + C7*x^10 + C6*x^8 + C5*x^6 + C4*x^4 + C3*x^2 + C2
912 fma.s1 fP98 = fP98, fX8, fP54
913 nop.i 0
914 }
915 ;;
917 { .mfi
918 nop.m 0
919 // C9*x^18 + C8*x^16 + C7*x^14 + C6*x^12 + C5*x^10 + C4*x^8 + C3*x^6 +
920 // C2*x^4 + C1*x^2 + C0
921 fma.s1 fP98 = fP98, fX4, fP10
922 nop.i 0
923 }
924 ;;
926 { .mfb
927 nop.m 0
928 // C9*x^21 + C8*x^19 + C7*x^17 + C6*x^15 + C5*x^13 + C4*x^11 + C3*x^9 +
929 // C2*x^7 + C1*x^5 + C0*x^3 + x
930 fma.d.s0 f8 = fP98, fX3, fNormX
931 br.ret.sptk b0 // Exit for 0 < |x| < 0.25
932 }
933 ;;
935 ATANH_UNORM:
936 // Here if x=unorm
937 { .mfi
938 getf.exp rArgSExpb = fNormX // Recompute if x unorm
939 fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
940 nop.i 0
941 }
942 ;;
944 { .mfb
945 nop.m 0
946 fcmp.eq.s0 p7,p0 = f8, f0 // Dummy to set denormal flag
947 (p13) br.cond.sptk ATANH_COMMON // Continue if x unorm and not denorm
948 }
949 ;;
951 .pred.rel "mutex",p10,p11
952 { .mfi
953 nop.m 0
954 (p10) fnma.d.s0 f8 = f8,f8,f8 // Result x-x^2 if x=-denorm
955 nop.i 0
956 }
957 { .mfb
958 nop.m 0
959 (p11) fma.d.s0 f8 = f8,f8,f8 // Result x+x^2 if x=+denorm
960 br.ret.spnt b0 // Exit if denorm
961 }
962 ;;
964 // Here if |x| >= 1.0
965 atanh_ge_one:
966 { .mfi
967 alloc r32 = ar.pfs,1,3,4,0
968 fmerge.s fAbsX = f0, f8 // Form |x|
969 nop.i 0
970 }
971 ;;
973 { .mfi
974 nop.m 0
975 fmerge.s f10 = f8, f8 // Save input for error call
976 nop.i 0
977 }
978 ;;
980 { .mfi
981 nop.m 0
982 fcmp.eq.s1 p6,p7 = fAbsX, f1 // Test for |x| = 1.0
983 nop.i 0
984 }
985 ;;
987 // Set error tag and result, and raise invalid flag if |x| > 1.0
988 { .mfi
989 (p7) mov atanh_GR_tag = 131
990 (p7) frcpa.s0 f8, p0 = f0, f0 // Get QNaN, and raise invalid
991 nop.i 0
992 }
993 ;;
995 // Set error tag and result, and raise Z flag if |x| = 1.0
996 { .mfi
997 nop.m 0
998 (p6) frcpa.s0 fRcp, p0 = f1, f0 // Get inf, and raise Z flag
999 nop.i 0
1000 }
1001 ;;
1003 { .mfb
1004 (p6) mov atanh_GR_tag = 132
1005 (p6) fmerge.s f8 = f8, fRcp // result is +-inf
1006 br.cond.sptk __libm_error_region // Exit if |x| >= 1.0
1007 }
1008 ;;
1010 GLOBAL_LIBM_END(atanh)
1013 LOCAL_LIBM_ENTRY(__libm_error_region)
1014 .prologue
1016 { .mfi
1017 add GR_Parameter_Y=-32,sp // Parameter 2 value
1018 nop.f 0
1019 .save ar.pfs,GR_SAVE_PFS
1020 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1021 }
1022 { .mfi
1023 .fframe 64
1024 add sp=-64,sp // Create new stack
1025 nop.f 0
1026 mov GR_SAVE_GP=gp // Save gp
1027 };;
1029 { .mmi
1030 stfd [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
1031 add GR_Parameter_X = 16,sp // Parameter 1 address
1032 .save b0, GR_SAVE_B0
1033 mov GR_SAVE_B0=b0 // Save b0
1034 };;
1036 .body
1037 { .mib
1038 stfd [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
1039 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1040 nop.b 0
1041 }
1042 { .mib
1043 stfd [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
1044 add GR_Parameter_Y = -16,GR_Parameter_Y
1045 br.call.sptk b0=__libm_error_support# // Call error handling function
1046 };;
1048 { .mmi
1049 add GR_Parameter_RESULT = 48,sp
1050 nop.m 0
1051 nop.i 0
1052 };;
1054 { .mmi
1055 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
1056 .restore sp
1057 add sp = 64,sp // Restore stack pointer
1058 mov b0 = GR_SAVE_B0 // Restore return address
1059 };;
1061 { .mib
1062 mov gp = GR_SAVE_GP // Restore gp
1063 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1064 br.ret.sptk b0 // Return
1065 };;
1067 LOCAL_LIBM_END(__libm_error_region)
1070 .type __libm_error_support#,@function
1071 .global __libm_error_support#