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