| blob | 1ec1408e35576930b266aa801867656f9186db8e |
1 .file "atanhf.s"
4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 05/22/01 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 08/06/02 Improved Itanium 2 performance
45 // 02/06/03 Reordered header: .section, .global, .proc, .align
46 // 05/26/03 Improved performance, fixed to handle unorms
47 //
48 // API
49 //==============================================================
50 // float atanhf(float)
51 //
52 // Overview of operation
53 //==============================================================
54 // Background
55 //
56 //
57 // There are 7 paths:
58 // 1. x = +/-0.0
59 // Return atanhf(x) = +/-0.0
60 //
61 // 2. 0.0 < |x| <= MAX_DENORMAL_ABS
62 // Return atanhf(x) = x + sign(x)*x^2
63 //
64 // 3. MAX_DENORMAL_ABS < |x| < 2^(-20)
65 // Return atanhf(x) = Pol3(x), where Pol3(x) = x + x^3
66 //
67 // 4. 2^(-20) <= |x| < 1
68 // Return atanhf(x) = 0.5 * (log(1 + x) - log(1 - x))
69 // Algorithm description for log function see below.
70 //
71 // 5. |x| = 1
72 // Return atanhf(x) = sign(x) * +INF
73 //
74 // 6. 1 < |x| <= +INF
75 // Return atanhf(x) = QNaN
76 //
77 // 7. x = [S,Q]NaN
78 // Return atanhf(x) = QNaN
79 //
80 //==============================================================
81 // Algorithm Description for log(x) function
82 //
83 // Consider x = 2^N * 1.f1 f2 f3 f4...f63
84 // log(x) = log(x * frcpa(x) / frcpa(x))
85 // = log(x * frcpa(x)) + log(1/frcpa(x))
86 // = log(x * frcpa(x)) - log(frcpa(x))
87 //
88 // frcpa(x) = 2^(-N) * frcpa(1.f1 f2 ... f63)
89 //
90 // -log(frcpa(x)) = -log(C)
91 // = -log(2^(-N)) - log(frcpa(1.f1 f2 ... f63))
92 //
93 // -log(frcpa(x)) = -log(C)
94 // = N*log2 - log(frcpa(1.f1 f2 ... f63))
95 //
96 //
97 // log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
98 //
99 // log(x) = N*log2 + log(1./frcpa(1.f1 f2 ... f63)) + log(x * frcpa(x))
100 // log(x) = N*log2 + T + log(frcpa(x) x)
101 //
102 // Log(x) = N*log2 + T + log(C * x)
103 //
104 // C * x = 1 + r
105 //
106 // log(x) = N*log2 + T + log(1 + r)
107 // log(x) = N*log2 + T + Series(r)
108 //
109 // 1.f1 f2 ... f8 has 256 entries.
110 // They are 1 + k/2^8, k = 0 ... 255
111 // These 256 values are the table entries.
112 //
113 // Implementation
114 //==============================================================
115 // C = frcpa(x)
116 // r = C * x - 1
117 //
118 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
119 //
120 // x = f * 2*N where f is 1.f_1f_2f_3...f_63
121 // Nfloat = float(n) where n is the true unbiased exponent
122 // pre-index = f_1f_2....f_8
123 // index = pre_index * 16
124 // get the dxt table entry at index + offset = T
125 //
126 // result = (T + Nfloat * log(2)) + rseries
127 //
128 // The T table is calculated as follows
129 // Form x_k = 1 + k/2^8 where k goes from 0... 255
130 // y_k = frcpa(x_k)
131 // log(1/y_k) in quad and round to double-extended
133 // Registers used
134 //==============================================================
135 // Floating Point registers used:
136 // f8, input
137 // f32 -> f59
139 // General registers used:
140 // r14 -> r29, r32 -> r39
142 // Predicate registers used:
143 // p6 -> p9
145 // p6 to filter out case when |x| >= 1
146 // p7 to filter out case when x = [Q,S]NaN or +/-0
147 // p8 to filter out case when |x| < 2^(-20)
148 // p9 to filter out case when x = denormal
151 // Assembly macros
152 //==============================================================
153 DataPtr = r14
154 RcpTablePtrM = r15
155 RcpTablePtrP = r16
156 rExpbMask = r17
157 rBias = r18
158 rNearZeroBound = r19
159 rArgSExpb = r20
160 rArgExpb = r21
161 rExpbm = r22
162 rExpbp = r23
163 rSigm = r24
164 rSigp = r25
165 rNm = r26
166 rNp = r27
167 rIndm = r28
168 rIndp = r29
170 GR_SAVE_B0 = r33
171 GR_SAVE_GP = r34
172 GR_SAVE_PFS = r35
174 GR_Parameter_X = r36
175 GR_Parameter_Y = r37
176 GR_Parameter_RESULT = r38
177 atanh_GR_tag = r39
179 //==============================================================
180 fOneMx = f33
181 fOnePx = f34
182 fRm2 = f35
183 fRm3 = f36
184 fRp2 = f37
185 fRp3 = f38
186 fRcpM = f39
187 fRcpP = f40
188 fRp = f41
189 fRm = f42
190 fN4CvtM = f43
191 fN4CvtP = f44
192 fNm = f45
193 fNp = f46
194 fLogTm = f47
195 fLogTp = f48
196 fLog2 = f49
197 fArgAbs = f50
198 fNormX = f50
199 fP32m = f51
200 fP32p = f52
201 fP10m = f53
202 fP10p = f54
203 fX2 = f55
204 fP3 = f56
205 fP2 = f57
206 fP1 = f58
207 fHalf = f59
211 // Data tables
212 //==============================================================
214 RODATA
216 .align 16
218 LOCAL_OBJECT_START(atanhf_data)
219 data8 0xbfc0001008f39d59 // P3*0.5
220 data8 0x3fc5556073e0c45a // P2*0.5
221 data8 0xbfcffffffffaea15 // P1*0.5
222 data8 0x3fe0000000000000 // 0.5
223 data8 0x3fd62e42fefa39ef // 0.5*ln(2)
224 data8 0x0000000000000000 // pad
225 LOCAL_OBJECT_END(atanhf_data)
227 LOCAL_OBJECT_START(atanhf_data2)
228 data8 0x3f50040155d5889e //log(1/frcpa(1+0/256))/2
229 data8 0x3f68121214586b54 //log(1/frcpa(1+1/256))/2
230 data8 0x3f741929f96832f0 //log(1/frcpa(1+2/256))/2
231 data8 0x3f7c317384c75f06 //log(1/frcpa(1+3/256))/2
232 data8 0x3f81a6b91ac73386 //log(1/frcpa(1+4/256))/2
233 data8 0x3f85ba9a5d9ac039 //log(1/frcpa(1+5/256))/2
234 data8 0x3f89d2a8074325f4 //log(1/frcpa(1+6/256))/2
235 data8 0x3f8d6b2725979802 //log(1/frcpa(1+7/256))/2
236 data8 0x3f90c58fa19dfaaa //log(1/frcpa(1+8/256))/2
237 data8 0x3f92954c78cbce1b //log(1/frcpa(1+9/256))/2
238 data8 0x3f94a94d2da96c56 //log(1/frcpa(1+10/256))/2
239 data8 0x3f967c94f2d4bb58 //log(1/frcpa(1+11/256))/2
240 data8 0x3f985188b630f068 //log(1/frcpa(1+12/256))/2
241 data8 0x3f9a6b8abe73af4c //log(1/frcpa(1+13/256))/2
242 data8 0x3f9c441e06f72a9e //log(1/frcpa(1+14/256))/2
243 data8 0x3f9e1e6713606d07 //log(1/frcpa(1+15/256))/2
244 data8 0x3f9ffa6911ab9301 //log(1/frcpa(1+16/256))/2
245 data8 0x3fa0ec139c5da601 //log(1/frcpa(1+17/256))/2
246 data8 0x3fa1dbd2643d190b //log(1/frcpa(1+18/256))/2
247 data8 0x3fa2cc7284fe5f1c //log(1/frcpa(1+19/256))/2
248 data8 0x3fa3bdf5a7d1ee64 //log(1/frcpa(1+20/256))/2
249 data8 0x3fa4b05d7aa012e0 //log(1/frcpa(1+21/256))/2
250 data8 0x3fa580db7ceb5702 //log(1/frcpa(1+22/256))/2
251 data8 0x3fa674f089365a7a //log(1/frcpa(1+23/256))/2
252 data8 0x3fa769ef2c6b568d //log(1/frcpa(1+24/256))/2
253 data8 0x3fa85fd927506a48 //log(1/frcpa(1+25/256))/2
254 data8 0x3fa9335e5d594989 //log(1/frcpa(1+26/256))/2
255 data8 0x3faa2b0220c8e5f5 //log(1/frcpa(1+27/256))/2
256 data8 0x3fab0004ac1a86ac //log(1/frcpa(1+28/256))/2
257 data8 0x3fabf968769fca11 //log(1/frcpa(1+29/256))/2
258 data8 0x3faccfedbfee13a8 //log(1/frcpa(1+30/256))/2
259 data8 0x3fada727638446a2 //log(1/frcpa(1+31/256))/2
260 data8 0x3faea3257fe10f7a //log(1/frcpa(1+32/256))/2
261 data8 0x3faf7be9fedbfde6 //log(1/frcpa(1+33/256))/2
262 data8 0x3fb02ab352ff25f4 //log(1/frcpa(1+34/256))/2
263 data8 0x3fb097ce579d204d //log(1/frcpa(1+35/256))/2
264 data8 0x3fb1178e8227e47c //log(1/frcpa(1+36/256))/2
265 data8 0x3fb185747dbecf34 //log(1/frcpa(1+37/256))/2
266 data8 0x3fb1f3b925f25d41 //log(1/frcpa(1+38/256))/2
267 data8 0x3fb2625d1e6ddf57 //log(1/frcpa(1+39/256))/2
268 data8 0x3fb2d1610c86813a //log(1/frcpa(1+40/256))/2
269 data8 0x3fb340c59741142e //log(1/frcpa(1+41/256))/2
270 data8 0x3fb3b08b6757f2a9 //log(1/frcpa(1+42/256))/2
271 data8 0x3fb40dfb08378003 //log(1/frcpa(1+43/256))/2
272 data8 0x3fb47e74e8ca5f7c //log(1/frcpa(1+44/256))/2
273 data8 0x3fb4ef51f6466de4 //log(1/frcpa(1+45/256))/2
274 data8 0x3fb56092e02ba516 //log(1/frcpa(1+46/256))/2
275 data8 0x3fb5d23857cd74d5 //log(1/frcpa(1+47/256))/2
276 data8 0x3fb6313a37335d76 //log(1/frcpa(1+48/256))/2
277 data8 0x3fb6a399dabbd383 //log(1/frcpa(1+49/256))/2
278 data8 0x3fb70337dd3ce41b //log(1/frcpa(1+50/256))/2
279 data8 0x3fb77654128f6127 //log(1/frcpa(1+51/256))/2
280 data8 0x3fb7e9d82a0b022d //log(1/frcpa(1+52/256))/2
281 data8 0x3fb84a6b759f512f //log(1/frcpa(1+53/256))/2
282 data8 0x3fb8ab47d5f5a310 //log(1/frcpa(1+54/256))/2
283 data8 0x3fb91fe49096581b //log(1/frcpa(1+55/256))/2
284 data8 0x3fb981634011aa75 //log(1/frcpa(1+56/256))/2
285 data8 0x3fb9f6c407089664 //log(1/frcpa(1+57/256))/2
286 data8 0x3fba58e729348f43 //log(1/frcpa(1+58/256))/2
287 data8 0x3fbabb55c31693ad //log(1/frcpa(1+59/256))/2
288 data8 0x3fbb1e104919efd0 //log(1/frcpa(1+60/256))/2
289 data8 0x3fbb94ee93e367cb //log(1/frcpa(1+61/256))/2
290 data8 0x3fbbf851c067555f //log(1/frcpa(1+62/256))/2
291 data8 0x3fbc5c0254bf23a6 //log(1/frcpa(1+63/256))/2
292 data8 0x3fbcc000c9db3c52 //log(1/frcpa(1+64/256))/2
293 data8 0x3fbd244d99c85674 //log(1/frcpa(1+65/256))/2
294 data8 0x3fbd88e93fb2f450 //log(1/frcpa(1+66/256))/2
295 data8 0x3fbdedd437eaef01 //log(1/frcpa(1+67/256))/2
296 data8 0x3fbe530effe71012 //log(1/frcpa(1+68/256))/2
297 data8 0x3fbeb89a1648b971 //log(1/frcpa(1+69/256))/2
298 data8 0x3fbf1e75fadf9bde //log(1/frcpa(1+70/256))/2
299 data8 0x3fbf84a32ead7c35 //log(1/frcpa(1+71/256))/2
300 data8 0x3fbfeb2233ea07cd //log(1/frcpa(1+72/256))/2
301 data8 0x3fc028f9c7035c1c //log(1/frcpa(1+73/256))/2
302 data8 0x3fc05c8be0d9635a //log(1/frcpa(1+74/256))/2
303 data8 0x3fc085eb8f8ae797 //log(1/frcpa(1+75/256))/2
304 data8 0x3fc0b9c8e32d1911 //log(1/frcpa(1+76/256))/2
305 data8 0x3fc0edd060b78081 //log(1/frcpa(1+77/256))/2
306 data8 0x3fc122024cf0063f //log(1/frcpa(1+78/256))/2
307 data8 0x3fc14be2927aecd4 //log(1/frcpa(1+79/256))/2
308 data8 0x3fc180618ef18adf //log(1/frcpa(1+80/256))/2
309 data8 0x3fc1b50bbe2fc63b //log(1/frcpa(1+81/256))/2
310 data8 0x3fc1df4cc7cf242d //log(1/frcpa(1+82/256))/2
311 data8 0x3fc214456d0eb8d4 //log(1/frcpa(1+83/256))/2
312 data8 0x3fc23ec5991eba49 //log(1/frcpa(1+84/256))/2
313 data8 0x3fc2740d9f870afb //log(1/frcpa(1+85/256))/2
314 data8 0x3fc29ecdabcdfa04 //log(1/frcpa(1+86/256))/2
315 data8 0x3fc2d46602adccee //log(1/frcpa(1+87/256))/2
316 data8 0x3fc2ff66b04ea9d4 //log(1/frcpa(1+88/256))/2
317 data8 0x3fc335504b355a37 //log(1/frcpa(1+89/256))/2
318 data8 0x3fc360925ec44f5d //log(1/frcpa(1+90/256))/2
319 data8 0x3fc38bf1c3337e75 //log(1/frcpa(1+91/256))/2
320 data8 0x3fc3c25277333184 //log(1/frcpa(1+92/256))/2
321 data8 0x3fc3edf463c1683e //log(1/frcpa(1+93/256))/2
322 data8 0x3fc419b423d5e8c7 //log(1/frcpa(1+94/256))/2
323 data8 0x3fc44591e0539f49 //log(1/frcpa(1+95/256))/2
324 data8 0x3fc47c9175b6f0ad //log(1/frcpa(1+96/256))/2
325 data8 0x3fc4a8b341552b09 //log(1/frcpa(1+97/256))/2
326 data8 0x3fc4d4f3908901a0 //log(1/frcpa(1+98/256))/2
327 data8 0x3fc501528da1f968 //log(1/frcpa(1+99/256))/2
328 data8 0x3fc52dd06347d4f6 //log(1/frcpa(1+100/256))/2
329 data8 0x3fc55a6d3c7b8a8a //log(1/frcpa(1+101/256))/2
330 data8 0x3fc5925d2b112a59 //log(1/frcpa(1+102/256))/2
331 data8 0x3fc5bf406b543db2 //log(1/frcpa(1+103/256))/2
332 data8 0x3fc5ec433d5c35ae //log(1/frcpa(1+104/256))/2
333 data8 0x3fc61965cdb02c1f //log(1/frcpa(1+105/256))/2
334 data8 0x3fc646a84935b2a2 //log(1/frcpa(1+106/256))/2
335 data8 0x3fc6740add31de94 //log(1/frcpa(1+107/256))/2
336 data8 0x3fc6a18db74a58c5 //log(1/frcpa(1+108/256))/2
337 data8 0x3fc6cf31058670ec //log(1/frcpa(1+109/256))/2
338 data8 0x3fc6f180e852f0ba //log(1/frcpa(1+110/256))/2
339 data8 0x3fc71f5d71b894f0 //log(1/frcpa(1+111/256))/2
340 data8 0x3fc74d5aefd66d5c //log(1/frcpa(1+112/256))/2
341 data8 0x3fc77b79922bd37e //log(1/frcpa(1+113/256))/2
342 data8 0x3fc7a9b9889f19e2 //log(1/frcpa(1+114/256))/2
343 data8 0x3fc7d81b037eb6a6 //log(1/frcpa(1+115/256))/2
344 data8 0x3fc8069e33827231 //log(1/frcpa(1+116/256))/2
345 data8 0x3fc82996d3ef8bcb //log(1/frcpa(1+117/256))/2
346 data8 0x3fc85855776dcbfb //log(1/frcpa(1+118/256))/2
347 data8 0x3fc8873658327ccf //log(1/frcpa(1+119/256))/2
348 data8 0x3fc8aa75973ab8cf //log(1/frcpa(1+120/256))/2
349 data8 0x3fc8d992dc8824e5 //log(1/frcpa(1+121/256))/2
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352 data8 0x3fc95bd750ee3ed3 //log(1/frcpa(1+124/256))/2
353 data8 0x3fc98b7811a3ee5b //log(1/frcpa(1+125/256))/2
354 data8 0x3fc9af47f33d406c //log(1/frcpa(1+126/256))/2
355 data8 0x3fc9df270c1914a8 //log(1/frcpa(1+127/256))/2
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357 data8 0x3fca33440224fa79 //log(1/frcpa(1+129/256))/2
358 data8 0x3fca57725e80c383 //log(1/frcpa(1+130/256))/2
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362 data8 0x3fcb015b3eb1e790 //log(1/frcpa(1+134/256))/2
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364 data8 0x3fcb56fa04462909 //log(1/frcpa(1+136/256))/2
365 data8 0x3fcb881aa659bc93 //log(1/frcpa(1+137/256))/2
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378 data8 0x3fcd9509707ae52f //log(1/frcpa(1+150/256))/2
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380 data8 0x3fcdee2f3445e4af //log(1/frcpa(1+152/256))/2
381 data8 0x3fce148a1a2726ce //log(1/frcpa(1+153/256))/2
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387 data8 0x3fcefc9326d16ab9 //log(1/frcpa(1+159/256))/2
388 data8 0x3fcf2391a2157600 //log(1/frcpa(1+160/256))/2
389 data8 0x3fcf4aa7ee03192d //log(1/frcpa(1+161/256))/2
390 data8 0x3fcf71d627c30bb0 //log(1/frcpa(1+162/256))/2
391 data8 0x3fcf991c6cb3b379 //log(1/frcpa(1+163/256))/2
392 data8 0x3fcfc07ada69a910 //log(1/frcpa(1+164/256))/2
393 data8 0x3fcfe7f18eb03d3e //log(1/frcpa(1+165/256))/2
394 data8 0x3fd007c053c5002e //log(1/frcpa(1+166/256))/2
395 data8 0x3fd01b942198a5a1 //log(1/frcpa(1+167/256))/2
396 data8 0x3fd02f74400c64eb //log(1/frcpa(1+168/256))/2
397 data8 0x3fd04360be7603ad //log(1/frcpa(1+169/256))/2
398 data8 0x3fd05759ac47fe34 //log(1/frcpa(1+170/256))/2
399 data8 0x3fd06b5f1911cf52 //log(1/frcpa(1+171/256))/2
400 data8 0x3fd078bf0533c568 //log(1/frcpa(1+172/256))/2
401 data8 0x3fd08cd9687e7b0e //log(1/frcpa(1+173/256))/2
402 data8 0x3fd0a10074cf9019 //log(1/frcpa(1+174/256))/2
403 data8 0x3fd0b5343a234477 //log(1/frcpa(1+175/256))/2
404 data8 0x3fd0c974c89431ce //log(1/frcpa(1+176/256))/2
405 data8 0x3fd0ddc2305b9886 //log(1/frcpa(1+177/256))/2
406 data8 0x3fd0eb524bafc918 //log(1/frcpa(1+178/256))/2
407 data8 0x3fd0ffb54213a476 //log(1/frcpa(1+179/256))/2
408 data8 0x3fd114253da97d9f //log(1/frcpa(1+180/256))/2
409 data8 0x3fd128a24f1d9aff //log(1/frcpa(1+181/256))/2
410 data8 0x3fd1365252bf0865 //log(1/frcpa(1+182/256))/2
411 data8 0x3fd14ae558b4a92d //log(1/frcpa(1+183/256))/2
412 data8 0x3fd15f85a19c765b //log(1/frcpa(1+184/256))/2
413 data8 0x3fd16d4d38c119fa //log(1/frcpa(1+185/256))/2
414 data8 0x3fd18203c20dd133 //log(1/frcpa(1+186/256))/2
415 data8 0x3fd196c7bc4b1f3b //log(1/frcpa(1+187/256))/2
416 data8 0x3fd1a4a738b7a33c //log(1/frcpa(1+188/256))/2
417 data8 0x3fd1b981c0c9653d //log(1/frcpa(1+189/256))/2
418 data8 0x3fd1ce69e8bb106b //log(1/frcpa(1+190/256))/2
419 data8 0x3fd1dc619de06944 //log(1/frcpa(1+191/256))/2
420 data8 0x3fd1f160a2ad0da4 //log(1/frcpa(1+192/256))/2
421 data8 0x3fd2066d7740737e //log(1/frcpa(1+193/256))/2
422 data8 0x3fd2147dba47a394 //log(1/frcpa(1+194/256))/2
423 data8 0x3fd229a1bc5ebac3 //log(1/frcpa(1+195/256))/2
424 data8 0x3fd237c1841a502e //log(1/frcpa(1+196/256))/2
425 data8 0x3fd24cfce6f80d9a //log(1/frcpa(1+197/256))/2
426 data8 0x3fd25b2c55cd5762 //log(1/frcpa(1+198/256))/2
427 data8 0x3fd2707f4d5f7c41 //log(1/frcpa(1+199/256))/2
428 data8 0x3fd285e0842ca384 //log(1/frcpa(1+200/256))/2
429 data8 0x3fd294294708b773 //log(1/frcpa(1+201/256))/2
430 data8 0x3fd2a9a2670aff0c //log(1/frcpa(1+202/256))/2
431 data8 0x3fd2b7fb2c8d1cc1 //log(1/frcpa(1+203/256))/2
432 data8 0x3fd2c65a6395f5f5 //log(1/frcpa(1+204/256))/2
433 data8 0x3fd2dbf557b0df43 //log(1/frcpa(1+205/256))/2
434 data8 0x3fd2ea64c3f97655 //log(1/frcpa(1+206/256))/2
435 data8 0x3fd3001823684d73 //log(1/frcpa(1+207/256))/2
436 data8 0x3fd30e97e9a8b5cd //log(1/frcpa(1+208/256))/2
437 data8 0x3fd32463ebdd34ea //log(1/frcpa(1+209/256))/2
438 data8 0x3fd332f4314ad796 //log(1/frcpa(1+210/256))/2
439 data8 0x3fd348d90e7464d0 //log(1/frcpa(1+211/256))/2
440 data8 0x3fd35779f8c43d6e //log(1/frcpa(1+212/256))/2
441 data8 0x3fd36621961a6a99 //log(1/frcpa(1+213/256))/2
442 data8 0x3fd37c299f3c366a //log(1/frcpa(1+214/256))/2
443 data8 0x3fd38ae2171976e7 //log(1/frcpa(1+215/256))/2
444 data8 0x3fd399a157a603e7 //log(1/frcpa(1+216/256))/2
445 data8 0x3fd3afccfe77b9d1 //log(1/frcpa(1+217/256))/2
446 data8 0x3fd3be9d503533b5 //log(1/frcpa(1+218/256))/2
447 data8 0x3fd3cd7480b4a8a3 //log(1/frcpa(1+219/256))/2
448 data8 0x3fd3e3c43918f76c //log(1/frcpa(1+220/256))/2
449 data8 0x3fd3f2acb27ed6c7 //log(1/frcpa(1+221/256))/2
450 data8 0x3fd4019c2125ca93 //log(1/frcpa(1+222/256))/2
451 data8 0x3fd4181061389722 //log(1/frcpa(1+223/256))/2
452 data8 0x3fd42711518df545 //log(1/frcpa(1+224/256))/2
453 data8 0x3fd436194e12b6bf //log(1/frcpa(1+225/256))/2
454 data8 0x3fd445285d68ea69 //log(1/frcpa(1+226/256))/2
455 data8 0x3fd45bcc464c893a //log(1/frcpa(1+227/256))/2
456 data8 0x3fd46aed21f117fc //log(1/frcpa(1+228/256))/2
457 data8 0x3fd47a1527e8a2d3 //log(1/frcpa(1+229/256))/2
458 data8 0x3fd489445efffccc //log(1/frcpa(1+230/256))/2
459 data8 0x3fd4a018bcb69835 //log(1/frcpa(1+231/256))/2
460 data8 0x3fd4af5a0c9d65d7 //log(1/frcpa(1+232/256))/2
461 data8 0x3fd4bea2a5bdbe87 //log(1/frcpa(1+233/256))/2
462 data8 0x3fd4cdf28f10ac46 //log(1/frcpa(1+234/256))/2
463 data8 0x3fd4dd49cf994058 //log(1/frcpa(1+235/256))/2
464 data8 0x3fd4eca86e64a684 //log(1/frcpa(1+236/256))/2
465 data8 0x3fd503c43cd8eb68 //log(1/frcpa(1+237/256))/2
466 data8 0x3fd513356667fc57 //log(1/frcpa(1+238/256))/2
467 data8 0x3fd522ae0738a3d8 //log(1/frcpa(1+239/256))/2
468 data8 0x3fd5322e26867857 //log(1/frcpa(1+240/256))/2
469 data8 0x3fd541b5cb979809 //log(1/frcpa(1+241/256))/2
470 data8 0x3fd55144fdbcbd62 //log(1/frcpa(1+242/256))/2
471 data8 0x3fd560dbc45153c7 //log(1/frcpa(1+243/256))/2
472 data8 0x3fd5707a26bb8c66 //log(1/frcpa(1+244/256))/2
473 data8 0x3fd587f60ed5b900 //log(1/frcpa(1+245/256))/2
474 data8 0x3fd597a7977c8f31 //log(1/frcpa(1+246/256))/2
475 data8 0x3fd5a760d634bb8b //log(1/frcpa(1+247/256))/2
476 data8 0x3fd5b721d295f10f //log(1/frcpa(1+248/256))/2
477 data8 0x3fd5c6ea94431ef9 //log(1/frcpa(1+249/256))/2
478 data8 0x3fd5d6bb22ea86f6 //log(1/frcpa(1+250/256))/2
479 data8 0x3fd5e6938645d390 //log(1/frcpa(1+251/256))/2
480 data8 0x3fd5f673c61a2ed2 //log(1/frcpa(1+252/256))/2
481 data8 0x3fd6065bea385926 //log(1/frcpa(1+253/256))/2
482 data8 0x3fd6164bfa7cc06b //log(1/frcpa(1+254/256))/2
483 data8 0x3fd62643fecf9743 //log(1/frcpa(1+255/256))/2
484 LOCAL_OBJECT_END(atanhf_data2)
487 .section .text
488 GLOBAL_LIBM_ENTRY(atanhf)
490 { .mfi
491 getf.exp rArgSExpb = f8
492 fclass.m p9,p0 = f8, 0x0b // is arg denormal ?
493 mov rExpbMask = 0x1ffff
494 }
495 { .mfi
496 addl DataPtr = @ltoff(atanhf_data), gp
497 fnma.s1 fOneMx = f8, f1, f1 // 1 - x
498 mov rBias = 0xffff
499 }
500 ;;
502 { .mfi
503 nop.m 0
504 fclass.m p7,p0 = f8, 0xc7 // is arg NaN or +/-0 ?
505 mov rNearZeroBound = 0xffeb // 2^(-20)
506 }
507 { .mfi
508 ld8 DataPtr = [DataPtr]
509 fma.s1 fOnePx = f8, f1, f1 // 1 + x
510 nop.i 0
511 }
512 ;;
514 { .mfb
515 nop.m 0
516 fnorm.s1 fNormX = f8 // Normalize x
517 (p9) br.cond.spnt ATANH_UNORM // Branch if x=unorm
518 }
519 ;;
521 ATANH_COMMON:
522 // Return here if x=unorm and not denorm
523 { .mfi
524 ldfpd fP3, fP2 = [DataPtr], 16
525 fma.s1 fX2 = f8, f8, f0 // x^2
526 nop.i 0
527 }
528 { .mfb
529 nop.m 0
530 (p7) fma.s.s0 f8 = f8,f1,f8 // NaN or +/-0
531 (p7) br.ret.spnt b0
532 }
533 ;;
535 { .mfi
536 ldfpd fP1, fHalf = [DataPtr], 16
537 frcpa.s1 fRcpM, p9 = f1, fOneMx // rcpm = frcpa(1 - x)
538 nop.i 0
539 }
540 ;;
542 { .mfi
543 getf.exp rExpbm = fOneMx
544 frcpa.s1 fRcpP, p0 = f1, fOnePx // rcpp = frcpa(1 + x)
545 // biased exponent
546 and rArgExpb = rArgSExpb, rExpbMask
547 }
548 ;;
550 { .mmi
551 getf.exp rExpbp = fOnePx
552 // is |x| < 2^(-20) ?
553 cmp.gt p8,p0 = rNearZeroBound, rArgExpb
554 cmp.ge p6,p0 = rArgExpb, rBias // is |x| >= 1 ?
555 }
556 ;;
558 { .mmb
559 getf.sig rSigm = fOneMx
560 nop.m 0
561 (p6) br.cond.spnt atanhf_ge_one
562 }
563 ;;
565 { .mfb
566 getf.sig rSigp = fOnePx
567 (p8) fma.s.s0 f8 = fX2, f8, f8 // x + x^3
568 (p8) br.ret.spnt b0 // Exit for MAX_DENORM_ABS < |x| < 2^-20
569 }
570 ;;
572 { .mfi
573 ldfd fLog2 = [DataPtr], 16
574 fms.s1 fRm = fRcpM, fOneMx, f1 // rm = rcpm * (1 - x) - 1
575 nop.i 0
576 }
577 ;;
579 { .mmf
580 // (1 - x) is always positive here and we need not mask sign bit
581 sub rNm = rExpbm, rBias
582 // (1 + x) is always positive here and we need not mask sign bit
583 sub rNp = rExpbp, rBias
584 fms.s1 fRp = fRcpP, fOnePx, f1 // rp = rcpp * (1 + x) - 1
585 }
586 ;;
588 { .mmi
589 setf.sig fN4CvtM = rNm
590 setf.sig fN4CvtP = rNp
591 extr.u rIndm = rSigm,55,8 // Extract 8 bits
592 }
593 ;;
595 { .mmi
596 shladd RcpTablePtrM = rIndm, 3, DataPtr
597 nop.m 0
598 extr.u rIndp = rSigp,55,8 // Extract 8 bits
599 }
600 ;;
602 { .mmi
603 ldfd fLogTm = [RcpTablePtrM]
604 shladd RcpTablePtrP = rIndp, 3, DataPtr
605 nop.i 0
606 }
607 ;;
609 { .mfi
610 ldfd fLogTp = [RcpTablePtrP]
611 fma.s1 fRm2 = fRm, fRm, f0 // rm^2
612 nop.i 0
613 }
614 { .mfi
615 nop.m 0
616 fma.s1 fP32m = fP3, fRm, fP2 // P3*rm + P2
617 nop.i 0
618 }
619 ;;
621 { .mfi
622 nop.m 0
623 fma.s1 fRp2 = fRp, fRp, f0 // rp^2
624 nop.i 0
625 }
626 { .mfi
627 nop.m 0
628 fma.s1 fP10m = fP1, fRm, fHalf // P1*rm + 1
629 nop.i 0
630 }
631 ;;
633 { .mfi
634 nop.m 0
635 fma.s1 fP32p = fP3, fRp, fP2 // P3*rp + P2
636 nop.i 0
637 }
638 { .mfi
639 nop.m 0
640 fma.s1 fP10p = fP1, fRp, fHalf // P1*rp + 1
641 nop.i 0
642 }
643 ;;
645 { .mfi
646 nop.m 0
647 fcvt.xf fNm = fN4CvtM
648 nop.i 0
649 }
650 { .mfi
651 nop.m 0
652 fcvt.xf fNp = fN4CvtP
653 nop.i 0
654 }
655 ;;
657 { .mfi
658 nop.m 0
659 // (P3*rm + P2)*rm^2 + (P1*rm + 1)
660 fma.s1 fP32m = fP32m, fRm2, fP10m
661 nop.i 0
662 }
663 { .mfi
664 nop.m 0
665 // (P3*rp + P2)*rp^2 + (P1*rp + 1)
666 fma.s1 fP32p = fP32p, fRp2, fP10p
667 nop.i 0
668 }
669 ;;
671 { .mfi
672 nop.m 0
673 // Nm*ln(2)/2 + Tm/2
674 fma.s1 fLogTm = fNm, fLog2, fLogTm
675 nop.i 0
676 }
677 { .mfi
678 nop.m 0
679 // Np*ln(2)/2 + Tp/2
680 fma.s1 fLogTp = fNp, fLog2, fLogTp
681 nop.i 0
682 }
683 ;;
685 { .mfi
686 nop.m 0
687 // ((P3*rm + P2)*rm^2 + (P3*rm + 1))*0.5*rm + (Nm*ln(2)/2 + Tm/2)
688 fma.d.s1 fP32m = fP32m, fRm, fLogTm
689 nop.i 0
690 }
691 { .mfi
692 nop.m 0
693 // ((P3*rp + P2)*rp^2 + (P3*rp + 1))*0.5*rp + (Np*ln(2)/2 + Tp/2)
694 fma.d.s1 fP32p = fP32p, fRp, fLogTp
695 nop.i 0
696 }
697 ;;
699 { .mfb
700 nop.m 0
701 // atanhf(x) = 0.5 * (log(1 + x) - log(1 - x))
702 fnma.s.s0 f8 = fP32m, f1, fP32p
703 br.ret.sptk b0 // Exit for 2^(-20) <= |x| < 1.0
704 }
705 ;;
708 ATANH_UNORM:
709 // Here if x=unorm
710 { .mfi
711 getf.exp rArgSExpb = fNormX // Recompute if x unorm
712 fclass.m p0,p9 = fNormX, 0x0b // Test x denorm
713 nop.i 0
714 }
715 ;;
717 { .mfb
718 nop.m 0
719 fcmp.lt.s0 p10,p11 = f8, f0 // Set denormal flag
720 (p9) br.cond.sptk ATANH_COMMON // Continue if x unorm and not denorm
721 }
722 ;;
724 .pred.rel "mutex",p6,p7
725 { .mfi
726 nop.m 0
727 (p6) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=-denorm
728 nop.i 0
729 }
730 { .mfb
731 nop.m 0
732 (p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=+denorm
733 br.ret.spnt b0 // Exit if denorm
734 }
735 ;;
737 // Here if |x| >= 1.0
738 atanhf_ge_one:
739 { .mfi
740 alloc r32 = ar.pfs,1,3,4,0
741 fmerge.s fArgAbs = f0, f8 // Form |x|
742 nop.i 0
743 }
744 ;;
746 { .mfi
747 nop.m 0
748 fmerge.s f10 = f8, f8 // Save input for error call
749 nop.i 0
750 }
751 ;;
753 { .mfi
754 nop.m 0
755 fcmp.eq.s1 p6,p7 = fArgAbs, f1 // Test for |x| = 1.0
756 nop.i 0
757 }
758 ;;
760 // Set error tag and result, and raise invalid flag if |x| > 1.0
761 { .mfi
762 (p7) mov atanh_GR_tag = 133
763 (p7) frcpa.s0 f8, p0 = f0, f0 // Get QNaN, and raise invalid
764 nop.i 0
765 }
766 ;;
768 // Set error tag and result, and raise Z flag if |x| = 1.0
769 { .mfi
770 nop.m 0
771 (p6) frcpa.s0 fRm, p0 = f1, f0 // Get inf, and raise Z flag
772 nop.i 0
773 }
774 ;;
776 { .mfb
777 (p6) mov atanh_GR_tag = 134
778 (p6) fmerge.s f8 = f8, fRm // result is +-inf
779 br.cond.sptk __libm_error_region // Exit if |x| >= 1.0
780 }
781 ;;
783 GLOBAL_LIBM_END(atanhf)
786 LOCAL_LIBM_ENTRY(__libm_error_region)
787 .prologue
789 { .mfi
790 add GR_Parameter_Y=-32,sp // Parameter 2 value
791 nop.f 0
792 .save ar.pfs,GR_SAVE_PFS
793 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
794 }
795 { .mfi
796 .fframe 64
797 add sp=-64,sp // Create new stack
798 nop.f 0
799 mov GR_SAVE_GP=gp // Save gp
800 };;
802 { .mmi
803 stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
804 add GR_Parameter_X = 16,sp // Parameter 1 address
805 .save b0, GR_SAVE_B0
806 mov GR_SAVE_B0=b0 // Save b0
807 };;
809 .body
810 { .mib
811 stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
812 // Parameter 3 address
813 add GR_Parameter_RESULT = 0,GR_Parameter_Y
814 nop.b 0
815 }
816 { .mib
817 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
818 add GR_Parameter_Y = -16,GR_Parameter_Y
819 br.call.sptk b0=__libm_error_support# // Call error handling function
820 };;
822 { .mmi
823 add GR_Parameter_RESULT = 48,sp
824 nop.m 0
825 nop.i 0
826 };;
828 { .mmi
829 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
830 .restore sp
831 add sp = 64,sp // Restore stack pointer
832 mov b0 = GR_SAVE_B0 // Restore return address
833 };;
835 { .mib
836 mov gp = GR_SAVE_GP // Restore gp
837 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
838 br.ret.sptk b0 // Return
839 };;
841 LOCAL_LIBM_END(__libm_error_region)
844 .type __libm_error_support#,@function
845 .global __libm_error_support#