1.file "logf.s" 2 3 4// Copyright (c) 2000 - 2005, 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// 03/01/00 Initial version 42// 08/15/00 Bundle added after call to __libm_error_support to properly 43// set [the previously overwritten] GR_Parameter_RESULT. 44// 01/10/01 Improved speed, fixed flags for neg denormals 45// 05/20/02 Cleaned up namespace and sf0 syntax 46// 05/23/02 Modified algorithm. Now only one polynomial is used 47// for |x-1| >= 1/256 and for |x-1| < 1/256 48// 02/10/03 Reordered header: .section, .global, .proc, .align 49// 03/31/05 Reformatted delimiters between data tables 50// 51// API 52//============================================================== 53// float logf(float) 54// float log10f(float) 55// 56// 57// Overview of operation 58//============================================================== 59// Background 60// ---------- 61// 62// This algorithm is based on fact that 63// log(a b) = log(a) + log(b). 64// 65// In our case we have x = 2^N f, where 1 <= f < 2. 66// So 67// log(x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) 68// 69// To calculate log(f) we do following 70// log(f) = log(f * frcpa(f) / frcpa(f)) = 71// = log(f * frcpa(f)) + log(1/frcpa(f)) 72// 73// According to definition of IA-64's frcpa instruction it's a 74// floating point that approximates 1/f using a lookup on the 75// top of 8 bits of the input number's significand with relative 76// error < 2^(-8.886). So we have following 77// 78// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 79// 80// and 81// 82// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = 83// = log(1 + r) + T 84// 85// The first value can be computed by polynomial P(r) approximating 86// log(1 + r) on |r| < 1/256 and the second is precomputed tabular 87// value defined by top 8 bit of f. 88// 89// Finally we have that log(x) ~ (N*log(2) + T) + P(r) 90// 91// Note that if input argument is close to 1.0 (in our case it means 92// that |1 - x| < 1/256) we can use just polynomial approximation 93// because x = 2^0 * f = f = 1 + r and 94// log(x) = log(1 + r) ~ P(r) 95// 96// 97// To compute log10(x) we just use identity: 98// 99// log10(x) = log(x)/log(10) 100// 101// so we have that 102// 103// log10(x) = (N*log(2) + T + log(1+r)) / log(10) = 104// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10) 105// 106// 107// Implementation 108// -------------- 109// It can be seen that formulas for log and log10 differ from one another 110// only by coefficients and tabular values. Namely as log as log10 are 111// calculated as (N*L1 + T) + L2*Series(r) where in case of log 112// L1 = log(2) 113// T = log(1/frcpa(x)) 114// L2 = 1.0 115// and in case of log10 116// L1 = log(2)/log(10) 117// T = log(1/frcpa(x))/log(10) 118// L2 = 1.0/log(10) 119// 120// So common code with two different entry points those set pointers 121// to the base address of coresponding data sets containing values 122// of L2,T and prepare integer representation of L1 needed for following 123// setf instruction can be used. 124// 125// Note that both log and log10 use common approximation polynomial 126// it means we need only one set of coefficients of approximation. 127// 128// 1. Computation of log(x) for |x-1| >= 1/256 129// InvX = frcpa(x) 130// r = InvX*x - 1 131// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r), 132// A4,A3,A2 are created with setf inctruction. 133// We use Taylor series and so A4 = 1/4, A3 = 1/3, 134// A2 = 1/2 rounded to double. 135// 136// N = float(n) where n is true unbiased exponent of x 137// 138// T is tabular value of log(1/frcpa(x)) calculated in quad precision 139// and rounded to double. To T we get bits from 55 to 62 of register 140// format significand of x and calculate address 141// ad_T = table_base_addr + 8 * index 142// 143// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad 144// precision and rounded to double; it's loaded from memory 145// 146// L1 (log(2) or log10(2) depending on function) is calculated in quad 147// precision and rounded to double; it's created with setf. 148// 149// And final result = P2(r)*(r*L2) + (T + N*L1) 150// 151// 152// 2. Computation of log(x) for |x-1| < 1/256 153// r = x - 1 154// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r), 155// A4,A3,A2 are the same as in case |x-1| >= 1/256 156// 157// And final result = P2(r)*(r*L2) 158// 159// 3. How we define is input argument such that |x-1| < 1/256 or not. 160// 161// To do it we analyze biased exponent and significand of input argument. 162// 163// a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e. 164// we test is 0.5 <= x < 2). This comparison can be performed using 165// unsigned version of cmp instruction in such a way 166// biased_exponent_of_x - 0xFFFE < 2 167// 168// 169// b) Second (in case when result of a) is true) we need to compare x 170// with 1-1/256 and 1+1/256 or in register format representation with 171// 0xFFFEFF00000000000000 and 0xFFFF8080000000000000 correspondingly. 172// As far as biased exponent of x here can be equal only to 0xFFFE or 173// 0xFFFF we need to test only last bit of it. Also signifigand always 174// has implicit bit set to 1 that can be exluded from comparison. 175// Thus it's quite enough to generate 64-bit integer bits of that are 176// ix[63] = biased_exponent_of_x[0] and ix[62-0] = significand_of_x[62-0] 177// and compare it with 0x7F00000000000000 and 0x80800000000000000 (those 178// obtained like ix from register representatinos of 255/256 and 179// 257/256). This comparison can be made like in a), using unsigned 180// version of cmp i.e. ix - 0x7F00000000000000 < 0x0180000000000000. 181// 0x0180000000000000 is difference between 0x80800000000000000 and 182// 0x7F00000000000000. 183// 184// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are 185// filtered and processed on special branches. 186// 187// 188// Special values 189//============================================================== 190// 191// logf(+0) = -inf 192// logf(-0) = -inf 193// 194// logf(+qnan) = +qnan 195// logf(-qnan) = -qnan 196// logf(+snan) = +qnan 197// logf(-snan) = -qnan 198// 199// logf(-n) = QNAN Indefinite 200// logf(-inf) = QNAN Indefinite 201// 202// logf(+inf) = +inf 203// 204// Registers used 205//============================================================== 206// Floating Point registers used: 207// f8, input 208// f12 -> f14, f33 -> f39 209// 210// General registers used: 211// r8 -> r11 212// r14 -> r19 213// 214// Predicate registers used: 215// p6 -> p12 216 217 218// Assembly macros 219//============================================================== 220 221GR_TAG = r8 222GR_ad_T = r8 223GR_N = r9 224GR_Exp = r10 225GR_Sig = r11 226 227GR_025 = r14 228GR_05 = r15 229GR_A3 = r16 230GR_Ind = r17 231GR_dx = r15 232GR_Ln2 = r19 233GR_de = r20 234GR_x = r21 235GR_xorg = r22 236 237GR_SAVE_B0 = r33 238GR_SAVE_PFS = r34 239GR_SAVE_GP = r35 240GR_SAVE_SP = r36 241 242GR_Parameter_X = r37 243GR_Parameter_Y = r38 244GR_Parameter_RESULT = r39 245GR_Parameter_TAG = r40 246 247 248FR_A2 = f12 249FR_A3 = f13 250FR_A4 = f14 251 252FR_RcpX = f33 253FR_r = f34 254FR_r2 = f35 255FR_tmp = f35 256FR_Ln2 = f36 257FR_T = f37 258FR_N = f38 259FR_NxLn2pT = f38 260FR_NormX = f39 261FR_InvLn10 = f40 262 263 264FR_Y = f1 265FR_X = f10 266FR_RESULT = f8 267 268 269// Data tables 270//============================================================== 271RODATA 272.align 16 273LOCAL_OBJECT_START(logf_data) 274data8 0x3FF0000000000000 // 1.0 275// 276// ln(1/frcpa(1+i/256)), i=0...255 277data8 0x3F60040155D5889E // 0 278data8 0x3F78121214586B54 // 1 279data8 0x3F841929F96832F0 // 2 280data8 0x3F8C317384C75F06 // 3 281data8 0x3F91A6B91AC73386 // 4 282data8 0x3F95BA9A5D9AC039 // 5 283data8 0x3F99D2A8074325F4 // 6 284data8 0x3F9D6B2725979802 // 7 285data8 0x3FA0C58FA19DFAAA // 8 286data8 0x3FA2954C78CBCE1B // 9 287data8 0x3FA4A94D2DA96C56 // 10 288data8 0x3FA67C94F2D4BB58 // 11 289data8 0x3FA85188B630F068 // 12 290data8 0x3FAA6B8ABE73AF4C // 13 291data8 0x3FAC441E06F72A9E // 14 292data8 0x3FAE1E6713606D07 // 15 293data8 0x3FAFFA6911AB9301 // 16 294data8 0x3FB0EC139C5DA601 // 17 295data8 0x3FB1DBD2643D190B // 18 296data8 0x3FB2CC7284FE5F1C // 19 297data8 0x3FB3BDF5A7D1EE64 // 20 298data8 0x3FB4B05D7AA012E0 // 21 299data8 0x3FB580DB7CEB5702 // 22 300data8 0x3FB674F089365A7A // 23 301data8 0x3FB769EF2C6B568D // 24 302data8 0x3FB85FD927506A48 // 25 303data8 0x3FB9335E5D594989 // 26 304data8 0x3FBA2B0220C8E5F5 // 27 305data8 0x3FBB0004AC1A86AC // 28 306data8 0x3FBBF968769FCA11 // 29 307data8 0x3FBCCFEDBFEE13A8 // 30 308data8 0x3FBDA727638446A2 // 31 309data8 0x3FBEA3257FE10F7A // 32 310data8 0x3FBF7BE9FEDBFDE6 // 33 311data8 0x3FC02AB352FF25F4 // 34 312data8 0x3FC097CE579D204D // 35 313data8 0x3FC1178E8227E47C // 36 314data8 0x3FC185747DBECF34 // 37 315data8 0x3FC1F3B925F25D41 // 38 316data8 0x3FC2625D1E6DDF57 // 39 317data8 0x3FC2D1610C86813A // 40 318data8 0x3FC340C59741142E // 41 319data8 0x3FC3B08B6757F2A9 // 42 320data8 0x3FC40DFB08378003 // 43 321data8 0x3FC47E74E8CA5F7C // 44 322data8 0x3FC4EF51F6466DE4 // 45 323data8 0x3FC56092E02BA516 // 46 324data8 0x3FC5D23857CD74D5 // 47 325data8 0x3FC6313A37335D76 // 48 326data8 0x3FC6A399DABBD383 // 49 327data8 0x3FC70337DD3CE41B // 50 328data8 0x3FC77654128F6127 // 51 329data8 0x3FC7E9D82A0B022D // 52 330data8 0x3FC84A6B759F512F // 53 331data8 0x3FC8AB47D5F5A310 // 54 332data8 0x3FC91FE49096581B // 55 333data8 0x3FC981634011AA75 // 56 334data8 0x3FC9F6C407089664 // 57 335data8 0x3FCA58E729348F43 // 58 336data8 0x3FCABB55C31693AD // 59 337data8 0x3FCB1E104919EFD0 // 60 338data8 0x3FCB94EE93E367CB // 61 339data8 0x3FCBF851C067555F // 62 340data8 0x3FCC5C0254BF23A6 // 63 341data8 0x3FCCC000C9DB3C52 // 64 342data8 0x3FCD244D99C85674 // 65 343data8 0x3FCD88E93FB2F450 // 66 344data8 0x3FCDEDD437EAEF01 // 67 345data8 0x3FCE530EFFE71012 // 68 346data8 0x3FCEB89A1648B971 // 69 347data8 0x3FCF1E75FADF9BDE // 70 348data8 0x3FCF84A32EAD7C35 // 71 349data8 0x3FCFEB2233EA07CD // 72 350data8 0x3FD028F9C7035C1C // 73 351data8 0x3FD05C8BE0D9635A // 74 352data8 0x3FD085EB8F8AE797 // 75 353data8 0x3FD0B9C8E32D1911 // 76 354data8 0x3FD0EDD060B78081 // 77 355data8 0x3FD122024CF0063F // 78 356data8 0x3FD14BE2927AECD4 // 79 357data8 0x3FD180618EF18ADF // 80 358data8 0x3FD1B50BBE2FC63B // 81 359data8 0x3FD1DF4CC7CF242D // 82 360data8 0x3FD214456D0EB8D4 // 83 361data8 0x3FD23EC5991EBA49 // 84 362data8 0x3FD2740D9F870AFB // 85 363data8 0x3FD29ECDABCDFA04 // 86 364data8 0x3FD2D46602ADCCEE // 87 365data8 0x3FD2FF66B04EA9D4 // 88 366data8 0x3FD335504B355A37 // 89 367data8 0x3FD360925EC44F5D // 90 368data8 0x3FD38BF1C3337E75 // 91 369data8 0x3FD3C25277333184 // 92 370data8 0x3FD3EDF463C1683E // 93 371data8 0x3FD419B423D5E8C7 // 94 372data8 0x3FD44591E0539F49 // 95 373data8 0x3FD47C9175B6F0AD // 96 374data8 0x3FD4A8B341552B09 // 97 375data8 0x3FD4D4F3908901A0 // 98 376data8 0x3FD501528DA1F968 // 99 377data8 0x3FD52DD06347D4F6 // 100 378data8 0x3FD55A6D3C7B8A8A // 101 379data8 0x3FD5925D2B112A59 // 102 380data8 0x3FD5BF406B543DB2 // 103 381data8 0x3FD5EC433D5C35AE // 104 382data8 0x3FD61965CDB02C1F // 105 383data8 0x3FD646A84935B2A2 // 106 384data8 0x3FD6740ADD31DE94 // 107 385data8 0x3FD6A18DB74A58C5 // 108 386data8 0x3FD6CF31058670EC // 109 387data8 0x3FD6F180E852F0BA // 110 388data8 0x3FD71F5D71B894F0 // 111 389data8 0x3FD74D5AEFD66D5C // 112 390data8 0x3FD77B79922BD37E // 113 391data8 0x3FD7A9B9889F19E2 // 114 392data8 0x3FD7D81B037EB6A6 // 115 393data8 0x3FD8069E33827231 // 116 394data8 0x3FD82996D3EF8BCB // 117 395data8 0x3FD85855776DCBFB // 118 396data8 0x3FD8873658327CCF // 119 397data8 0x3FD8AA75973AB8CF // 120 398data8 0x3FD8D992DC8824E5 // 121 399data8 0x3FD908D2EA7D9512 // 122 400data8 0x3FD92C59E79C0E56 // 123 401data8 0x3FD95BD750EE3ED3 // 124 402data8 0x3FD98B7811A3EE5B // 125 403data8 0x3FD9AF47F33D406C // 126 404data8 0x3FD9DF270C1914A8 // 127 405data8 0x3FDA0325ED14FDA4 // 128 406data8 0x3FDA33440224FA79 // 129 407data8 0x3FDA57725E80C383 // 130 408data8 0x3FDA87D0165DD199 // 131 409data8 0x3FDAAC2E6C03F896 // 132 410data8 0x3FDADCCC6FDF6A81 // 133 411data8 0x3FDB015B3EB1E790 // 134 412data8 0x3FDB323A3A635948 // 135 413data8 0x3FDB56FA04462909 // 136 414data8 0x3FDB881AA659BC93 // 137 415data8 0x3FDBAD0BEF3DB165 // 138 416data8 0x3FDBD21297781C2F // 139 417data8 0x3FDC039236F08819 // 140 418data8 0x3FDC28CB1E4D32FD // 141 419data8 0x3FDC4E19B84723C2 // 142 420data8 0x3FDC7FF9C74554C9 // 143 421data8 0x3FDCA57B64E9DB05 // 144 422data8 0x3FDCCB130A5CEBB0 // 145 423data8 0x3FDCF0C0D18F326F // 146 424data8 0x3FDD232075B5A201 // 147 425data8 0x3FDD490246DEFA6B // 148 426data8 0x3FDD6EFA918D25CD // 149 427data8 0x3FDD9509707AE52F // 150 428data8 0x3FDDBB2EFE92C554 // 151 429data8 0x3FDDEE2F3445E4AF // 152 430data8 0x3FDE148A1A2726CE // 153 431data8 0x3FDE3AFC0A49FF40 // 154 432data8 0x3FDE6185206D516E // 155 433data8 0x3FDE882578823D52 // 156 434data8 0x3FDEAEDD2EAC990C // 157 435data8 0x3FDED5AC5F436BE3 // 158 436data8 0x3FDEFC9326D16AB9 // 159 437data8 0x3FDF2391A2157600 // 160 438data8 0x3FDF4AA7EE03192D // 161 439data8 0x3FDF71D627C30BB0 // 162 440data8 0x3FDF991C6CB3B379 // 163 441data8 0x3FDFC07ADA69A910 // 164 442data8 0x3FDFE7F18EB03D3E // 165 443data8 0x3FE007C053C5002E // 166 444data8 0x3FE01B942198A5A1 // 167 445data8 0x3FE02F74400C64EB // 168 446data8 0x3FE04360BE7603AD // 169 447data8 0x3FE05759AC47FE34 // 170 448data8 0x3FE06B5F1911CF52 // 171 449data8 0x3FE078BF0533C568 // 172 450data8 0x3FE08CD9687E7B0E // 173 451data8 0x3FE0A10074CF9019 // 174 452data8 0x3FE0B5343A234477 // 175 453data8 0x3FE0C974C89431CE // 176 454data8 0x3FE0DDC2305B9886 // 177 455data8 0x3FE0EB524BAFC918 // 178 456data8 0x3FE0FFB54213A476 // 179 457data8 0x3FE114253DA97D9F // 180 458data8 0x3FE128A24F1D9AFF // 181 459data8 0x3FE1365252BF0865 // 182 460data8 0x3FE14AE558B4A92D // 183 461data8 0x3FE15F85A19C765B // 184 462data8 0x3FE16D4D38C119FA // 185 463data8 0x3FE18203C20DD133 // 186 464data8 0x3FE196C7BC4B1F3B // 187 465data8 0x3FE1A4A738B7A33C // 188 466data8 0x3FE1B981C0C9653D // 189 467data8 0x3FE1CE69E8BB106B // 190 468data8 0x3FE1DC619DE06944 // 191 469data8 0x3FE1F160A2AD0DA4 // 192 470data8 0x3FE2066D7740737E // 193 471data8 0x3FE2147DBA47A394 // 194 472data8 0x3FE229A1BC5EBAC3 // 195 473data8 0x3FE237C1841A502E // 196 474data8 0x3FE24CFCE6F80D9A // 197 475data8 0x3FE25B2C55CD5762 // 198 476data8 0x3FE2707F4D5F7C41 // 199 477data8 0x3FE285E0842CA384 // 200 478data8 0x3FE294294708B773 // 201 479data8 0x3FE2A9A2670AFF0C // 202 480data8 0x3FE2B7FB2C8D1CC1 // 203 481data8 0x3FE2C65A6395F5F5 // 204 482data8 0x3FE2DBF557B0DF43 // 205 483data8 0x3FE2EA64C3F97655 // 206 484data8 0x3FE3001823684D73 // 207 485data8 0x3FE30E97E9A8B5CD // 208 486data8 0x3FE32463EBDD34EA // 209 487data8 0x3FE332F4314AD796 // 210 488data8 0x3FE348D90E7464D0 // 211 489data8 0x3FE35779F8C43D6E // 212 490data8 0x3FE36621961A6A99 // 213 491data8 0x3FE37C299F3C366A // 214 492data8 0x3FE38AE2171976E7 // 215 493data8 0x3FE399A157A603E7 // 216 494data8 0x3FE3AFCCFE77B9D1 // 217 495data8 0x3FE3BE9D503533B5 // 218 496data8 0x3FE3CD7480B4A8A3 // 219 497data8 0x3FE3E3C43918F76C // 220 498data8 0x3FE3F2ACB27ED6C7 // 221 499data8 0x3FE4019C2125CA93 // 222 500data8 0x3FE4181061389722 // 223 501data8 0x3FE42711518DF545 // 224 502data8 0x3FE436194E12B6BF // 225 503data8 0x3FE445285D68EA69 // 226 504data8 0x3FE45BCC464C893A // 227 505data8 0x3FE46AED21F117FC // 228 506data8 0x3FE47A1527E8A2D3 // 229 507data8 0x3FE489445EFFFCCC // 230 508data8 0x3FE4A018BCB69835 // 231 509data8 0x3FE4AF5A0C9D65D7 // 232 510data8 0x3FE4BEA2A5BDBE87 // 233 511data8 0x3FE4CDF28F10AC46 // 234 512data8 0x3FE4DD49CF994058 // 235 513data8 0x3FE4ECA86E64A684 // 236 514data8 0x3FE503C43CD8EB68 // 237 515data8 0x3FE513356667FC57 // 238 516data8 0x3FE522AE0738A3D8 // 239 517data8 0x3FE5322E26867857 // 240 518data8 0x3FE541B5CB979809 // 241 519data8 0x3FE55144FDBCBD62 // 242 520data8 0x3FE560DBC45153C7 // 243 521data8 0x3FE5707A26BB8C66 // 244 522data8 0x3FE587F60ED5B900 // 245 523data8 0x3FE597A7977C8F31 // 246 524data8 0x3FE5A760D634BB8B // 247 525data8 0x3FE5B721D295F10F // 248 526data8 0x3FE5C6EA94431EF9 // 249 527data8 0x3FE5D6BB22EA86F6 // 250 528data8 0x3FE5E6938645D390 // 251 529data8 0x3FE5F673C61A2ED2 // 252 530data8 0x3FE6065BEA385926 // 253 531data8 0x3FE6164BFA7CC06B // 254 532data8 0x3FE62643FECF9743 // 255 533LOCAL_OBJECT_END(logf_data) 534 535LOCAL_OBJECT_START(log10f_data) 536data8 0x3FDBCB7B1526E50E // 1/ln(10) 537// 538// ln(1/frcpa(1+i/256))/ln(10), i=0...255 539data8 0x3F4BD27045BFD025 // 0 540data8 0x3F64E84E793A474A // 1 541data8 0x3F7175085AB85FF0 // 2 542data8 0x3F787CFF9D9147A5 // 3 543data8 0x3F7EA9D372B89FC8 // 4 544data8 0x3F82DF9D95DA961C // 5 545data8 0x3F866DF172D6372C // 6 546data8 0x3F898D79EF5EEDF0 // 7 547data8 0x3F8D22ADF3F9579D // 8 548data8 0x3F9024231D30C398 // 9 549data8 0x3F91F23A98897D4A // 10 550data8 0x3F93881A7B818F9E // 11 551data8 0x3F951F6E1E759E35 // 12 552data8 0x3F96F2BCE7ADC5B4 // 13 553data8 0x3F988D362CDF359E // 14 554data8 0x3F9A292BAF010982 // 15 555data8 0x3F9BC6A03117EB97 // 16 556data8 0x3F9D65967DE3AB09 // 17 557data8 0x3F9F061167FC31E8 // 18 558data8 0x3FA05409E4F7819C // 19 559data8 0x3FA125D0432EA20E // 20 560data8 0x3FA1F85D440D299B // 21 561data8 0x3FA2AD755749617D // 22 562data8 0x3FA381772A00E604 // 23 563data8 0x3FA45643E165A70B // 24 564data8 0x3FA52BDD034475B8 // 25 565data8 0x3FA5E3966B7E9295 // 26 566data8 0x3FA6BAAF47C5B245 // 27 567data8 0x3FA773B3E8C4F3C8 // 28 568data8 0x3FA84C51EBEE8D15 // 29 569data8 0x3FA906A6786FC1CB // 30 570data8 0x3FA9C197ABF00DD7 // 31 571data8 0x3FAA9C78712191F7 // 32 572data8 0x3FAB58C09C8D637C // 33 573data8 0x3FAC15A8BCDD7B7E // 34 574data8 0x3FACD331E2C2967C // 35 575data8 0x3FADB11ED766ABF4 // 36 576data8 0x3FAE70089346A9E6 // 37 577data8 0x3FAF2F96C6754AEE // 38 578data8 0x3FAFEFCA8D451FD6 // 39 579data8 0x3FB0585283764178 // 40 580data8 0x3FB0B913AAC7D3A7 // 41 581data8 0x3FB11A294F2569F6 // 42 582data8 0x3FB16B51A2696891 // 43 583data8 0x3FB1CD03ADACC8BE // 44 584data8 0x3FB22F0BDD7745F5 // 45 585data8 0x3FB2916ACA38D1E8 // 46 586data8 0x3FB2F4210DF7663D // 47 587data8 0x3FB346A6C3C49066 // 48 588data8 0x3FB3A9FEBC60540A // 49 589data8 0x3FB3FD0C10A3AA54 // 50 590data8 0x3FB46107D3540A82 // 51 591data8 0x3FB4C55DD16967FE // 52 592data8 0x3FB51940330C000B // 53 593data8 0x3FB56D620EE7115E // 54 594data8 0x3FB5D2ABCF26178E // 55 595data8 0x3FB6275AA5DEBF81 // 56 596data8 0x3FB68D4EAF26D7EE // 57 597data8 0x3FB6E28C5C54A28D // 58 598data8 0x3FB7380B9665B7C8 // 59 599data8 0x3FB78DCCC278E85B // 60 600data8 0x3FB7F50C2CF2557A // 61 601data8 0x3FB84B5FD5EAEFD8 // 62 602data8 0x3FB8A1F6BAB2B226 // 63 603data8 0x3FB8F8D144557BDF // 64 604data8 0x3FB94FEFDCD61D92 // 65 605data8 0x3FB9A752EF316149 // 66 606data8 0x3FB9FEFAE7611EE0 // 67 607data8 0x3FBA56E8325F5C87 // 68 608data8 0x3FBAAF1B3E297BB4 // 69 609data8 0x3FBB079479C372AD // 70 610data8 0x3FBB6054553B12F7 // 71 611data8 0x3FBBB95B41AB5CE6 // 72 612data8 0x3FBC12A9B13FE079 // 73 613data8 0x3FBC6C4017382BEA // 74 614data8 0x3FBCB41FBA42686D // 75 615data8 0x3FBD0E38CE73393F // 76 616data8 0x3FBD689B2193F133 // 77 617data8 0x3FBDC3472B1D2860 // 78 618data8 0x3FBE0C06300D528B // 79 619data8 0x3FBE6738190E394C // 80 620data8 0x3FBEC2B50D208D9B // 81 621data8 0x3FBF0C1C2B936828 // 82 622data8 0x3FBF68216C9CC727 // 83 623data8 0x3FBFB1F6381856F4 // 84 624data8 0x3FC00742AF4CE5F8 // 85 625data8 0x3FC02C64906512D2 // 86 626data8 0x3FC05AF1E63E03B4 // 87 627data8 0x3FC0804BEA723AA9 // 88 628data8 0x3FC0AF1FD6711527 // 89 629data8 0x3FC0D4B2A8805A00 // 90 630data8 0x3FC0FA5EF136A06C // 91 631data8 0x3FC1299A4FB3E306 // 92 632data8 0x3FC14F806253C3ED // 93 633data8 0x3FC175805D1587C1 // 94 634data8 0x3FC19B9A637CA295 // 95 635data8 0x3FC1CB5FC26EDE17 // 96 636data8 0x3FC1F1B4E65F2590 // 97 637data8 0x3FC218248B5DC3E5 // 98 638data8 0x3FC23EAED62ADC76 // 99 639data8 0x3FC26553EBD337BD // 100 640data8 0x3FC28C13F1B11900 // 101 641data8 0x3FC2BCAA14381386 // 102 642data8 0x3FC2E3A740B7800F // 103 643data8 0x3FC30ABFD8F333B6 // 104 644data8 0x3FC331F403985097 // 105 645data8 0x3FC35943E7A60690 // 106 646data8 0x3FC380AFAC6E7C07 // 107 647data8 0x3FC3A8377997B9E6 // 108 648data8 0x3FC3CFDB771C9ADB // 109 649data8 0x3FC3EDA90D39A5DF // 110 650data8 0x3FC4157EC09505CD // 111 651data8 0x3FC43D7113FB04C1 // 112 652data8 0x3FC4658030AD1CCF // 113 653data8 0x3FC48DAC404638F6 // 114 654data8 0x3FC4B5F56CBBB869 // 115 655data8 0x3FC4DE5BE05E7583 // 116 656data8 0x3FC4FCBC0776FD85 // 117 657data8 0x3FC525561E9256EE // 118 658data8 0x3FC54E0DF3198865 // 119 659data8 0x3FC56CAB7112BDE2 // 120 660data8 0x3FC59597BA735B15 // 121 661data8 0x3FC5BEA23A506FDA // 122 662data8 0x3FC5DD7E08DE382F // 123 663data8 0x3FC606BDD3F92355 // 124 664data8 0x3FC6301C518A501F // 125 665data8 0x3FC64F3770618916 // 126 666data8 0x3FC678CC14C1E2D8 // 127 667data8 0x3FC6981005ED2947 // 128 668data8 0x3FC6C1DB5F9BB336 // 129 669data8 0x3FC6E1488ECD2881 // 130 670data8 0x3FC70B4B2E7E41B9 // 131 671data8 0x3FC72AE209146BF9 // 132 672data8 0x3FC7551C81BD8DCF // 133 673data8 0x3FC774DD76CC43BE // 134 674data8 0x3FC79F505DB00E88 // 135 675data8 0x3FC7BF3BDE099F30 // 136 676data8 0x3FC7E9E7CAC437F9 // 137 677data8 0x3FC809FE4902D00D // 138 678data8 0x3FC82A2757995CBE // 139 679data8 0x3FC85525C625E098 // 140 680data8 0x3FC8757A79831887 // 141 681data8 0x3FC895E2058D8E03 // 142 682data8 0x3FC8C13437695532 // 143 683data8 0x3FC8E1C812EF32BE // 144 684data8 0x3FC9026F112197E8 // 145 685data8 0x3FC923294888880B // 146 686data8 0x3FC94EEA4B8334F3 // 147 687data8 0x3FC96FD1B639FC09 // 148 688data8 0x3FC990CCA66229AC // 149 689data8 0x3FC9B1DB33334843 // 150 690data8 0x3FC9D2FD740E6607 // 151 691data8 0x3FC9FF49EEDCB553 // 152 692data8 0x3FCA209A84FBCFF8 // 153 693data8 0x3FCA41FF1E43F02B // 154 694data8 0x3FCA6377D2CE9378 // 155 695data8 0x3FCA8504BAE0D9F6 // 156 696data8 0x3FCAA6A5EEEBEFE3 // 157 697data8 0x3FCAC85B878D7879 // 158 698data8 0x3FCAEA259D8FFA0B // 159 699data8 0x3FCB0C0449EB4B6B // 160 700data8 0x3FCB2DF7A5C50299 // 161 701data8 0x3FCB4FFFCA70E4D1 // 162 702data8 0x3FCB721CD17157E3 // 163 703data8 0x3FCB944ED477D4ED // 164 704data8 0x3FCBB695ED655C7D // 165 705data8 0x3FCBD8F2364AEC0F // 166 706data8 0x3FCBFB63C969F4FF // 167 707data8 0x3FCC1DEAC134D4E9 // 168 708data8 0x3FCC4087384F4F80 // 169 709data8 0x3FCC6339498F09E2 // 170 710data8 0x3FCC86010FFC076C // 171 711data8 0x3FCC9D3D065C5B42 // 172 712data8 0x3FCCC029375BA07A // 173 713data8 0x3FCCE32B66978BA4 // 174 714data8 0x3FCD0643AFD51404 // 175 715data8 0x3FCD29722F0DEA45 // 176 716data8 0x3FCD4CB70070FE44 // 177 717data8 0x3FCD6446AB3F8C96 // 178 718data8 0x3FCD87B0EF71DB45 // 179 719data8 0x3FCDAB31D1FE99A7 // 180 720data8 0x3FCDCEC96FDC888F // 181 721data8 0x3FCDE6908876357A // 182 722data8 0x3FCE0A4E4A25C200 // 183 723data8 0x3FCE2E2315755E33 // 184 724data8 0x3FCE461322D1648A // 185 725data8 0x3FCE6A0E95C7787B // 186 726data8 0x3FCE8E216243DD60 // 187 727data8 0x3FCEA63AF26E007C // 188 728data8 0x3FCECA74ED15E0B7 // 189 729data8 0x3FCEEEC692CCD25A // 190 730data8 0x3FCF070A36B8D9C1 // 191 731data8 0x3FCF2B8393E34A2D // 192 732data8 0x3FCF5014EF538A5B // 193 733data8 0x3FCF68833AF1B180 // 194 734data8 0x3FCF8D3CD9F3F04F // 195 735data8 0x3FCFA5C61ADD93E9 // 196 736data8 0x3FCFCAA8567EBA7A // 197 737data8 0x3FCFE34CC8743DD8 // 198 738data8 0x3FD0042BFD74F519 // 199 739data8 0x3FD016BDF6A18017 // 200 740data8 0x3FD023262F907322 // 201 741data8 0x3FD035CCED8D32A1 // 202 742data8 0x3FD042430E869FFC // 203 743data8 0x3FD04EBEC842B2E0 // 204 744data8 0x3FD06182E84FD4AC // 205 745data8 0x3FD06E0CB609D383 // 206 746data8 0x3FD080E60BEC8F12 // 207 747data8 0x3FD08D7E0D894735 // 208 748data8 0x3FD0A06CC96A2056 // 209 749data8 0x3FD0AD131F3B3C55 // 210 750data8 0x3FD0C01771E775FB // 211 751data8 0x3FD0CCCC3CAD6F4B // 212 752data8 0x3FD0D986D91A34A9 // 213 753data8 0x3FD0ECA9B8861A2D // 214 754data8 0x3FD0F972F87FF3D6 // 215 755data8 0x3FD106421CF0E5F7 // 216 756data8 0x3FD11983EBE28A9D // 217 757data8 0x3FD12661E35B785A // 218 758data8 0x3FD13345D2779D3B // 219 759data8 0x3FD146A6F597283A // 220 760data8 0x3FD15399E81EA83D // 221 761data8 0x3FD16092E5D3A9A6 // 222 762data8 0x3FD17413C3B7AB5E // 223 763data8 0x3FD1811BF629D6FB // 224 764data8 0x3FD18E2A47B46686 // 225 765data8 0x3FD19B3EBE1A4418 // 226 766data8 0x3FD1AEE9017CB450 // 227 767data8 0x3FD1BC0CED7134E2 // 228 768data8 0x3FD1C93712ABC7FF // 229 769data8 0x3FD1D66777147D3F // 230 770data8 0x3FD1EA3BD1286E1C // 231 771data8 0x3FD1F77BED932C4C // 232 772data8 0x3FD204C25E1B031F // 233 773data8 0x3FD2120F28CE69B1 // 234 774data8 0x3FD21F6253C48D01 // 235 775data8 0x3FD22CBBE51D60AA // 236 776data8 0x3FD240CE4C975444 // 237 777data8 0x3FD24E37F8ECDAE8 // 238 778data8 0x3FD25BA8215AF7FC // 239 779data8 0x3FD2691ECC29F042 // 240 780data8 0x3FD2769BFFAB2E00 // 241 781data8 0x3FD2841FC23952C9 // 242 782data8 0x3FD291AA1A384978 // 243 783data8 0x3FD29F3B0E15584B // 244 784data8 0x3FD2B3A0EE479DF7 // 245 785data8 0x3FD2C142842C09E6 // 246 786data8 0x3FD2CEEACCB7BD6D // 247 787data8 0x3FD2DC99CE82FF21 // 248 788data8 0x3FD2EA4F902FD7DA // 249 789data8 0x3FD2F80C186A25FD // 250 790data8 0x3FD305CF6DE7B0F7 // 251 791data8 0x3FD3139997683CE7 // 252 792data8 0x3FD3216A9BB59E7C // 253 793data8 0x3FD32F4281A3CEFF // 254 794data8 0x3FD33D2150110092 // 255 795LOCAL_OBJECT_END(log10f_data) 796 797 798// Code 799//============================================================== 800.section .text 801 802// logf has p13 true, p14 false 803// log10f has p14 true, p13 false 804 805GLOBAL_IEEE754_ENTRY(log10f) 806{ .mfi 807 getf.exp GR_Exp = f8 // if x is unorm then must recompute 808 frcpa.s1 FR_RcpX,p0 = f1,f8 809 mov GR_05 = 0xFFFE // biased exponent of A2=0.5 810} 811{ .mlx 812 addl GR_ad_T = @ltoff(log10f_data),gp 813 movl GR_A3 = 0x3FD5555555555555 // double precision memory 814 // representation of A3 815};; 816{ .mfi 817 getf.sig GR_Sig = f8 // if x is unorm then must recompute 818 fclass.m p8,p0 = f8,9 // is x positive unorm? 819 sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25 820} 821{ .mlx 822 ld8 GR_ad_T = [GR_ad_T] 823 movl GR_Ln2 = 0x3FD34413509F79FF // double precision memory 824 // representation of 825 // log(2)/ln(10) 826};; 827{ .mfi 828 setf.d FR_A3 = GR_A3 // create A3 829 fcmp.eq.s1 p14,p13 = f0,f0 // set p14 to 1 for log10f 830 dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number 831 // bits of that are 832 // GR_xorg[63] = last bit of biased 833 // exponent of 255/256 834 // GR_xorg[62-0] = bits from 62 to 0 835 // of significand of 255/256 836} 837{ .mib 838 setf.exp FR_A2 = GR_05 // create A2 839 sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE 840 // needed for comparison with 0.5 and 2.0 841 br.cond.sptk logf_log10f_common 842};; 843GLOBAL_IEEE754_END(log10f) 844libm_alias_float_other (__log10, log10) 845 846GLOBAL_IEEE754_ENTRY(logf) 847{ .mfi 848 getf.exp GR_Exp = f8 // if x is unorm then must recompute 849 frcpa.s1 FR_RcpX,p0 = f1,f8 850 mov GR_05 = 0xFFFE // biased exponent of A2=-0.5 851} 852{ .mlx 853 addl GR_ad_T = @ltoff(logf_data),gp 854 movl GR_A3 = 0x3FD5555555555555 // double precision memory 855 // representation of A3 856};; 857{ .mfi 858 getf.sig GR_Sig = f8 // if x is unorm then must recompute 859 fclass.m p8,p0 = f8,9 // is x positive unorm? 860 dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number 861 // bits of that are 862 // GR_xorg[63] = last bit of biased 863 // exponent of 255/256 864 // GR_xorg[62-0] = bits from 62 to 0 865 // of significand of 255/256 866} 867{ .mfi 868 ld8 GR_ad_T = [GR_ad_T] 869 nop.f 0 870 sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25 871};; 872{ .mfi 873 setf.d FR_A3 = GR_A3 // create A3 874 fcmp.eq.s1 p13,p14 = f0,f0 // p13 - true for logf 875 sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE 876 // needed for comparison with 0.5 and 2.0 877} 878{ .mlx 879 setf.exp FR_A2 = GR_05 // create A2 880 movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory 881 // representation of log(2) 882};; 883logf_log10f_common: 884{ .mfi 885 setf.exp FR_A4 = GR_025 // create A4=0.25 886 fclass.m p9,p0 = f8,0x3A // is x < 0 (including negateve unnormals)? 887 dep GR_x = GR_Exp,GR_Sig,63,1 // produce integer that bits are 888 // GR_x[63] = GR_Exp[0] 889 // GR_x[62-0] = GR_Sig[62-0] 890} 891{ .mib 892 sub GR_N = GR_Exp,GR_05,1 // unbiased exponent of x 893 cmp.gtu p6,p7 = 2,GR_de // is 0.5 <= x < 2.0? 894(p8) br.cond.spnt logf_positive_unorm 895};; 896logf_core: 897{ .mfi 898 setf.sig FR_N = GR_N // copy unbiased exponent of x to the 899 // significand field of FR_N 900 fclass.m p10,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? 901 dep.z GR_dx = GR_05,54,3 // 0x0180000000000000 - difference 902 // between our integer representations 903 // of 257/256 and 255/256 904} 905{ .mfi 906 nop.m 0 907 nop.f 0 908 sub GR_x = GR_x,GR_xorg // difference between representations 909 // of x and 255/256 910};; 911{ .mfi 912 ldfd FR_InvLn10 = [GR_ad_T],8 913 fcmp.eq.s1 p11,p0 = f8,f1 // is x equal to 1.0? 914 extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index 915} 916{ .mib 917 setf.d FR_Ln2 = GR_Ln2 // create log(2) or log10(2) 918(p6) cmp.gtu p6,p7 = GR_dx,GR_x // set p6 if 255/256 <= x < 257/256 919(p9) br.cond.spnt logf_negatives // jump if input argument is negative number 920};; 921// p6 is true if |x-1| < 1/256 922// p7 is true if |x-1| >= 1/256 923.pred.rel "mutex",p6,p7 924{ .mfi 925 shladd GR_ad_T = GR_Ind,3,GR_ad_T // calculate address of T 926(p7) fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256 927 extr.u GR_Exp = GR_Exp,0,17 // exponent without sign 928} 929{ .mfb 930 nop.m 0 931(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256 932(p10) br.cond.spnt logf_nan_nat_pinf // exit for NaN, NaT or +Inf 933};; 934{ .mfb 935 ldfd FR_T = [GR_ad_T] // load T 936(p11) fma.s.s0 f8 = f0,f0,f0 937(p11) br.ret.spnt b0 // exit for x = 1.0 938};; 939{ .mib 940 nop.m 0 941 cmp.eq p12,p0 = r0,GR_Exp // is x +/-0? (here it's quite enough 942 // only to compare exponent with 0 943 // because all unnormals already 944 // have been filtered) 945(p12) br.cond.spnt logf_zeroes // Branch if input argument is +/-0 946};; 947{ .mfi 948 nop.m 0 949 fnma.s1 FR_A2 = FR_A2,FR_r,f1 // A2*r+1 950 nop.i 0 951} 952{ .mfi 953 nop.m 0 954 fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 955 nop.i 0 956};; 957{ .mfi 958 nop.m 0 959 fcvt.xf FR_N = FR_N // convert integer N in significand of FR_N 960 // to floating-point representation 961 nop.i 0 962} 963{ .mfi 964 nop.m 0 965 fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3 966 nop.i 0 967};; 968{ .mfi 969 nop.m 0 970 fma.s1 FR_r = FR_r,FR_InvLn10,f0 // For log10f we have r/log(10) 971 nop.i 0 972} 973{ .mfi 974 nop.m 0 975 nop.f 0 976 nop.i 0 977};; 978{ .mfi 979 nop.m 0 980 fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1) 981 nop.i 0 982} 983{ .mfi 984 nop.m 0 985 fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T // N*Ln2+T 986 nop.i 0 987};; 988.pred.rel "mutex",p6,p7 989{ .mfi 990 nop.m 0 991(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result for |x-1|>=1/256 992 nop.i 0 993} 994{ .mfb 995 nop.m 0 996(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result for |x-1|<1/256 997 br.ret.sptk b0 998};; 999 1000.align 32 1001logf_positive_unorm: 1002{ .mfi 1003 nop.m 0 1004(p8) fma.s0 f8 = f8,f1,f0 // Normalize & set D-flag 1005 nop.i 0 1006};; 1007{ .mfi 1008 getf.exp GR_Exp = f8 // recompute biased exponent 1009 nop.f 0 1010 cmp.ne p6,p7 = r0,r0 // p6 <- 0, p7 <- 1 because 1011 // in case of unorm we are out 1012 // interval [255/256; 257/256] 1013};; 1014{ .mfi 1015 getf.sig GR_Sig = f8 // recompute significand 1016 nop.f 0 1017 nop.i 0 1018};; 1019{ .mib 1020 sub GR_N = GR_Exp,GR_05,1 // unbiased exponent N 1021 nop.i 0 1022 br.cond.sptk logf_core // return into main path 1023};; 1024 1025.align 32 1026logf_nan_nat_pinf: 1027{ .mfi 1028 nop.m 0 1029 fma.s.s0 f8 = f8,f1,f0 // set V-flag 1030 nop.i 0 1031} 1032{ .mfb 1033 nop.m 0 1034 nop.f 0 1035 br.ret.sptk b0 // exit for NaN, NaT or +Inf 1036};; 1037 1038.align 32 1039logf_zeroes: 1040{ .mfi 1041 nop.m 0 1042 fmerge.s FR_X = f8,f8 // keep input argument for subsequent 1043 // call of __libm_error_support# 1044 nop.i 0 1045} 1046{ .mfi 1047(p13) mov GR_TAG = 4 // set libm error in case of logf 1048 fms.s1 FR_tmp = f0,f0,f1 // -1.0 1049 nop.i 0 1050};; 1051{ .mfi 1052 nop.m 0 1053 frcpa.s0 f8,p0 = FR_tmp,f0 // log(+/-0) should be equal to -INF. 1054 // We can get it using frcpa because it 1055 // sets result to the IEEE-754 mandated 1056 // quotient of FR_tmp/f0. 1057 // As far as FR_tmp is -1 it'll be -INF 1058 nop.i 0 1059} 1060{ .mib 1061(p14) mov GR_TAG = 10 // set libm error in case of log10f 1062 nop.i 0 1063 br.cond.sptk logf_libm_err 1064};; 1065 1066.align 32 1067logf_negatives: 1068{ .mfi 1069(p13) mov GR_TAG = 5 // set libm error in case of logf 1070 fmerge.s FR_X = f8,f8 // keep input argument for subsequent 1071 // call of __libm_error_support# 1072 nop.i 0 1073};; 1074{ .mfi 1075(p14) mov GR_TAG = 11 // set libm error in case of log10f 1076 frcpa.s0 f8,p0 = f0,f0 // log(negatives) should be equal to NaN. 1077 // We can get it using frcpa because it 1078 // sets result to the IEEE-754 mandated 1079 // quotient of f0/f0 i.e. NaN. 1080 nop.i 0 1081};; 1082 1083.align 32 1084logf_libm_err: 1085{ .mmi 1086 alloc r32 = ar.pfs,1,4,4,0 1087 mov GR_Parameter_TAG = GR_TAG 1088 nop.i 0 1089};; 1090GLOBAL_IEEE754_END(logf) 1091libm_alias_float_other (__log, log) 1092#ifdef SHARED 1093.symver logf,logf@@GLIBC_2.27 1094.weak __logf_compat 1095.set __logf_compat,__logf 1096.symver __logf_compat,logf@GLIBC_2.2 1097#endif 1098 1099 1100// Stack operations when calling error support. 1101// (1) (2) (3) (call) (4) 1102// sp -> + psp -> + psp -> + sp -> + 1103// | | | | 1104// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8 1105// | | | | 1106// | <-GR_Y Y2->| Y2 ->| <- GR_Y | 1107// | | | | 1108// | | <- GR_X X1 ->| | 1109// | | | | 1110// sp-64 -> + sp -> + sp -> + + 1111// save ar.pfs save b0 restore gp 1112// save gp restore ar.pfs 1113 1114LOCAL_LIBM_ENTRY(__libm_error_region) 1115.prologue 1116{ .mfi 1117 add GR_Parameter_Y=-32,sp // Parameter 2 value 1118 nop.f 0 1119.save ar.pfs,GR_SAVE_PFS 1120 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 1121} 1122{ .mfi 1123.fframe 64 1124 add sp=-64,sp // Create new stack 1125 nop.f 0 1126 mov GR_SAVE_GP=gp // Save gp 1127};; 1128{ .mmi 1129 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack 1130 add GR_Parameter_X = 16,sp // Parameter 1 address 1131.save b0, GR_SAVE_B0 1132 mov GR_SAVE_B0=b0 // Save b0 1133};; 1134.body 1135{ .mib 1136 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack 1137 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 1138 nop.b 0 1139} 1140{ .mib 1141 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack 1142 add GR_Parameter_Y = -16,GR_Parameter_Y 1143 br.call.sptk b0=__libm_error_support# // Call error handling function 1144};; 1145{ .mmi 1146 nop.m 0 1147 nop.m 0 1148 add GR_Parameter_RESULT = 48,sp 1149};; 1150{ .mmi 1151 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack 1152.restore sp 1153 add sp = 64,sp // Restore stack pointer 1154 mov b0 = GR_SAVE_B0 // Restore return address 1155};; 1156{ .mib 1157 mov gp = GR_SAVE_GP // Restore gp 1158 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 1159 br.ret.sptk b0 // Return 1160};; 1161 1162LOCAL_LIBM_END(__libm_error_region) 1163 1164.type __libm_error_support#,@function 1165.global __libm_error_support# 1166