| blob | df616deae07e7ec608402953ea4587873a762d4a |
1 .file "asinhf.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 // ==============================================================
41 // History
42 // ==============================================================
43 // 04/02/01 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 // 05/21/03 Improved performance, fixed to handle unorms
48 //
49 // API
50 // ==============================================================
51 // float asinhf(float)
52 //
53 // Overview of operation
54 // ==============================================================
55 //
56 // There are 7 paths:
57 // 1. x = 0.0
58 // Return asinhf(x) = 0.0
59 // 2. 0.0 <|x| < 2^(-5)
60 // Return asinhf(x) = Pol5(x), where Pol5(x) = ((x^2)*C1 + C0)*x^3 + x
62 // 3. 2^(-5) <= |x| < 2^51
63 // Return asinhf(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
64 // To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
65 // (2 iterations)
66 // Algorithm description for log function see below.
67 //
68 // 4. 2^51 <= |x| < +INF
69 // Return asinhf(x) = sign(x)*log(2*|x|)
70 // Algorithm description for log function see below.
71 //
72 // 5. x = INF
73 // Return asinhf(x) = INF
74 //
75 // 6. x = [S,Q]NaN
76 // Return asinhf(x) = QNaN
77 //
78 // 7. x = denormal
79 // Return asinhf(x) = x
80 //
81 //==============================================================
82 // Algorithm Description for log(x) function
83 // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
84 // true for this asinh implementation
85 //
86 // Consider x = 2^N 1.f1 f2 f3 f4...f63
87 // Log(x) = log(frcpa(x) x/frcpa(x))
88 // = log(1/frcpa(x)) + log(frcpa(x) x)
89 // = -log(frcpa(x)) + log(frcpa(x) x)
90 //
91 // frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
92 //
93 // -log(frcpa(x)) = -log(C)
94 // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
95 //
96 // -log(frcpa(x)) = -log(C)
97 // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
98 //
99 // -log(frcpa(x)) = -log(C)
100 // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
101 //
102 // Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
103 //
104 // Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
105 // Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
106 // Log(x) = +Nlog2 + T + log(frcpa(x) x)
107 //
108 // Log(x) = +Nlog2 + T + log(C x)
109 //
110 // Cx = 1 + r
111 //
112 // Log(x) = +Nlog2 + T + log(1+r)
113 // Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
114 //
115 // 1.f1 f2 ... f8 has 256 entries.
116 // They are 1 + k/2^8, k = 0 ... 255
117 // These 256 values are the table entries.
118 //
119 // Implementation
120 //==============================================================
121 // C = frcpa(x)
122 // r = C * x - 1
123 //
124 // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
125 //
126 // x = f * 2*n where f is 1.f_1f_2f_3....f_63
127 // Nfloat = float(n) where n is the true unbiased exponent
128 // pre-index = f_1f_2....f_8
129 // index = pre_index * 8
130 // get the dxt table entry at index + offset = T
131 //
132 // result = (T + Nfloat * log(2)) + rseries
133 //
134 // The T table is calculated as follows
135 // Form x_k = 1 + k/2^8 where k goes from 0... 255
136 // y_k = frcpa(x_k)
137 // log(1/y_k) in quad and round to double-extended
138 //
139 //
140 // Registers used
141 //==============================================================
142 // Floating Point registers used:
143 // f8, input
144 // f9 -> f15, f32 -> f55
146 // General registers used:
147 // r14 -> r27
149 // Predicate registers used:
150 // p6 -> p14
152 // p6 to filter out case when x = [Q,S]NaN or INF or zero
153 // p7 to filter out case when x < 0.0
154 // p8 to select path #2
156 // p11 to filter out case when x >= 0
157 // p12 to filter out case when x = + denormal
158 // p13 to select path #4
159 // p14 to filtef out case when x = - denormal
160 // Assembly macros
161 //==============================================================
162 log_GR_exp_17_ones = r14
163 log_GR_signexp_f8 = r15
164 log_table_address2 = r16
165 log_GR_exp_16_ones = r17
166 log_GR_exp_f8 = r18
167 log_GR_true_exp_f8 = r19
168 log_GR_significand_f8 = r20
169 log_GR_index = r21
170 log_GR_comp2 = r22
171 asinh_GR_f8 = r23
172 asinh_GR_comp = r24
173 asinh_GR_f8 = r25
174 log_table_address3 = r26
175 NR_table_address = r27
177 //==============================================================
178 log_y = f9
179 NR1 = f10
180 NR2 = f11
181 log_y_rs = f12
182 log_y_rs_iter = f13
183 log_y_rs_iter1 = f14
184 fNormX = f15
185 asinh_w_sq = f32
186 log_arg_early = f33
187 log_y_rs_iter2 = f34
188 log_P3 = f35
189 log_P2 = f36
190 log_P1 = f37
191 log2 = f38
192 log_C0 = f39
193 log_C1 = f40
194 asinh_f8 = f41
195 log_C = f42
196 log_arg = f43
197 asinh_w_cube = f44
198 log_int_Nfloat = f45
199 log_r = f46
200 log_rsq = f47
201 asinh_w_1 = f48
202 log_rp_p32 = f49
203 log_rcube = f50
204 log_rp_p10 = f51
205 log_rp_p2 = f52
206 log_Nfloat = f53
207 log_T = f54
208 log_T_plus_Nlog2 = f55
210 // Data tables
211 //==============================================================
213 RODATA
214 .align 16
216 LOCAL_OBJECT_START(log_table_1)
218 data8 0xbfd0001008f39d59 // p3
219 data8 0x3fd5556073e0c45a // p2
220 data8 0xbfdffffffffaea15 // p1
221 data8 0x3fe62e42fefa39ef // log(2)
222 LOCAL_OBJECT_END(log_table_1)
224 LOCAL_OBJECT_START(log_table_2)
225 data8 0x3FE0000000000000 // 0.5
226 data8 0x4008000000000000 // 3.0
227 data8 0x9979C79685A5EB16, 0x00003FFB // C1 3FFB9979C79685A5EB16
228 data8 0xAAAAA96F80786D62, 0x0000BFFC // C0 BFFCAAAAA96F80786D62
229 LOCAL_OBJECT_END(log_table_2)
231 LOCAL_OBJECT_START(log_table_3)
232 data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)
233 data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)
234 data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)
235 data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)
236 data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)
237 data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)
238 data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)
239 data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)
240 data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)
241 data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)
242 data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)
243 data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)
244 data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)
245 data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)
246 data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)
247 data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)
248 data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)
249 data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)
250 data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)
251 data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)
252 data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)
253 data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)
254 data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)
255 data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)
256 data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)
257 data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)
258 data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)
259 data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)
260 data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)
261 data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)
262 data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)
263 data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)
264 data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)
265 data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)
266 data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)
267 data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)
268 data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)
269 data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)
270 data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)
271 data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)
272 data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)
273 data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)
274 data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)
275 data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)
276 data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)
277 data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)
278 data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)
279 data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)
280 data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)
281 data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)
282 data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)
283 data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)
284 data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)
285 data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)
286 data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)
287 data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)
288 data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)
289 data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)
290 data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)
291 data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)
292 data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)
293 data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)
294 data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)
295 data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)
296 data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)
297 data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)
298 data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)
299 data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)
300 data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)
301 data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)
302 data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)
303 data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)
304 data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)
305 data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)
306 data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)
307 data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)
308 data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)
309 data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)
310 data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)
311 data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)
312 data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)
313 data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)
314 data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)
315 data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)
316 data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)
317 data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)
318 data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)
319 data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)
320 data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)
321 data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)
322 data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)
323 data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)
324 data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)
325 data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)
326 data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)
327 data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)
328 data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)
329 data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)
330 data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)
331 data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)
332 data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)
333 data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)
334 data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)
335 data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)
336 data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)
337 data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)
338 data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)
339 data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)
340 data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)
341 data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)
342 data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)
343 data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)
344 data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)
345 data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)
346 data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)
347 data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)
348 data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)
349 data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)
350 data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)
351 data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)
352 data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)
353 data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)
354 data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)
355 data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)
356 data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)
357 data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)
358 data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)
359 data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)
360 data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)
361 data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)
362 data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)
363 data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)
364 data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)
365 data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)
366 data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)
367 data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)
368 data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)
369 data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)
370 data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)
371 data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)
372 data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)
373 data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)
374 data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)
375 data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)
376 data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)
377 data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)
378 data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)
379 data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)
380 data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)
381 data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)
382 data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)
383 data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)
384 data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)
385 data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)
386 data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)
387 data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)
388 data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)
389 data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)
390 data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)
391 data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)
392 data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)
393 data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)
394 data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)
395 data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)
396 data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)
397 data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)
398 data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)
399 data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)
400 data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)
401 data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)
402 data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)
403 data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)
404 data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)
405 data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)
406 data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)
407 data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)
408 data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)
409 data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)
410 data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)
411 data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)
412 data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)
413 data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)
414 data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)
415 data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)
416 data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)
417 data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)
418 data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)
419 data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)
420 data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)
421 data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)
422 data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)
423 data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)
424 data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)
425 data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)
426 data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)
427 data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)
428 data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)
429 data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)
430 data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)
431 data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)
432 data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)
433 data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)
434 data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)
435 data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)
436 data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)
437 data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)
438 data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)
439 data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)
440 data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)
441 data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)
442 data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)
443 data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)
444 data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)
445 data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)
446 data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)
447 data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)
448 data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)
449 data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)
450 data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)
451 data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)
452 data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)
453 data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)
454 data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)
455 data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)
456 data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)
457 data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)
458 data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)
459 data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)
460 data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)
461 data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)
462 data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)
463 data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)
464 data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)
465 data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)
466 data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)
467 data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)
468 data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)
469 data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)
470 data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)
471 data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)
472 data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)
473 data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)
474 data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)
475 data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)
476 data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)
477 data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)
478 data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)
479 data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)
480 data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)
481 data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)
482 data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)
483 data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)
484 data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)
485 data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)
486 data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)
487 data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
488 LOCAL_OBJECT_END(log_table_3)
491 .section .text
492 GLOBAL_LIBM_ENTRY(asinhf)
494 { .mfi
495 getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
496 fclass.m p12,p0 = f8, 0x0b // Test x unorm
497 mov log_GR_exp_17_ones = 0x1ffff
498 }
499 { .mfi
500 addl NR_table_address = @ltoff(log_table_1), gp
501 fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
502 mov asinh_GR_comp = 0xfffa
503 }
504 ;;
506 { .mfi
507 mov log_GR_exp_16_ones = 0xffff //BIAS
508 fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
509 mov log_GR_comp2 = 0x10032
510 }
511 { .mfi
512 ld8 NR_table_address = [NR_table_address]
513 fma.s1 asinh_w_sq = f8,f8,f0 // x^2
514 nop.i 0
515 }
516 ;;
518 { .mfi
519 nop.m 0
520 fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
521 nop.i 0
522 }
523 { .mfb
524 nop.m 0
525 fnorm.s1 fNormX = f8 // Normalize x
526 (p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
527 }
528 ;;
530 ASINH_COMMON:
531 // Return here if x=unorm and not denorm
532 { .mfi
533 //to get second table address
534 adds log_table_address2 = 0x20, NR_table_address
535 fma.s1 log_arg = f8,f1,f8
536 }
537 { .mfb
538 nop.m 0
539 (p6) fma.s.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
540 (p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
541 }
542 ;;
544 { .mfi
545 ldfpd NR1,NR2 = [log_table_address2],16
546 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
547 nop.i 0
548 }
549 ;;
551 { .mfi
552 ldfe log_C1 = [log_table_address2],16
553 nop.f 0
554 and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
555 }
556 ;;
558 { .mib
559 ldfe log_C0 = [log_table_address2],16
560 cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
561 (p13) br.cond.spnt LOG_COMMON1 // Branch if path 4: |x| >= 2^51
562 }
563 ;;
565 { .mfi
566 nop.m 0
567 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
568 nop.i 0
569 }
570 ;;
572 .pred.rel "mutex",p7,p11
573 { .mfi
574 nop.m 0
575 (p11) mov asinh_f8 = fNormX
576 nop.i 0
577 }
578 { .mfb
579 cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
580 (p7) fnma.s1 asinh_f8 = fNormX,f1,f0
581 (p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2: 0 < |x| < 2^-5
582 }
583 ;;
585 // Here if main path, 2^-5 <= |x| < 2^51
586 ///////////////////////////////// The first iteration /////////////////////////
587 { .mfi
588 ldfpd log_P3,log_P2 = [NR_table_address],16
589 fnma.s1 log_y_rs_iter2 = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
590 nop.i 0
591 }
592 { .mfi
593 nop.m 0
594 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
595 nop.i 0
596 }
597 ;;
599 { .mfi
600 ldfpd log_P1,log2 = [NR_table_address],16
601 // (0.5*z)*(3-(y*z)*z)
602 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter2,f0
603 nop.i 0
604 }
605 { .mfi
606 nop.m 0
607 // (0.5*z)*(3-(y*z)*z)
608 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs_iter2,f0
609 nop.i 0
610 }
611 ;;
613 ////////////////////////////////// The second iteration ////////////////////////
614 { .mfi
615 nop.m 0
616 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
617 nop.i 0
618 }
619 { .mfi
620 nop.m 0
621 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
622 nop.i 0
623 }
624 ;;
626 { .mfi
627 nop.m 0
628 fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
629 nop.i 0
630 }
631 ;;
633 { .mfi
634 nop.m 0
635 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
636 nop.i 0
637 }
638 { .mfi
639 nop.m 0
640 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
641 nop.i 0
642 }
643 ;;
645 { .mfi
646 nop.m 0
647 frcpa.s1 log_C,p0 = f1,log_arg_early
648 nop.i 0
649 }
650 ;;
652 { .mfi
653 getf.exp log_GR_signexp_f8 = log_arg_early
654 nop.f 0
655 nop.i 0
656 }
657 ;;
659 { .mfi
660 getf.sig log_GR_significand_f8 = log_arg_early
661 // (0.5*z)*(3-(y*z)*z)*y + |x|
662 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
663 //to get third table address
664 adds log_table_address3 = 0x30, NR_table_address
665 }
666 ;;
668 /////////////////////////////////////////// The end NR iterations /////////////
670 { .mfi
671 nop.m 0
672 nop.f 0
673 //significant bit destruction
674 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
675 }
676 ;;
678 { .mfi
679 //BIAS subtraction
680 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
681 (p7) fnma.s1 log2 = log2,f1,f0
682 nop.i 0
683 }
684 ;;
686 { .mfi
687 setf.sig log_int_Nfloat = log_GR_true_exp_f8
688 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
689 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
690 }
691 ;;
693 { .mmi
694 //pre-index*16 + index
695 shladd log_table_address3 = log_GR_index,3,log_table_address3
696 ;;
697 ldfd log_T = [log_table_address3]
698 nop.i 0
699 }
700 ;;
702 { .mfi
703 nop.m 0
704 fma.s1 log_rsq = log_r, log_r, f0 //r^2
705 nop.i 0
706 }
707 { .mfi
708 nop.m 0
709 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
710 nop.i 0
711 }
712 ;;
714 { .mfi
715 nop.m 0
716 fma.s1 log_rp_p10 = log_P1, log_r, f1
717 nop.i 0
718 }
719 ;;
721 { .mfi
722 nop.m 0
723 //convert N to the floating-point format
724 fcvt.xf log_Nfloat = log_int_Nfloat
725 nop.i 0
726 }
727 ;;
729 { .mfi
730 nop.m 0
731 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
732 nop.i 0
733 }
734 ;;
736 .pred.rel "mutex",p7,p11
737 { .mfi
738 nop.m 0
739 (p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
740 nop.i 0
741 }
742 { .mfi
743 nop.m 0
744 (p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
745 nop.i 0
746 }
747 ;;
749 { .mfi
750 nop.m 0
751 (p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
752 nop.i 0
753 }
754 { .mfb
755 nop.m 0
756 (p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
757 br.ret.sptk b0 // Exit main path, path 3: 2^-5 <= |x| < 2^51
758 }
759 ;;
762 // Here if path 4, |x| >= 2^51
763 LOG_COMMON1:
764 { .mfi
765 ldfpd log_P3,log_P2 = [NR_table_address],16
766 nop.f 0
767 nop.i 0
768 }
769 ;;
771 { .mfi
772 ldfpd log_P1,log2 = [NR_table_address],16
773 frcpa.s1 log_C,p0 = f1,log_arg
774 nop.i 0
775 }
776 ;;
778 { .mfi
779 getf.exp log_GR_signexp_f8 = log_arg
780 nop.f 0
781 //to get third table address
782 adds log_table_address3 = 0x30, NR_table_address
783 }
784 ;;
786 { .mfi
787 getf.sig log_GR_significand_f8 = log_arg
788 nop.f 0
789 nop.i 0
790 }
791 ;;
793 { .mfi
794 nop.m 0
795 nop.f 0
796 //to destroy the most bit in the significant area
797 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
798 }
799 ;;
801 { .mmf
802 nop.m 0
803 //BIAS subtraction
804 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
805 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
806 }
807 ;;
809 { .mfi
810 setf.sig log_int_Nfloat = log_GR_true_exp_f8
811 nop.f 0
812 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
813 }
814 ;;
816 { .mmi
817 //pre-index*16 + index
818 shladd log_table_address3 = log_GR_index,3,log_table_address3
819 ;;
820 ldfd log_T = [log_table_address3]
821 nop.i 0
822 }
823 ;;
825 { .mfi
826 nop.m 0
827 fma.s1 log_rsq = log_r, log_r, f0 //r^2
828 nop.i 0
829 }
830 { .mfi
831 nop.m 0
832 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
833 nop.i 0
834 }
835 ;;
837 { .mfi
838 nop.m 0
839 fma.s1 log_rp_p10 = log_P1, log_r, f1
840 nop.i 0
841 }
842 { .mfi
843 nop.m 0
844 (p7) fnma.s1 log2 = log2,f1,f0
845 nop.i 0
846 }
847 ;;
849 { .mfi
850 nop.m 0
851 //convert N to the floating-point format
852 fcvt.xf log_Nfloat = log_int_Nfloat
853 nop.i 0
854 }
855 { .mfi
856 nop.m 0
857 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
858 nop.i 0
859 }
860 ;;
862 .pred.rel "mutex",p7,p11
863 { .mfi
864 nop.m 0
865 (p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
866 nop.i 0
867 }
868 { .mfi
869 nop.m 0
870 (p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
871 nop.i 0
872 }
873 ;;
875 { .mfi
876 nop.m 0
877 (p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
878 nop.i 0
879 }
880 { .mfb
881 nop.m 0
882 (p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
883 br.ret.sptk b0 // Exit path 4, |x| >= 2^51
884 }
885 ;;
887 // Here if path 2, 0 < |x| < 2^-5
888 ASINH_NEAR_ZERO:
889 { .mfi
890 nop.m 0
891 fma.s1 asinh_w_1 = asinh_w_sq,log_C1,log_C0
892 nop.i 0
893 }
894 { .mfi
895 nop.m 0
896 fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
897 nop.i 0
898 }
899 ;;
901 { .mfb
902 nop.m 0
903 fma.s.s0 f8 = asinh_w_1,asinh_w_cube,fNormX
904 br.ret.sptk b0 // Exit path 2, 0 < |x| < 2^-5
905 }
906 ;;
908 ASINH_UNORM:
909 // Here if x=unorm
910 { .mfi
911 getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
912 fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
913 nop.i 0
914 }
915 ;;
917 { .mfb
918 nop.m 0
919 fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
920 (p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
921 }
922 ;;
924 .pred.rel "mutex",p7,p11
925 { .mfi
926 nop.m 0
927 (p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
928 nop.i 0
929 }
930 { .mfb
931 nop.m 0
932 (p11) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
933 br.ret.spnt b0 // Exit if denorm
934 }
935 ;;
937 GLOBAL_LIBM_END(asinhf)