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Diffstat (limited to 'sysdeps/ia64/fpu/e_log.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_log.S | 1728 |
1 files changed, 1728 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_log.S b/sysdeps/ia64/fpu/e_log.S new file mode 100644 index 0000000000..50eed956da --- /dev/null +++ b/sysdeps/ia64/fpu/e_log.S @@ -0,0 +1,1728 @@ +.file "log.s" + + +// Copyright (c) 2000 - 2005, Intel Corporation +// All rights reserved. +// +// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 02/02/00 Initial version +// 04/04/00 Unwind support added +// 06/16/00 Updated table to be rounded correctly +// 08/15/00 Bundle added after call to __libm_error_support to properly +// set [the previously overwritten] GR_Parameter_RESULT. +// 08/17/00 Improved speed of main path by 5 cycles +// Shortened path for x=1.0 +// 01/09/01 Improved speed, fixed flags for neg denormals +// 05/20/02 Cleaned up namespace and sf0 syntax +// 05/23/02 Modified algorithm. Now only one polynomial is used +// for |x-1| >= 1/256 and for |x-1| < 1/256 +// 12/11/02 Improved performance for Itanium 2 +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// double log(double) +// double log10(double) +// +// +// Overview of operation +//============================================================== +// Background +// ---------- +// +// This algorithm is based on fact that +// log(a b) = log(a) + log(b). +// In our case we have x = 2^N f, where 1 <= f < 2. +// So +// log(x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) +// +// To calculate log(f) we do following +// log(f) = log(f * frcpa(f) / frcpa(f)) = +// = log(f * frcpa(f)) + log(1/frcpa(f)) +// +// According to definition of IA-64's frcpa instruction it's a +// floating point that approximates 1/f using a lookup on the +// top of 8 bits of the input number's significand with relative +// error < 2^(-8.886). So we have following +// +// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 +// +// and +// +// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = +// = log(1 + r) + T +// +// The first value can be computed by polynomial P(r) approximating +// log(1 + r) on |r| < 1/256 and the second is precomputed tabular +// value defined by top 8 bit of f. +// +// Finally we have that log(x) ~ (N*log(2) + T) + P(r) +// +// Note that if input argument is close to 1.0 (in our case it means +// that |1 - x| < 1/256) we can use just polynomial approximation +// because x = 2^0 * f = f = 1 + r and +// log(x) = log(1 + r) ~ P(r) +// +// +// To compute log10(x) we use the simple identity +// +// log10(x) = log(x)/log(10) +// +// so we have that +// +// log10(x) = (N*log(2) + T + log(1+r)) / log(10) = +// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10) +// +// +// Implementation +// -------------- +// It can be seen that formulas for log and log10 differ from one another +// only by coefficients and tabular values. Namely as log as log10 are +// calculated as (N*L1 + T) + L2*Series(r) where in case of log +// L1 = log(2) +// T = log(1/frcpa(x)) +// L2 = 1.0 +// and in case of log10 +// L1 = log(2)/log(10) +// T = log(1/frcpa(x))/log(10) +// L2 = 1.0/log(10) +// +// So common code with two different entry points those set pointers +// to the base address of coresponding data sets containing values +// of L2,T and prepare integer representation of L1 needed for following +// setf instruction. +// +// Note that both log and log10 use common approximation polynomial +// it means we need only one set of coefficients of approximation. +// +// +// 1. |x-1| >= 1/256 +// InvX = frcpa(x) +// r = InvX*x - 1 +// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), +// all coefficients are calculated in quad and rounded to double +// precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2 +// created with setf. +// +// N = float(n) where n is true unbiased exponent of x +// +// T is tabular value of log(1/frcpa(x)) calculated in quad precision +// and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo. +// To load Thi,Tlo we get bits from 55 to 62 of register format significand +// as index and calculate two addresses +// ad_Thi = Thi_table_base_addr + 8 * index +// ad_Tlo = Tlo_table_base_addr + 4 * index +// +// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad +// precision and rounded to double extended; it's loaded from memory. +// +// L1 (log(2) or log10(2) depending on function) is calculated in quad +// precision and represented by two floating-point 64-bit numbers L1hi,L1lo +// stored in memory. +// +// And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + L2*P(r) +// +// +// 2. |x-1| < 1/256 +// r = x - 1 +// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), +// A7,A6,A5A4,A3,A2 are the same as in case |x-1| >= 1/256 +// +// And final results +// log(x) = P(r) +// log10(x) = L2*P(r) +// +// 3. How we define is input argument such that |x-1| < 1/256 or not. +// +// To do it we analyze biased exponent and integer representation of +// input argument +// +// a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e. +// we test is 0.5 <= x < 2). This comparison can be performed using +// unsigned version of cmp instruction in such a way +// biased_exponent_of_x - 0xFFFE < 2 +// +// +// b) Second (in case when result of a) is true) we need to compare x +// with 1-1/256 and 1+1/256 or in double precision memory representation +// with 0x3FEFE00000000000 and 0x3FF0100000000000 correspondingly. +// This comparison can be made like in a), using unsigned +// version of cmp i.e. ix - 0x3FEFE00000000000 < 0x0000300000000000. +// 0x0000300000000000 is difference between 0x3FF0100000000000 and +// 0x3FEFE00000000000 +// +// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are +// filtered and processed on special branches. +// + +// +// Special values +//============================================================== +// +// log(+0) = -inf +// log(-0) = -inf +// +// log(+qnan) = +qnan +// log(-qnan) = -qnan +// log(+snan) = +qnan +// log(-snan) = -qnan +// +// log(-n) = QNAN Indefinite +// log(-inf) = QNAN Indefinite +// +// log(+inf) = +inf +// +// +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f7 -> f15, f32 -> f42 +// +// General registers used: +// r8 -> r11 +// r14 -> r23 +// +// Predicate registers used: +// p6 -> p15 + +// Assembly macros +//============================================================== +GR_TAG = r8 +GR_ad_1 = r8 +GR_ad_2 = r9 +GR_Exp = r10 +GR_N = r11 + +GR_x = r14 +GR_dx = r15 +GR_NearOne = r15 +GR_xorg = r16 +GR_mask = r16 +GR_05 = r17 +GR_A3 = r18 +GR_Sig = r19 +GR_Ind = r19 +GR_Nm1 = r20 +GR_bias = r21 +GR_ad_3 = r22 +GR_rexp = r23 + + +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 +GR_SAVE_SP = r36 + +GR_Parameter_X = r37 +GR_Parameter_Y = r38 +GR_Parameter_RESULT = r39 +GR_Parameter_TAG = r40 + + + +FR_NormX = f7 +FR_RcpX = f9 +FR_tmp = f9 +FR_r = f10 +FR_r2 = f11 +FR_r4 = f12 +FR_N = f13 +FR_Ln2hi = f14 +FR_Ln2lo = f15 + +FR_A7 = f32 +FR_A6 = f33 +FR_A5 = f34 +FR_A4 = f35 +FR_A3 = f36 +FR_A2 = f37 + +FR_Thi = f38 +FR_NxLn2hipThi = f38 +FR_NxLn2pT = f38 +FR_Tlo = f39 +FR_NxLn2lopTlo = f39 + +FR_InvLn10 = f40 +FR_A32 = f41 +FR_A321 = f42 + + +FR_Y = f1 +FR_X = f10 +FR_RESULT = f8 + + +// Data +//============================================================== +RODATA +.align 16 + +LOCAL_OBJECT_START(log_data) +// coefficients of polynomial approximation +data8 0x3FC2494104381A8E // A7 +data8 0xBFC5556D556BBB69 // A6 +// +// two parts of ln(2) +data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED +// +data8 0x8000000000000000,0x3FFF // 1.0 +// +data8 0x3FC999999988B5E9 // A5 +data8 0xBFCFFFFFFFF6FFF5 // A4 +// +// hi parts of ln(1/frcpa(1+i/256)), i=0...255 +data8 0x3F60040155D5889D // 0 +data8 0x3F78121214586B54 // 1 +data8 0x3F841929F96832EF // 2 +data8 0x3F8C317384C75F06 // 3 +data8 0x3F91A6B91AC73386 // 4 +data8 0x3F95BA9A5D9AC039 // 5 +data8 0x3F99D2A8074325F3 // 6 +data8 0x3F9D6B2725979802 // 7 +data8 0x3FA0C58FA19DFAA9 // 8 +data8 0x3FA2954C78CBCE1A // 9 +data8 0x3FA4A94D2DA96C56 // 10 +data8 0x3FA67C94F2D4BB58 // 11 +data8 0x3FA85188B630F068 // 12 +data8 0x3FAA6B8ABE73AF4C // 13 +data8 0x3FAC441E06F72A9E // 14 +data8 0x3FAE1E6713606D06 // 15 +data8 0x3FAFFA6911AB9300 // 16 +data8 0x3FB0EC139C5DA600 // 17 +data8 0x3FB1DBD2643D190B // 18 +data8 0x3FB2CC7284FE5F1C // 19 +data8 0x3FB3BDF5A7D1EE64 // 20 +data8 0x3FB4B05D7AA012E0 // 21 +data8 0x3FB580DB7CEB5701 // 22 +data8 0x3FB674F089365A79 // 23 +data8 0x3FB769EF2C6B568D // 24 +data8 0x3FB85FD927506A47 // 25 +data8 0x3FB9335E5D594988 // 26 +data8 0x3FBA2B0220C8E5F4 // 27 +data8 0x3FBB0004AC1A86AB // 28 +data8 0x3FBBF968769FCA10 // 29 +data8 0x3FBCCFEDBFEE13A8 // 30 +data8 0x3FBDA727638446A2 // 31 +data8 0x3FBEA3257FE10F79 // 32 +data8 0x3FBF7BE9FEDBFDE5 // 33 +data8 0x3FC02AB352FF25F3 // 34 +data8 0x3FC097CE579D204C // 35 +data8 0x3FC1178E8227E47B // 36 +data8 0x3FC185747DBECF33 // 37 +data8 0x3FC1F3B925F25D41 // 38 +data8 0x3FC2625D1E6DDF56 // 39 +data8 0x3FC2D1610C868139 // 40 +data8 0x3FC340C59741142E // 41 +data8 0x3FC3B08B6757F2A9 // 42 +data8 0x3FC40DFB08378003 // 43 +data8 0x3FC47E74E8CA5F7C // 44 +data8 0x3FC4EF51F6466DE4 // 45 +data8 0x3FC56092E02BA516 // 46 +data8 0x3FC5D23857CD74D4 // 47 +data8 0x3FC6313A37335D76 // 48 +data8 0x3FC6A399DABBD383 // 49 +data8 0x3FC70337DD3CE41A // 50 +data8 0x3FC77654128F6127 // 51 +data8 0x3FC7E9D82A0B022D // 52 +data8 0x3FC84A6B759F512E // 53 +data8 0x3FC8AB47D5F5A30F // 54 +data8 0x3FC91FE49096581B // 55 +data8 0x3FC981634011AA75 // 56 +data8 0x3FC9F6C407089664 // 57 +data8 0x3FCA58E729348F43 // 58 +data8 0x3FCABB55C31693AC // 59 +data8 0x3FCB1E104919EFD0 // 60 +data8 0x3FCB94EE93E367CA // 61 +data8 0x3FCBF851C067555E // 62 +data8 0x3FCC5C0254BF23A5 // 63 +data8 0x3FCCC000C9DB3C52 // 64 +data8 0x3FCD244D99C85673 // 65 +data8 0x3FCD88E93FB2F450 // 66 +data8 0x3FCDEDD437EAEF00 // 67 +data8 0x3FCE530EFFE71012 // 68 +data8 0x3FCEB89A1648B971 // 69 +data8 0x3FCF1E75FADF9BDE // 70 +data8 0x3FCF84A32EAD7C35 // 71 +data8 0x3FCFEB2233EA07CD // 72 +data8 0x3FD028F9C7035C1C // 73 +data8 0x3FD05C8BE0D9635A // 74 +data8 0x3FD085EB8F8AE797 // 75 +data8 0x3FD0B9C8E32D1911 // 76 +data8 0x3FD0EDD060B78080 // 77 +data8 0x3FD122024CF0063F // 78 +data8 0x3FD14BE2927AECD4 // 79 +data8 0x3FD180618EF18ADF // 80 +data8 0x3FD1B50BBE2FC63B // 81 +data8 0x3FD1DF4CC7CF242D // 82 +data8 0x3FD214456D0EB8D4 // 83 +data8 0x3FD23EC5991EBA49 // 84 +data8 0x3FD2740D9F870AFB // 85 +data8 0x3FD29ECDABCDFA03 // 86 +data8 0x3FD2D46602ADCCEE // 87 +data8 0x3FD2FF66B04EA9D4 // 88 +data8 0x3FD335504B355A37 // 89 +data8 0x3FD360925EC44F5C // 90 +data8 0x3FD38BF1C3337E74 // 91 +data8 0x3FD3C25277333183 // 92 +data8 0x3FD3EDF463C1683E // 93 +data8 0x3FD419B423D5E8C7 // 94 +data8 0x3FD44591E0539F48 // 95 +data8 0x3FD47C9175B6F0AD // 96 +data8 0x3FD4A8B341552B09 // 97 +data8 0x3FD4D4F39089019F // 98 +data8 0x3FD501528DA1F967 // 99 +data8 0x3FD52DD06347D4F6 // 100 +data8 0x3FD55A6D3C7B8A89 // 101 +data8 0x3FD5925D2B112A59 // 102 +data8 0x3FD5BF406B543DB1 // 103 +data8 0x3FD5EC433D5C35AD // 104 +data8 0x3FD61965CDB02C1E // 105 +data8 0x3FD646A84935B2A1 // 106 +data8 0x3FD6740ADD31DE94 // 107 +data8 0x3FD6A18DB74A58C5 // 108 +data8 0x3FD6CF31058670EC // 109 +data8 0x3FD6F180E852F0B9 // 110 +data8 0x3FD71F5D71B894EF // 111 +data8 0x3FD74D5AEFD66D5C // 112 +data8 0x3FD77B79922BD37D // 113 +data8 0x3FD7A9B9889F19E2 // 114 +data8 0x3FD7D81B037EB6A6 // 115 +data8 0x3FD8069E33827230 // 116 +data8 0x3FD82996D3EF8BCA // 117 +data8 0x3FD85855776DCBFA // 118 +data8 0x3FD8873658327CCE // 119 +data8 0x3FD8AA75973AB8CE // 120 +data8 0x3FD8D992DC8824E4 // 121 +data8 0x3FD908D2EA7D9511 // 122 +data8 0x3FD92C59E79C0E56 // 123 +data8 0x3FD95BD750EE3ED2 // 124 +data8 0x3FD98B7811A3EE5B // 125 +data8 0x3FD9AF47F33D406B // 126 +data8 0x3FD9DF270C1914A7 // 127 +data8 0x3FDA0325ED14FDA4 // 128 +data8 0x3FDA33440224FA78 // 129 +data8 0x3FDA57725E80C382 // 130 +data8 0x3FDA87D0165DD199 // 131 +data8 0x3FDAAC2E6C03F895 // 132 +data8 0x3FDADCCC6FDF6A81 // 133 +data8 0x3FDB015B3EB1E790 // 134 +data8 0x3FDB323A3A635948 // 135 +data8 0x3FDB56FA04462909 // 136 +data8 0x3FDB881AA659BC93 // 137 +data8 0x3FDBAD0BEF3DB164 // 138 +data8 0x3FDBD21297781C2F // 139 +data8 0x3FDC039236F08818 // 140 +data8 0x3FDC28CB1E4D32FC // 141 +data8 0x3FDC4E19B84723C1 // 142 +data8 0x3FDC7FF9C74554C9 // 143 +data8 0x3FDCA57B64E9DB05 // 144 +data8 0x3FDCCB130A5CEBAF // 145 +data8 0x3FDCF0C0D18F326F // 146 +data8 0x3FDD232075B5A201 // 147 +data8 0x3FDD490246DEFA6B // 148 +data8 0x3FDD6EFA918D25CD // 149 +data8 0x3FDD9509707AE52F // 150 +data8 0x3FDDBB2EFE92C554 // 151 +data8 0x3FDDEE2F3445E4AE // 152 +data8 0x3FDE148A1A2726CD // 153 +data8 0x3FDE3AFC0A49FF3F // 154 +data8 0x3FDE6185206D516D // 155 +data8 0x3FDE882578823D51 // 156 +data8 0x3FDEAEDD2EAC990C // 157 +data8 0x3FDED5AC5F436BE2 // 158 +data8 0x3FDEFC9326D16AB8 // 159 +data8 0x3FDF2391A21575FF // 160 +data8 0x3FDF4AA7EE03192C // 161 +data8 0x3FDF71D627C30BB0 // 162 +data8 0x3FDF991C6CB3B379 // 163 +data8 0x3FDFC07ADA69A90F // 164 +data8 0x3FDFE7F18EB03D3E // 165 +data8 0x3FE007C053C5002E // 166 +data8 0x3FE01B942198A5A0 // 167 +data8 0x3FE02F74400C64EA // 168 +data8 0x3FE04360BE7603AC // 169 +data8 0x3FE05759AC47FE33 // 170 +data8 0x3FE06B5F1911CF51 // 171 +data8 0x3FE078BF0533C568 // 172 +data8 0x3FE08CD9687E7B0E // 173 +data8 0x3FE0A10074CF9019 // 174 +data8 0x3FE0B5343A234476 // 175 +data8 0x3FE0C974C89431CD // 176 +data8 0x3FE0DDC2305B9886 // 177 +data8 0x3FE0EB524BAFC918 // 178 +data8 0x3FE0FFB54213A475 // 179 +data8 0x3FE114253DA97D9F // 180 +data8 0x3FE128A24F1D9AFF // 181 +data8 0x3FE1365252BF0864 // 182 +data8 0x3FE14AE558B4A92D // 183 +data8 0x3FE15F85A19C765B // 184 +data8 0x3FE16D4D38C119FA // 185 +data8 0x3FE18203C20DD133 // 186 +data8 0x3FE196C7BC4B1F3A // 187 +data8 0x3FE1A4A738B7A33C // 188 +data8 0x3FE1B981C0C9653C // 189 +data8 0x3FE1CE69E8BB106A // 190 +data8 0x3FE1DC619DE06944 // 191 +data8 0x3FE1F160A2AD0DA3 // 192 +data8 0x3FE2066D7740737E // 193 +data8 0x3FE2147DBA47A393 // 194 +data8 0x3FE229A1BC5EBAC3 // 195 +data8 0x3FE237C1841A502E // 196 +data8 0x3FE24CFCE6F80D9A // 197 +data8 0x3FE25B2C55CD5762 // 198 +data8 0x3FE2707F4D5F7C40 // 199 +data8 0x3FE285E0842CA383 // 200 +data8 0x3FE294294708B773 // 201 +data8 0x3FE2A9A2670AFF0C // 202 +data8 0x3FE2B7FB2C8D1CC0 // 203 +data8 0x3FE2C65A6395F5F5 // 204 +data8 0x3FE2DBF557B0DF42 // 205 +data8 0x3FE2EA64C3F97654 // 206 +data8 0x3FE3001823684D73 // 207 +data8 0x3FE30E97E9A8B5CC // 208 +data8 0x3FE32463EBDD34E9 // 209 +data8 0x3FE332F4314AD795 // 210 +data8 0x3FE348D90E7464CF // 211 +data8 0x3FE35779F8C43D6D // 212 +data8 0x3FE36621961A6A99 // 213 +data8 0x3FE37C299F3C366A // 214 +data8 0x3FE38AE2171976E7 // 215 +data8 0x3FE399A157A603E7 // 216 +data8 0x3FE3AFCCFE77B9D1 // 217 +data8 0x3FE3BE9D503533B5 // 218 +data8 0x3FE3CD7480B4A8A2 // 219 +data8 0x3FE3E3C43918F76C // 220 +data8 0x3FE3F2ACB27ED6C6 // 221 +data8 0x3FE4019C2125CA93 // 222 +data8 0x3FE4181061389722 // 223 +data8 0x3FE42711518DF545 // 224 +data8 0x3FE436194E12B6BF // 225 +data8 0x3FE445285D68EA69 // 226 +data8 0x3FE45BCC464C893A // 227 +data8 0x3FE46AED21F117FC // 228 +data8 0x3FE47A1527E8A2D3 // 229 +data8 0x3FE489445EFFFCCB // 230 +data8 0x3FE4A018BCB69835 // 231 +data8 0x3FE4AF5A0C9D65D7 // 232 +data8 0x3FE4BEA2A5BDBE87 // 233 +data8 0x3FE4CDF28F10AC46 // 234 +data8 0x3FE4DD49CF994058 // 235 +data8 0x3FE4ECA86E64A683 // 236 +data8 0x3FE503C43CD8EB68 // 237 +data8 0x3FE513356667FC57 // 238 +data8 0x3FE522AE0738A3D7 // 239 +data8 0x3FE5322E26867857 // 240 +data8 0x3FE541B5CB979809 // 241 +data8 0x3FE55144FDBCBD62 // 242 +data8 0x3FE560DBC45153C6 // 243 +data8 0x3FE5707A26BB8C66 // 244 +data8 0x3FE587F60ED5B8FF // 245 +data8 0x3FE597A7977C8F31 // 246 +data8 0x3FE5A760D634BB8A // 247 +data8 0x3FE5B721D295F10E // 248 +data8 0x3FE5C6EA94431EF9 // 249 +data8 0x3FE5D6BB22EA86F5 // 250 +data8 0x3FE5E6938645D38F // 251 +data8 0x3FE5F673C61A2ED1 // 252 +data8 0x3FE6065BEA385926 // 253 +data8 0x3FE6164BFA7CC06B // 254 +data8 0x3FE62643FECF9742 // 255 +// +// lo parts of ln(1/frcpa(1+i/256)), i=0...255 +data4 0x20E70672 // 0 +data4 0x1F60A5D0 // 1 +data4 0x218EABA0 // 2 +data4 0x21403104 // 3 +data4 0x20E9B54E // 4 +data4 0x21EE1382 // 5 +data4 0x226014E3 // 6 +data4 0x2095E5C9 // 7 +data4 0x228BA9D4 // 8 +data4 0x22932B86 // 9 +data4 0x22608A57 // 10 +data4 0x220209F3 // 11 +data4 0x212882CC // 12 +data4 0x220D46E2 // 13 +data4 0x21FA4C28 // 14 +data4 0x229E5BD9 // 15 +data4 0x228C9838 // 16 +data4 0x2311F954 // 17 +data4 0x221365DF // 18 +data4 0x22BD0CB3 // 19 +data4 0x223D4BB7 // 20 +data4 0x22A71BBE // 21 +data4 0x237DB2FA // 22 +data4 0x23194C9D // 23 +data4 0x22EC639E // 24 +data4 0x2367E669 // 25 +data4 0x232E1D5F // 26 +data4 0x234A639B // 27 +data4 0x2365C0E0 // 28 +data4 0x234646C1 // 29 +data4 0x220CBF9C // 30 +data4 0x22A00FD4 // 31 +data4 0x2306A3F2 // 32 +data4 0x23745A9B // 33 +data4 0x2398D756 // 34 +data4 0x23DD0B6A // 35 +data4 0x23DE338B // 36 +data4 0x23A222DF // 37 +data4 0x223164F8 // 38 +data4 0x23B4E87B // 39 +data4 0x23D6CCB8 // 40 +data4 0x220C2099 // 41 +data4 0x21B86B67 // 42 +data4 0x236D14F1 // 43 +data4 0x225A923F // 44 +data4 0x22748723 // 45 +data4 0x22200D13 // 46 +data4 0x23C296EA // 47 +data4 0x2302AC38 // 48 +data4 0x234B1996 // 49 +data4 0x2385E298 // 50 +data4 0x23175BE5 // 51 +data4 0x2193F482 // 52 +data4 0x23BFEA90 // 53 +data4 0x23D70A0C // 54 +data4 0x231CF30A // 55 +data4 0x235D9E90 // 56 +data4 0x221AD0CB // 57 +data4 0x22FAA08B // 58 +data4 0x23D29A87 // 59 +data4 0x20C4B2FE // 60 +data4 0x2381B8B7 // 61 +data4 0x23F8D9FC // 62 +data4 0x23EAAE7B // 63 +data4 0x2329E8AA // 64 +data4 0x23EC0322 // 65 +data4 0x2357FDCB // 66 +data4 0x2392A9AD // 67 +data4 0x22113B02 // 68 +data4 0x22DEE901 // 69 +data4 0x236A6D14 // 70 +data4 0x2371D33E // 71 +data4 0x2146F005 // 72 +data4 0x23230B06 // 73 +data4 0x22F1C77D // 74 +data4 0x23A89FA3 // 75 +data4 0x231D1241 // 76 +data4 0x244DA96C // 77 +data4 0x23ECBB7D // 78 +data4 0x223E42B4 // 79 +data4 0x23801BC9 // 80 +data4 0x23573263 // 81 +data4 0x227C1158 // 82 +data4 0x237BD749 // 83 +data4 0x21DDBAE9 // 84 +data4 0x23401735 // 85 +data4 0x241D9DEE // 86 +data4 0x23BC88CB // 87 +data4 0x2396D5F1 // 88 +data4 0x23FC89CF // 89 +data4 0x2414F9A2 // 90 +data4 0x2474A0F5 // 91 +data4 0x24354B60 // 92 +data4 0x23C1EB40 // 93 +data4 0x2306DD92 // 94 +data4 0x24353B6B // 95 +data4 0x23CD1701 // 96 +data4 0x237C7A1C // 97 +data4 0x245793AA // 98 +data4 0x24563695 // 99 +data4 0x23C51467 // 100 +data4 0x24476B68 // 101 +data4 0x212585A9 // 102 +data4 0x247B8293 // 103 +data4 0x2446848A // 104 +data4 0x246A53F8 // 105 +data4 0x246E496D // 106 +data4 0x23ED1D36 // 107 +data4 0x2314C258 // 108 +data4 0x233244A7 // 109 +data4 0x245B7AF0 // 110 +data4 0x24247130 // 111 +data4 0x22D67B38 // 112 +data4 0x2449F620 // 113 +data4 0x23BBC8B8 // 114 +data4 0x237D3BA0 // 115 +data4 0x245E8F13 // 116 +data4 0x2435573F // 117 +data4 0x242DE666 // 118 +data4 0x2463BC10 // 119 +data4 0x2466587D // 120 +data4 0x2408144B // 121 +data4 0x2405F0E5 // 122 +data4 0x22381CFF // 123 +data4 0x24154F9B // 124 +data4 0x23A4E96E // 125 +data4 0x24052967 // 126 +data4 0x2406963F // 127 +data4 0x23F7D3CB // 128 +data4 0x2448AFF4 // 129 +data4 0x24657A21 // 130 +data4 0x22FBC230 // 131 +data4 0x243C8DEA // 132 +data4 0x225DC4B7 // 133 +data4 0x23496EBF // 134 +data4 0x237C2B2B // 135 +data4 0x23A4A5B1 // 136 +data4 0x2394E9D1 // 137 +data4 0x244BC950 // 138 +data4 0x23C7448F // 139 +data4 0x2404A1AD // 140 +data4 0x246511D5 // 141 +data4 0x24246526 // 142 +data4 0x23111F57 // 143 +data4 0x22868951 // 144 +data4 0x243EB77F // 145 +data4 0x239F3DFF // 146 +data4 0x23089666 // 147 +data4 0x23EBFA6A // 148 +data4 0x23C51312 // 149 +data4 0x23E1DD5E // 150 +data4 0x232C0944 // 151 +data4 0x246A741F // 152 +data4 0x2414DF8D // 153 +data4 0x247B5546 // 154 +data4 0x2415C980 // 155 +data4 0x24324ABD // 156 +data4 0x234EB5E5 // 157 +data4 0x2465E43E // 158 +data4 0x242840D1 // 159 +data4 0x24444057 // 160 +data4 0x245E56F0 // 161 +data4 0x21AE30F8 // 162 +data4 0x23FB3283 // 163 +data4 0x247A4D07 // 164 +data4 0x22AE314D // 165 +data4 0x246B7727 // 166 +data4 0x24EAD526 // 167 +data4 0x24B41DC9 // 168 +data4 0x24EE8062 // 169 +data4 0x24A0C7C4 // 170 +data4 0x24E8DA67 // 171 +data4 0x231120F7 // 172 +data4 0x24401FFB // 173 +data4 0x2412DD09 // 174 +data4 0x248C131A // 175 +data4 0x24C0A7CE // 176 +data4 0x243DD4C8 // 177 +data4 0x24457FEB // 178 +data4 0x24DEEFBB // 179 +data4 0x243C70AE // 180 +data4 0x23E7A6FA // 181 +data4 0x24C2D311 // 182 +data4 0x23026255 // 183 +data4 0x2437C9B9 // 184 +data4 0x246BA847 // 185 +data4 0x2420B448 // 186 +data4 0x24C4CF5A // 187 +data4 0x242C4981 // 188 +data4 0x24DE1525 // 189 +data4 0x24F5CC33 // 190 +data4 0x235A85DA // 191 +data4 0x24A0B64F // 192 +data4 0x244BA0A4 // 193 +data4 0x24AAF30A // 194 +data4 0x244C86F9 // 195 +data4 0x246D5B82 // 196 +data4 0x24529347 // 197 +data4 0x240DD008 // 198 +data4 0x24E98790 // 199 +data4 0x2489B0CE // 200 +data4 0x22BC29AC // 201 +data4 0x23F37C7A // 202 +data4 0x24987FE8 // 203 +data4 0x22AFE20B // 204 +data4 0x24C8D7C2 // 205 +data4 0x24B28B7D // 206 +data4 0x23B6B271 // 207 +data4 0x24C77CB6 // 208 +data4 0x24EF1DCA // 209 +data4 0x24A4F0AC // 210 +data4 0x24CF113E // 211 +data4 0x2496BBAB // 212 +data4 0x23C7CC8A // 213 +data4 0x23AE3961 // 214 +data4 0x2410A895 // 215 +data4 0x23CE3114 // 216 +data4 0x2308247D // 217 +data4 0x240045E9 // 218 +data4 0x24974F60 // 219 +data4 0x242CB39F // 220 +data4 0x24AB8D69 // 221 +data4 0x23436788 // 222 +data4 0x24305E9E // 223 +data4 0x243E71A9 // 224 +data4 0x23C2A6B3 // 225 +data4 0x23FFE6CF // 226 +data4 0x2322D801 // 227 +data4 0x24515F21 // 228 +data4 0x2412A0D6 // 229 +data4 0x24E60D44 // 230 +data4 0x240D9251 // 231 +data4 0x247076E2 // 232 +data4 0x229B101B // 233 +data4 0x247B12DE // 234 +data4 0x244B9127 // 235 +data4 0x2499EC42 // 236 +data4 0x21FC3963 // 237 +data4 0x23E53266 // 238 +data4 0x24CE102D // 239 +data4 0x23CC45D2 // 240 +data4 0x2333171D // 241 +data4 0x246B3533 // 242 +data4 0x24931129 // 243 +data4 0x24405FFA // 244 +data4 0x24CF464D // 245 +data4 0x237095CD // 246 +data4 0x24F86CBD // 247 +data4 0x24E2D84B // 248 +data4 0x21ACBB44 // 249 +data4 0x24F43A8C // 250 +data4 0x249DB931 // 251 +data4 0x24A385EF // 252 +data4 0x238B1279 // 253 +data4 0x2436213E // 254 +data4 0x24F18A3B // 255 +LOCAL_OBJECT_END(log_data) + + +LOCAL_OBJECT_START(log10_data) +// coefficients of polynoimal approximation +data8 0x3FC2494104381A8E // A7 +data8 0xBFC5556D556BBB69 // A6 +// +// two parts of ln(2)/ln(10) +data8 0x3FD3441350900000, 0x3DCEF3FDE623E256 +// +data8 0xDE5BD8A937287195,0x3FFD // 1/ln(10) +// +data8 0x3FC999999988B5E9 // A5 +data8 0xBFCFFFFFFFF6FFF5 // A4 +// +// Hi parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255 +data8 0x3F4BD27045BFD024 // 0 +data8 0x3F64E84E793A474A // 1 +data8 0x3F7175085AB85FF0 // 2 +data8 0x3F787CFF9D9147A5 // 3 +data8 0x3F7EA9D372B89FC8 // 4 +data8 0x3F82DF9D95DA961C // 5 +data8 0x3F866DF172D6372B // 6 +data8 0x3F898D79EF5EEDEF // 7 +data8 0x3F8D22ADF3F9579C // 8 +data8 0x3F9024231D30C398 // 9 +data8 0x3F91F23A98897D49 // 10 +data8 0x3F93881A7B818F9E // 11 +data8 0x3F951F6E1E759E35 // 12 +data8 0x3F96F2BCE7ADC5B4 // 13 +data8 0x3F988D362CDF359E // 14 +data8 0x3F9A292BAF010981 // 15 +data8 0x3F9BC6A03117EB97 // 16 +data8 0x3F9D65967DE3AB08 // 17 +data8 0x3F9F061167FC31E7 // 18 +data8 0x3FA05409E4F7819B // 19 +data8 0x3FA125D0432EA20D // 20 +data8 0x3FA1F85D440D299B // 21 +data8 0x3FA2AD755749617C // 22 +data8 0x3FA381772A00E603 // 23 +data8 0x3FA45643E165A70A // 24 +data8 0x3FA52BDD034475B8 // 25 +data8 0x3FA5E3966B7E9295 // 26 +data8 0x3FA6BAAF47C5B244 // 27 +data8 0x3FA773B3E8C4F3C7 // 28 +data8 0x3FA84C51EBEE8D15 // 29 +data8 0x3FA906A6786FC1CA // 30 +data8 0x3FA9C197ABF00DD6 // 31 +data8 0x3FAA9C78712191F7 // 32 +data8 0x3FAB58C09C8D637C // 33 +data8 0x3FAC15A8BCDD7B7E // 34 +data8 0x3FACD331E2C2967B // 35 +data8 0x3FADB11ED766ABF4 // 36 +data8 0x3FAE70089346A9E6 // 37 +data8 0x3FAF2F96C6754AED // 38 +data8 0x3FAFEFCA8D451FD5 // 39 +data8 0x3FB0585283764177 // 40 +data8 0x3FB0B913AAC7D3A6 // 41 +data8 0x3FB11A294F2569F5 // 42 +data8 0x3FB16B51A2696890 // 43 +data8 0x3FB1CD03ADACC8BD // 44 +data8 0x3FB22F0BDD7745F5 // 45 +data8 0x3FB2916ACA38D1E7 // 46 +data8 0x3FB2F4210DF7663C // 47 +data8 0x3FB346A6C3C49065 // 48 +data8 0x3FB3A9FEBC605409 // 49 +data8 0x3FB3FD0C10A3AA54 // 50 +data8 0x3FB46107D3540A81 // 51 +data8 0x3FB4C55DD16967FE // 52 +data8 0x3FB51940330C000A // 53 +data8 0x3FB56D620EE7115E // 54 +data8 0x3FB5D2ABCF26178D // 55 +data8 0x3FB6275AA5DEBF81 // 56 +data8 0x3FB68D4EAF26D7EE // 57 +data8 0x3FB6E28C5C54A28D // 58 +data8 0x3FB7380B9665B7C7 // 59 +data8 0x3FB78DCCC278E85B // 60 +data8 0x3FB7F50C2CF25579 // 61 +data8 0x3FB84B5FD5EAEFD7 // 62 +data8 0x3FB8A1F6BAB2B226 // 63 +data8 0x3FB8F8D144557BDF // 64 +data8 0x3FB94FEFDCD61D92 // 65 +data8 0x3FB9A752EF316149 // 66 +data8 0x3FB9FEFAE7611EDF // 67 +data8 0x3FBA56E8325F5C86 // 68 +data8 0x3FBAAF1B3E297BB3 // 69 +data8 0x3FBB079479C372AC // 70 +data8 0x3FBB6054553B12F7 // 71 +data8 0x3FBBB95B41AB5CE5 // 72 +data8 0x3FBC12A9B13FE079 // 73 +data8 0x3FBC6C4017382BEA // 74 +data8 0x3FBCB41FBA42686C // 75 +data8 0x3FBD0E38CE73393E // 76 +data8 0x3FBD689B2193F132 // 77 +data8 0x3FBDC3472B1D285F // 78 +data8 0x3FBE0C06300D528B // 79 +data8 0x3FBE6738190E394B // 80 +data8 0x3FBEC2B50D208D9A // 81 +data8 0x3FBF0C1C2B936827 // 82 +data8 0x3FBF68216C9CC726 // 83 +data8 0x3FBFB1F6381856F3 // 84 +data8 0x3FC00742AF4CE5F8 // 85 +data8 0x3FC02C64906512D2 // 86 +data8 0x3FC05AF1E63E03B4 // 87 +data8 0x3FC0804BEA723AA8 // 88 +data8 0x3FC0AF1FD6711526 // 89 +data8 0x3FC0D4B2A88059FF // 90 +data8 0x3FC0FA5EF136A06C // 91 +data8 0x3FC1299A4FB3E305 // 92 +data8 0x3FC14F806253C3EC // 93 +data8 0x3FC175805D1587C1 // 94 +data8 0x3FC19B9A637CA294 // 95 +data8 0x3FC1CB5FC26EDE16 // 96 +data8 0x3FC1F1B4E65F2590 // 97 +data8 0x3FC218248B5DC3E5 // 98 +data8 0x3FC23EAED62ADC76 // 99 +data8 0x3FC26553EBD337BC // 100 +data8 0x3FC28C13F1B118FF // 101 +data8 0x3FC2BCAA14381385 // 102 +data8 0x3FC2E3A740B7800E // 103 +data8 0x3FC30ABFD8F333B6 // 104 +data8 0x3FC331F403985096 // 105 +data8 0x3FC35943E7A6068F // 106 +data8 0x3FC380AFAC6E7C07 // 107 +data8 0x3FC3A8377997B9E5 // 108 +data8 0x3FC3CFDB771C9ADB // 109 +data8 0x3FC3EDA90D39A5DE // 110 +data8 0x3FC4157EC09505CC // 111 +data8 0x3FC43D7113FB04C0 // 112 +data8 0x3FC4658030AD1CCE // 113 +data8 0x3FC48DAC404638F5 // 114 +data8 0x3FC4B5F56CBBB869 // 115 +data8 0x3FC4DE5BE05E7582 // 116 +data8 0x3FC4FCBC0776FD85 // 117 +data8 0x3FC525561E9256EE // 118 +data8 0x3FC54E0DF3198865 // 119 +data8 0x3FC56CAB7112BDE2 // 120 +data8 0x3FC59597BA735B15 // 121 +data8 0x3FC5BEA23A506FD9 // 122 +data8 0x3FC5DD7E08DE382E // 123 +data8 0x3FC606BDD3F92355 // 124 +data8 0x3FC6301C518A501E // 125 +data8 0x3FC64F3770618915 // 126 +data8 0x3FC678CC14C1E2D7 // 127 +data8 0x3FC6981005ED2947 // 128 +data8 0x3FC6C1DB5F9BB335 // 129 +data8 0x3FC6E1488ECD2880 // 130 +data8 0x3FC70B4B2E7E41B8 // 131 +data8 0x3FC72AE209146BF8 // 132 +data8 0x3FC7551C81BD8DCF // 133 +data8 0x3FC774DD76CC43BD // 134 +data8 0x3FC79F505DB00E88 // 135 +data8 0x3FC7BF3BDE099F30 // 136 +data8 0x3FC7E9E7CAC437F8 // 137 +data8 0x3FC809FE4902D00D // 138 +data8 0x3FC82A2757995CBD // 139 +data8 0x3FC85525C625E098 // 140 +data8 0x3FC8757A79831887 // 141 +data8 0x3FC895E2058D8E02 // 142 +data8 0x3FC8C13437695531 // 143 +data8 0x3FC8E1C812EF32BE // 144 +data8 0x3FC9026F112197E8 // 145 +data8 0x3FC923294888880A // 146 +data8 0x3FC94EEA4B8334F2 // 147 +data8 0x3FC96FD1B639FC09 // 148 +data8 0x3FC990CCA66229AB // 149 +data8 0x3FC9B1DB33334842 // 150 +data8 0x3FC9D2FD740E6606 // 151 +data8 0x3FC9FF49EEDCB553 // 152 +data8 0x3FCA209A84FBCFF7 // 153 +data8 0x3FCA41FF1E43F02B // 154 +data8 0x3FCA6377D2CE9377 // 155 +data8 0x3FCA8504BAE0D9F5 // 156 +data8 0x3FCAA6A5EEEBEFE2 // 157 +data8 0x3FCAC85B878D7878 // 158 +data8 0x3FCAEA259D8FFA0B // 159 +data8 0x3FCB0C0449EB4B6A // 160 +data8 0x3FCB2DF7A5C50299 // 161 +data8 0x3FCB4FFFCA70E4D1 // 162 +data8 0x3FCB721CD17157E2 // 163 +data8 0x3FCB944ED477D4EC // 164 +data8 0x3FCBB695ED655C7C // 165 +data8 0x3FCBD8F2364AEC0F // 166 +data8 0x3FCBFB63C969F4FF // 167 +data8 0x3FCC1DEAC134D4E9 // 168 +data8 0x3FCC4087384F4F80 // 169 +data8 0x3FCC6339498F09E1 // 170 +data8 0x3FCC86010FFC076B // 171 +data8 0x3FCC9D3D065C5B41 // 172 +data8 0x3FCCC029375BA079 // 173 +data8 0x3FCCE32B66978BA4 // 174 +data8 0x3FCD0643AFD51404 // 175 +data8 0x3FCD29722F0DEA45 // 176 +data8 0x3FCD4CB70070FE43 // 177 +data8 0x3FCD6446AB3F8C95 // 178 +data8 0x3FCD87B0EF71DB44 // 179 +data8 0x3FCDAB31D1FE99A6 // 180 +data8 0x3FCDCEC96FDC888E // 181 +data8 0x3FCDE69088763579 // 182 +data8 0x3FCE0A4E4A25C1FF // 183 +data8 0x3FCE2E2315755E32 // 184 +data8 0x3FCE461322D1648A // 185 +data8 0x3FCE6A0E95C7787B // 186 +data8 0x3FCE8E216243DD60 // 187 +data8 0x3FCEA63AF26E007C // 188 +data8 0x3FCECA74ED15E0B7 // 189 +data8 0x3FCEEEC692CCD259 // 190 +data8 0x3FCF070A36B8D9C0 // 191 +data8 0x3FCF2B8393E34A2D // 192 +data8 0x3FCF5014EF538A5A // 193 +data8 0x3FCF68833AF1B17F // 194 +data8 0x3FCF8D3CD9F3F04E // 195 +data8 0x3FCFA5C61ADD93E9 // 196 +data8 0x3FCFCAA8567EBA79 // 197 +data8 0x3FCFE34CC8743DD8 // 198 +data8 0x3FD0042BFD74F519 // 199 +data8 0x3FD016BDF6A18017 // 200 +data8 0x3FD023262F907322 // 201 +data8 0x3FD035CCED8D32A1 // 202 +data8 0x3FD042430E869FFB // 203 +data8 0x3FD04EBEC842B2DF // 204 +data8 0x3FD06182E84FD4AB // 205 +data8 0x3FD06E0CB609D383 // 206 +data8 0x3FD080E60BEC8F12 // 207 +data8 0x3FD08D7E0D894735 // 208 +data8 0x3FD0A06CC96A2055 // 209 +data8 0x3FD0AD131F3B3C55 // 210 +data8 0x3FD0C01771E775FB // 211 +data8 0x3FD0CCCC3CAD6F4B // 212 +data8 0x3FD0D986D91A34A8 // 213 +data8 0x3FD0ECA9B8861A2D // 214 +data8 0x3FD0F972F87FF3D5 // 215 +data8 0x3FD106421CF0E5F7 // 216 +data8 0x3FD11983EBE28A9C // 217 +data8 0x3FD12661E35B7859 // 218 +data8 0x3FD13345D2779D3B // 219 +data8 0x3FD146A6F597283A // 220 +data8 0x3FD15399E81EA83D // 221 +data8 0x3FD16092E5D3A9A6 // 222 +data8 0x3FD17413C3B7AB5D // 223 +data8 0x3FD1811BF629D6FA // 224 +data8 0x3FD18E2A47B46685 // 225 +data8 0x3FD19B3EBE1A4418 // 226 +data8 0x3FD1AEE9017CB450 // 227 +data8 0x3FD1BC0CED7134E1 // 228 +data8 0x3FD1C93712ABC7FF // 229 +data8 0x3FD1D66777147D3E // 230 +data8 0x3FD1EA3BD1286E1C // 231 +data8 0x3FD1F77BED932C4C // 232 +data8 0x3FD204C25E1B031F // 233 +data8 0x3FD2120F28CE69B1 // 234 +data8 0x3FD21F6253C48D00 // 235 +data8 0x3FD22CBBE51D60A9 // 236 +data8 0x3FD240CE4C975444 // 237 +data8 0x3FD24E37F8ECDAE7 // 238 +data8 0x3FD25BA8215AF7FC // 239 +data8 0x3FD2691ECC29F042 // 240 +data8 0x3FD2769BFFAB2DFF // 241 +data8 0x3FD2841FC23952C9 // 242 +data8 0x3FD291AA1A384978 // 243 +data8 0x3FD29F3B0E15584A // 244 +data8 0x3FD2B3A0EE479DF7 // 245 +data8 0x3FD2C142842C09E5 // 246 +data8 0x3FD2CEEACCB7BD6C // 247 +data8 0x3FD2DC99CE82FF20 // 248 +data8 0x3FD2EA4F902FD7D9 // 249 +data8 0x3FD2F80C186A25FC // 250 +data8 0x3FD305CF6DE7B0F6 // 251 +data8 0x3FD3139997683CE7 // 252 +data8 0x3FD3216A9BB59E7C // 253 +data8 0x3FD32F4281A3CEFE // 254 +data8 0x3FD33D2150110091 // 255 +// +// Lo parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255 +data4 0x1FB0EB5A // 0 +data4 0x206E5EE3 // 1 +data4 0x208F3609 // 2 +data4 0x2070EB03 // 3 +data4 0x1F314BAE // 4 +data4 0x217A889D // 5 +data4 0x21E63650 // 6 +data4 0x21C2F4A3 // 7 +data4 0x2192A10C // 8 +data4 0x1F84B73E // 9 +data4 0x2243FBCA // 10 +data4 0x21BD9C51 // 11 +data4 0x213C542B // 12 +data4 0x21047386 // 13 +data4 0x21217D8F // 14 +data4 0x226791B7 // 15 +data4 0x204CCE66 // 16 +data4 0x2234CE9F // 17 +data4 0x220675E2 // 18 +data4 0x22B8E5BA // 19 +data4 0x22C12D14 // 20 +data4 0x211D41F0 // 21 +data4 0x228507F3 // 22 +data4 0x22F7274B // 23 +data4 0x22A7FDD1 // 24 +data4 0x2244A06E // 25 +data4 0x215DCE69 // 26 +data4 0x22F5C961 // 27 +data4 0x22EBEF29 // 28 +data4 0x222A2CB6 // 29 +data4 0x22B9FE00 // 30 +data4 0x22E79EB7 // 31 +data4 0x222F9607 // 32 +data4 0x2189D87F // 33 +data4 0x2236DB45 // 34 +data4 0x22ED77FB // 35 +data4 0x21CB70F0 // 36 +data4 0x21B8ACE8 // 37 +data4 0x22EC58C1 // 38 +data4 0x22CFCC1C // 39 +data4 0x2343E77A // 40 +data4 0x237FBC7F // 41 +data4 0x230D472E // 42 +data4 0x234686FB // 43 +data4 0x23770425 // 44 +data4 0x223977EC // 45 +data4 0x2345800A // 46 +data4 0x237BC351 // 47 +data4 0x23191502 // 48 +data4 0x232BAC12 // 49 +data4 0x22692421 // 50 +data4 0x234D409D // 51 +data4 0x22EC3214 // 52 +data4 0x2376C916 // 53 +data4 0x22B00DD1 // 54 +data4 0x2309D910 // 55 +data4 0x22F925FD // 56 +data4 0x22A63A7B // 57 +data4 0x2106264A // 58 +data4 0x234227F9 // 59 +data4 0x1ECB1978 // 60 +data4 0x23460A62 // 61 +data4 0x232ED4B1 // 62 +data4 0x226DDC38 // 63 +data4 0x1F101A73 // 64 +data4 0x21B1F82B // 65 +data4 0x22752F19 // 66 +data4 0x2320BC15 // 67 +data4 0x236EEC5E // 68 +data4 0x23404D3E // 69 +data4 0x2304C517 // 70 +data4 0x22F7441A // 71 +data4 0x230D3D7A // 72 +data4 0x2264A9DF // 73 +data4 0x22410CC8 // 74 +data4 0x2342CCCB // 75 +data4 0x23560BD4 // 76 +data4 0x237BBFFE // 77 +data4 0x2373A206 // 78 +data4 0x22C871B9 // 79 +data4 0x2354B70C // 80 +data4 0x232EDB33 // 81 +data4 0x235DB680 // 82 +data4 0x230EF422 // 83 +data4 0x235316CA // 84 +data4 0x22EEEE8B // 85 +data4 0x2375C88C // 86 +data4 0x235ABD21 // 87 +data4 0x23A0D232 // 88 +data4 0x23F5FFB5 // 89 +data4 0x23D3CEC8 // 90 +data4 0x22A92204 // 91 +data4 0x238C64DF // 92 +data4 0x23B82896 // 93 +data4 0x22D633B8 // 94 +data4 0x23861E93 // 95 +data4 0x23CB594B // 96 +data4 0x2330387E // 97 +data4 0x21CD4702 // 98 +data4 0x2284C505 // 99 +data4 0x23D6995C // 100 +data4 0x23F6C807 // 101 +data4 0x239CEF5C // 102 +data4 0x239442B0 // 103 +data4 0x22B35EE5 // 104 +data4 0x2391E9A4 // 105 +data4 0x23A390F5 // 106 +data4 0x2349AC9C // 107 +data4 0x23FA5535 // 108 +data4 0x21E3A46A // 109 +data4 0x23B44ABA // 110 +data4 0x23CEA8E0 // 111 +data4 0x23F647DC // 112 +data4 0x2390D1A8 // 113 +data4 0x23D0CFA2 // 114 +data4 0x236E0872 // 115 +data4 0x23B88B91 // 116 +data4 0x2283C359 // 117 +data4 0x232F647F // 118 +data4 0x23122CD7 // 119 +data4 0x232CF564 // 120 +data4 0x232630FD // 121 +data4 0x23BEE1C8 // 122 +data4 0x23B2BD30 // 123 +data4 0x2301F1C0 // 124 +data4 0x23CE4D67 // 125 +data4 0x23A353C9 // 126 +data4 0x238086E8 // 127 +data4 0x22D0D29E // 128 +data4 0x23A3B3C8 // 129 +data4 0x23F69F4B // 130 +data4 0x23EA3C21 // 131 +data4 0x23951C88 // 132 +data4 0x2372AFFC // 133 +data4 0x23A6D1A8 // 134 +data4 0x22BBBAF4 // 135 +data4 0x227FA3DD // 136 +data4 0x23804D9B // 137 +data4 0x232D771F // 138 +data4 0x239CB57B // 139 +data4 0x2303CF34 // 140 +data4 0x22218C2A // 141 +data4 0x23991BEE // 142 +data4 0x23EB3596 // 143 +data4 0x230487FA // 144 +data4 0x2135DF4C // 145 +data4 0x2380FD2D // 146 +data4 0x23EB75E9 // 147 +data4 0x211C62C8 // 148 +data4 0x23F518F1 // 149 +data4 0x23FEF882 // 150 +data4 0x239097C7 // 151 +data4 0x223E2BDA // 152 +data4 0x23988F89 // 153 +data4 0x22E4A4AD // 154 +data4 0x23F03D9C // 155 +data4 0x23F5018F // 156 +data4 0x23E1E250 // 157 +data4 0x23FD3D90 // 158 +data4 0x22DEE2FF // 159 +data4 0x238342AB // 160 +data4 0x22E6736F // 161 +data4 0x233AFC28 // 162 +data4 0x2395F661 // 163 +data4 0x23D8B991 // 164 +data4 0x23CD58D5 // 165 +data4 0x21941FD6 // 166 +data4 0x23352915 // 167 +data4 0x235D09EE // 168 +data4 0x22DC7EF9 // 169 +data4 0x238BC9F3 // 170 +data4 0x2397DF8F // 171 +data4 0x2380A7BB // 172 +data4 0x23EFF48C // 173 +data4 0x21E67408 // 174 +data4 0x236420F7 // 175 +data4 0x22C8DFB5 // 176 +data4 0x239B5D35 // 177 +data4 0x23BDC09D // 178 +data4 0x239E822C // 179 +data4 0x23984F0A // 180 +data4 0x23EF2119 // 181 +data4 0x23F738B8 // 182 +data4 0x23B66187 // 183 +data4 0x23B06AD7 // 184 +data4 0x2369140F // 185 +data4 0x218DACE6 // 186 +data4 0x21DF23F1 // 187 +data4 0x235D8B34 // 188 +data4 0x23460333 // 189 +data4 0x23F11D62 // 190 +data4 0x23C37147 // 191 +data4 0x22B2AE2A // 192 +data4 0x23949211 // 193 +data4 0x23B69799 // 194 +data4 0x23DBEC75 // 195 +data4 0x229A6FB3 // 196 +data4 0x23FC6C60 // 197 +data4 0x22D01FFC // 198 +data4 0x235985F0 // 199 +data4 0x23F7ECA5 // 200 +data4 0x23F924D3 // 201 +data4 0x2381B92F // 202 +data4 0x243A0FBE // 203 +data4 0x24712D72 // 204 +data4 0x24594E2F // 205 +data4 0x220CD12A // 206 +data4 0x23D87FB0 // 207 +data4 0x2338288A // 208 +data4 0x242BB2CC // 209 +data4 0x220F6265 // 210 +data4 0x23BB7FE3 // 211 +data4 0x2301C0A2 // 212 +data4 0x246709AB // 213 +data4 0x23A619E2 // 214 +data4 0x24030E3B // 215 +data4 0x233C36CC // 216 +data4 0x241AAB77 // 217 +data4 0x243D41A3 // 218 +data4 0x23834A60 // 219 +data4 0x236AC7BF // 220 +data4 0x23B6D597 // 221 +data4 0x210E9474 // 222 +data4 0x242156E6 // 223 +data4 0x243A1D68 // 224 +data4 0x2472187C // 225 +data4 0x23834E86 // 226 +data4 0x23CA0807 // 227 +data4 0x24745887 // 228 +data4 0x23E2B0E1 // 229 +data4 0x2421EB67 // 230 +data4 0x23DCC64E // 231 +data4 0x22DF71D1 // 232 +data4 0x238D5ECA // 233 +data4 0x23CDE86F // 234 +data4 0x24131F45 // 235 +data4 0x240FE4E2 // 236 +data4 0x2317731A // 237 +data4 0x24015C76 // 238 +data4 0x2301A4E8 // 239 +data4 0x23E52A6D // 240 +data4 0x247D8A0D // 241 +data4 0x23DFEEBA // 242 +data4 0x22139FEC // 243 +data4 0x2454A112 // 244 +data4 0x23C21E28 // 245 +data4 0x2460D813 // 246 +data4 0x24258924 // 247 +data4 0x2425680F // 248 +data4 0x24194D1E // 249 +data4 0x24242C2F // 250 +data4 0x243DDE5E // 251 +data4 0x23DEB388 // 252 +data4 0x23E0E6EB // 253 +data4 0x24393E74 // 254 +data4 0x241B1863 // 255 +LOCAL_OBJECT_END(log10_data) + + + +// Code +//============================================================== + +// log has p13 true, p14 false +// log10 has p14 true, p13 false + +.section .text +GLOBAL_IEEE754_ENTRY(log10) +{ .mfi + getf.exp GR_Exp = f8 // if x is unorm then must recompute + frcpa.s1 FR_RcpX,p0 = f1,f8 + mov GR_05 = 0xFFFE // biased exponent of A2=0.5 +} +{ .mlx + addl GR_ad_1 = @ltoff(log10_data),gp + movl GR_A3 = 0x3fd5555555555557 // double precision memory + // representation of A3 +};; + +{ .mfi + getf.sig GR_Sig = f8 // get significand to calculate index + fclass.m p8,p0 = f8,9 // is x positive unorm? + mov GR_xorg = 0x3fefe // double precision memory msb of 255/256 +} +{ .mib + ld8 GR_ad_1 = [GR_ad_1] + cmp.eq p14,p13 = r0,r0 // set p14 to 1 for log10 + br.cond.sptk log_log10_common +};; +GLOBAL_IEEE754_END(log10) + + +GLOBAL_IEEE754_ENTRY(log) +{ .mfi + getf.exp GR_Exp = f8 // if x is unorm then must recompute + frcpa.s1 FR_RcpX,p0 = f1,f8 + mov GR_05 = 0xfffe +} +{ .mlx + addl GR_ad_1 = @ltoff(log_data),gp + movl GR_A3 = 0x3fd5555555555557 // double precision memory + // representation of A3 +};; + +{ .mfi + getf.sig GR_Sig = f8 // get significand to calculate index + fclass.m p8,p0 = f8,9 // is x positive unorm? + mov GR_xorg = 0x3fefe // double precision memory msb of 255/256 +} +{ .mfi + ld8 GR_ad_1 = [GR_ad_1] + nop.f 0 + cmp.eq p13,p14 = r0,r0 // set p13 to 1 for log +};; + +log_log10_common: +{ .mfi + getf.d GR_x = f8 // double precision memory representation of x + fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? + dep.z GR_dx = 3, 44, 2 // Create 0x0000300000000000 + // Difference between double precision + // memory representations of 257/256 and + // 255/256 +} +{ .mfi + setf.exp FR_A2 = GR_05 // create A2 + fnorm.s1 FR_NormX = f8 + mov GR_bias = 0xffff +};; + +{ .mfi + setf.d FR_A3 = GR_A3 // create A3 + fcmp.eq.s1 p12,p0 = f1,f8 // is x equal to 1.0? + dep.z GR_xorg = GR_xorg, 44, 19 // 0x3fefe00000000000 + // double precision memory + // representation of 255/256 +} +{ .mib + add GR_ad_2 = 0x30,GR_ad_1 // address of A5,A4 + add GR_ad_3 = 0x840,GR_ad_1 // address of ln(1/frcpa) lo parts +(p8) br.cond.spnt log_positive_unorms +};; + +log_core: +{ .mfi + ldfpd FR_A7,FR_A6 = [GR_ad_1],16 + fclass.m p10,p0 = f8,0x3A // is x < 0? + sub GR_Nm1 = GR_Exp,GR_05 // unbiased_exponent_of_x - 1 +} +{ .mfi + ldfpd FR_A5,FR_A4 = [GR_ad_2],16 +(p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag + sub GR_N = GR_Exp,GR_bias // unbiased_exponent_of_x +};; + +{ .mfi + setf.sig FR_N = GR_N // copy unbiased exponent of x to significand + fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256 + extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index +} +{ .mib + sub GR_x = GR_x, GR_xorg // get diff between x and 255/256 + cmp.gtu p6, p7 = 2, GR_Nm1 // p6 true if 0.5 <= x < 2 +(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf +};; + +{ .mfi + ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16 + fclass.m p11,p0 = f8,0x07 // is x = 0? + shladd GR_ad_3 = GR_Ind,2,GR_ad_3 // address of Tlo +} +{ .mib + shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi +(p6) cmp.leu p6, p7 = GR_x, GR_dx // 255/256 <= x <= 257/256 +(p10) br.cond.spnt log_negatives // jump if x is negative +};; + +// p6 is true if |x-1| < 1/256 +// p7 is true if |x-1| >= 1/256 +{ .mfi + ldfd FR_Thi = [GR_ad_2] +(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256 + nop.i 0 +};; + +{ .mmi +(p7) ldfs FR_Tlo = [GR_ad_3] + nop.m 0 + nop.i 0 +} +{ .mfb + nop.m 0 +(p12) fma.d.s0 f8 = f0,f0,f0 +(p12) br.ret.spnt b0 // exit for +1.0 +};; + +.pred.rel "mutex",p6,p7 +{ .mfi +(p6) mov GR_NearOne = 1 + fms.s1 FR_A32 = FR_A3,FR_r,FR_A2 // A3*r-A2 +(p7) mov GR_NearOne = 0 +} +{ .mfb + ldfe FR_InvLn10 = [GR_ad_1],16 + fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 +(p11) br.cond.spnt log_zeroes // jump if x is zero +};; + +{ .mfi + nop.m 0 + fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6 + nop.i 0 +} +{ .mfi +(p7) cmp.eq.unc p9,p0 = r0,r0 // set p9 if |x-1| > 1/256 + fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4 +(p14) cmp.eq.unc p8,p0 = 1,GR_NearOne // set p8 to 1 if it's log10 + // and argument near 1.0 +};; + +{ .mfi +(p6) getf.exp GR_rexp = FR_r // Get signexp of x-1 +(p7) fcvt.xf FR_N = FR_N +(p8) cmp.eq p9,p6 = r0,r0 // Also set p9 and clear p6 if log10 + // and arg near 1 +};; + +{ .mfi + nop.m 0 + fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4 + nop.i 0 +} +{ .mfi + nop.m 0 +(p8) fma.s1 FR_NxLn2pT = f0,f0,f0 // Clear NxLn2pT if log10 near 1 + nop.i 0 +};; + +{ .mfi + nop.m 0 + // (A3*r+A2)*r^2+r + fma.s1 FR_A321 = FR_A32,FR_r2,FR_r + mov GR_mask = 0x1ffff +} +{ .mfi + nop.m 0 + // (A7*r+A6)*r^2+(A5*r+A4) + fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4 + nop.i 0 +};; + +{ .mfi +(p6) and GR_rexp = GR_rexp, GR_mask + // N*Ln2hi+Thi +(p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi + nop.i 0 +} +{ .mfi + nop.m 0 + // N*Ln2lo+Tlo +(p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo + nop.i 0 +};; + +{ .mfi +(p6) sub GR_rexp = GR_rexp, GR_bias // unbiased exponent of x-1 +(p9) fma.s1 f8 = FR_A4,FR_r4,FR_A321 // P(r) if |x-1| >= 1/256 or + // log10 and |x-1| < 1/256 + nop.i 0 +} +{ .mfi + nop.m 0 + // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo) +(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo + nop.i 0 +};; + +{ .mfi +(p6) cmp.gt.unc p10, p6 = -40, GR_rexp // Test |x-1| < 2^-40 + nop.f 0 + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p10) fma.d.s0 f8 = FR_A32,FR_r2,FR_r // log(x) if |x-1| < 2^-40 + nop.i 0 +};; + +.pred.rel "mutex",p6,p9 +{ .mfi + nop.m 0 +(p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A321 // log(x) if 2^-40 <= |x-1| < 1/256 + nop.i 0 +} +{ .mfb + nop.m 0 +(p9) fma.d.s0 f8 = f8,FR_InvLn10,FR_NxLn2pT // result if |x-1| >= 1/256 + // or log10 and |x-1| < 1/256 + br.ret.sptk b0 +};; + +.align 32 +log_positive_unorms: +{ .mmf + getf.exp GR_Exp = FR_NormX // recompute biased exponent + getf.d GR_x = FR_NormX // recompute double precision x + fcmp.eq.s1 p12,p0 = f1,FR_NormX // is x equal to 1.0? +};; + +{ .mfb + getf.sig GR_Sig = FR_NormX // recompute significand + fcmp.eq.s0 p15, p0 = f8, f0 // set denormal flag + br.cond.sptk log_core +};; + +.align 32 +log_zeroes: +{ .mfi + nop.m 0 + fmerge.s FR_X = f8,f8 // keep input argument for subsequent + // call of __libm_error_support# + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_tmp = f0,f0,f1 // -1.0 + nop.i 0 +};; + +.pred.rel "mutex",p13,p14 +{ .mfi +(p13) mov GR_TAG = 2 // set libm error in case of log + frcpa.s0 f8,p0 = FR_tmp,f0 // log(+/-0) should be equal to -INF. + // We can get it using frcpa because it + // sets result to the IEEE-754 mandated + // quotient of FR_tmp/f0. + // As far as FR_tmp is -1 it'll be -INF + nop.i 0 +} +{ .mib +(p14) mov GR_TAG = 8 // set libm error in case of log10 + nop.i 0 + br.cond.sptk log_libm_err +};; + +.align 32 +log_negatives: +{ .mfi + nop.m 0 + fmerge.s FR_X = f8,f8 + nop.i 0 +};; + +.pred.rel "mutex",p13,p14 +{ .mfi +(p13) mov GR_TAG = 3 // set libm error in case of log + frcpa.s0 f8,p0 = f0,f0 // log(negatives) should be equal to NaN. + // We can get it using frcpa because it + // sets result to the IEEE-754 mandated + // quotient of f0/f0 i.e. NaN. +(p14) mov GR_TAG = 9 // set libm error in case of log10 +};; + +.align 32 +log_libm_err: +{ .mmi + alloc r32 = ar.pfs,1,4,4,0 + mov GR_Parameter_TAG = GR_TAG + nop.i 0 +};; +GLOBAL_IEEE754_END(log) + + +LOCAL_LIBM_ENTRY(__libm_error_region) +.prologue +{ .mfi + add GR_Parameter_Y = -32,sp // Parameter 2 value + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS = ar.pfs // Save ar.pfs +} +{ .mfi +.fframe 64 + add sp = -64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP = gp // Save gp +};; + +{ .mmi + stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0 = b0 // Save b0 +};; + +.body +{ .mib + stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 +} +{ .mib + stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack + add GR_Parameter_Y = -16,GR_Parameter_Y + br.call.sptk b0=__libm_error_support# // Call error handling function +};; + +{ .mmi + add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 +};; + +{ .mmi + ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack +.restore sp + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address +};; + +{ .mib + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return +};; +LOCAL_LIBM_END(__libm_error_region) + +.type __libm_error_support#,@function +.global __libm_error_support# |