1.file "asinhf.s" 2 3 4// Copyright (c) 2000 - 2003, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// ============================================================== 40// History 41// ============================================================== 42// 04/02/01 Initial version 43// 04/19/01 Improved speed of the paths #1,2,3,4,5 44// 05/20/02 Cleaned up namespace and sf0 syntax 45// 02/06/03 Reordered header: .section, .global, .proc, .align 46// 05/21/03 Improved performance, fixed to handle unorms 47// 48// API 49// ============================================================== 50// float asinhf(float) 51// 52// Overview of operation 53// ============================================================== 54// 55// There are 7 paths: 56// 1. x = 0.0 57// Return asinhf(x) = 0.0 58// 2. 0.0 <|x| < 2^(-5) 59// Return asinhf(x) = Pol5(x), where Pol5(x) = ((x^2)*C1 + C0)*x^3 + x 60 61// 3. 2^(-5) <= |x| < 2^51 62// Return asinhf(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0))) 63// To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used 64// (2 iterations) 65// Algorithm description for log function see below. 66// 67// 4. 2^51 <= |x| < +INF 68// Return asinhf(x) = sign(x)*log(2*|x|) 69// Algorithm description for log function see below. 70// 71// 5. x = INF 72// Return asinhf(x) = INF 73// 74// 6. x = [S,Q]NaN 75// Return asinhf(x) = QNaN 76// 77// 7. x = denormal 78// Return asinhf(x) = x 79// 80//============================================================== 81// Algorithm Description for log(x) function 82// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always 83// true for this asinh implementation 84// 85// Consider x = 2^N 1.f1 f2 f3 f4...f63 86// Log(x) = log(frcpa(x) x/frcpa(x)) 87// = log(1/frcpa(x)) + log(frcpa(x) x) 88// = -log(frcpa(x)) + log(frcpa(x) x) 89// 90// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63) 91// 92// -log(frcpa(x)) = -log(C) 93// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63)) 94// 95// -log(frcpa(x)) = -log(C) 96// = +Nlog2 - log(frcpa(1.f1 f2 ... f63)) 97// 98// -log(frcpa(x)) = -log(C) 99// = +Nlog2 + log(frcpa(1.f1 f2 ... f63)) 100// 101// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x) 102// 103// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) 104// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) 105// Log(x) = +Nlog2 + T + log(frcpa(x) x) 106// 107// Log(x) = +Nlog2 + T + log(C x) 108// 109// Cx = 1 + r 110// 111// Log(x) = +Nlog2 + T + log(1+r) 112// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....) 113// 114// 1.f1 f2 ... f8 has 256 entries. 115// They are 1 + k/2^8, k = 0 ... 255 116// These 256 values are the table entries. 117// 118// Implementation 119//============================================================== 120// C = frcpa(x) 121// r = C * x - 1 122// 123// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 124// 125// x = f * 2*n where f is 1.f_1f_2f_3....f_63 126// Nfloat = float(n) where n is the true unbiased exponent 127// pre-index = f_1f_2....f_8 128// index = pre_index * 8 129// get the dxt table entry at index + offset = T 130// 131// result = (T + Nfloat * log(2)) + rseries 132// 133// The T table is calculated as follows 134// Form x_k = 1 + k/2^8 where k goes from 0... 255 135// y_k = frcpa(x_k) 136// log(1/y_k) in quad and round to double-extended 137// 138// 139// Registers used 140//============================================================== 141// Floating Point registers used: 142// f8, input 143// f9 -> f15, f32 -> f55 144 145// General registers used: 146// r14 -> r27 147 148// Predicate registers used: 149// p6 -> p14 150 151// p6 to filter out case when x = [Q,S]NaN or INF or zero 152// p7 to filter out case when x < 0.0 153// p8 to select path #2 154 155// p11 to filter out case when x >= 0 156// p12 to filter out case when x = + denormal 157// p13 to select path #4 158// p14 to filtef out case when x = - denormal 159// Assembly macros 160//============================================================== 161log_GR_exp_17_ones = r14 162log_GR_signexp_f8 = r15 163log_table_address2 = r16 164log_GR_exp_16_ones = r17 165log_GR_exp_f8 = r18 166log_GR_true_exp_f8 = r19 167log_GR_significand_f8 = r20 168log_GR_index = r21 169log_GR_comp2 = r22 170asinh_GR_f8 = r23 171asinh_GR_comp = r24 172asinh_GR_f8 = r25 173log_table_address3 = r26 174NR_table_address = r27 175 176//============================================================== 177log_y = f9 178NR1 = f10 179NR2 = f11 180log_y_rs = f12 181log_y_rs_iter = f13 182log_y_rs_iter1 = f14 183fNormX = f15 184asinh_w_sq = f32 185log_arg_early = f33 186log_y_rs_iter2 = f34 187log_P3 = f35 188log_P2 = f36 189log_P1 = f37 190log2 = f38 191log_C0 = f39 192log_C1 = f40 193asinh_f8 = f41 194log_C = f42 195log_arg = f43 196asinh_w_cube = f44 197log_int_Nfloat = f45 198log_r = f46 199log_rsq = f47 200asinh_w_1 = f48 201log_rp_p32 = f49 202log_rcube = f50 203log_rp_p10 = f51 204log_rp_p2 = f52 205log_Nfloat = f53 206log_T = f54 207log_T_plus_Nlog2 = f55 208 209// Data tables 210//============================================================== 211 212RODATA 213.align 16 214 215LOCAL_OBJECT_START(log_table_1) 216 217data8 0xbfd0001008f39d59 // p3 218data8 0x3fd5556073e0c45a // p2 219data8 0xbfdffffffffaea15 // p1 220data8 0x3fe62e42fefa39ef // log(2) 221LOCAL_OBJECT_END(log_table_1) 222 223LOCAL_OBJECT_START(log_table_2) 224data8 0x3FE0000000000000 // 0.5 225data8 0x4008000000000000 // 3.0 226data8 0x9979C79685A5EB16, 0x00003FFB // C1 3FFB9979C79685A5EB16 227data8 0xAAAAA96F80786D62, 0x0000BFFC // C0 BFFCAAAAA96F80786D62 228LOCAL_OBJECT_END(log_table_2) 229 230LOCAL_OBJECT_START(log_table_3) 231data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256) 232data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256) 233data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256) 234data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256) 235data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256) 236data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256) 237data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256) 238data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256) 239data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256) 240data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256) 241data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256) 242data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256) 243data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256) 244data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256) 245data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256) 246data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256) 247data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256) 248data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256) 249data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256) 250data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256) 251data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256) 252data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256) 253data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256) 254data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256) 255data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256) 256data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256) 257data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256) 258data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256) 259data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256) 260data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256) 261data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256) 262data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256) 263data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256) 264data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256) 265data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256) 266data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256) 267data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256) 268data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256) 269data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256) 270data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256) 271data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256) 272data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256) 273data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256) 274data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256) 275data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256) 276data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256) 277data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256) 278data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256) 279data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256) 280data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256) 281data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256) 282data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256) 283data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256) 284data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256) 285data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256) 286data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256) 287data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256) 288data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256) 289data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256) 290data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256) 291data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256) 292data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256) 293data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256) 294data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256) 295data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256) 296data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256) 297data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256) 298data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256) 299data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256) 300data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256) 301data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256) 302data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256) 303data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256) 304data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256) 305data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256) 306data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256) 307data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256) 308data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256) 309data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256) 310data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256) 311data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256) 312data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256) 313data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256) 314data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256) 315data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256) 316data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256) 317data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256) 318data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256) 319data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256) 320data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256) 321data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256) 322data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256) 323data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256) 324data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256) 325data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256) 326data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256) 327data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256) 328data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256) 329data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256) 330data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256) 331data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256) 332data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256) 333data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256) 334data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256) 335data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256) 336data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256) 337data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256) 338data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256) 339data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256) 340data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256) 341data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256) 342data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256) 343data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256) 344data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256) 345data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256) 346data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256) 347data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256) 348data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256) 349data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256) 350data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256) 351data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256) 352data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256) 353data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256) 354data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256) 355data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256) 356data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256) 357data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256) 358data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256) 359data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256) 360data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256) 361data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256) 362data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256) 363data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256) 364data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256) 365data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256) 366data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256) 367data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256) 368data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256) 369data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256) 370data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256) 371data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256) 372data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256) 373data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256) 374data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256) 375data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256) 376data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256) 377data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256) 378data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256) 379data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256) 380data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256) 381data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256) 382data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256) 383data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256) 384data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256) 385data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256) 386data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256) 387data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256) 388data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256) 389data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256) 390data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256) 391data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256) 392data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256) 393data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256) 394data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256) 395data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256) 396data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256) 397data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256) 398data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256) 399data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256) 400data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256) 401data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256) 402data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256) 403data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256) 404data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256) 405data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256) 406data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256) 407data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256) 408data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256) 409data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256) 410data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256) 411data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256) 412data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256) 413data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256) 414data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256) 415data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256) 416data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256) 417data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256) 418data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256) 419data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256) 420data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256) 421data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256) 422data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256) 423data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256) 424data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256) 425data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256) 426data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256) 427data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256) 428data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256) 429data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256) 430data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256) 431data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256) 432data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256) 433data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256) 434data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256) 435data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256) 436data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256) 437data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256) 438data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256) 439data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256) 440data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256) 441data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256) 442data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256) 443data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256) 444data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256) 445data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256) 446data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256) 447data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256) 448data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256) 449data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256) 450data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256) 451data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256) 452data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256) 453data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256) 454data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256) 455data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256) 456data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256) 457data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256) 458data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256) 459data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256) 460data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256) 461data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256) 462data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256) 463data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256) 464data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256) 465data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256) 466data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256) 467data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256) 468data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256) 469data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256) 470data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256) 471data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256) 472data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256) 473data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256) 474data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256) 475data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256) 476data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256) 477data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256) 478data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256) 479data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256) 480data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256) 481data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256) 482data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256) 483data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256) 484data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256) 485data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256) 486data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256) 487LOCAL_OBJECT_END(log_table_3) 488 489 490.section .text 491GLOBAL_LIBM_ENTRY(asinhf) 492 493{ .mfi 494 getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm 495 fclass.m p12,p0 = f8, 0x0b // Test x unorm 496 mov log_GR_exp_17_ones = 0x1ffff 497} 498{ .mfi 499 addl NR_table_address = @ltoff(log_table_1), gp 500 fma.s1 log_y = f8, f8, f1 // y = x^2 + 1 501 mov asinh_GR_comp = 0xfffa 502} 503;; 504 505{ .mfi 506 mov log_GR_exp_16_ones = 0xffff //BIAS 507 fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero 508 mov log_GR_comp2 = 0x10032 509} 510{ .mfi 511 ld8 NR_table_address = [NR_table_address] 512 fma.s1 asinh_w_sq = f8,f8,f0 // x^2 513 nop.i 0 514} 515;; 516 517{ .mfi 518 nop.m 0 519 fcmp.lt.s1 p7,p11 = f8,f0 // if x<0 520 nop.i 0 521} 522{ .mfb 523 nop.m 0 524 fnorm.s1 fNormX = f8 // Normalize x 525(p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm 526} 527;; 528 529ASINH_COMMON: 530// Return here if x=unorm and not denorm 531{ .mfi 532 //to get second table address 533 adds log_table_address2 = 0x20, NR_table_address 534 fma.s1 log_arg = f8,f1,f8 535} 536{ .mfb 537 nop.m 0 538(p6) fma.s.s0 f8 = f8,f1,f8 // quietize nan result if x=nan 539(p6) br.ret.spnt b0 // Exit for x=nan and inf and zero 540} 541;; 542 543{ .mfi 544 ldfpd NR1,NR2 = [log_table_address2],16 545 frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y) 546 nop.i 0 547} 548;; 549 550{ .mfi 551 ldfe log_C1 = [log_table_address2],16 552 nop.f 0 553 and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones 554} 555;; 556 557{ .mib 558 ldfe log_C0 = [log_table_address2],16 559 cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8 560(p13) br.cond.spnt LOG_COMMON1 // Branch if path 4: |x| >= 2^51 561} 562;; 563 564{ .mfi 565 nop.m 0 566 fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z 567 nop.i 0 568} 569;; 570 571.pred.rel "mutex",p7,p11 572{ .mfi 573 nop.m 0 574(p11) mov asinh_f8 = fNormX 575 nop.i 0 576} 577{ .mfb 578 cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8 579(p7) fnma.s1 asinh_f8 = fNormX,f1,f0 580(p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2: 0 < |x| < 2^-5 581} 582;; 583 584// Here if main path, 2^-5 <= |x| < 2^51 585///////////////////////////////// The first iteration ///////////////////////// 586{ .mfi 587 ldfpd log_P3,log_P2 = [NR_table_address],16 588 fnma.s1 log_y_rs_iter2 = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z 589 nop.i 0 590} 591{ .mfi 592 nop.m 0 593 fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z 594 nop.i 0 595} 596;; 597 598{ .mfi 599 ldfpd log_P1,log2 = [NR_table_address],16 600 // (0.5*z)*(3-(y*z)*z) 601 fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter2,f0 602 nop.i 0 603} 604{ .mfi 605 nop.m 0 606 // (0.5*z)*(3-(y*z)*z) 607 fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs_iter2,f0 608 nop.i 0 609} 610;; 611 612////////////////////////////////// The second iteration //////////////////////// 613{ .mfi 614 nop.m 0 615 fma.s1 log_y_rs = log_y_rs_iter,log_y,f0 616 nop.i 0 617} 618{ .mfi 619 nop.m 0 620 fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0 621 nop.i 0 622} 623;; 624 625{ .mfi 626 nop.m 0 627 fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8 628 nop.i 0 629} 630;; 631 632{ .mfi 633 nop.m 0 634 fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2 635 nop.i 0 636} 637{ .mfi 638 nop.m 0 639 fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0 640 nop.i 0 641} 642;; 643 644{ .mfi 645 nop.m 0 646 frcpa.s1 log_C,p0 = f1,log_arg_early 647 nop.i 0 648} 649;; 650 651{ .mfi 652 getf.exp log_GR_signexp_f8 = log_arg_early 653 nop.f 0 654 nop.i 0 655} 656;; 657 658{ .mfi 659 getf.sig log_GR_significand_f8 = log_arg_early 660 // (0.5*z)*(3-(y*z)*z)*y + |x| 661 fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8 662 //to get third table address 663 adds log_table_address3 = 0x30, NR_table_address 664} 665;; 666 667/////////////////////////////////////////// The end NR iterations ///////////// 668 669{ .mfi 670 nop.m 0 671 nop.f 0 672 //significant bit destruction 673 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones 674} 675;; 676 677{ .mfi 678 //BIAS subtraction 679 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones 680(p7) fnma.s1 log2 = log2,f1,f0 681 nop.i 0 682} 683;; 684 685{ .mfi 686 setf.sig log_int_Nfloat = log_GR_true_exp_f8 687 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1 688 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits 689} 690;; 691 692{ .mmi 693 //pre-index*16 + index 694 shladd log_table_address3 = log_GR_index,3,log_table_address3 695;; 696 ldfd log_T = [log_table_address3] 697 nop.i 0 698} 699;; 700 701{ .mfi 702 nop.m 0 703 fma.s1 log_rsq = log_r, log_r, f0 //r^2 704 nop.i 0 705} 706{ .mfi 707 nop.m 0 708 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2 709 nop.i 0 710} 711;; 712 713{ .mfi 714 nop.m 0 715 fma.s1 log_rp_p10 = log_P1, log_r, f1 716 nop.i 0 717} 718;; 719 720{ .mfi 721 nop.m 0 722 //convert N to the floating-point format 723 fcvt.xf log_Nfloat = log_int_Nfloat 724 nop.i 0 725} 726;; 727 728{ .mfi 729 nop.m 0 730 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 731 nop.i 0 732} 733;; 734 735.pred.rel "mutex",p7,p11 736{ .mfi 737 nop.m 0 738(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0 739 nop.i 0 740} 741{ .mfi 742 nop.m 0 743(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0 744 nop.i 0 745} 746;; 747 748{ .mfi 749 nop.m 0 750(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2 751 nop.i 0 752} 753{ .mfb 754 nop.m 0 755(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2 756 br.ret.sptk b0 // Exit main path, path 3: 2^-5 <= |x| < 2^51 757} 758;; 759 760 761// Here if path 4, |x| >= 2^51 762LOG_COMMON1: 763{ .mfi 764 ldfpd log_P3,log_P2 = [NR_table_address],16 765 nop.f 0 766 nop.i 0 767} 768;; 769 770{ .mfi 771 ldfpd log_P1,log2 = [NR_table_address],16 772 frcpa.s1 log_C,p0 = f1,log_arg 773 nop.i 0 774} 775;; 776 777{ .mfi 778 getf.exp log_GR_signexp_f8 = log_arg 779 nop.f 0 780 //to get third table address 781 adds log_table_address3 = 0x30, NR_table_address 782} 783;; 784 785{ .mfi 786 getf.sig log_GR_significand_f8 = log_arg 787 nop.f 0 788 nop.i 0 789} 790;; 791 792{ .mfi 793 nop.m 0 794 nop.f 0 795 //to destroy the most bit in the significant area 796 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones 797} 798;; 799 800{ .mmf 801 nop.m 0 802 //BIAS subtraction 803 sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones 804 fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1 805} 806;; 807 808{ .mfi 809 setf.sig log_int_Nfloat = log_GR_true_exp_f8 810 nop.f 0 811 extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits 812} 813;; 814 815{ .mmi 816 //pre-index*16 + index 817 shladd log_table_address3 = log_GR_index,3,log_table_address3 818;; 819 ldfd log_T = [log_table_address3] 820 nop.i 0 821} 822;; 823 824{ .mfi 825 nop.m 0 826 fma.s1 log_rsq = log_r, log_r, f0 //r^2 827 nop.i 0 828} 829{ .mfi 830 nop.m 0 831 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2 832 nop.i 0 833} 834;; 835 836{ .mfi 837 nop.m 0 838 fma.s1 log_rp_p10 = log_P1, log_r, f1 839 nop.i 0 840} 841{ .mfi 842 nop.m 0 843(p7) fnma.s1 log2 = log2,f1,f0 844 nop.i 0 845} 846;; 847 848{ .mfi 849 nop.m 0 850 //convert N to the floating-point format 851 fcvt.xf log_Nfloat = log_int_Nfloat 852 nop.i 0 853} 854{ .mfi 855 nop.m 0 856 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 857 nop.i 0 858} 859;; 860 861.pred.rel "mutex",p7,p11 862{ .mfi 863 nop.m 0 864(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0 865 nop.i 0 866} 867{ .mfi 868 nop.m 0 869(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0 870 nop.i 0 871} 872;; 873 874{ .mfi 875 nop.m 0 876(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2 877 nop.i 0 878} 879{ .mfb 880 nop.m 0 881(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2 882 br.ret.sptk b0 // Exit path 4, |x| >= 2^51 883} 884;; 885 886// Here if path 2, 0 < |x| < 2^-5 887ASINH_NEAR_ZERO: 888{ .mfi 889 nop.m 0 890 fma.s1 asinh_w_1 = asinh_w_sq,log_C1,log_C0 891 nop.i 0 892} 893{ .mfi 894 nop.m 0 895 fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0 896 nop.i 0 897} 898;; 899 900{ .mfb 901 nop.m 0 902 fma.s.s0 f8 = asinh_w_1,asinh_w_cube,fNormX 903 br.ret.sptk b0 // Exit path 2, 0 < |x| < 2^-5 904} 905;; 906 907ASINH_UNORM: 908// Here if x=unorm 909{ .mfi 910 getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm 911 fclass.m p0,p13 = fNormX, 0x0b // Test x denorm 912 nop.i 0 913} 914;; 915 916{ .mfb 917 nop.m 0 918 fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag 919(p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm 920} 921;; 922 923.pred.rel "mutex",p7,p11 924{ .mfi 925 nop.m 0 926(p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm 927 nop.i 0 928} 929{ .mfb 930 nop.m 0 931(p11) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm 932 br.ret.spnt b0 // Exit if denorm 933} 934;; 935 936GLOBAL_LIBM_END(asinhf) 937libm_alias_float_other (asinh, asinh) 938