1.file "log1pf.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// History 40//============================================================== 41// 02/02/00 Initial version 42// 04/04/00 Unwind support added 43// 08/15/00 Bundle added after call to __libm_error_support to properly 44// set [the previously overwritten] GR_Parameter_RESULT. 45// 06/29/01 Improved speed of all paths 46// 05/20/02 Cleaned up namespace and sf0 syntax 47// 10/02/02 Improved performance by basing on log algorithm 48// 02/10/03 Reordered header: .section, .global, .proc, .align 49// 04/18/03 Eliminate possible WAW dependency warning 50// 12/16/03 Fixed parameter passing to/from error handling routine 51// 52// API 53//============================================================== 54// float log1pf(float) 55// 56// log1p(x) = log(x+1) 57// 58// Overview of operation 59//============================================================== 60// Background 61// ---------- 62// 63// This algorithm is based on fact that 64// log1p(x) = log(1+x) and 65// log(a b) = log(a) + log(b). 66// In our case we have 1+x = 2^N f, where 1 <= f < 2. 67// So 68// log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) 69// 70// To calculate log(f) we do following 71// log(f) = log(f * frcpa(f) / frcpa(f)) = 72// = log(f * frcpa(f)) + log(1/frcpa(f)) 73// 74// According to definition of IA-64's frcpa instruction it's a 75// floating point that approximates 1/f using a lookup on the 76// top of 8 bits of the input number's + 1 significand with relative 77// error < 2^(-8.886). So we have following 78// 79// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 80// 81// and 82// 83// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = 84// = log(1 + r) + T 85// 86// The first value can be computed by polynomial P(r) approximating 87// log(1 + r) on |r| < 1/256 and the second is precomputed tabular 88// value defined by top 8 bit of f. 89// 90// Finally we have that log(1+x) ~ (N*log(2) + T) + P(r) 91// 92// Note that if input argument is close to 0.0 (in our case it means 93// that |x| < 1/256) we can use just polynomial approximation 94// because 1+x = 2^0 * f = f = 1 + r and 95// log(1+x) = log(1 + r) ~ P(r) 96// 97// 98// Implementation 99// -------------- 100// 101// 1. |x| >= 2^(-8), and x > -1 102// InvX = frcpa(x+1) 103// r = InvX*(x+1) - 1 104// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r), 105// A4,A3,A2 are created with setf instruction. 106// We use Taylor series and so A4 = 1/4, A3 = 1/3, 107// A2 = 1/2 rounded to double. 108// 109// N = float(n) where n is true unbiased exponent of x 110// 111// T is tabular value of log(1/frcpa(x)) calculated in quad precision 112// and rounded to double. To load T we get bits from 55 to 62 of register 113// format significand as index and calculate address 114// ad_T = table_base_addr + 8 * index 115// 116// L1 (log(2)) is calculated in quad precision and rounded to double; 117// it's created with setf 118// 119// And final result = P2(r)*r + (T + N*L1) 120// 121// 122// 2. 2^(-40) <= |x| < 2^(-8) 123// r = x 124// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r), 125// A4,A3,A2 are the same as in case |x| >= 1/256 126// 127// And final result = P2(r)*r 128// 129// 3. 0 < |x| < 2^(-40) 130// Although log1p(x) is basically x, we would like to preserve the inexactness 131// nature as well as consistent behavior under different rounding modes. 132// We can do this by computing the result as 133// 134// log1p(x) = x - x*x 135// 136// 137// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are 138// filtered and processed on special branches. 139// 140 141// 142// Special values 143//============================================================== 144// 145// log1p(-1) = -inf // Call error support 146// 147// log1p(+qnan) = +qnan 148// log1p(-qnan) = -qnan 149// log1p(+snan) = +qnan 150// log1p(-snan) = -qnan 151// 152// log1p(x),x<-1= QNAN Indefinite // Call error support 153// log1p(-inf) = QNAN Indefinite 154// log1p(+inf) = +inf 155// log1p(+/-0) = +/-0 156// 157// 158// Registers used 159//============================================================== 160// Floating Point registers used: 161// f8, input 162// f7 -> f15, f32 -> f36 163// 164// General registers used: 165// r8 -> r11 166// r14 -> r22 167// 168// Predicate registers used: 169// p6 -> p12 170 171// Assembly macros 172//============================================================== 173GR_TAG = r8 174GR_ad_T = r9 175GR_Exp = r10 176GR_N = r11 177 178GR_signexp_x = r14 179GR_exp_mask = r15 180GR_exp_bias = r16 181GR_05 = r17 182GR_A3 = r18 183GR_Sig = r19 184GR_Ind = r19 185GR_exp_x = r20 186GR_Ln2 = r21 187GR_025 = r22 188 189 190GR_SAVE_B0 = r33 191GR_SAVE_PFS = r34 192GR_SAVE_GP = r35 193GR_SAVE_SP = r36 194 195GR_Parameter_X = r37 196GR_Parameter_Y = r38 197GR_Parameter_RESULT = r39 198GR_Parameter_TAG = r40 199 200 201 202FR_NormX = f7 203FR_RcpX = f9 204FR_r = f10 205FR_r2 = f11 206FR_r4 = f12 207FR_N = f13 208FR_Ln2 = f14 209FR_Xp1 = f15 210 211FR_A4 = f33 212FR_A3 = f34 213FR_A2 = f35 214 215FR_T = f36 216FR_NxLn2pT = f36 217 218 219 220FR_Y = f1 221FR_X = f10 222FR_RESULT = f8 223 224 225// Data 226//============================================================== 227RODATA 228.align 16 229 230LOCAL_OBJECT_START(log_data) 231// ln(1/frcpa(1+i/256)), i=0...255 232data8 0x3F60040155D5889E // 0 233data8 0x3F78121214586B54 // 1 234data8 0x3F841929F96832F0 // 2 235data8 0x3F8C317384C75F06 // 3 236data8 0x3F91A6B91AC73386 // 4 237data8 0x3F95BA9A5D9AC039 // 5 238data8 0x3F99D2A8074325F4 // 6 239data8 0x3F9D6B2725979802 // 7 240data8 0x3FA0C58FA19DFAAA // 8 241data8 0x3FA2954C78CBCE1B // 9 242data8 0x3FA4A94D2DA96C56 // 10 243data8 0x3FA67C94F2D4BB58 // 11 244data8 0x3FA85188B630F068 // 12 245data8 0x3FAA6B8ABE73AF4C // 13 246data8 0x3FAC441E06F72A9E // 14 247data8 0x3FAE1E6713606D07 // 15 248data8 0x3FAFFA6911AB9301 // 16 249data8 0x3FB0EC139C5DA601 // 17 250data8 0x3FB1DBD2643D190B // 18 251data8 0x3FB2CC7284FE5F1C // 19 252data8 0x3FB3BDF5A7D1EE64 // 20 253data8 0x3FB4B05D7AA012E0 // 21 254data8 0x3FB580DB7CEB5702 // 22 255data8 0x3FB674F089365A7A // 23 256data8 0x3FB769EF2C6B568D // 24 257data8 0x3FB85FD927506A48 // 25 258data8 0x3FB9335E5D594989 // 26 259data8 0x3FBA2B0220C8E5F5 // 27 260data8 0x3FBB0004AC1A86AC // 28 261data8 0x3FBBF968769FCA11 // 29 262data8 0x3FBCCFEDBFEE13A8 // 30 263data8 0x3FBDA727638446A2 // 31 264data8 0x3FBEA3257FE10F7A // 32 265data8 0x3FBF7BE9FEDBFDE6 // 33 266data8 0x3FC02AB352FF25F4 // 34 267data8 0x3FC097CE579D204D // 35 268data8 0x3FC1178E8227E47C // 36 269data8 0x3FC185747DBECF34 // 37 270data8 0x3FC1F3B925F25D41 // 38 271data8 0x3FC2625D1E6DDF57 // 39 272data8 0x3FC2D1610C86813A // 40 273data8 0x3FC340C59741142E // 41 274data8 0x3FC3B08B6757F2A9 // 42 275data8 0x3FC40DFB08378003 // 43 276data8 0x3FC47E74E8CA5F7C // 44 277data8 0x3FC4EF51F6466DE4 // 45 278data8 0x3FC56092E02BA516 // 46 279data8 0x3FC5D23857CD74D5 // 47 280data8 0x3FC6313A37335D76 // 48 281data8 0x3FC6A399DABBD383 // 49 282data8 0x3FC70337DD3CE41B // 50 283data8 0x3FC77654128F6127 // 51 284data8 0x3FC7E9D82A0B022D // 52 285data8 0x3FC84A6B759F512F // 53 286data8 0x3FC8AB47D5F5A310 // 54 287data8 0x3FC91FE49096581B // 55 288data8 0x3FC981634011AA75 // 56 289data8 0x3FC9F6C407089664 // 57 290data8 0x3FCA58E729348F43 // 58 291data8 0x3FCABB55C31693AD // 59 292data8 0x3FCB1E104919EFD0 // 60 293data8 0x3FCB94EE93E367CB // 61 294data8 0x3FCBF851C067555F // 62 295data8 0x3FCC5C0254BF23A6 // 63 296data8 0x3FCCC000C9DB3C52 // 64 297data8 0x3FCD244D99C85674 // 65 298data8 0x3FCD88E93FB2F450 // 66 299data8 0x3FCDEDD437EAEF01 // 67 300data8 0x3FCE530EFFE71012 // 68 301data8 0x3FCEB89A1648B971 // 69 302data8 0x3FCF1E75FADF9BDE // 70 303data8 0x3FCF84A32EAD7C35 // 71 304data8 0x3FCFEB2233EA07CD // 72 305data8 0x3FD028F9C7035C1C // 73 306data8 0x3FD05C8BE0D9635A // 74 307data8 0x3FD085EB8F8AE797 // 75 308data8 0x3FD0B9C8E32D1911 // 76 309data8 0x3FD0EDD060B78081 // 77 310data8 0x3FD122024CF0063F // 78 311data8 0x3FD14BE2927AECD4 // 79 312data8 0x3FD180618EF18ADF // 80 313data8 0x3FD1B50BBE2FC63B // 81 314data8 0x3FD1DF4CC7CF242D // 82 315data8 0x3FD214456D0EB8D4 // 83 316data8 0x3FD23EC5991EBA49 // 84 317data8 0x3FD2740D9F870AFB // 85 318data8 0x3FD29ECDABCDFA04 // 86 319data8 0x3FD2D46602ADCCEE // 87 320data8 0x3FD2FF66B04EA9D4 // 88 321data8 0x3FD335504B355A37 // 89 322data8 0x3FD360925EC44F5D // 90 323data8 0x3FD38BF1C3337E75 // 91 324data8 0x3FD3C25277333184 // 92 325data8 0x3FD3EDF463C1683E // 93 326data8 0x3FD419B423D5E8C7 // 94 327data8 0x3FD44591E0539F49 // 95 328data8 0x3FD47C9175B6F0AD // 96 329data8 0x3FD4A8B341552B09 // 97 330data8 0x3FD4D4F3908901A0 // 98 331data8 0x3FD501528DA1F968 // 99 332data8 0x3FD52DD06347D4F6 // 100 333data8 0x3FD55A6D3C7B8A8A // 101 334data8 0x3FD5925D2B112A59 // 102 335data8 0x3FD5BF406B543DB2 // 103 336data8 0x3FD5EC433D5C35AE // 104 337data8 0x3FD61965CDB02C1F // 105 338data8 0x3FD646A84935B2A2 // 106 339data8 0x3FD6740ADD31DE94 // 107 340data8 0x3FD6A18DB74A58C5 // 108 341data8 0x3FD6CF31058670EC // 109 342data8 0x3FD6F180E852F0BA // 110 343data8 0x3FD71F5D71B894F0 // 111 344data8 0x3FD74D5AEFD66D5C // 112 345data8 0x3FD77B79922BD37E // 113 346data8 0x3FD7A9B9889F19E2 // 114 347data8 0x3FD7D81B037EB6A6 // 115 348data8 0x3FD8069E33827231 // 116 349data8 0x3FD82996D3EF8BCB // 117 350data8 0x3FD85855776DCBFB // 118 351data8 0x3FD8873658327CCF // 119 352data8 0x3FD8AA75973AB8CF // 120 353data8 0x3FD8D992DC8824E5 // 121 354data8 0x3FD908D2EA7D9512 // 122 355data8 0x3FD92C59E79C0E56 // 123 356data8 0x3FD95BD750EE3ED3 // 124 357data8 0x3FD98B7811A3EE5B // 125 358data8 0x3FD9AF47F33D406C // 126 359data8 0x3FD9DF270C1914A8 // 127 360data8 0x3FDA0325ED14FDA4 // 128 361data8 0x3FDA33440224FA79 // 129 362data8 0x3FDA57725E80C383 // 130 363data8 0x3FDA87D0165DD199 // 131 364data8 0x3FDAAC2E6C03F896 // 132 365data8 0x3FDADCCC6FDF6A81 // 133 366data8 0x3FDB015B3EB1E790 // 134 367data8 0x3FDB323A3A635948 // 135 368data8 0x3FDB56FA04462909 // 136 369data8 0x3FDB881AA659BC93 // 137 370data8 0x3FDBAD0BEF3DB165 // 138 371data8 0x3FDBD21297781C2F // 139 372data8 0x3FDC039236F08819 // 140 373data8 0x3FDC28CB1E4D32FD // 141 374data8 0x3FDC4E19B84723C2 // 142 375data8 0x3FDC7FF9C74554C9 // 143 376data8 0x3FDCA57B64E9DB05 // 144 377data8 0x3FDCCB130A5CEBB0 // 145 378data8 0x3FDCF0C0D18F326F // 146 379data8 0x3FDD232075B5A201 // 147 380data8 0x3FDD490246DEFA6B // 148 381data8 0x3FDD6EFA918D25CD // 149 382data8 0x3FDD9509707AE52F // 150 383data8 0x3FDDBB2EFE92C554 // 151 384data8 0x3FDDEE2F3445E4AF // 152 385data8 0x3FDE148A1A2726CE // 153 386data8 0x3FDE3AFC0A49FF40 // 154 387data8 0x3FDE6185206D516E // 155 388data8 0x3FDE882578823D52 // 156 389data8 0x3FDEAEDD2EAC990C // 157 390data8 0x3FDED5AC5F436BE3 // 158 391data8 0x3FDEFC9326D16AB9 // 159 392data8 0x3FDF2391A2157600 // 160 393data8 0x3FDF4AA7EE03192D // 161 394data8 0x3FDF71D627C30BB0 // 162 395data8 0x3FDF991C6CB3B379 // 163 396data8 0x3FDFC07ADA69A910 // 164 397data8 0x3FDFE7F18EB03D3E // 165 398data8 0x3FE007C053C5002E // 166 399data8 0x3FE01B942198A5A1 // 167 400data8 0x3FE02F74400C64EB // 168 401data8 0x3FE04360BE7603AD // 169 402data8 0x3FE05759AC47FE34 // 170 403data8 0x3FE06B5F1911CF52 // 171 404data8 0x3FE078BF0533C568 // 172 405data8 0x3FE08CD9687E7B0E // 173 406data8 0x3FE0A10074CF9019 // 174 407data8 0x3FE0B5343A234477 // 175 408data8 0x3FE0C974C89431CE // 176 409data8 0x3FE0DDC2305B9886 // 177 410data8 0x3FE0EB524BAFC918 // 178 411data8 0x3FE0FFB54213A476 // 179 412data8 0x3FE114253DA97D9F // 180 413data8 0x3FE128A24F1D9AFF // 181 414data8 0x3FE1365252BF0865 // 182 415data8 0x3FE14AE558B4A92D // 183 416data8 0x3FE15F85A19C765B // 184 417data8 0x3FE16D4D38C119FA // 185 418data8 0x3FE18203C20DD133 // 186 419data8 0x3FE196C7BC4B1F3B // 187 420data8 0x3FE1A4A738B7A33C // 188 421data8 0x3FE1B981C0C9653D // 189 422data8 0x3FE1CE69E8BB106B // 190 423data8 0x3FE1DC619DE06944 // 191 424data8 0x3FE1F160A2AD0DA4 // 192 425data8 0x3FE2066D7740737E // 193 426data8 0x3FE2147DBA47A394 // 194 427data8 0x3FE229A1BC5EBAC3 // 195 428data8 0x3FE237C1841A502E // 196 429data8 0x3FE24CFCE6F80D9A // 197 430data8 0x3FE25B2C55CD5762 // 198 431data8 0x3FE2707F4D5F7C41 // 199 432data8 0x3FE285E0842CA384 // 200 433data8 0x3FE294294708B773 // 201 434data8 0x3FE2A9A2670AFF0C // 202 435data8 0x3FE2B7FB2C8D1CC1 // 203 436data8 0x3FE2C65A6395F5F5 // 204 437data8 0x3FE2DBF557B0DF43 // 205 438data8 0x3FE2EA64C3F97655 // 206 439data8 0x3FE3001823684D73 // 207 440data8 0x3FE30E97E9A8B5CD // 208 441data8 0x3FE32463EBDD34EA // 209 442data8 0x3FE332F4314AD796 // 210 443data8 0x3FE348D90E7464D0 // 211 444data8 0x3FE35779F8C43D6E // 212 445data8 0x3FE36621961A6A99 // 213 446data8 0x3FE37C299F3C366A // 214 447data8 0x3FE38AE2171976E7 // 215 448data8 0x3FE399A157A603E7 // 216 449data8 0x3FE3AFCCFE77B9D1 // 217 450data8 0x3FE3BE9D503533B5 // 218 451data8 0x3FE3CD7480B4A8A3 // 219 452data8 0x3FE3E3C43918F76C // 220 453data8 0x3FE3F2ACB27ED6C7 // 221 454data8 0x3FE4019C2125CA93 // 222 455data8 0x3FE4181061389722 // 223 456data8 0x3FE42711518DF545 // 224 457data8 0x3FE436194E12B6BF // 225 458data8 0x3FE445285D68EA69 // 226 459data8 0x3FE45BCC464C893A // 227 460data8 0x3FE46AED21F117FC // 228 461data8 0x3FE47A1527E8A2D3 // 229 462data8 0x3FE489445EFFFCCC // 230 463data8 0x3FE4A018BCB69835 // 231 464data8 0x3FE4AF5A0C9D65D7 // 232 465data8 0x3FE4BEA2A5BDBE87 // 233 466data8 0x3FE4CDF28F10AC46 // 234 467data8 0x3FE4DD49CF994058 // 235 468data8 0x3FE4ECA86E64A684 // 236 469data8 0x3FE503C43CD8EB68 // 237 470data8 0x3FE513356667FC57 // 238 471data8 0x3FE522AE0738A3D8 // 239 472data8 0x3FE5322E26867857 // 240 473data8 0x3FE541B5CB979809 // 241 474data8 0x3FE55144FDBCBD62 // 242 475data8 0x3FE560DBC45153C7 // 243 476data8 0x3FE5707A26BB8C66 // 244 477data8 0x3FE587F60ED5B900 // 245 478data8 0x3FE597A7977C8F31 // 246 479data8 0x3FE5A760D634BB8B // 247 480data8 0x3FE5B721D295F10F // 248 481data8 0x3FE5C6EA94431EF9 // 249 482data8 0x3FE5D6BB22EA86F6 // 250 483data8 0x3FE5E6938645D390 // 251 484data8 0x3FE5F673C61A2ED2 // 252 485data8 0x3FE6065BEA385926 // 253 486data8 0x3FE6164BFA7CC06B // 254 487data8 0x3FE62643FECF9743 // 255 488LOCAL_OBJECT_END(log_data) 489 490 491// Code 492//============================================================== 493 494.section .text 495GLOBAL_IEEE754_ENTRY(log1pf) 496{ .mfi 497 getf.exp GR_signexp_x = f8 // if x is unorm then must recompute 498 fadd.s1 FR_Xp1 = f8, f1 // Form 1+x 499 mov GR_05 = 0xfffe 500} 501{ .mlx 502 addl GR_ad_T = @ltoff(log_data),gp 503 movl GR_A3 = 0x3fd5555555555555 // double precision memory 504 // representation of A3 505} 506;; 507 508{ .mfi 509 ld8 GR_ad_T = [GR_ad_T] 510 fclass.m p8,p0 = f8,0xb // Is x unorm? 511 mov GR_exp_mask = 0x1ffff 512} 513{ .mfi 514 mov GR_025 = 0xfffd // Exponent of 0.25 515 fnorm.s1 FR_NormX = f8 // Normalize x 516 mov GR_exp_bias = 0xffff 517} 518;; 519 520{ .mfi 521 setf.exp FR_A2 = GR_05 // create A2 = 0.5 522 fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? 523 nop.i 0 524} 525{ .mib 526 setf.d FR_A3 = GR_A3 // create A3 527 nop.i 0 528(p8) br.cond.spnt log1p_unorm // Branch if x=unorm 529} 530;; 531 532log1p_common: 533{ .mfi 534 setf.exp FR_A4 = GR_025 // create A4 = 0.25 535 frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1 536 nop.i 0 537} 538{ .mfb 539 nop.m 0 540(p9) fma.s.s0 f8 = f8,f1,f0 // set V-flag 541(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf 542} 543;; 544 545{ .mfi 546 getf.exp GR_Exp = FR_Xp1 // signexp of x+1 547 fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0? 548 and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x 549} 550{ .mlx 551 nop.m 0 552 movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory 553 // representation of log(2) 554} 555;; 556 557{ .mfi 558 getf.sig GR_Sig = FR_Xp1 // get significand to calculate index 559 // for T if |x| >= 2^-8 560 fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0? 561 sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x 562} 563;; 564 565{ .mfi 566 sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1 567 fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1? 568 cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8 569} 570{ .mfb 571 nop.m 0 572 nop.f 0 573(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1 574} 575;; 576 577// p6 is true if |x| < 1/256 578// p7 is true if |x| >= 1/256 579.pred.rel "mutex",p6,p7 580{ .mfi 581 nop.m 0 582(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256 583(p6) cmp.gt.unc p10,p0 = -40, GR_exp_x // Is |x| < 2^-40 584} 585{ .mfb 586(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the 587 // significand field of FR_N 588(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256 589(p12) br.ret.spnt b0 // exit for x=0, return x 590} 591;; 592 593{ .mib 594 setf.d FR_Ln2 = GR_Ln2 // create log(2) 595(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index 596(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1 597} 598;; 599 600{ .mmf 601(p7) shladd GR_ad_T = GR_Ind,3,GR_ad_T // address of T 602 nop.m 0 603(p10) fnma.s.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x 604} 605;; 606 607{ .mmb 608(p7) ldfd FR_T = [GR_ad_T] 609 nop.m 0 610(p10) br.ret.spnt b0 // Exit if |x| < 2^-40 611} 612;; 613 614{ .mfi 615 nop.m 0 616 fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 617 nop.i 0 618} 619{ .mfi 620 nop.m 0 621 fnma.s1 FR_A2 = FR_A2,FR_r,f1 // 1.0 - A2*r 622 nop.i 0 623} 624;; 625 626{ .mfi 627 nop.m 0 628 fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A3 - A4*r 629 nop.i 0 630} 631;; 632 633{ .mfi 634 nop.m 0 635(p7) fcvt.xf FR_N = FR_N 636 nop.i 0 637} 638;; 639 640{ .mfi 641 nop.m 0 642 // (A3*r+A2)*r^2+r 643 fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1) 644 nop.i 0 645} 646;; 647 648{ .mfi 649 nop.m 0 650 // N*Ln2hi+T 651(p7) fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T 652 nop.i 0 653} 654;; 655 656.pred.rel "mutex",p6,p7 657{ .mfi 658 nop.m 0 659(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result if 2^(-40) <= |x| < 1/256 660 nop.i 0 661} 662{ .mfb 663 nop.m 0 664(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result if |x| >= 1/256 665 br.ret.sptk b0 // Exit if |x| >= 2^(-40) 666} 667;; 668 669.align 32 670log1p_unorm: 671// Here if x=unorm 672{ .mfb 673 getf.exp GR_signexp_x = FR_NormX // recompute biased exponent 674 nop.f 0 675 br.cond.sptk log1p_common 676} 677;; 678 679.align 32 680log1p_eq_minus_1: 681// Here if x=-1 682{ .mfi 683 nop.m 0 684 fmerge.s FR_X = f8,f8 // keep input argument for subsequent 685 // call of __libm_error_support# 686 nop.i 0 687} 688;; 689 690{ .mfi 691 mov GR_TAG = 142 // set libm error in case of log1p(-1). 692 frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF. 693 // We can get it using frcpa because it 694 // sets result to the IEEE-754 mandated 695 // quotient of f8/f0. 696 nop.i 0 697} 698{ .mib 699 nop.m 0 700 nop.i 0 701 br.cond.sptk log_libm_err 702} 703;; 704 705.align 32 706log1p_lt_minus_1: 707// Here if x < -1 708{ .mfi 709 nop.m 0 710 fmerge.s FR_X = f8,f8 711 nop.i 0 712} 713;; 714 715{ .mfi 716 mov GR_TAG = 143 // set libm error in case of x < -1. 717 frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN. 718 // We can get it using frcpa because it 719 // sets result to the IEEE-754 mandated 720 // quotient of f0/f0 i.e. NaN. 721 nop.i 0 722} 723;; 724 725.align 32 726log_libm_err: 727{ .mmi 728 alloc r32 = ar.pfs,1,4,4,0 729 mov GR_Parameter_TAG = GR_TAG 730 nop.i 0 731} 732;; 733 734GLOBAL_IEEE754_END(log1pf) 735libm_alias_float_other (__log1p, log1p) 736 737 738LOCAL_LIBM_ENTRY(__libm_error_region) 739.prologue 740{ .mfi 741 add GR_Parameter_Y = -32,sp // Parameter 2 value 742 nop.f 0 743.save ar.pfs,GR_SAVE_PFS 744 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs 745} 746{ .mfi 747.fframe 64 748 add sp = -64,sp // Create new stack 749 nop.f 0 750 mov GR_SAVE_GP = gp // Save gp 751};; 752{ .mmi 753 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack 754 add GR_Parameter_X = 16,sp // Parameter 1 address 755.save b0, GR_SAVE_B0 756 mov GR_SAVE_B0 = b0 // Save b0 757};; 758.body 759{ .mib 760 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack 761 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 762 nop.b 0 763} 764{ .mib 765 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack 766 add GR_Parameter_Y = -16,GR_Parameter_Y 767 br.call.sptk b0=__libm_error_support# // Call error handling function 768};; 769{ .mmi 770 add GR_Parameter_RESULT = 48,sp 771 nop.m 0 772 nop.i 0 773};; 774{ .mmi 775 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack 776.restore sp 777 add sp = 64,sp // Restore stack pointer 778 mov b0 = GR_SAVE_B0 // Restore return address 779};; 780{ .mib 781 mov gp = GR_SAVE_GP // Restore gp 782 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 783 br.ret.sptk b0 // Return 784};; 785LOCAL_LIBM_END(__libm_error_region) 786 787.type __libm_error_support#,@function 788.global __libm_error_support# 789