1.file "log.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// 02/02/00 Initial version 42// 04/04/00 Unwind support added 43// 06/16/00 Updated table to be rounded correctly 44// 08/15/00 Bundle added after call to __libm_error_support to properly 45// set [the previously overwritten] GR_Parameter_RESULT. 46// 08/17/00 Improved speed of main path by 5 cycles 47// Shortened path for x=1.0 48// 01/09/01 Improved speed, fixed flags for neg denormals 49// 05/20/02 Cleaned up namespace and sf0 syntax 50// 05/23/02 Modified algorithm. Now only one polynomial is used 51// for |x-1| >= 1/256 and for |x-1| < 1/256 52// 12/11/02 Improved performance for Itanium 2 53// 03/31/05 Reformatted delimiters between data tables 54// 55// API 56//============================================================== 57// double log(double) 58// double log10(double) 59// 60// 61// Overview of operation 62//============================================================== 63// Background 64// ---------- 65// 66// This algorithm is based on fact that 67// log(a b) = log(a) + log(b). 68// In our case we have x = 2^N f, where 1 <= f < 2. 69// So 70// log(x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) 71// 72// To calculate log(f) we do following 73// log(f) = log(f * frcpa(f) / frcpa(f)) = 74// = log(f * frcpa(f)) + log(1/frcpa(f)) 75// 76// According to definition of IA-64's frcpa instruction it's a 77// floating point that approximates 1/f using a lookup on the 78// top of 8 bits of the input number's significand with relative 79// error < 2^(-8.886). So we have following 80// 81// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 82// 83// and 84// 85// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = 86// = log(1 + r) + T 87// 88// The first value can be computed by polynomial P(r) approximating 89// log(1 + r) on |r| < 1/256 and the second is precomputed tabular 90// value defined by top 8 bit of f. 91// 92// Finally we have that log(x) ~ (N*log(2) + T) + P(r) 93// 94// Note that if input argument is close to 1.0 (in our case it means 95// that |1 - x| < 1/256) we can use just polynomial approximation 96// because x = 2^0 * f = f = 1 + r and 97// log(x) = log(1 + r) ~ P(r) 98// 99// 100// To compute log10(x) we use the simple identity 101// 102// log10(x) = log(x)/log(10) 103// 104// so we have that 105// 106// log10(x) = (N*log(2) + T + log(1+r)) / log(10) = 107// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10) 108// 109// 110// Implementation 111// -------------- 112// It can be seen that formulas for log and log10 differ from one another 113// only by coefficients and tabular values. Namely as log as log10 are 114// calculated as (N*L1 + T) + L2*Series(r) where in case of log 115// L1 = log(2) 116// T = log(1/frcpa(x)) 117// L2 = 1.0 118// and in case of log10 119// L1 = log(2)/log(10) 120// T = log(1/frcpa(x))/log(10) 121// L2 = 1.0/log(10) 122// 123// So common code with two different entry points those set pointers 124// to the base address of coresponding data sets containing values 125// of L2,T and prepare integer representation of L1 needed for following 126// setf instruction. 127// 128// Note that both log and log10 use common approximation polynomial 129// it means we need only one set of coefficients of approximation. 130// 131// 132// 1. |x-1| >= 1/256 133// InvX = frcpa(x) 134// r = InvX*x - 1 135// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), 136// all coefficients are calculated in quad and rounded to double 137// precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2 138// created with setf. 139// 140// N = float(n) where n is true unbiased exponent of x 141// 142// T is tabular value of log(1/frcpa(x)) calculated in quad precision 143// and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo. 144// To load Thi,Tlo we get bits from 55 to 62 of register format significand 145// as index and calculate two addresses 146// ad_Thi = Thi_table_base_addr + 8 * index 147// ad_Tlo = Tlo_table_base_addr + 4 * index 148// 149// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad 150// precision and rounded to double extended; it's loaded from memory. 151// 152// L1 (log(2) or log10(2) depending on function) is calculated in quad 153// precision and represented by two floating-point 64-bit numbers L1hi,L1lo 154// stored in memory. 155// 156// And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + L2*P(r) 157// 158// 159// 2. |x-1| < 1/256 160// r = x - 1 161// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), 162// A7,A6,A5A4,A3,A2 are the same as in case |x-1| >= 1/256 163// 164// And final results 165// log(x) = P(r) 166// log10(x) = L2*P(r) 167// 168// 3. How we define is input argument such that |x-1| < 1/256 or not. 169// 170// To do it we analyze biased exponent and integer representation of 171// input argument 172// 173// a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e. 174// we test is 0.5 <= x < 2). This comparison can be performed using 175// unsigned version of cmp instruction in such a way 176// biased_exponent_of_x - 0xFFFE < 2 177// 178// 179// b) Second (in case when result of a) is true) we need to compare x 180// with 1-1/256 and 1+1/256 or in double precision memory representation 181// with 0x3FEFE00000000000 and 0x3FF0100000000000 correspondingly. 182// This comparison can be made like in a), using unsigned 183// version of cmp i.e. ix - 0x3FEFE00000000000 < 0x0000300000000000. 184// 0x0000300000000000 is difference between 0x3FF0100000000000 and 185// 0x3FEFE00000000000 186// 187// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are 188// filtered and processed on special branches. 189// 190 191// 192// Special values 193//============================================================== 194// 195// log(+0) = -inf 196// log(-0) = -inf 197// 198// log(+qnan) = +qnan 199// log(-qnan) = -qnan 200// log(+snan) = +qnan 201// log(-snan) = -qnan 202// 203// log(-n) = QNAN Indefinite 204// log(-inf) = QNAN Indefinite 205// 206// log(+inf) = +inf 207// 208// 209// Registers used 210//============================================================== 211// Floating Point registers used: 212// f8, input 213// f7 -> f15, f32 -> f42 214// 215// General registers used: 216// r8 -> r11 217// r14 -> r23 218// 219// Predicate registers used: 220// p6 -> p15 221 222// Assembly macros 223//============================================================== 224GR_TAG = r8 225GR_ad_1 = r8 226GR_ad_2 = r9 227GR_Exp = r10 228GR_N = r11 229 230GR_x = r14 231GR_dx = r15 232GR_NearOne = r15 233GR_xorg = r16 234GR_mask = r16 235GR_05 = r17 236GR_A3 = r18 237GR_Sig = r19 238GR_Ind = r19 239GR_Nm1 = r20 240GR_bias = r21 241GR_ad_3 = r22 242GR_rexp = r23 243 244 245GR_SAVE_B0 = r33 246GR_SAVE_PFS = r34 247GR_SAVE_GP = r35 248GR_SAVE_SP = r36 249 250GR_Parameter_X = r37 251GR_Parameter_Y = r38 252GR_Parameter_RESULT = r39 253GR_Parameter_TAG = r40 254 255 256 257FR_NormX = f7 258FR_RcpX = f9 259FR_tmp = f9 260FR_r = f10 261FR_r2 = f11 262FR_r4 = f12 263FR_N = f13 264FR_Ln2hi = f14 265FR_Ln2lo = f15 266 267FR_A7 = f32 268FR_A6 = f33 269FR_A5 = f34 270FR_A4 = f35 271FR_A3 = f36 272FR_A2 = f37 273 274FR_Thi = f38 275FR_NxLn2hipThi = f38 276FR_NxLn2pT = f38 277FR_Tlo = f39 278FR_NxLn2lopTlo = f39 279 280FR_InvLn10 = f40 281FR_A32 = f41 282FR_A321 = f42 283 284 285FR_Y = f1 286FR_X = f10 287FR_RESULT = f8 288 289 290// Data 291//============================================================== 292RODATA 293.align 16 294 295LOCAL_OBJECT_START(log_data) 296// coefficients of polynomial approximation 297data8 0x3FC2494104381A8E // A7 298data8 0xBFC5556D556BBB69 // A6 299// 300// two parts of ln(2) 301data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED 302// 303data8 0x8000000000000000,0x3FFF // 1.0 304// 305data8 0x3FC999999988B5E9 // A5 306data8 0xBFCFFFFFFFF6FFF5 // A4 307// 308// hi parts of ln(1/frcpa(1+i/256)), i=0...255 309data8 0x3F60040155D5889D // 0 310data8 0x3F78121214586B54 // 1 311data8 0x3F841929F96832EF // 2 312data8 0x3F8C317384C75F06 // 3 313data8 0x3F91A6B91AC73386 // 4 314data8 0x3F95BA9A5D9AC039 // 5 315data8 0x3F99D2A8074325F3 // 6 316data8 0x3F9D6B2725979802 // 7 317data8 0x3FA0C58FA19DFAA9 // 8 318data8 0x3FA2954C78CBCE1A // 9 319data8 0x3FA4A94D2DA96C56 // 10 320data8 0x3FA67C94F2D4BB58 // 11 321data8 0x3FA85188B630F068 // 12 322data8 0x3FAA6B8ABE73AF4C // 13 323data8 0x3FAC441E06F72A9E // 14 324data8 0x3FAE1E6713606D06 // 15 325data8 0x3FAFFA6911AB9300 // 16 326data8 0x3FB0EC139C5DA600 // 17 327data8 0x3FB1DBD2643D190B // 18 328data8 0x3FB2CC7284FE5F1C // 19 329data8 0x3FB3BDF5A7D1EE64 // 20 330data8 0x3FB4B05D7AA012E0 // 21 331data8 0x3FB580DB7CEB5701 // 22 332data8 0x3FB674F089365A79 // 23 333data8 0x3FB769EF2C6B568D // 24 334data8 0x3FB85FD927506A47 // 25 335data8 0x3FB9335E5D594988 // 26 336data8 0x3FBA2B0220C8E5F4 // 27 337data8 0x3FBB0004AC1A86AB // 28 338data8 0x3FBBF968769FCA10 // 29 339data8 0x3FBCCFEDBFEE13A8 // 30 340data8 0x3FBDA727638446A2 // 31 341data8 0x3FBEA3257FE10F79 // 32 342data8 0x3FBF7BE9FEDBFDE5 // 33 343data8 0x3FC02AB352FF25F3 // 34 344data8 0x3FC097CE579D204C // 35 345data8 0x3FC1178E8227E47B // 36 346data8 0x3FC185747DBECF33 // 37 347data8 0x3FC1F3B925F25D41 // 38 348data8 0x3FC2625D1E6DDF56 // 39 349data8 0x3FC2D1610C868139 // 40 350data8 0x3FC340C59741142E // 41 351data8 0x3FC3B08B6757F2A9 // 42 352data8 0x3FC40DFB08378003 // 43 353data8 0x3FC47E74E8CA5F7C // 44 354data8 0x3FC4EF51F6466DE4 // 45 355data8 0x3FC56092E02BA516 // 46 356data8 0x3FC5D23857CD74D4 // 47 357data8 0x3FC6313A37335D76 // 48 358data8 0x3FC6A399DABBD383 // 49 359data8 0x3FC70337DD3CE41A // 50 360data8 0x3FC77654128F6127 // 51 361data8 0x3FC7E9D82A0B022D // 52 362data8 0x3FC84A6B759F512E // 53 363data8 0x3FC8AB47D5F5A30F // 54 364data8 0x3FC91FE49096581B // 55 365data8 0x3FC981634011AA75 // 56 366data8 0x3FC9F6C407089664 // 57 367data8 0x3FCA58E729348F43 // 58 368data8 0x3FCABB55C31693AC // 59 369data8 0x3FCB1E104919EFD0 // 60 370data8 0x3FCB94EE93E367CA // 61 371data8 0x3FCBF851C067555E // 62 372data8 0x3FCC5C0254BF23A5 // 63 373data8 0x3FCCC000C9DB3C52 // 64 374data8 0x3FCD244D99C85673 // 65 375data8 0x3FCD88E93FB2F450 // 66 376data8 0x3FCDEDD437EAEF00 // 67 377data8 0x3FCE530EFFE71012 // 68 378data8 0x3FCEB89A1648B971 // 69 379data8 0x3FCF1E75FADF9BDE // 70 380data8 0x3FCF84A32EAD7C35 // 71 381data8 0x3FCFEB2233EA07CD // 72 382data8 0x3FD028F9C7035C1C // 73 383data8 0x3FD05C8BE0D9635A // 74 384data8 0x3FD085EB8F8AE797 // 75 385data8 0x3FD0B9C8E32D1911 // 76 386data8 0x3FD0EDD060B78080 // 77 387data8 0x3FD122024CF0063F // 78 388data8 0x3FD14BE2927AECD4 // 79 389data8 0x3FD180618EF18ADF // 80 390data8 0x3FD1B50BBE2FC63B // 81 391data8 0x3FD1DF4CC7CF242D // 82 392data8 0x3FD214456D0EB8D4 // 83 393data8 0x3FD23EC5991EBA49 // 84 394data8 0x3FD2740D9F870AFB // 85 395data8 0x3FD29ECDABCDFA03 // 86 396data8 0x3FD2D46602ADCCEE // 87 397data8 0x3FD2FF66B04EA9D4 // 88 398data8 0x3FD335504B355A37 // 89 399data8 0x3FD360925EC44F5C // 90 400data8 0x3FD38BF1C3337E74 // 91 401data8 0x3FD3C25277333183 // 92 402data8 0x3FD3EDF463C1683E // 93 403data8 0x3FD419B423D5E8C7 // 94 404data8 0x3FD44591E0539F48 // 95 405data8 0x3FD47C9175B6F0AD // 96 406data8 0x3FD4A8B341552B09 // 97 407data8 0x3FD4D4F39089019F // 98 408data8 0x3FD501528DA1F967 // 99 409data8 0x3FD52DD06347D4F6 // 100 410data8 0x3FD55A6D3C7B8A89 // 101 411data8 0x3FD5925D2B112A59 // 102 412data8 0x3FD5BF406B543DB1 // 103 413data8 0x3FD5EC433D5C35AD // 104 414data8 0x3FD61965CDB02C1E // 105 415data8 0x3FD646A84935B2A1 // 106 416data8 0x3FD6740ADD31DE94 // 107 417data8 0x3FD6A18DB74A58C5 // 108 418data8 0x3FD6CF31058670EC // 109 419data8 0x3FD6F180E852F0B9 // 110 420data8 0x3FD71F5D71B894EF // 111 421data8 0x3FD74D5AEFD66D5C // 112 422data8 0x3FD77B79922BD37D // 113 423data8 0x3FD7A9B9889F19E2 // 114 424data8 0x3FD7D81B037EB6A6 // 115 425data8 0x3FD8069E33827230 // 116 426data8 0x3FD82996D3EF8BCA // 117 427data8 0x3FD85855776DCBFA // 118 428data8 0x3FD8873658327CCE // 119 429data8 0x3FD8AA75973AB8CE // 120 430data8 0x3FD8D992DC8824E4 // 121 431data8 0x3FD908D2EA7D9511 // 122 432data8 0x3FD92C59E79C0E56 // 123 433data8 0x3FD95BD750EE3ED2 // 124 434data8 0x3FD98B7811A3EE5B // 125 435data8 0x3FD9AF47F33D406B // 126 436data8 0x3FD9DF270C1914A7 // 127 437data8 0x3FDA0325ED14FDA4 // 128 438data8 0x3FDA33440224FA78 // 129 439data8 0x3FDA57725E80C382 // 130 440data8 0x3FDA87D0165DD199 // 131 441data8 0x3FDAAC2E6C03F895 // 132 442data8 0x3FDADCCC6FDF6A81 // 133 443data8 0x3FDB015B3EB1E790 // 134 444data8 0x3FDB323A3A635948 // 135 445data8 0x3FDB56FA04462909 // 136 446data8 0x3FDB881AA659BC93 // 137 447data8 0x3FDBAD0BEF3DB164 // 138 448data8 0x3FDBD21297781C2F // 139 449data8 0x3FDC039236F08818 // 140 450data8 0x3FDC28CB1E4D32FC // 141 451data8 0x3FDC4E19B84723C1 // 142 452data8 0x3FDC7FF9C74554C9 // 143 453data8 0x3FDCA57B64E9DB05 // 144 454data8 0x3FDCCB130A5CEBAF // 145 455data8 0x3FDCF0C0D18F326F // 146 456data8 0x3FDD232075B5A201 // 147 457data8 0x3FDD490246DEFA6B // 148 458data8 0x3FDD6EFA918D25CD // 149 459data8 0x3FDD9509707AE52F // 150 460data8 0x3FDDBB2EFE92C554 // 151 461data8 0x3FDDEE2F3445E4AE // 152 462data8 0x3FDE148A1A2726CD // 153 463data8 0x3FDE3AFC0A49FF3F // 154 464data8 0x3FDE6185206D516D // 155 465data8 0x3FDE882578823D51 // 156 466data8 0x3FDEAEDD2EAC990C // 157 467data8 0x3FDED5AC5F436BE2 // 158 468data8 0x3FDEFC9326D16AB8 // 159 469data8 0x3FDF2391A21575FF // 160 470data8 0x3FDF4AA7EE03192C // 161 471data8 0x3FDF71D627C30BB0 // 162 472data8 0x3FDF991C6CB3B379 // 163 473data8 0x3FDFC07ADA69A90F // 164 474data8 0x3FDFE7F18EB03D3E // 165 475data8 0x3FE007C053C5002E // 166 476data8 0x3FE01B942198A5A0 // 167 477data8 0x3FE02F74400C64EA // 168 478data8 0x3FE04360BE7603AC // 169 479data8 0x3FE05759AC47FE33 // 170 480data8 0x3FE06B5F1911CF51 // 171 481data8 0x3FE078BF0533C568 // 172 482data8 0x3FE08CD9687E7B0E // 173 483data8 0x3FE0A10074CF9019 // 174 484data8 0x3FE0B5343A234476 // 175 485data8 0x3FE0C974C89431CD // 176 486data8 0x3FE0DDC2305B9886 // 177 487data8 0x3FE0EB524BAFC918 // 178 488data8 0x3FE0FFB54213A475 // 179 489data8 0x3FE114253DA97D9F // 180 490data8 0x3FE128A24F1D9AFF // 181 491data8 0x3FE1365252BF0864 // 182 492data8 0x3FE14AE558B4A92D // 183 493data8 0x3FE15F85A19C765B // 184 494data8 0x3FE16D4D38C119FA // 185 495data8 0x3FE18203C20DD133 // 186 496data8 0x3FE196C7BC4B1F3A // 187 497data8 0x3FE1A4A738B7A33C // 188 498data8 0x3FE1B981C0C9653C // 189 499data8 0x3FE1CE69E8BB106A // 190 500data8 0x3FE1DC619DE06944 // 191 501data8 0x3FE1F160A2AD0DA3 // 192 502data8 0x3FE2066D7740737E // 193 503data8 0x3FE2147DBA47A393 // 194 504data8 0x3FE229A1BC5EBAC3 // 195 505data8 0x3FE237C1841A502E // 196 506data8 0x3FE24CFCE6F80D9A // 197 507data8 0x3FE25B2C55CD5762 // 198 508data8 0x3FE2707F4D5F7C40 // 199 509data8 0x3FE285E0842CA383 // 200 510data8 0x3FE294294708B773 // 201 511data8 0x3FE2A9A2670AFF0C // 202 512data8 0x3FE2B7FB2C8D1CC0 // 203 513data8 0x3FE2C65A6395F5F5 // 204 514data8 0x3FE2DBF557B0DF42 // 205 515data8 0x3FE2EA64C3F97654 // 206 516data8 0x3FE3001823684D73 // 207 517data8 0x3FE30E97E9A8B5CC // 208 518data8 0x3FE32463EBDD34E9 // 209 519data8 0x3FE332F4314AD795 // 210 520data8 0x3FE348D90E7464CF // 211 521data8 0x3FE35779F8C43D6D // 212 522data8 0x3FE36621961A6A99 // 213 523data8 0x3FE37C299F3C366A // 214 524data8 0x3FE38AE2171976E7 // 215 525data8 0x3FE399A157A603E7 // 216 526data8 0x3FE3AFCCFE77B9D1 // 217 527data8 0x3FE3BE9D503533B5 // 218 528data8 0x3FE3CD7480B4A8A2 // 219 529data8 0x3FE3E3C43918F76C // 220 530data8 0x3FE3F2ACB27ED6C6 // 221 531data8 0x3FE4019C2125CA93 // 222 532data8 0x3FE4181061389722 // 223 533data8 0x3FE42711518DF545 // 224 534data8 0x3FE436194E12B6BF // 225 535data8 0x3FE445285D68EA69 // 226 536data8 0x3FE45BCC464C893A // 227 537data8 0x3FE46AED21F117FC // 228 538data8 0x3FE47A1527E8A2D3 // 229 539data8 0x3FE489445EFFFCCB // 230 540data8 0x3FE4A018BCB69835 // 231 541data8 0x3FE4AF5A0C9D65D7 // 232 542data8 0x3FE4BEA2A5BDBE87 // 233 543data8 0x3FE4CDF28F10AC46 // 234 544data8 0x3FE4DD49CF994058 // 235 545data8 0x3FE4ECA86E64A683 // 236 546data8 0x3FE503C43CD8EB68 // 237 547data8 0x3FE513356667FC57 // 238 548data8 0x3FE522AE0738A3D7 // 239 549data8 0x3FE5322E26867857 // 240 550data8 0x3FE541B5CB979809 // 241 551data8 0x3FE55144FDBCBD62 // 242 552data8 0x3FE560DBC45153C6 // 243 553data8 0x3FE5707A26BB8C66 // 244 554data8 0x3FE587F60ED5B8FF // 245 555data8 0x3FE597A7977C8F31 // 246 556data8 0x3FE5A760D634BB8A // 247 557data8 0x3FE5B721D295F10E // 248 558data8 0x3FE5C6EA94431EF9 // 249 559data8 0x3FE5D6BB22EA86F5 // 250 560data8 0x3FE5E6938645D38F // 251 561data8 0x3FE5F673C61A2ED1 // 252 562data8 0x3FE6065BEA385926 // 253 563data8 0x3FE6164BFA7CC06B // 254 564data8 0x3FE62643FECF9742 // 255 565// 566// lo parts of ln(1/frcpa(1+i/256)), i=0...255 567data4 0x20E70672 // 0 568data4 0x1F60A5D0 // 1 569data4 0x218EABA0 // 2 570data4 0x21403104 // 3 571data4 0x20E9B54E // 4 572data4 0x21EE1382 // 5 573data4 0x226014E3 // 6 574data4 0x2095E5C9 // 7 575data4 0x228BA9D4 // 8 576data4 0x22932B86 // 9 577data4 0x22608A57 // 10 578data4 0x220209F3 // 11 579data4 0x212882CC // 12 580data4 0x220D46E2 // 13 581data4 0x21FA4C28 // 14 582data4 0x229E5BD9 // 15 583data4 0x228C9838 // 16 584data4 0x2311F954 // 17 585data4 0x221365DF // 18 586data4 0x22BD0CB3 // 19 587data4 0x223D4BB7 // 20 588data4 0x22A71BBE // 21 589data4 0x237DB2FA // 22 590data4 0x23194C9D // 23 591data4 0x22EC639E // 24 592data4 0x2367E669 // 25 593data4 0x232E1D5F // 26 594data4 0x234A639B // 27 595data4 0x2365C0E0 // 28 596data4 0x234646C1 // 29 597data4 0x220CBF9C // 30 598data4 0x22A00FD4 // 31 599data4 0x2306A3F2 // 32 600data4 0x23745A9B // 33 601data4 0x2398D756 // 34 602data4 0x23DD0B6A // 35 603data4 0x23DE338B // 36 604data4 0x23A222DF // 37 605data4 0x223164F8 // 38 606data4 0x23B4E87B // 39 607data4 0x23D6CCB8 // 40 608data4 0x220C2099 // 41 609data4 0x21B86B67 // 42 610data4 0x236D14F1 // 43 611data4 0x225A923F // 44 612data4 0x22748723 // 45 613data4 0x22200D13 // 46 614data4 0x23C296EA // 47 615data4 0x2302AC38 // 48 616data4 0x234B1996 // 49 617data4 0x2385E298 // 50 618data4 0x23175BE5 // 51 619data4 0x2193F482 // 52 620data4 0x23BFEA90 // 53 621data4 0x23D70A0C // 54 622data4 0x231CF30A // 55 623data4 0x235D9E90 // 56 624data4 0x221AD0CB // 57 625data4 0x22FAA08B // 58 626data4 0x23D29A87 // 59 627data4 0x20C4B2FE // 60 628data4 0x2381B8B7 // 61 629data4 0x23F8D9FC // 62 630data4 0x23EAAE7B // 63 631data4 0x2329E8AA // 64 632data4 0x23EC0322 // 65 633data4 0x2357FDCB // 66 634data4 0x2392A9AD // 67 635data4 0x22113B02 // 68 636data4 0x22DEE901 // 69 637data4 0x236A6D14 // 70 638data4 0x2371D33E // 71 639data4 0x2146F005 // 72 640data4 0x23230B06 // 73 641data4 0x22F1C77D // 74 642data4 0x23A89FA3 // 75 643data4 0x231D1241 // 76 644data4 0x244DA96C // 77 645data4 0x23ECBB7D // 78 646data4 0x223E42B4 // 79 647data4 0x23801BC9 // 80 648data4 0x23573263 // 81 649data4 0x227C1158 // 82 650data4 0x237BD749 // 83 651data4 0x21DDBAE9 // 84 652data4 0x23401735 // 85 653data4 0x241D9DEE // 86 654data4 0x23BC88CB // 87 655data4 0x2396D5F1 // 88 656data4 0x23FC89CF // 89 657data4 0x2414F9A2 // 90 658data4 0x2474A0F5 // 91 659data4 0x24354B60 // 92 660data4 0x23C1EB40 // 93 661data4 0x2306DD92 // 94 662data4 0x24353B6B // 95 663data4 0x23CD1701 // 96 664data4 0x237C7A1C // 97 665data4 0x245793AA // 98 666data4 0x24563695 // 99 667data4 0x23C51467 // 100 668data4 0x24476B68 // 101 669data4 0x212585A9 // 102 670data4 0x247B8293 // 103 671data4 0x2446848A // 104 672data4 0x246A53F8 // 105 673data4 0x246E496D // 106 674data4 0x23ED1D36 // 107 675data4 0x2314C258 // 108 676data4 0x233244A7 // 109 677data4 0x245B7AF0 // 110 678data4 0x24247130 // 111 679data4 0x22D67B38 // 112 680data4 0x2449F620 // 113 681data4 0x23BBC8B8 // 114 682data4 0x237D3BA0 // 115 683data4 0x245E8F13 // 116 684data4 0x2435573F // 117 685data4 0x242DE666 // 118 686data4 0x2463BC10 // 119 687data4 0x2466587D // 120 688data4 0x2408144B // 121 689data4 0x2405F0E5 // 122 690data4 0x22381CFF // 123 691data4 0x24154F9B // 124 692data4 0x23A4E96E // 125 693data4 0x24052967 // 126 694data4 0x2406963F // 127 695data4 0x23F7D3CB // 128 696data4 0x2448AFF4 // 129 697data4 0x24657A21 // 130 698data4 0x22FBC230 // 131 699data4 0x243C8DEA // 132 700data4 0x225DC4B7 // 133 701data4 0x23496EBF // 134 702data4 0x237C2B2B // 135 703data4 0x23A4A5B1 // 136 704data4 0x2394E9D1 // 137 705data4 0x244BC950 // 138 706data4 0x23C7448F // 139 707data4 0x2404A1AD // 140 708data4 0x246511D5 // 141 709data4 0x24246526 // 142 710data4 0x23111F57 // 143 711data4 0x22868951 // 144 712data4 0x243EB77F // 145 713data4 0x239F3DFF // 146 714data4 0x23089666 // 147 715data4 0x23EBFA6A // 148 716data4 0x23C51312 // 149 717data4 0x23E1DD5E // 150 718data4 0x232C0944 // 151 719data4 0x246A741F // 152 720data4 0x2414DF8D // 153 721data4 0x247B5546 // 154 722data4 0x2415C980 // 155 723data4 0x24324ABD // 156 724data4 0x234EB5E5 // 157 725data4 0x2465E43E // 158 726data4 0x242840D1 // 159 727data4 0x24444057 // 160 728data4 0x245E56F0 // 161 729data4 0x21AE30F8 // 162 730data4 0x23FB3283 // 163 731data4 0x247A4D07 // 164 732data4 0x22AE314D // 165 733data4 0x246B7727 // 166 734data4 0x24EAD526 // 167 735data4 0x24B41DC9 // 168 736data4 0x24EE8062 // 169 737data4 0x24A0C7C4 // 170 738data4 0x24E8DA67 // 171 739data4 0x231120F7 // 172 740data4 0x24401FFB // 173 741data4 0x2412DD09 // 174 742data4 0x248C131A // 175 743data4 0x24C0A7CE // 176 744data4 0x243DD4C8 // 177 745data4 0x24457FEB // 178 746data4 0x24DEEFBB // 179 747data4 0x243C70AE // 180 748data4 0x23E7A6FA // 181 749data4 0x24C2D311 // 182 750data4 0x23026255 // 183 751data4 0x2437C9B9 // 184 752data4 0x246BA847 // 185 753data4 0x2420B448 // 186 754data4 0x24C4CF5A // 187 755data4 0x242C4981 // 188 756data4 0x24DE1525 // 189 757data4 0x24F5CC33 // 190 758data4 0x235A85DA // 191 759data4 0x24A0B64F // 192 760data4 0x244BA0A4 // 193 761data4 0x24AAF30A // 194 762data4 0x244C86F9 // 195 763data4 0x246D5B82 // 196 764data4 0x24529347 // 197 765data4 0x240DD008 // 198 766data4 0x24E98790 // 199 767data4 0x2489B0CE // 200 768data4 0x22BC29AC // 201 769data4 0x23F37C7A // 202 770data4 0x24987FE8 // 203 771data4 0x22AFE20B // 204 772data4 0x24C8D7C2 // 205 773data4 0x24B28B7D // 206 774data4 0x23B6B271 // 207 775data4 0x24C77CB6 // 208 776data4 0x24EF1DCA // 209 777data4 0x24A4F0AC // 210 778data4 0x24CF113E // 211 779data4 0x2496BBAB // 212 780data4 0x23C7CC8A // 213 781data4 0x23AE3961 // 214 782data4 0x2410A895 // 215 783data4 0x23CE3114 // 216 784data4 0x2308247D // 217 785data4 0x240045E9 // 218 786data4 0x24974F60 // 219 787data4 0x242CB39F // 220 788data4 0x24AB8D69 // 221 789data4 0x23436788 // 222 790data4 0x24305E9E // 223 791data4 0x243E71A9 // 224 792data4 0x23C2A6B3 // 225 793data4 0x23FFE6CF // 226 794data4 0x2322D801 // 227 795data4 0x24515F21 // 228 796data4 0x2412A0D6 // 229 797data4 0x24E60D44 // 230 798data4 0x240D9251 // 231 799data4 0x247076E2 // 232 800data4 0x229B101B // 233 801data4 0x247B12DE // 234 802data4 0x244B9127 // 235 803data4 0x2499EC42 // 236 804data4 0x21FC3963 // 237 805data4 0x23E53266 // 238 806data4 0x24CE102D // 239 807data4 0x23CC45D2 // 240 808data4 0x2333171D // 241 809data4 0x246B3533 // 242 810data4 0x24931129 // 243 811data4 0x24405FFA // 244 812data4 0x24CF464D // 245 813data4 0x237095CD // 246 814data4 0x24F86CBD // 247 815data4 0x24E2D84B // 248 816data4 0x21ACBB44 // 249 817data4 0x24F43A8C // 250 818data4 0x249DB931 // 251 819data4 0x24A385EF // 252 820data4 0x238B1279 // 253 821data4 0x2436213E // 254 822data4 0x24F18A3B // 255 823LOCAL_OBJECT_END(log_data) 824 825 826LOCAL_OBJECT_START(log10_data) 827// coefficients of polynoimal approximation 828data8 0x3FC2494104381A8E // A7 829data8 0xBFC5556D556BBB69 // A6 830// 831// two parts of ln(2)/ln(10) 832data8 0x3FD3441350900000, 0x3DCEF3FDE623E256 833// 834data8 0xDE5BD8A937287195,0x3FFD // 1/ln(10) 835// 836data8 0x3FC999999988B5E9 // A5 837data8 0xBFCFFFFFFFF6FFF5 // A4 838// 839// Hi parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255 840data8 0x3F4BD27045BFD024 // 0 841data8 0x3F64E84E793A474A // 1 842data8 0x3F7175085AB85FF0 // 2 843data8 0x3F787CFF9D9147A5 // 3 844data8 0x3F7EA9D372B89FC8 // 4 845data8 0x3F82DF9D95DA961C // 5 846data8 0x3F866DF172D6372B // 6 847data8 0x3F898D79EF5EEDEF // 7 848data8 0x3F8D22ADF3F9579C // 8 849data8 0x3F9024231D30C398 // 9 850data8 0x3F91F23A98897D49 // 10 851data8 0x3F93881A7B818F9E // 11 852data8 0x3F951F6E1E759E35 // 12 853data8 0x3F96F2BCE7ADC5B4 // 13 854data8 0x3F988D362CDF359E // 14 855data8 0x3F9A292BAF010981 // 15 856data8 0x3F9BC6A03117EB97 // 16 857data8 0x3F9D65967DE3AB08 // 17 858data8 0x3F9F061167FC31E7 // 18 859data8 0x3FA05409E4F7819B // 19 860data8 0x3FA125D0432EA20D // 20 861data8 0x3FA1F85D440D299B // 21 862data8 0x3FA2AD755749617C // 22 863data8 0x3FA381772A00E603 // 23 864data8 0x3FA45643E165A70A // 24 865data8 0x3FA52BDD034475B8 // 25 866data8 0x3FA5E3966B7E9295 // 26 867data8 0x3FA6BAAF47C5B244 // 27 868data8 0x3FA773B3E8C4F3C7 // 28 869data8 0x3FA84C51EBEE8D15 // 29 870data8 0x3FA906A6786FC1CA // 30 871data8 0x3FA9C197ABF00DD6 // 31 872data8 0x3FAA9C78712191F7 // 32 873data8 0x3FAB58C09C8D637C // 33 874data8 0x3FAC15A8BCDD7B7E // 34 875data8 0x3FACD331E2C2967B // 35 876data8 0x3FADB11ED766ABF4 // 36 877data8 0x3FAE70089346A9E6 // 37 878data8 0x3FAF2F96C6754AED // 38 879data8 0x3FAFEFCA8D451FD5 // 39 880data8 0x3FB0585283764177 // 40 881data8 0x3FB0B913AAC7D3A6 // 41 882data8 0x3FB11A294F2569F5 // 42 883data8 0x3FB16B51A2696890 // 43 884data8 0x3FB1CD03ADACC8BD // 44 885data8 0x3FB22F0BDD7745F5 // 45 886data8 0x3FB2916ACA38D1E7 // 46 887data8 0x3FB2F4210DF7663C // 47 888data8 0x3FB346A6C3C49065 // 48 889data8 0x3FB3A9FEBC605409 // 49 890data8 0x3FB3FD0C10A3AA54 // 50 891data8 0x3FB46107D3540A81 // 51 892data8 0x3FB4C55DD16967FE // 52 893data8 0x3FB51940330C000A // 53 894data8 0x3FB56D620EE7115E // 54 895data8 0x3FB5D2ABCF26178D // 55 896data8 0x3FB6275AA5DEBF81 // 56 897data8 0x3FB68D4EAF26D7EE // 57 898data8 0x3FB6E28C5C54A28D // 58 899data8 0x3FB7380B9665B7C7 // 59 900data8 0x3FB78DCCC278E85B // 60 901data8 0x3FB7F50C2CF25579 // 61 902data8 0x3FB84B5FD5EAEFD7 // 62 903data8 0x3FB8A1F6BAB2B226 // 63 904data8 0x3FB8F8D144557BDF // 64 905data8 0x3FB94FEFDCD61D92 // 65 906data8 0x3FB9A752EF316149 // 66 907data8 0x3FB9FEFAE7611EDF // 67 908data8 0x3FBA56E8325F5C86 // 68 909data8 0x3FBAAF1B3E297BB3 // 69 910data8 0x3FBB079479C372AC // 70 911data8 0x3FBB6054553B12F7 // 71 912data8 0x3FBBB95B41AB5CE5 // 72 913data8 0x3FBC12A9B13FE079 // 73 914data8 0x3FBC6C4017382BEA // 74 915data8 0x3FBCB41FBA42686C // 75 916data8 0x3FBD0E38CE73393E // 76 917data8 0x3FBD689B2193F132 // 77 918data8 0x3FBDC3472B1D285F // 78 919data8 0x3FBE0C06300D528B // 79 920data8 0x3FBE6738190E394B // 80 921data8 0x3FBEC2B50D208D9A // 81 922data8 0x3FBF0C1C2B936827 // 82 923data8 0x3FBF68216C9CC726 // 83 924data8 0x3FBFB1F6381856F3 // 84 925data8 0x3FC00742AF4CE5F8 // 85 926data8 0x3FC02C64906512D2 // 86 927data8 0x3FC05AF1E63E03B4 // 87 928data8 0x3FC0804BEA723AA8 // 88 929data8 0x3FC0AF1FD6711526 // 89 930data8 0x3FC0D4B2A88059FF // 90 931data8 0x3FC0FA5EF136A06C // 91 932data8 0x3FC1299A4FB3E305 // 92 933data8 0x3FC14F806253C3EC // 93 934data8 0x3FC175805D1587C1 // 94 935data8 0x3FC19B9A637CA294 // 95 936data8 0x3FC1CB5FC26EDE16 // 96 937data8 0x3FC1F1B4E65F2590 // 97 938data8 0x3FC218248B5DC3E5 // 98 939data8 0x3FC23EAED62ADC76 // 99 940data8 0x3FC26553EBD337BC // 100 941data8 0x3FC28C13F1B118FF // 101 942data8 0x3FC2BCAA14381385 // 102 943data8 0x3FC2E3A740B7800E // 103 944data8 0x3FC30ABFD8F333B6 // 104 945data8 0x3FC331F403985096 // 105 946data8 0x3FC35943E7A6068F // 106 947data8 0x3FC380AFAC6E7C07 // 107 948data8 0x3FC3A8377997B9E5 // 108 949data8 0x3FC3CFDB771C9ADB // 109 950data8 0x3FC3EDA90D39A5DE // 110 951data8 0x3FC4157EC09505CC // 111 952data8 0x3FC43D7113FB04C0 // 112 953data8 0x3FC4658030AD1CCE // 113 954data8 0x3FC48DAC404638F5 // 114 955data8 0x3FC4B5F56CBBB869 // 115 956data8 0x3FC4DE5BE05E7582 // 116 957data8 0x3FC4FCBC0776FD85 // 117 958data8 0x3FC525561E9256EE // 118 959data8 0x3FC54E0DF3198865 // 119 960data8 0x3FC56CAB7112BDE2 // 120 961data8 0x3FC59597BA735B15 // 121 962data8 0x3FC5BEA23A506FD9 // 122 963data8 0x3FC5DD7E08DE382E // 123 964data8 0x3FC606BDD3F92355 // 124 965data8 0x3FC6301C518A501E // 125 966data8 0x3FC64F3770618915 // 126 967data8 0x3FC678CC14C1E2D7 // 127 968data8 0x3FC6981005ED2947 // 128 969data8 0x3FC6C1DB5F9BB335 // 129 970data8 0x3FC6E1488ECD2880 // 130 971data8 0x3FC70B4B2E7E41B8 // 131 972data8 0x3FC72AE209146BF8 // 132 973data8 0x3FC7551C81BD8DCF // 133 974data8 0x3FC774DD76CC43BD // 134 975data8 0x3FC79F505DB00E88 // 135 976data8 0x3FC7BF3BDE099F30 // 136 977data8 0x3FC7E9E7CAC437F8 // 137 978data8 0x3FC809FE4902D00D // 138 979data8 0x3FC82A2757995CBD // 139 980data8 0x3FC85525C625E098 // 140 981data8 0x3FC8757A79831887 // 141 982data8 0x3FC895E2058D8E02 // 142 983data8 0x3FC8C13437695531 // 143 984data8 0x3FC8E1C812EF32BE // 144 985data8 0x3FC9026F112197E8 // 145 986data8 0x3FC923294888880A // 146 987data8 0x3FC94EEA4B8334F2 // 147 988data8 0x3FC96FD1B639FC09 // 148 989data8 0x3FC990CCA66229AB // 149 990data8 0x3FC9B1DB33334842 // 150 991data8 0x3FC9D2FD740E6606 // 151 992data8 0x3FC9FF49EEDCB553 // 152 993data8 0x3FCA209A84FBCFF7 // 153 994data8 0x3FCA41FF1E43F02B // 154 995data8 0x3FCA6377D2CE9377 // 155 996data8 0x3FCA8504BAE0D9F5 // 156 997data8 0x3FCAA6A5EEEBEFE2 // 157 998data8 0x3FCAC85B878D7878 // 158 999data8 0x3FCAEA259D8FFA0B // 159 1000data8 0x3FCB0C0449EB4B6A // 160 1001data8 0x3FCB2DF7A5C50299 // 161 1002data8 0x3FCB4FFFCA70E4D1 // 162 1003data8 0x3FCB721CD17157E2 // 163 1004data8 0x3FCB944ED477D4EC // 164 1005data8 0x3FCBB695ED655C7C // 165 1006data8 0x3FCBD8F2364AEC0F // 166 1007data8 0x3FCBFB63C969F4FF // 167 1008data8 0x3FCC1DEAC134D4E9 // 168 1009data8 0x3FCC4087384F4F80 // 169 1010data8 0x3FCC6339498F09E1 // 170 1011data8 0x3FCC86010FFC076B // 171 1012data8 0x3FCC9D3D065C5B41 // 172 1013data8 0x3FCCC029375BA079 // 173 1014data8 0x3FCCE32B66978BA4 // 174 1015data8 0x3FCD0643AFD51404 // 175 1016data8 0x3FCD29722F0DEA45 // 176 1017data8 0x3FCD4CB70070FE43 // 177 1018data8 0x3FCD6446AB3F8C95 // 178 1019data8 0x3FCD87B0EF71DB44 // 179 1020data8 0x3FCDAB31D1FE99A6 // 180 1021data8 0x3FCDCEC96FDC888E // 181 1022data8 0x3FCDE69088763579 // 182 1023data8 0x3FCE0A4E4A25C1FF // 183 1024data8 0x3FCE2E2315755E32 // 184 1025data8 0x3FCE461322D1648A // 185 1026data8 0x3FCE6A0E95C7787B // 186 1027data8 0x3FCE8E216243DD60 // 187 1028data8 0x3FCEA63AF26E007C // 188 1029data8 0x3FCECA74ED15E0B7 // 189 1030data8 0x3FCEEEC692CCD259 // 190 1031data8 0x3FCF070A36B8D9C0 // 191 1032data8 0x3FCF2B8393E34A2D // 192 1033data8 0x3FCF5014EF538A5A // 193 1034data8 0x3FCF68833AF1B17F // 194 1035data8 0x3FCF8D3CD9F3F04E // 195 1036data8 0x3FCFA5C61ADD93E9 // 196 1037data8 0x3FCFCAA8567EBA79 // 197 1038data8 0x3FCFE34CC8743DD8 // 198 1039data8 0x3FD0042BFD74F519 // 199 1040data8 0x3FD016BDF6A18017 // 200 1041data8 0x3FD023262F907322 // 201 1042data8 0x3FD035CCED8D32A1 // 202 1043data8 0x3FD042430E869FFB // 203 1044data8 0x3FD04EBEC842B2DF // 204 1045data8 0x3FD06182E84FD4AB // 205 1046data8 0x3FD06E0CB609D383 // 206 1047data8 0x3FD080E60BEC8F12 // 207 1048data8 0x3FD08D7E0D894735 // 208 1049data8 0x3FD0A06CC96A2055 // 209 1050data8 0x3FD0AD131F3B3C55 // 210 1051data8 0x3FD0C01771E775FB // 211 1052data8 0x3FD0CCCC3CAD6F4B // 212 1053data8 0x3FD0D986D91A34A8 // 213 1054data8 0x3FD0ECA9B8861A2D // 214 1055data8 0x3FD0F972F87FF3D5 // 215 1056data8 0x3FD106421CF0E5F7 // 216 1057data8 0x3FD11983EBE28A9C // 217 1058data8 0x3FD12661E35B7859 // 218 1059data8 0x3FD13345D2779D3B // 219 1060data8 0x3FD146A6F597283A // 220 1061data8 0x3FD15399E81EA83D // 221 1062data8 0x3FD16092E5D3A9A6 // 222 1063data8 0x3FD17413C3B7AB5D // 223 1064data8 0x3FD1811BF629D6FA // 224 1065data8 0x3FD18E2A47B46685 // 225 1066data8 0x3FD19B3EBE1A4418 // 226 1067data8 0x3FD1AEE9017CB450 // 227 1068data8 0x3FD1BC0CED7134E1 // 228 1069data8 0x3FD1C93712ABC7FF // 229 1070data8 0x3FD1D66777147D3E // 230 1071data8 0x3FD1EA3BD1286E1C // 231 1072data8 0x3FD1F77BED932C4C // 232 1073data8 0x3FD204C25E1B031F // 233 1074data8 0x3FD2120F28CE69B1 // 234 1075data8 0x3FD21F6253C48D00 // 235 1076data8 0x3FD22CBBE51D60A9 // 236 1077data8 0x3FD240CE4C975444 // 237 1078data8 0x3FD24E37F8ECDAE7 // 238 1079data8 0x3FD25BA8215AF7FC // 239 1080data8 0x3FD2691ECC29F042 // 240 1081data8 0x3FD2769BFFAB2DFF // 241 1082data8 0x3FD2841FC23952C9 // 242 1083data8 0x3FD291AA1A384978 // 243 1084data8 0x3FD29F3B0E15584A // 244 1085data8 0x3FD2B3A0EE479DF7 // 245 1086data8 0x3FD2C142842C09E5 // 246 1087data8 0x3FD2CEEACCB7BD6C // 247 1088data8 0x3FD2DC99CE82FF20 // 248 1089data8 0x3FD2EA4F902FD7D9 // 249 1090data8 0x3FD2F80C186A25FC // 250 1091data8 0x3FD305CF6DE7B0F6 // 251 1092data8 0x3FD3139997683CE7 // 252 1093data8 0x3FD3216A9BB59E7C // 253 1094data8 0x3FD32F4281A3CEFE // 254 1095data8 0x3FD33D2150110091 // 255 1096// 1097// Lo parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255 1098data4 0x1FB0EB5A // 0 1099data4 0x206E5EE3 // 1 1100data4 0x208F3609 // 2 1101data4 0x2070EB03 // 3 1102data4 0x1F314BAE // 4 1103data4 0x217A889D // 5 1104data4 0x21E63650 // 6 1105data4 0x21C2F4A3 // 7 1106data4 0x2192A10C // 8 1107data4 0x1F84B73E // 9 1108data4 0x2243FBCA // 10 1109data4 0x21BD9C51 // 11 1110data4 0x213C542B // 12 1111data4 0x21047386 // 13 1112data4 0x21217D8F // 14 1113data4 0x226791B7 // 15 1114data4 0x204CCE66 // 16 1115data4 0x2234CE9F // 17 1116data4 0x220675E2 // 18 1117data4 0x22B8E5BA // 19 1118data4 0x22C12D14 // 20 1119data4 0x211D41F0 // 21 1120data4 0x228507F3 // 22 1121data4 0x22F7274B // 23 1122data4 0x22A7FDD1 // 24 1123data4 0x2244A06E // 25 1124data4 0x215DCE69 // 26 1125data4 0x22F5C961 // 27 1126data4 0x22EBEF29 // 28 1127data4 0x222A2CB6 // 29 1128data4 0x22B9FE00 // 30 1129data4 0x22E79EB7 // 31 1130data4 0x222F9607 // 32 1131data4 0x2189D87F // 33 1132data4 0x2236DB45 // 34 1133data4 0x22ED77FB // 35 1134data4 0x21CB70F0 // 36 1135data4 0x21B8ACE8 // 37 1136data4 0x22EC58C1 // 38 1137data4 0x22CFCC1C // 39 1138data4 0x2343E77A // 40 1139data4 0x237FBC7F // 41 1140data4 0x230D472E // 42 1141data4 0x234686FB // 43 1142data4 0x23770425 // 44 1143data4 0x223977EC // 45 1144data4 0x2345800A // 46 1145data4 0x237BC351 // 47 1146data4 0x23191502 // 48 1147data4 0x232BAC12 // 49 1148data4 0x22692421 // 50 1149data4 0x234D409D // 51 1150data4 0x22EC3214 // 52 1151data4 0x2376C916 // 53 1152data4 0x22B00DD1 // 54 1153data4 0x2309D910 // 55 1154data4 0x22F925FD // 56 1155data4 0x22A63A7B // 57 1156data4 0x2106264A // 58 1157data4 0x234227F9 // 59 1158data4 0x1ECB1978 // 60 1159data4 0x23460A62 // 61 1160data4 0x232ED4B1 // 62 1161data4 0x226DDC38 // 63 1162data4 0x1F101A73 // 64 1163data4 0x21B1F82B // 65 1164data4 0x22752F19 // 66 1165data4 0x2320BC15 // 67 1166data4 0x236EEC5E // 68 1167data4 0x23404D3E // 69 1168data4 0x2304C517 // 70 1169data4 0x22F7441A // 71 1170data4 0x230D3D7A // 72 1171data4 0x2264A9DF // 73 1172data4 0x22410CC8 // 74 1173data4 0x2342CCCB // 75 1174data4 0x23560BD4 // 76 1175data4 0x237BBFFE // 77 1176data4 0x2373A206 // 78 1177data4 0x22C871B9 // 79 1178data4 0x2354B70C // 80 1179data4 0x232EDB33 // 81 1180data4 0x235DB680 // 82 1181data4 0x230EF422 // 83 1182data4 0x235316CA // 84 1183data4 0x22EEEE8B // 85 1184data4 0x2375C88C // 86 1185data4 0x235ABD21 // 87 1186data4 0x23A0D232 // 88 1187data4 0x23F5FFB5 // 89 1188data4 0x23D3CEC8 // 90 1189data4 0x22A92204 // 91 1190data4 0x238C64DF // 92 1191data4 0x23B82896 // 93 1192data4 0x22D633B8 // 94 1193data4 0x23861E93 // 95 1194data4 0x23CB594B // 96 1195data4 0x2330387E // 97 1196data4 0x21CD4702 // 98 1197data4 0x2284C505 // 99 1198data4 0x23D6995C // 100 1199data4 0x23F6C807 // 101 1200data4 0x239CEF5C // 102 1201data4 0x239442B0 // 103 1202data4 0x22B35EE5 // 104 1203data4 0x2391E9A4 // 105 1204data4 0x23A390F5 // 106 1205data4 0x2349AC9C // 107 1206data4 0x23FA5535 // 108 1207data4 0x21E3A46A // 109 1208data4 0x23B44ABA // 110 1209data4 0x23CEA8E0 // 111 1210data4 0x23F647DC // 112 1211data4 0x2390D1A8 // 113 1212data4 0x23D0CFA2 // 114 1213data4 0x236E0872 // 115 1214data4 0x23B88B91 // 116 1215data4 0x2283C359 // 117 1216data4 0x232F647F // 118 1217data4 0x23122CD7 // 119 1218data4 0x232CF564 // 120 1219data4 0x232630FD // 121 1220data4 0x23BEE1C8 // 122 1221data4 0x23B2BD30 // 123 1222data4 0x2301F1C0 // 124 1223data4 0x23CE4D67 // 125 1224data4 0x23A353C9 // 126 1225data4 0x238086E8 // 127 1226data4 0x22D0D29E // 128 1227data4 0x23A3B3C8 // 129 1228data4 0x23F69F4B // 130 1229data4 0x23EA3C21 // 131 1230data4 0x23951C88 // 132 1231data4 0x2372AFFC // 133 1232data4 0x23A6D1A8 // 134 1233data4 0x22BBBAF4 // 135 1234data4 0x227FA3DD // 136 1235data4 0x23804D9B // 137 1236data4 0x232D771F // 138 1237data4 0x239CB57B // 139 1238data4 0x2303CF34 // 140 1239data4 0x22218C2A // 141 1240data4 0x23991BEE // 142 1241data4 0x23EB3596 // 143 1242data4 0x230487FA // 144 1243data4 0x2135DF4C // 145 1244data4 0x2380FD2D // 146 1245data4 0x23EB75E9 // 147 1246data4 0x211C62C8 // 148 1247data4 0x23F518F1 // 149 1248data4 0x23FEF882 // 150 1249data4 0x239097C7 // 151 1250data4 0x223E2BDA // 152 1251data4 0x23988F89 // 153 1252data4 0x22E4A4AD // 154 1253data4 0x23F03D9C // 155 1254data4 0x23F5018F // 156 1255data4 0x23E1E250 // 157 1256data4 0x23FD3D90 // 158 1257data4 0x22DEE2FF // 159 1258data4 0x238342AB // 160 1259data4 0x22E6736F // 161 1260data4 0x233AFC28 // 162 1261data4 0x2395F661 // 163 1262data4 0x23D8B991 // 164 1263data4 0x23CD58D5 // 165 1264data4 0x21941FD6 // 166 1265data4 0x23352915 // 167 1266data4 0x235D09EE // 168 1267data4 0x22DC7EF9 // 169 1268data4 0x238BC9F3 // 170 1269data4 0x2397DF8F // 171 1270data4 0x2380A7BB // 172 1271data4 0x23EFF48C // 173 1272data4 0x21E67408 // 174 1273data4 0x236420F7 // 175 1274data4 0x22C8DFB5 // 176 1275data4 0x239B5D35 // 177 1276data4 0x23BDC09D // 178 1277data4 0x239E822C // 179 1278data4 0x23984F0A // 180 1279data4 0x23EF2119 // 181 1280data4 0x23F738B8 // 182 1281data4 0x23B66187 // 183 1282data4 0x23B06AD7 // 184 1283data4 0x2369140F // 185 1284data4 0x218DACE6 // 186 1285data4 0x21DF23F1 // 187 1286data4 0x235D8B34 // 188 1287data4 0x23460333 // 189 1288data4 0x23F11D62 // 190 1289data4 0x23C37147 // 191 1290data4 0x22B2AE2A // 192 1291data4 0x23949211 // 193 1292data4 0x23B69799 // 194 1293data4 0x23DBEC75 // 195 1294data4 0x229A6FB3 // 196 1295data4 0x23FC6C60 // 197 1296data4 0x22D01FFC // 198 1297data4 0x235985F0 // 199 1298data4 0x23F7ECA5 // 200 1299data4 0x23F924D3 // 201 1300data4 0x2381B92F // 202 1301data4 0x243A0FBE // 203 1302data4 0x24712D72 // 204 1303data4 0x24594E2F // 205 1304data4 0x220CD12A // 206 1305data4 0x23D87FB0 // 207 1306data4 0x2338288A // 208 1307data4 0x242BB2CC // 209 1308data4 0x220F6265 // 210 1309data4 0x23BB7FE3 // 211 1310data4 0x2301C0A2 // 212 1311data4 0x246709AB // 213 1312data4 0x23A619E2 // 214 1313data4 0x24030E3B // 215 1314data4 0x233C36CC // 216 1315data4 0x241AAB77 // 217 1316data4 0x243D41A3 // 218 1317data4 0x23834A60 // 219 1318data4 0x236AC7BF // 220 1319data4 0x23B6D597 // 221 1320data4 0x210E9474 // 222 1321data4 0x242156E6 // 223 1322data4 0x243A1D68 // 224 1323data4 0x2472187C // 225 1324data4 0x23834E86 // 226 1325data4 0x23CA0807 // 227 1326data4 0x24745887 // 228 1327data4 0x23E2B0E1 // 229 1328data4 0x2421EB67 // 230 1329data4 0x23DCC64E // 231 1330data4 0x22DF71D1 // 232 1331data4 0x238D5ECA // 233 1332data4 0x23CDE86F // 234 1333data4 0x24131F45 // 235 1334data4 0x240FE4E2 // 236 1335data4 0x2317731A // 237 1336data4 0x24015C76 // 238 1337data4 0x2301A4E8 // 239 1338data4 0x23E52A6D // 240 1339data4 0x247D8A0D // 241 1340data4 0x23DFEEBA // 242 1341data4 0x22139FEC // 243 1342data4 0x2454A112 // 244 1343data4 0x23C21E28 // 245 1344data4 0x2460D813 // 246 1345data4 0x24258924 // 247 1346data4 0x2425680F // 248 1347data4 0x24194D1E // 249 1348data4 0x24242C2F // 250 1349data4 0x243DDE5E // 251 1350data4 0x23DEB388 // 252 1351data4 0x23E0E6EB // 253 1352data4 0x24393E74 // 254 1353data4 0x241B1863 // 255 1354LOCAL_OBJECT_END(log10_data) 1355 1356 1357 1358// Code 1359//============================================================== 1360 1361// log has p13 true, p14 false 1362// log10 has p14 true, p13 false 1363 1364.section .text 1365GLOBAL_IEEE754_ENTRY(log10) 1366{ .mfi 1367 getf.exp GR_Exp = f8 // if x is unorm then must recompute 1368 frcpa.s1 FR_RcpX,p0 = f1,f8 1369 mov GR_05 = 0xFFFE // biased exponent of A2=0.5 1370} 1371{ .mlx 1372 addl GR_ad_1 = @ltoff(log10_data),gp 1373 movl GR_A3 = 0x3fd5555555555557 // double precision memory 1374 // representation of A3 1375};; 1376 1377{ .mfi 1378 getf.sig GR_Sig = f8 // get significand to calculate index 1379 fclass.m p8,p0 = f8,9 // is x positive unorm? 1380 mov GR_xorg = 0x3fefe // double precision memory msb of 255/256 1381} 1382{ .mib 1383 ld8 GR_ad_1 = [GR_ad_1] 1384 cmp.eq p14,p13 = r0,r0 // set p14 to 1 for log10 1385 br.cond.sptk log_log10_common 1386};; 1387GLOBAL_IEEE754_END(log10) 1388libm_alias_double_other (__log10, log10) 1389 1390 1391GLOBAL_IEEE754_ENTRY(log) 1392{ .mfi 1393 getf.exp GR_Exp = f8 // if x is unorm then must recompute 1394 frcpa.s1 FR_RcpX,p0 = f1,f8 1395 mov GR_05 = 0xfffe 1396} 1397{ .mlx 1398 addl GR_ad_1 = @ltoff(log_data),gp 1399 movl GR_A3 = 0x3fd5555555555557 // double precision memory 1400 // representation of A3 1401};; 1402 1403{ .mfi 1404 getf.sig GR_Sig = f8 // get significand to calculate index 1405 fclass.m p8,p0 = f8,9 // is x positive unorm? 1406 mov GR_xorg = 0x3fefe // double precision memory msb of 255/256 1407} 1408{ .mfi 1409 ld8 GR_ad_1 = [GR_ad_1] 1410 nop.f 0 1411 cmp.eq p13,p14 = r0,r0 // set p13 to 1 for log 1412};; 1413 1414log_log10_common: 1415{ .mfi 1416 getf.d GR_x = f8 // double precision memory representation of x 1417 fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? 1418 dep.z GR_dx = 3, 44, 2 // Create 0x0000300000000000 1419 // Difference between double precision 1420 // memory representations of 257/256 and 1421 // 255/256 1422} 1423{ .mfi 1424 setf.exp FR_A2 = GR_05 // create A2 1425 fnorm.s1 FR_NormX = f8 1426 mov GR_bias = 0xffff 1427};; 1428 1429{ .mfi 1430 setf.d FR_A3 = GR_A3 // create A3 1431 fcmp.eq.s1 p12,p0 = f1,f8 // is x equal to 1.0? 1432 dep.z GR_xorg = GR_xorg, 44, 19 // 0x3fefe00000000000 1433 // double precision memory 1434 // representation of 255/256 1435} 1436{ .mib 1437 add GR_ad_2 = 0x30,GR_ad_1 // address of A5,A4 1438 add GR_ad_3 = 0x840,GR_ad_1 // address of ln(1/frcpa) lo parts 1439(p8) br.cond.spnt log_positive_unorms 1440};; 1441 1442log_core: 1443{ .mfi 1444 ldfpd FR_A7,FR_A6 = [GR_ad_1],16 1445 fclass.m p10,p0 = f8,0x3A // is x < 0? 1446 sub GR_Nm1 = GR_Exp,GR_05 // unbiased_exponent_of_x - 1 1447} 1448{ .mfi 1449 ldfpd FR_A5,FR_A4 = [GR_ad_2],16 1450(p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag 1451 sub GR_N = GR_Exp,GR_bias // unbiased_exponent_of_x 1452};; 1453 1454{ .mfi 1455 setf.sig FR_N = GR_N // copy unbiased exponent of x to significand 1456 fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256 1457 extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index 1458} 1459{ .mib 1460 sub GR_x = GR_x, GR_xorg // get diff between x and 255/256 1461 cmp.gtu p6, p7 = 2, GR_Nm1 // p6 true if 0.5 <= x < 2 1462(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf 1463};; 1464 1465{ .mfi 1466 ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16 1467 fclass.m p11,p0 = f8,0x07 // is x = 0? 1468 shladd GR_ad_3 = GR_Ind,2,GR_ad_3 // address of Tlo 1469} 1470{ .mib 1471 shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi 1472(p6) cmp.leu p6, p7 = GR_x, GR_dx // 255/256 <= x <= 257/256 1473(p10) br.cond.spnt log_negatives // jump if x is negative 1474};; 1475 1476// p6 is true if |x-1| < 1/256 1477// p7 is true if |x-1| >= 1/256 1478{ .mfi 1479 ldfd FR_Thi = [GR_ad_2] 1480(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256 1481 nop.i 0 1482};; 1483 1484{ .mmi 1485(p7) ldfs FR_Tlo = [GR_ad_3] 1486 nop.m 0 1487 nop.i 0 1488} 1489{ .mfb 1490 nop.m 0 1491(p12) fma.d.s0 f8 = f0,f0,f0 1492(p12) br.ret.spnt b0 // exit for +1.0 1493};; 1494 1495.pred.rel "mutex",p6,p7 1496{ .mfi 1497(p6) mov GR_NearOne = 1 1498 fms.s1 FR_A32 = FR_A3,FR_r,FR_A2 // A3*r-A2 1499(p7) mov GR_NearOne = 0 1500} 1501{ .mfb 1502 ldfe FR_InvLn10 = [GR_ad_1],16 1503 fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 1504(p11) br.cond.spnt log_zeroes // jump if x is zero 1505};; 1506 1507{ .mfi 1508 nop.m 0 1509 fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6 1510 nop.i 0 1511} 1512{ .mfi 1513(p7) cmp.eq.unc p9,p0 = r0,r0 // set p9 if |x-1| > 1/256 1514 fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4 1515(p14) cmp.eq.unc p8,p0 = 1,GR_NearOne // set p8 to 1 if it's log10 1516 // and argument near 1.0 1517};; 1518 1519{ .mfi 1520(p6) getf.exp GR_rexp = FR_r // Get signexp of x-1 1521(p7) fcvt.xf FR_N = FR_N 1522(p8) cmp.eq p9,p6 = r0,r0 // Also set p9 and clear p6 if log10 1523 // and arg near 1 1524};; 1525 1526{ .mfi 1527 nop.m 0 1528 fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4 1529 nop.i 0 1530} 1531{ .mfi 1532 nop.m 0 1533(p8) fma.s1 FR_NxLn2pT = f0,f0,f0 // Clear NxLn2pT if log10 near 1 1534 nop.i 0 1535};; 1536 1537{ .mfi 1538 nop.m 0 1539 // (A3*r+A2)*r^2+r 1540 fma.s1 FR_A321 = FR_A32,FR_r2,FR_r 1541 mov GR_mask = 0x1ffff 1542} 1543{ .mfi 1544 nop.m 0 1545 // (A7*r+A6)*r^2+(A5*r+A4) 1546 fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4 1547 nop.i 0 1548};; 1549 1550{ .mfi 1551(p6) and GR_rexp = GR_rexp, GR_mask 1552 // N*Ln2hi+Thi 1553(p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi 1554 nop.i 0 1555} 1556{ .mfi 1557 nop.m 0 1558 // N*Ln2lo+Tlo 1559(p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo 1560 nop.i 0 1561};; 1562 1563{ .mfi 1564(p6) sub GR_rexp = GR_rexp, GR_bias // unbiased exponent of x-1 1565(p9) fma.s1 f8 = FR_A4,FR_r4,FR_A321 // P(r) if |x-1| >= 1/256 or 1566 // log10 and |x-1| < 1/256 1567 nop.i 0 1568} 1569{ .mfi 1570 nop.m 0 1571 // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo) 1572(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo 1573 nop.i 0 1574};; 1575 1576{ .mfi 1577(p6) cmp.gt.unc p10, p6 = -40, GR_rexp // Test |x-1| < 2^-40 1578 nop.f 0 1579 nop.i 0 1580};; 1581 1582{ .mfi 1583 nop.m 0 1584(p10) fma.d.s0 f8 = FR_A32,FR_r2,FR_r // log(x) if |x-1| < 2^-40 1585 nop.i 0 1586};; 1587 1588.pred.rel "mutex",p6,p9 1589{ .mfi 1590 nop.m 0 1591(p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A321 // log(x) if 2^-40 <= |x-1| < 1/256 1592 nop.i 0 1593} 1594{ .mfb 1595 nop.m 0 1596(p9) fma.d.s0 f8 = f8,FR_InvLn10,FR_NxLn2pT // result if |x-1| >= 1/256 1597 // or log10 and |x-1| < 1/256 1598 br.ret.sptk b0 1599};; 1600 1601.align 32 1602log_positive_unorms: 1603{ .mmf 1604 getf.exp GR_Exp = FR_NormX // recompute biased exponent 1605 getf.d GR_x = FR_NormX // recompute double precision x 1606 fcmp.eq.s1 p12,p0 = f1,FR_NormX // is x equal to 1.0? 1607};; 1608 1609{ .mfb 1610 getf.sig GR_Sig = FR_NormX // recompute significand 1611 fcmp.eq.s0 p15, p0 = f8, f0 // set denormal flag 1612 br.cond.sptk log_core 1613};; 1614 1615.align 32 1616log_zeroes: 1617{ .mfi 1618 nop.m 0 1619 fmerge.s FR_X = f8,f8 // keep input argument for subsequent 1620 // call of __libm_error_support# 1621 nop.i 0 1622} 1623{ .mfi 1624 nop.m 0 1625 fms.s1 FR_tmp = f0,f0,f1 // -1.0 1626 nop.i 0 1627};; 1628 1629.pred.rel "mutex",p13,p14 1630{ .mfi 1631(p13) mov GR_TAG = 2 // set libm error in case of log 1632 frcpa.s0 f8,p0 = FR_tmp,f0 // log(+/-0) should be equal to -INF. 1633 // We can get it using frcpa because it 1634 // sets result to the IEEE-754 mandated 1635 // quotient of FR_tmp/f0. 1636 // As far as FR_tmp is -1 it'll be -INF 1637 nop.i 0 1638} 1639{ .mib 1640(p14) mov GR_TAG = 8 // set libm error in case of log10 1641 nop.i 0 1642 br.cond.sptk log_libm_err 1643};; 1644 1645.align 32 1646log_negatives: 1647{ .mfi 1648 nop.m 0 1649 fmerge.s FR_X = f8,f8 1650 nop.i 0 1651};; 1652 1653.pred.rel "mutex",p13,p14 1654{ .mfi 1655(p13) mov GR_TAG = 3 // set libm error in case of log 1656 frcpa.s0 f8,p0 = f0,f0 // log(negatives) should be equal to NaN. 1657 // We can get it using frcpa because it 1658 // sets result to the IEEE-754 mandated 1659 // quotient of f0/f0 i.e. NaN. 1660(p14) mov GR_TAG = 9 // set libm error in case of log10 1661};; 1662 1663.align 32 1664log_libm_err: 1665{ .mmi 1666 alloc r32 = ar.pfs,1,4,4,0 1667 mov GR_Parameter_TAG = GR_TAG 1668 nop.i 0 1669};; 1670GLOBAL_IEEE754_END(log) 1671libm_alias_double_other (__log, log) 1672#ifdef SHARED 1673.symver log,log@@GLIBC_2.29 1674.weak __log_compat 1675.set __log_compat,__log 1676.symver __log_compat,log@GLIBC_2.2 1677#endif 1678 1679 1680LOCAL_LIBM_ENTRY(__libm_error_region) 1681.prologue 1682{ .mfi 1683 add GR_Parameter_Y = -32,sp // Parameter 2 value 1684 nop.f 0 1685.save ar.pfs,GR_SAVE_PFS 1686 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs 1687} 1688{ .mfi 1689.fframe 64 1690 add sp = -64,sp // Create new stack 1691 nop.f 0 1692 mov GR_SAVE_GP = gp // Save gp 1693};; 1694 1695{ .mmi 1696 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack 1697 add GR_Parameter_X = 16,sp // Parameter 1 address 1698.save b0, GR_SAVE_B0 1699 mov GR_SAVE_B0 = b0 // Save b0 1700};; 1701 1702.body 1703{ .mib 1704 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack 1705 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 1706 nop.b 0 1707} 1708{ .mib 1709 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack 1710 add GR_Parameter_Y = -16,GR_Parameter_Y 1711 br.call.sptk b0=__libm_error_support# // Call error handling function 1712};; 1713 1714{ .mmi 1715 add GR_Parameter_RESULT = 48,sp 1716 nop.m 0 1717 nop.i 0 1718};; 1719 1720{ .mmi 1721 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack 1722.restore sp 1723 add sp = 64,sp // Restore stack pointer 1724 mov b0 = GR_SAVE_B0 // Restore return address 1725};; 1726 1727{ .mib 1728 mov gp = GR_SAVE_GP // Restore gp 1729 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 1730 br.ret.sptk b0 // Return 1731};; 1732LOCAL_LIBM_END(__libm_error_region) 1733 1734.type __libm_error_support#,@function 1735.global __libm_error_support# 1736