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Diffstat (limited to 'sysdeps/ia64/fpu/e_logf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_logf.S | 1787 |
1 files changed, 795 insertions, 992 deletions
diff --git a/sysdeps/ia64/fpu/e_logf.S b/sysdeps/ia64/fpu/e_logf.S index 0ca6d3f2c8..829d0abed0 100644 --- a/sysdeps/ia64/fpu/e_logf.S +++ b/sysdeps/ia64/fpu/e_logf.S @@ -1,10 +1,10 @@ .file "logf.s" - -// Copyright (c) 2000 - 2003, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, +// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,1072 +20,861 @@ // * 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 +// +// 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 +// 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 +// 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. -// +// 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. +// problem reports or change requests be submitted to it directly at +// http://developer.intel.com/opensource. // // History //============================================================== -// 03/01/00 Initial version -// 08/15/00 Bundle added after call to __libm_error_support to properly +// 3/01/00 Initial version +// 8/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. -// 01/10/01 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 -// 02/10/03 Reordered header: .section, .global, .proc, .align +// 1/10/01 Improved speed, fixed flags for neg denormals +// // // API //============================================================== // float logf(float) // float log10f(float) // -// // Overview of operation //============================================================== // Background -// ---------- // -// This algorithm is based on fact that -// log(a b) = log(a) + log(b). +// Consider x = 2^N 1.f1 f2 f3 f4...f63 +// Log(x) = log(frcpa(x) x/frcpa(x)) +// = log(1/frcpa(x)) + log(frcpa(x) x) +// = -log(frcpa(x)) + log(frcpa(x) x) // -// 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) +// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63) // -// To calculate log(f) we do following -// log(f) = log(f * frcpa(f) / frcpa(f)) = -// = log(f * frcpa(f)) + log(1/frcpa(f)) +// -log(frcpa(x)) = -log(C) +// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63)) // -// 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 +// -log(frcpa(x)) = -log(C) +// = +Nlog2 - log(frcpa(1.f1 f2 ... f63)) // -// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 +// -log(frcpa(x)) = -log(C) +// = +Nlog2 + log(frcpa(1.f1 f2 ... f63)) // -// 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 just use identity: +// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x) + +// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) +// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) +// Log(x) = +Nlog2 + T + log(frcpa(x) x) // -// log10(x) = log(x)/log(10) +// Log(x) = +Nlog2 + T + log(C x) // -// so we have that +// Cx = 1 + r // -// log10(x) = (N*log(2) + T + log(1+r)) / log(10) = -// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10) +// Log(x) = +Nlog2 + T + log(1+r) +// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....) // +// 1.f1 f2 ... f8 has 256 entries. +// They are 1 + k/2^8, k = 0 ... 255 +// These 256 values are the table entries. // // 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 can be used. -// -// Note that both log and log10 use common approximation polynomial -// it means we need only one set of coefficients of approximation. -// -// 1. Computation of log(x) for |x-1| >= 1/256 -// InvX = frcpa(x) -// r = InvX*x - 1 -// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r), -// A4,A3,A2 are created with setf inctruction. -// We use Taylor series and so A4 = 1/4, A3 = 1/3, -// A2 = 1/2 rounded to double. -// -// 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 rounded to double. To T we get bits from 55 to 62 of register -// format significand of x and calculate address -// ad_T = table_base_addr + 8 * index -// -// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad -// precision and rounded to double; it's loaded from memory -// -// L1 (log(2) or log10(2) depending on function) is calculated in quad -// precision and rounded to double; it's created with setf. -// -// And final result = P2(r)*(r*L2) + (T + N*L1) -// -// -// 2. Computation of log(x) for |x-1| < 1/256 -// r = x - 1 -// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r), -// A4,A3,A2 are the same as in case |x-1| >= 1/256 -// -// And final result = P2(r)*(r*L2) -// -// 3. How we define is input argument such that |x-1| < 1/256 or not. -// -// To do it we analyze biased exponent and significand of input argment. +//=============== +// CASE 1: |x-1| >= 2^-8 +// C = frcpa(x) +// r = C * x - 1 // -// 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 +// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 // +// x = f * 2*n where f is 1.f_1f_2f_3....f_63 +// Nfloat = float(n) where n is the true unbiased exponent +// pre-index = f_1f_2....f_8 +// index = pre_index * 16 +// get the dxt table entry at index + offset = T // -// 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 register format representation with -// 0xFFFEFF00000000000000 and 0xFFFF8080000000000000 correspondingly. -// As far as biased exponent of x here can be equal only to 0xFFFE or -// 0xFFFF we need to test only last bit of it. Also signifigand always -// has implicit bit set to 1 that can be exluded from comparison. -// Thus it's quite enough to generate 64-bit integer bits of that are -// ix[63] = biased_exponent_of_x[0] and ix[62-0] = significand_of_x[62-0] -// and compare it with 0x7F00000000000000 and 0x80800000000000000 (those -// obtained like ix from register representatinos of 255/256 and -// 257/256). This comparison can be made like in a), using unsigned -// version of cmp i.e. ix - 0x7F00000000000000 < 0x0180000000000000. -// 0x0180000000000000 is difference between 0x80800000000000000 and -// 0x7F00000000000000. +// result = (T + Nfloat * log(2)) + rseries // -// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are -// filtered and processed on special branches. +// The T table is calculated as follows +// Form x_k = 1 + k/2^8 where k goes from 0... 255 +// y_k = frcpa(x_k) +// log(1/y_k) in quad and round to double + +// CASE 2: |x-1| < 2^-6 +// w = x - 1 // +// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4 // -// Special values +// result = wseries + +// Special values //============================================================== -// -// logf(+0) = -inf -// logf(-0) = -inf -// -// logf(+qnan) = +qnan -// logf(-qnan) = -qnan -// logf(+snan) = +qnan -// logf(-snan) = -qnan -// -// logf(-n) = QNAN Indefinite -// logf(-inf) = QNAN Indefinite -// -// logf(+inf) = +inf -// + + +// 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: +// Floating Point registers used: // f8, input -// f12 -> f14, f33 -> f39 -// -// General registers used: -// r8 -> r11 -// r14 -> r19 -// +// f9 -> f15, f32 -> f47 + +// General registers used: +// r32 -> r51 + // Predicate registers used: -// p6 -> p12 +// p6 -> p15 +// p8 log base e +// p6 log base e special +// p9 used in the frcpa +// p13 log base e large W +// p14 log base e small w + +// p7 log base 10 +// p10 log base 10 large W +// p11 log base 10 small w +// p12 log base 10 special + +#include "libm_support.h" // Assembly macros //============================================================== -GR_TAG = r8 -GR_ad_T = r8 -GR_N = r9 -GR_Exp = r10 -GR_Sig = r11 - -GR_025 = r14 -GR_05 = r15 -GR_A3 = r16 -GR_Ind = r17 -GR_dx = r15 -GR_Ln2 = r19 -GR_de = r20 -GR_x = r21 -GR_xorg = r22 - -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_A2 = f12 -FR_A3 = f13 -FR_A4 = f14 - -FR_RcpX = f33 -FR_r = f34 -FR_r2 = f35 -FR_tmp = f35 -FR_Ln2 = f36 -FR_T = f37 -FR_N = f38 -FR_NxLn2pT = f38 -FR_NormX = f39 -FR_InvLn10 = f40 - - -FR_Y = f1 -FR_X = f10 -FR_RESULT = f8 +log_int_Nfloat = f9 +log_Nfloat = f10 + +log_P3 = f11 +log_P2 = f12 +log_P1 = f13 +log_inv_ln10 = f14 +log_log2 = f15 + +log_w = f32 +log_T = f33 +log_rp_p32 = f34 +log_rp_p2 = f35 +log_rp_p10 = f36 +log_rsq = f37 +log_T_plus_Nlog2 = f38 +log_r = f39 +log_C = f40 +log_rp_q32 = f41 +log_rp_q2 = f42 +log_rp_q10 = f43 +log_wsq = f44 +log_Q = f45 +log_inv_ln10 = f46 +log_NORM_f8 = f47 + +// =================================== + +log_GR_exp_17_ones = r33 +log_GR_exp_16_ones = r34 +log_GR_exp_f8 = r35 +log_GR_signexp_f8 = r36 +log_GR_true_exp_f8 = r37 +log_GR_significand_f8 = r38 +log_GR_index = r39 +log_AD_1 = r40 +log_GR_signexp_w = r41 +log_GR_fff7 = r42 +log_AD_2 = r43 +log_GR_exp_w = r44 + +GR_SAVE_B0 = r45 +GR_SAVE_GP = r46 +GR_SAVE_PFS = r47 + +GR_Parameter_X = r48 +GR_Parameter_Y = r49 +GR_Parameter_RESULT = r50 +log_GR_tag = r51 // Data tables //============================================================== -RODATA + +#ifdef _LIBC +.rodata +#else +.data +#endif + .align 16 -LOCAL_OBJECT_START(logf_data) -data8 0x3FF0000000000000 // 1.0 -// -// ln(1/frcpa(1+i/256)), i=0...255 -data8 0x3F60040155D5889E // 0 -data8 0x3F78121214586B54 // 1 -data8 0x3F841929F96832F0 // 2 -data8 0x3F8C317384C75F06 // 3 -data8 0x3F91A6B91AC73386 // 4 -data8 0x3F95BA9A5D9AC039 // 5 -data8 0x3F99D2A8074325F4 // 6 -data8 0x3F9D6B2725979802 // 7 -data8 0x3FA0C58FA19DFAAA // 8 -data8 0x3FA2954C78CBCE1B // 9 -data8 0x3FA4A94D2DA96C56 // 10 -data8 0x3FA67C94F2D4BB58 // 11 -data8 0x3FA85188B630F068 // 12 -data8 0x3FAA6B8ABE73AF4C // 13 -data8 0x3FAC441E06F72A9E // 14 -data8 0x3FAE1E6713606D07 // 15 -data8 0x3FAFFA6911AB9301 // 16 -data8 0x3FB0EC139C5DA601 // 17 -data8 0x3FB1DBD2643D190B // 18 -data8 0x3FB2CC7284FE5F1C // 19 -data8 0x3FB3BDF5A7D1EE64 // 20 -data8 0x3FB4B05D7AA012E0 // 21 -data8 0x3FB580DB7CEB5702 // 22 -data8 0x3FB674F089365A7A // 23 -data8 0x3FB769EF2C6B568D // 24 -data8 0x3FB85FD927506A48 // 25 -data8 0x3FB9335E5D594989 // 26 -data8 0x3FBA2B0220C8E5F5 // 27 -data8 0x3FBB0004AC1A86AC // 28 -data8 0x3FBBF968769FCA11 // 29 -data8 0x3FBCCFEDBFEE13A8 // 30 -data8 0x3FBDA727638446A2 // 31 -data8 0x3FBEA3257FE10F7A // 32 -data8 0x3FBF7BE9FEDBFDE6 // 33 -data8 0x3FC02AB352FF25F4 // 34 -data8 0x3FC097CE579D204D // 35 -data8 0x3FC1178E8227E47C // 36 -data8 0x3FC185747DBECF34 // 37 -data8 0x3FC1F3B925F25D41 // 38 -data8 0x3FC2625D1E6DDF57 // 39 -data8 0x3FC2D1610C86813A // 40 -data8 0x3FC340C59741142E // 41 -data8 0x3FC3B08B6757F2A9 // 42 -data8 0x3FC40DFB08378003 // 43 -data8 0x3FC47E74E8CA5F7C // 44 -data8 0x3FC4EF51F6466DE4 // 45 -data8 0x3FC56092E02BA516 // 46 -data8 0x3FC5D23857CD74D5 // 47 -data8 0x3FC6313A37335D76 // 48 -data8 0x3FC6A399DABBD383 // 49 -data8 0x3FC70337DD3CE41B // 50 -data8 0x3FC77654128F6127 // 51 -data8 0x3FC7E9D82A0B022D // 52 -data8 0x3FC84A6B759F512F // 53 -data8 0x3FC8AB47D5F5A310 // 54 -data8 0x3FC91FE49096581B // 55 -data8 0x3FC981634011AA75 // 56 -data8 0x3FC9F6C407089664 // 57 -data8 0x3FCA58E729348F43 // 58 -data8 0x3FCABB55C31693AD // 59 -data8 0x3FCB1E104919EFD0 // 60 -data8 0x3FCB94EE93E367CB // 61 -data8 0x3FCBF851C067555F // 62 -data8 0x3FCC5C0254BF23A6 // 63 -data8 0x3FCCC000C9DB3C52 // 64 -data8 0x3FCD244D99C85674 // 65 -data8 0x3FCD88E93FB2F450 // 66 -data8 0x3FCDEDD437EAEF01 // 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 0x3FD0EDD060B78081 // 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 0x3FD29ECDABCDFA04 // 86 -data8 0x3FD2D46602ADCCEE // 87 -data8 0x3FD2FF66B04EA9D4 // 88 -data8 0x3FD335504B355A37 // 89 -data8 0x3FD360925EC44F5D // 90 -data8 0x3FD38BF1C3337E75 // 91 -data8 0x3FD3C25277333184 // 92 -data8 0x3FD3EDF463C1683E // 93 -data8 0x3FD419B423D5E8C7 // 94 -data8 0x3FD44591E0539F49 // 95 -data8 0x3FD47C9175B6F0AD // 96 -data8 0x3FD4A8B341552B09 // 97 -data8 0x3FD4D4F3908901A0 // 98 -data8 0x3FD501528DA1F968 // 99 -data8 0x3FD52DD06347D4F6 // 100 -data8 0x3FD55A6D3C7B8A8A // 101 -data8 0x3FD5925D2B112A59 // 102 -data8 0x3FD5BF406B543DB2 // 103 -data8 0x3FD5EC433D5C35AE // 104 -data8 0x3FD61965CDB02C1F // 105 -data8 0x3FD646A84935B2A2 // 106 -data8 0x3FD6740ADD31DE94 // 107 -data8 0x3FD6A18DB74A58C5 // 108 -data8 0x3FD6CF31058670EC // 109 -data8 0x3FD6F180E852F0BA // 110 -data8 0x3FD71F5D71B894F0 // 111 -data8 0x3FD74D5AEFD66D5C // 112 -data8 0x3FD77B79922BD37E // 113 -data8 0x3FD7A9B9889F19E2 // 114 -data8 0x3FD7D81B037EB6A6 // 115 -data8 0x3FD8069E33827231 // 116 -data8 0x3FD82996D3EF8BCB // 117 -data8 0x3FD85855776DCBFB // 118 -data8 0x3FD8873658327CCF // 119 -data8 0x3FD8AA75973AB8CF // 120 -data8 0x3FD8D992DC8824E5 // 121 -data8 0x3FD908D2EA7D9512 // 122 -data8 0x3FD92C59E79C0E56 // 123 -data8 0x3FD95BD750EE3ED3 // 124 -data8 0x3FD98B7811A3EE5B // 125 -data8 0x3FD9AF47F33D406C // 126 -data8 0x3FD9DF270C1914A8 // 127 -data8 0x3FDA0325ED14FDA4 // 128 -data8 0x3FDA33440224FA79 // 129 -data8 0x3FDA57725E80C383 // 130 -data8 0x3FDA87D0165DD199 // 131 -data8 0x3FDAAC2E6C03F896 // 132 -data8 0x3FDADCCC6FDF6A81 // 133 -data8 0x3FDB015B3EB1E790 // 134 -data8 0x3FDB323A3A635948 // 135 -data8 0x3FDB56FA04462909 // 136 -data8 0x3FDB881AA659BC93 // 137 -data8 0x3FDBAD0BEF3DB165 // 138 -data8 0x3FDBD21297781C2F // 139 -data8 0x3FDC039236F08819 // 140 -data8 0x3FDC28CB1E4D32FD // 141 -data8 0x3FDC4E19B84723C2 // 142 -data8 0x3FDC7FF9C74554C9 // 143 -data8 0x3FDCA57B64E9DB05 // 144 -data8 0x3FDCCB130A5CEBB0 // 145 -data8 0x3FDCF0C0D18F326F // 146 -data8 0x3FDD232075B5A201 // 147 -data8 0x3FDD490246DEFA6B // 148 -data8 0x3FDD6EFA918D25CD // 149 -data8 0x3FDD9509707AE52F // 150 -data8 0x3FDDBB2EFE92C554 // 151 -data8 0x3FDDEE2F3445E4AF // 152 -data8 0x3FDE148A1A2726CE // 153 -data8 0x3FDE3AFC0A49FF40 // 154 -data8 0x3FDE6185206D516E // 155 -data8 0x3FDE882578823D52 // 156 -data8 0x3FDEAEDD2EAC990C // 157 -data8 0x3FDED5AC5F436BE3 // 158 -data8 0x3FDEFC9326D16AB9 // 159 -data8 0x3FDF2391A2157600 // 160 -data8 0x3FDF4AA7EE03192D // 161 -data8 0x3FDF71D627C30BB0 // 162 -data8 0x3FDF991C6CB3B379 // 163 -data8 0x3FDFC07ADA69A910 // 164 -data8 0x3FDFE7F18EB03D3E // 165 -data8 0x3FE007C053C5002E // 166 -data8 0x3FE01B942198A5A1 // 167 -data8 0x3FE02F74400C64EB // 168 -data8 0x3FE04360BE7603AD // 169 -data8 0x3FE05759AC47FE34 // 170 -data8 0x3FE06B5F1911CF52 // 171 -data8 0x3FE078BF0533C568 // 172 -data8 0x3FE08CD9687E7B0E // 173 -data8 0x3FE0A10074CF9019 // 174 -data8 0x3FE0B5343A234477 // 175 -data8 0x3FE0C974C89431CE // 176 -data8 0x3FE0DDC2305B9886 // 177 -data8 0x3FE0EB524BAFC918 // 178 -data8 0x3FE0FFB54213A476 // 179 -data8 0x3FE114253DA97D9F // 180 -data8 0x3FE128A24F1D9AFF // 181 -data8 0x3FE1365252BF0865 // 182 -data8 0x3FE14AE558B4A92D // 183 -data8 0x3FE15F85A19C765B // 184 -data8 0x3FE16D4D38C119FA // 185 -data8 0x3FE18203C20DD133 // 186 -data8 0x3FE196C7BC4B1F3B // 187 -data8 0x3FE1A4A738B7A33C // 188 -data8 0x3FE1B981C0C9653D // 189 -data8 0x3FE1CE69E8BB106B // 190 -data8 0x3FE1DC619DE06944 // 191 -data8 0x3FE1F160A2AD0DA4 // 192 -data8 0x3FE2066D7740737E // 193 -data8 0x3FE2147DBA47A394 // 194 -data8 0x3FE229A1BC5EBAC3 // 195 -data8 0x3FE237C1841A502E // 196 -data8 0x3FE24CFCE6F80D9A // 197 -data8 0x3FE25B2C55CD5762 // 198 -data8 0x3FE2707F4D5F7C41 // 199 -data8 0x3FE285E0842CA384 // 200 -data8 0x3FE294294708B773 // 201 -data8 0x3FE2A9A2670AFF0C // 202 -data8 0x3FE2B7FB2C8D1CC1 // 203 -data8 0x3FE2C65A6395F5F5 // 204 -data8 0x3FE2DBF557B0DF43 // 205 -data8 0x3FE2EA64C3F97655 // 206 -data8 0x3FE3001823684D73 // 207 -data8 0x3FE30E97E9A8B5CD // 208 -data8 0x3FE32463EBDD34EA // 209 -data8 0x3FE332F4314AD796 // 210 -data8 0x3FE348D90E7464D0 // 211 -data8 0x3FE35779F8C43D6E // 212 -data8 0x3FE36621961A6A99 // 213 -data8 0x3FE37C299F3C366A // 214 -data8 0x3FE38AE2171976E7 // 215 -data8 0x3FE399A157A603E7 // 216 -data8 0x3FE3AFCCFE77B9D1 // 217 -data8 0x3FE3BE9D503533B5 // 218 -data8 0x3FE3CD7480B4A8A3 // 219 -data8 0x3FE3E3C43918F76C // 220 -data8 0x3FE3F2ACB27ED6C7 // 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 0x3FE489445EFFFCCC // 230 -data8 0x3FE4A018BCB69835 // 231 -data8 0x3FE4AF5A0C9D65D7 // 232 -data8 0x3FE4BEA2A5BDBE87 // 233 -data8 0x3FE4CDF28F10AC46 // 234 -data8 0x3FE4DD49CF994058 // 235 -data8 0x3FE4ECA86E64A684 // 236 -data8 0x3FE503C43CD8EB68 // 237 -data8 0x3FE513356667FC57 // 238 -data8 0x3FE522AE0738A3D8 // 239 -data8 0x3FE5322E26867857 // 240 -data8 0x3FE541B5CB979809 // 241 -data8 0x3FE55144FDBCBD62 // 242 -data8 0x3FE560DBC45153C7 // 243 -data8 0x3FE5707A26BB8C66 // 244 -data8 0x3FE587F60ED5B900 // 245 -data8 0x3FE597A7977C8F31 // 246 -data8 0x3FE5A760D634BB8B // 247 -data8 0x3FE5B721D295F10F // 248 -data8 0x3FE5C6EA94431EF9 // 249 -data8 0x3FE5D6BB22EA86F6 // 250 -data8 0x3FE5E6938645D390 // 251 -data8 0x3FE5F673C61A2ED2 // 252 -data8 0x3FE6065BEA385926 // 253 -data8 0x3FE6164BFA7CC06B // 254 -data8 0x3FE62643FECF9743 // 255 -LOCAL_OBJECT_END(logf_data) - -LOCAL_OBJECT_START(log10f_data) -data8 0x3FDBCB7B1526E50E // 1/ln(10) -// -// ln(1/frcpa(1+i/256))/ln(10), i=0...255 -data8 0x3F4BD27045BFD025 // 0 -data8 0x3F64E84E793A474A // 1 -data8 0x3F7175085AB85FF0 // 2 -data8 0x3F787CFF9D9147A5 // 3 -data8 0x3F7EA9D372B89FC8 // 4 -data8 0x3F82DF9D95DA961C // 5 -data8 0x3F866DF172D6372C // 6 -data8 0x3F898D79EF5EEDF0 // 7 -data8 0x3F8D22ADF3F9579D // 8 -data8 0x3F9024231D30C398 // 9 -data8 0x3F91F23A98897D4A // 10 -data8 0x3F93881A7B818F9E // 11 -data8 0x3F951F6E1E759E35 // 12 -data8 0x3F96F2BCE7ADC5B4 // 13 -data8 0x3F988D362CDF359E // 14 -data8 0x3F9A292BAF010982 // 15 -data8 0x3F9BC6A03117EB97 // 16 -data8 0x3F9D65967DE3AB09 // 17 -data8 0x3F9F061167FC31E8 // 18 -data8 0x3FA05409E4F7819C // 19 -data8 0x3FA125D0432EA20E // 20 -data8 0x3FA1F85D440D299B // 21 -data8 0x3FA2AD755749617D // 22 -data8 0x3FA381772A00E604 // 23 -data8 0x3FA45643E165A70B // 24 -data8 0x3FA52BDD034475B8 // 25 -data8 0x3FA5E3966B7E9295 // 26 -data8 0x3FA6BAAF47C5B245 // 27 -data8 0x3FA773B3E8C4F3C8 // 28 -data8 0x3FA84C51EBEE8D15 // 29 -data8 0x3FA906A6786FC1CB // 30 -data8 0x3FA9C197ABF00DD7 // 31 -data8 0x3FAA9C78712191F7 // 32 -data8 0x3FAB58C09C8D637C // 33 -data8 0x3FAC15A8BCDD7B7E // 34 -data8 0x3FACD331E2C2967C // 35 -data8 0x3FADB11ED766ABF4 // 36 -data8 0x3FAE70089346A9E6 // 37 -data8 0x3FAF2F96C6754AEE // 38 -data8 0x3FAFEFCA8D451FD6 // 39 -data8 0x3FB0585283764178 // 40 -data8 0x3FB0B913AAC7D3A7 // 41 -data8 0x3FB11A294F2569F6 // 42 -data8 0x3FB16B51A2696891 // 43 -data8 0x3FB1CD03ADACC8BE // 44 -data8 0x3FB22F0BDD7745F5 // 45 -data8 0x3FB2916ACA38D1E8 // 46 -data8 0x3FB2F4210DF7663D // 47 -data8 0x3FB346A6C3C49066 // 48 -data8 0x3FB3A9FEBC60540A // 49 -data8 0x3FB3FD0C10A3AA54 // 50 -data8 0x3FB46107D3540A82 // 51 -data8 0x3FB4C55DD16967FE // 52 -data8 0x3FB51940330C000B // 53 -data8 0x3FB56D620EE7115E // 54 -data8 0x3FB5D2ABCF26178E // 55 -data8 0x3FB6275AA5DEBF81 // 56 -data8 0x3FB68D4EAF26D7EE // 57 -data8 0x3FB6E28C5C54A28D // 58 -data8 0x3FB7380B9665B7C8 // 59 -data8 0x3FB78DCCC278E85B // 60 -data8 0x3FB7F50C2CF2557A // 61 -data8 0x3FB84B5FD5EAEFD8 // 62 -data8 0x3FB8A1F6BAB2B226 // 63 -data8 0x3FB8F8D144557BDF // 64 -data8 0x3FB94FEFDCD61D92 // 65 -data8 0x3FB9A752EF316149 // 66 -data8 0x3FB9FEFAE7611EE0 // 67 -data8 0x3FBA56E8325F5C87 // 68 -data8 0x3FBAAF1B3E297BB4 // 69 -data8 0x3FBB079479C372AD // 70 -data8 0x3FBB6054553B12F7 // 71 -data8 0x3FBBB95B41AB5CE6 // 72 -data8 0x3FBC12A9B13FE079 // 73 -data8 0x3FBC6C4017382BEA // 74 -data8 0x3FBCB41FBA42686D // 75 -data8 0x3FBD0E38CE73393F // 76 -data8 0x3FBD689B2193F133 // 77 -data8 0x3FBDC3472B1D2860 // 78 -data8 0x3FBE0C06300D528B // 79 -data8 0x3FBE6738190E394C // 80 -data8 0x3FBEC2B50D208D9B // 81 -data8 0x3FBF0C1C2B936828 // 82 -data8 0x3FBF68216C9CC727 // 83 -data8 0x3FBFB1F6381856F4 // 84 -data8 0x3FC00742AF4CE5F8 // 85 -data8 0x3FC02C64906512D2 // 86 -data8 0x3FC05AF1E63E03B4 // 87 -data8 0x3FC0804BEA723AA9 // 88 -data8 0x3FC0AF1FD6711527 // 89 -data8 0x3FC0D4B2A8805A00 // 90 -data8 0x3FC0FA5EF136A06C // 91 -data8 0x3FC1299A4FB3E306 // 92 -data8 0x3FC14F806253C3ED // 93 -data8 0x3FC175805D1587C1 // 94 -data8 0x3FC19B9A637CA295 // 95 -data8 0x3FC1CB5FC26EDE17 // 96 -data8 0x3FC1F1B4E65F2590 // 97 -data8 0x3FC218248B5DC3E5 // 98 -data8 0x3FC23EAED62ADC76 // 99 -data8 0x3FC26553EBD337BD // 100 -data8 0x3FC28C13F1B11900 // 101 -data8 0x3FC2BCAA14381386 // 102 -data8 0x3FC2E3A740B7800F // 103 -data8 0x3FC30ABFD8F333B6 // 104 -data8 0x3FC331F403985097 // 105 -data8 0x3FC35943E7A60690 // 106 -data8 0x3FC380AFAC6E7C07 // 107 -data8 0x3FC3A8377997B9E6 // 108 -data8 0x3FC3CFDB771C9ADB // 109 -data8 0x3FC3EDA90D39A5DF // 110 -data8 0x3FC4157EC09505CD // 111 -data8 0x3FC43D7113FB04C1 // 112 -data8 0x3FC4658030AD1CCF // 113 -data8 0x3FC48DAC404638F6 // 114 -data8 0x3FC4B5F56CBBB869 // 115 -data8 0x3FC4DE5BE05E7583 // 116 -data8 0x3FC4FCBC0776FD85 // 117 -data8 0x3FC525561E9256EE // 118 -data8 0x3FC54E0DF3198865 // 119 -data8 0x3FC56CAB7112BDE2 // 120 -data8 0x3FC59597BA735B15 // 121 -data8 0x3FC5BEA23A506FDA // 122 -data8 0x3FC5DD7E08DE382F // 123 -data8 0x3FC606BDD3F92355 // 124 -data8 0x3FC6301C518A501F // 125 -data8 0x3FC64F3770618916 // 126 -data8 0x3FC678CC14C1E2D8 // 127 -data8 0x3FC6981005ED2947 // 128 -data8 0x3FC6C1DB5F9BB336 // 129 -data8 0x3FC6E1488ECD2881 // 130 -data8 0x3FC70B4B2E7E41B9 // 131 -data8 0x3FC72AE209146BF9 // 132 -data8 0x3FC7551C81BD8DCF // 133 -data8 0x3FC774DD76CC43BE // 134 -data8 0x3FC79F505DB00E88 // 135 -data8 0x3FC7BF3BDE099F30 // 136 -data8 0x3FC7E9E7CAC437F9 // 137 -data8 0x3FC809FE4902D00D // 138 -data8 0x3FC82A2757995CBE // 139 -data8 0x3FC85525C625E098 // 140 -data8 0x3FC8757A79831887 // 141 -data8 0x3FC895E2058D8E03 // 142 -data8 0x3FC8C13437695532 // 143 -data8 0x3FC8E1C812EF32BE // 144 -data8 0x3FC9026F112197E8 // 145 -data8 0x3FC923294888880B // 146 -data8 0x3FC94EEA4B8334F3 // 147 -data8 0x3FC96FD1B639FC09 // 148 -data8 0x3FC990CCA66229AC // 149 -data8 0x3FC9B1DB33334843 // 150 -data8 0x3FC9D2FD740E6607 // 151 -data8 0x3FC9FF49EEDCB553 // 152 -data8 0x3FCA209A84FBCFF8 // 153 -data8 0x3FCA41FF1E43F02B // 154 -data8 0x3FCA6377D2CE9378 // 155 -data8 0x3FCA8504BAE0D9F6 // 156 -data8 0x3FCAA6A5EEEBEFE3 // 157 -data8 0x3FCAC85B878D7879 // 158 -data8 0x3FCAEA259D8FFA0B // 159 -data8 0x3FCB0C0449EB4B6B // 160 -data8 0x3FCB2DF7A5C50299 // 161 -data8 0x3FCB4FFFCA70E4D1 // 162 -data8 0x3FCB721CD17157E3 // 163 -data8 0x3FCB944ED477D4ED // 164 -data8 0x3FCBB695ED655C7D // 165 -data8 0x3FCBD8F2364AEC0F // 166 -data8 0x3FCBFB63C969F4FF // 167 -data8 0x3FCC1DEAC134D4E9 // 168 -data8 0x3FCC4087384F4F80 // 169 -data8 0x3FCC6339498F09E2 // 170 -data8 0x3FCC86010FFC076C // 171 -data8 0x3FCC9D3D065C5B42 // 172 -data8 0x3FCCC029375BA07A // 173 -data8 0x3FCCE32B66978BA4 // 174 -data8 0x3FCD0643AFD51404 // 175 -data8 0x3FCD29722F0DEA45 // 176 -data8 0x3FCD4CB70070FE44 // 177 -data8 0x3FCD6446AB3F8C96 // 178 -data8 0x3FCD87B0EF71DB45 // 179 -data8 0x3FCDAB31D1FE99A7 // 180 -data8 0x3FCDCEC96FDC888F // 181 -data8 0x3FCDE6908876357A // 182 -data8 0x3FCE0A4E4A25C200 // 183 -data8 0x3FCE2E2315755E33 // 184 -data8 0x3FCE461322D1648A // 185 -data8 0x3FCE6A0E95C7787B // 186 -data8 0x3FCE8E216243DD60 // 187 -data8 0x3FCEA63AF26E007C // 188 -data8 0x3FCECA74ED15E0B7 // 189 -data8 0x3FCEEEC692CCD25A // 190 -data8 0x3FCF070A36B8D9C1 // 191 -data8 0x3FCF2B8393E34A2D // 192 -data8 0x3FCF5014EF538A5B // 193 -data8 0x3FCF68833AF1B180 // 194 -data8 0x3FCF8D3CD9F3F04F // 195 -data8 0x3FCFA5C61ADD93E9 // 196 -data8 0x3FCFCAA8567EBA7A // 197 -data8 0x3FCFE34CC8743DD8 // 198 -data8 0x3FD0042BFD74F519 // 199 -data8 0x3FD016BDF6A18017 // 200 -data8 0x3FD023262F907322 // 201 -data8 0x3FD035CCED8D32A1 // 202 -data8 0x3FD042430E869FFC // 203 -data8 0x3FD04EBEC842B2E0 // 204 -data8 0x3FD06182E84FD4AC // 205 -data8 0x3FD06E0CB609D383 // 206 -data8 0x3FD080E60BEC8F12 // 207 -data8 0x3FD08D7E0D894735 // 208 -data8 0x3FD0A06CC96A2056 // 209 -data8 0x3FD0AD131F3B3C55 // 210 -data8 0x3FD0C01771E775FB // 211 -data8 0x3FD0CCCC3CAD6F4B // 212 -data8 0x3FD0D986D91A34A9 // 213 -data8 0x3FD0ECA9B8861A2D // 214 -data8 0x3FD0F972F87FF3D6 // 215 -data8 0x3FD106421CF0E5F7 // 216 -data8 0x3FD11983EBE28A9D // 217 -data8 0x3FD12661E35B785A // 218 -data8 0x3FD13345D2779D3B // 219 -data8 0x3FD146A6F597283A // 220 -data8 0x3FD15399E81EA83D // 221 -data8 0x3FD16092E5D3A9A6 // 222 -data8 0x3FD17413C3B7AB5E // 223 -data8 0x3FD1811BF629D6FB // 224 -data8 0x3FD18E2A47B46686 // 225 -data8 0x3FD19B3EBE1A4418 // 226 -data8 0x3FD1AEE9017CB450 // 227 -data8 0x3FD1BC0CED7134E2 // 228 -data8 0x3FD1C93712ABC7FF // 229 -data8 0x3FD1D66777147D3F // 230 -data8 0x3FD1EA3BD1286E1C // 231 -data8 0x3FD1F77BED932C4C // 232 -data8 0x3FD204C25E1B031F // 233 -data8 0x3FD2120F28CE69B1 // 234 -data8 0x3FD21F6253C48D01 // 235 -data8 0x3FD22CBBE51D60AA // 236 -data8 0x3FD240CE4C975444 // 237 -data8 0x3FD24E37F8ECDAE8 // 238 -data8 0x3FD25BA8215AF7FC // 239 -data8 0x3FD2691ECC29F042 // 240 -data8 0x3FD2769BFFAB2E00 // 241 -data8 0x3FD2841FC23952C9 // 242 -data8 0x3FD291AA1A384978 // 243 -data8 0x3FD29F3B0E15584B // 244 -data8 0x3FD2B3A0EE479DF7 // 245 -data8 0x3FD2C142842C09E6 // 246 -data8 0x3FD2CEEACCB7BD6D // 247 -data8 0x3FD2DC99CE82FF21 // 248 -data8 0x3FD2EA4F902FD7DA // 249 -data8 0x3FD2F80C186A25FD // 250 -data8 0x3FD305CF6DE7B0F7 // 251 -data8 0x3FD3139997683CE7 // 252 -data8 0x3FD3216A9BB59E7C // 253 -data8 0x3FD32F4281A3CEFF // 254 -data8 0x3FD33D2150110092 // 255 -LOCAL_OBJECT_END(log10f_data) - - -// Code -//============================================================== + +log_table_1: +ASM_TYPE_DIRECTIVE(log_table_1,@object) +data8 0xbfd0001008f39d59 // p3 +data8 0x3fd5556073e0c45a // p2 +ASM_SIZE_DIRECTIVE(log_table_1) + +log_table_2: +ASM_TYPE_DIRECTIVE(log_table_2,@object) +data8 0xbfdffffffffaea15 // p1 +data8 0x3fdbcb7b1526e50e // 1/ln10 +data8 0x3fe62e42fefa39ef // Log(2) +data8 0x0 // pad + +data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256) +data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256) +data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256) +data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256) +data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256) +data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256) +data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256) +data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256) +data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256) +data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256) +data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256) +data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256) +data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256) +data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256) +data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256) +data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256) +data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256) +data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256) +data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256) +data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256) +data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256) +data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256) +data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256) +data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256) +data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256) +data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256) +data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256) +data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256) +data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256) +data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256) +data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256) +data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256) +data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256) +data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256) +data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256) +data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256) +data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256) +data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256) +data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256) +data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256) +data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256) +data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256) +data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256) +data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256) +data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256) +data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256) +data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256) +data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256) +data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256) +data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256) +data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256) +data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256) +data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256) +data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256) +data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256) +data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256) +data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256) +data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256) +data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256) +data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256) +data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256) +data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256) +data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256) +data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256) +data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256) +data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256) +data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256) +data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256) +data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256) +data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256) +data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256) +data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256) +data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256) +data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256) +data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256) +data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256) +data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256) +data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256) +data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256) +data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256) +data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256) +data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256) +data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256) +data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256) +data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256) +data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256) +data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256) +data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256) +data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256) +data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256) +data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256) +data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256) +data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256) +data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256) +data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256) +data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256) +data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256) +data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256) +data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256) +data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256) +data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256) +data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256) +data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256) +data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256) +data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256) +data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256) +data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256) +data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256) +data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256) +data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256) +data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256) +data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256) +data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256) +data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256) +data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256) +data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256) +data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256) +data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256) +data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256) +data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256) +data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256) +data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256) +data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256) +data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256) +data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256) +data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256) +data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256) +data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256) +data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256) +data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256) +data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256) +data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256) +data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256) +data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256) +data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256) +data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256) +data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256) +data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256) +data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256) +data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256) +data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256) +data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256) +data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256) +data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256) +data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256) +data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256) +data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256) +data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256) +data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256) +data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256) +data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256) +data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256) +data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256) +data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256) +data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256) +data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256) +data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256) +data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256) +data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256) +data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256) +data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256) +data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256) +data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256) +data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256) +data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256) +data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256) +data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256) +data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256) +data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256) +data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256) +data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256) +data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256) +data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256) +data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256) +data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256) +data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256) +data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256) +data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256) +data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256) +data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256) +data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256) +data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256) +data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256) +data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256) +data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256) +data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256) +data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256) +data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256) +data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256) +data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256) +data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256) +data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256) +data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256) +data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256) +data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256) +data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256) +data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256) +data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256) +data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256) +data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256) +data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256) +data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256) +data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256) +data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256) +data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256) +data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256) +data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256) +data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256) +data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256) +data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256) +data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256) +data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256) +data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256) +data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256) +data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256) +data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256) +data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256) +data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256) +data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256) +data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256) +data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256) +data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256) +data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256) +data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256) +data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256) +data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256) +data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256) +data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256) +data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256) +data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256) +data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256) +data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256) +data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256) +data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256) +data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256) +data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256) +data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256) +data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256) +data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256) +data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256) +data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256) +data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256) +data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256) +data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256) +data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256) +data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256) +data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256) +data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256) +data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256) +data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256) +data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256) +data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256) +data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256) +data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256) +data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256) +data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256) +ASM_SIZE_DIRECTIVE(log_table_2) + + +.align 32 +.global logf# +.global log10f# + +// log10 has p7 true, p8 false +// log has p8 true, p7 false + .section .text +.proc log10f# +.align 32 -// logf has p13 true, p14 false -// log10f has p14 true, p13 false +log10f: +#ifdef _LIBC +.global __ieee754_log10f +.type __ieee754_log10f,@function +__ieee754_log10f: +#endif +{ .mfi + alloc r32=ar.pfs,1,15,4,0 + frcpa.s1 log_C,p9 = f1,f8 + cmp.eq.unc p7,p8 = r0, r0 +} +{ .mfb + addl log_AD_1 = @ltoff(log_table_1), gp + fnorm.s1 log_NORM_f8 = f8 + br.sptk L(LOG_LOG10_X) +} +;; + +.endp log10f +ASM_SIZE_DIRECTIVE(log10f) +ASM_SIZE_DIRECTIVE(__ieee754_log10f) + + + +.section .text +.proc logf# +.align 32 +logf: +#ifdef _LIBC +.global __ieee754_logf +.type __ieee754_logf,@function +__ieee754_logf: +#endif -GLOBAL_IEEE754_ENTRY(log10f) { .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 + alloc r32=ar.pfs,1,15,4,0 + frcpa.s1 log_C,p9 = f1,f8 + cmp.eq.unc p8,p7 = r0, r0 } -{ .mlx - addl GR_ad_T = @ltoff(log10f_data),gp - movl GR_A3 = 0x3FD5555555555555 // double precision memory - // representation of A3 -};; { .mfi - getf.sig GR_Sig = f8 // if x is unorm then must recompute - fclass.m p8,p0 = f8,9 // is x positive unorm? - sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25 + addl log_AD_1 = @ltoff(log_table_1), gp + fnorm.s1 log_NORM_f8 = f8 + nop.i 999 } -{ .mlx - ld8 GR_ad_T = [GR_ad_T] - movl GR_Ln2 = 0x3FD34413509F79FF // double precision memory - // representation of - // log(2)/ln(10) -};; +;; + +L(LOG_LOG10_X): + { .mfi - setf.d FR_A3 = GR_A3 // create A3 - fcmp.eq.s1 p14,p13 = f0,f0 // set p14 to 1 for log10f - dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number - // bits of that are - // GR_xorg[63] = last bit of biased - // exponent of 255/256 - // GR_xorg[62-0] = bits from 62 to 0 - // of significand of 255/256 + getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute + fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm + mov log_GR_fff7 = 0xfff7 } -{ .mib - setf.exp FR_A2 = GR_05 // create A2 - sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE - // needed to comparion with 0.5 and 2.0 - br.cond.sptk logf_log10f_common -};; -GLOBAL_IEEE754_END(log10f) -GLOBAL_IEEE754_ENTRY(logf) { .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 + ld8 log_AD_1 = [log_AD_1] + fms.s1 log_w = f8,f1,f1 + mov log_GR_exp_17_ones = 0x1ffff } -{ .mlx - addl GR_ad_T = @ltoff(logf_data),gp - movl GR_A3 = 0x3FD5555555555555 // double precision memory - // representation of A3 -};; +;; + +{ .mmi + getf.sig log_GR_significand_f8 = f8 // If x unorm then must recompute + mov log_GR_exp_16_ones = 0xffff + nop.i 999 +} +;; + +{ .mmb + adds log_AD_2 = 0x10, log_AD_1 + and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones +(p15) br.cond.spnt L(LOG_DENORM) +} +;; + +L(LOG_COMMON): +{.mfi + ldfpd log_P3,log_P2 = [log_AD_1],16 + fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan + shl log_GR_index = log_GR_significand_f8,1 +} +{.mfi + sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones + nop.f 999 + nop.i 999 +} +;; + { .mfi - getf.sig GR_Sig = f8 // if x is unorm then must recompute - fclass.m p8,p0 = f8,9 // is x positive unorm? - dep.z GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number - // bits of that are - // GR_xorg[63] = last bit of biased - // exponent of 255/256 - // GR_xorg[62-0] = bits from 62 to 0 - // of significand of 255/256 + ldfpd log_P1,log_inv_ln10 = [log_AD_2],16 + fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf + shr.u log_GR_index = log_GR_index,56 } { .mfi - ld8 GR_ad_T = [GR_ad_T] - nop.f 0 - sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25 -};; + setf.sig log_int_Nfloat = log_GR_true_exp_f8 + nop.f 999 + nop.i 999 +} +;; + + { .mfi - setf.d FR_A3 = GR_A3 // create A3 - fcmp.eq.s1 p13,p14 = f0,f0 // p13 - true for logf - sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE - // needed to comparion with 0.5 and 2.0 + ldfd log_log2 = [log_AD_2],16 + fma.s1 log_wsq = log_w, log_w, f0 + nop.i 999 } -{ .mlx - setf.exp FR_A2 = GR_05 // create A2 - movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory - // representation of log(2) -};; -logf_log10f_common: +{ .mfb + nop.m 999 +(p6) fma.s.s0 f8 = f8,f1,f0 // quietize nan result if x=nan +(p6) br.ret.spnt b0 // Exit for x=nan +} +;; + + { .mfi - setf.exp FR_A4 = GR_025 // create A4=0.25 - fclass.m p9,p0 = f8,0x3A // is x < 0 (including negateve unnormals)? - dep GR_x = GR_Exp,GR_Sig,63,1 // produce integer that bits are - // GR_x[63] = GR_Exp[0] - // GR_x[62-0] = GR_Sig[62-0] + shladd log_AD_2 = log_GR_index,3,log_AD_2 + fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0 + nop.i 999 } -{ .mib - sub GR_N = GR_Exp,GR_05,1 // unbiased exponent of x - cmp.gtu p6,p7 = 2,GR_de // is 0.5 <= x < 2.0? -(p8) br.cond.spnt logf_positive_unorm -};; -logf_core: +{ .mfb + nop.m 999 + fms.s1 log_r = log_C,f8,f1 +(p11) br.ret.spnt b0 // Exit for x=+inf +} +;; + + +{ .mmf + nop.m 999 + nop.m 999 + fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0 +} +;; + + +{ .mfb + ldfd log_T = [log_AD_2] +(p10) fmerge.s f8 = f0, f0 +(p10) br.ret.spnt b0 // Exit for x=1.0 +;; +} + { .mfi - setf.sig FR_N = GR_N // copy unbiased exponent of x to the - // significand field of FR_N - fclass.m p10,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? - dep.z GR_dx = GR_05,54,3 // 0x0180000000000000 - difference - // between our integer representations - // of 257/256 and 255/256 + getf.exp log_GR_signexp_w = log_w + fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf + nop.i 999 +} +;; + +{ .mmb + nop.m 999 + nop.m 999 +(p6) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x=0 +;; } + + { .mfi - nop.m 0 - nop.f 0 - sub GR_x = GR_x,GR_xorg // difference between representations - // of x and 255/256 -};; + and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w + nop.f 999 + nop.i 999 +} +{ .mfb + nop.m 999 + fma.s1 log_rsq = log_r, log_r, f0 +(p12) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x<0 +;; +} + { .mfi - ldfd FR_InvLn10 = [GR_ad_T],8 - fcmp.eq.s1 p11,p0 = f8,f1 // is x equal to 1.0? - extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index + nop.m 999 + fma.s1 log_rp_p32 = log_P3, log_r, log_P2 + nop.i 999 } -{ .mib - setf.d FR_Ln2 = GR_Ln2 // create log(2) or log10(2) -(p6) cmp.gtu p6,p7 = GR_dx,GR_x // set p6 if 255/256 <= x < 257/256 -(p9) br.cond.spnt logf_negatives // jump if input argument is negative number -};; -// p6 is true if |x-1| < 1/256 -// p7 is true if |x-1| >= 1/256 -.pred.rel "mutex",p6,p7 { .mfi - shladd GR_ad_T = GR_Ind,3,GR_ad_T // calculate address of T -(p7) fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256 - extr.u GR_Exp = GR_Exp,0,17 // exponent without sign + nop.m 999 + fma.s1 log_rp_q32 = log_P3, log_w, log_P2 + nop.i 999 +;; } -{ .mfb - nop.m 0 -(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256 -(p10) br.cond.spnt logf_nan_nat_pinf // exit for NaN, NaT or +Inf -};; -{ .mfb - ldfd FR_T = [GR_ad_T] // load T -(p11) fma.s.s0 f8 = f0,f0,f0 -(p11) br.ret.spnt b0 // exit for x = 1.0 -};; -{ .mib - nop.m 0 - cmp.eq p12,p0 = r0,GR_Exp // is x +/-0? (here it's quite enough - // only to compare exponent with 0 - // because all unnormals already - // have been filtered) -(p12) br.cond.spnt logf_zeroes // Branch if input argument is +/-0 -};; + { .mfi - nop.m 0 - fnma.s1 FR_A2 = FR_A2,FR_r,f1 // A2*r+1 - nop.i 0 + nop.m 999 + fcvt.xf log_Nfloat = log_int_Nfloat + nop.i 999 ;; } + { .mfi - nop.m 0 - fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 - nop.i 0 -};; + nop.m 999 + fma.s1 log_rp_p10 = log_P1, log_r, f1 + nop.i 999 +} { .mfi - nop.m 0 - fcvt.xf FR_N = FR_N // convert integer N in significand of FR_N - // to floating-point representation - nop.i 0 + nop.m 999 + fma.s1 log_rp_q10 = log_P1, log_w, f1 + nop.i 999 +;; } + +// p13 <== large w log +// p14 <== small w log { .mfi - nop.m 0 - fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3 - nop.i 0 -};; +(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff7 + fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input + nop.i 999 +;; +} + +// p10 <== large w log10 +// p11 <== small w log10 { .mfi - nop.m 0 - fma.s1 FR_r = FR_r,FR_InvLn10,f0 // For log10f we have r/log(10) - nop.i 0 +(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7 + nop.f 999 + nop.i 999 ;; } + { .mfi - nop.m 0 - nop.f 0 - nop.i 0 -};; + nop.m 999 + fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T + nop.i 999 ;; +} + + { .mfi - nop.m 0 - fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1) - nop.i 0 + nop.m 999 + fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 + nop.i 999 } { .mfi - nop.m 0 - fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T // N*Ln2+T - nop.i 0 -};; -.pred.rel "mutex",p6,p7 + nop.m 999 + fma.s1 log_rp_q2 = log_rp_q32, log_wsq, log_rp_q10 + nop.i 999 +;; +} + + +// small w, log <== p14 { .mfi - nop.m 0 -(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result for |x-1|>=1/256 - nop.i 0 + nop.m 999 +(p14) fma.s f8 = log_rp_q2, log_w, f0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p11) fma.s1 log_Q = log_rp_q2, log_w, f0 + nop.i 999 ;; } -{ .mfb - nop.m 0 -(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result for |x-1|<1/256 - br.ret.sptk b0 -};; -.align 32 -logf_positive_unorm: + +// large w, log <== p13 +.pred.rel "mutex",p13,p10 { .mfi - nop.m 0 -(p8) fma.s0 f8 = f8,f1,f0 // Normalize & set D-flag - nop.i 0 -};; + nop.m 999 +(p13) fma.s f8 = log_rp_p2, log_r, log_T_plus_Nlog2 + nop.i 999 +} { .mfi - getf.exp GR_Exp = f8 // recompute biased exponent - nop.f 0 - cmp.ne p6,p7 = r0,r0 // p6 <- 0, p7 <- 1 because - // in case of unorm we are out - // interval [255/256; 257/256] -};; + nop.m 999 +(p10) fma.s1 log_Q = log_rp_p2, log_r, log_T_plus_Nlog2 + nop.i 999 ;; +} + + +// log10 +{ .mfb + nop.m 999 +(p7) fma.s f8 = log_inv_ln10,log_Q,f0 + br.ret.sptk b0 +;; +} + + +L(LOG_DENORM): +{ .mmi + getf.exp log_GR_signexp_f8 = log_NORM_f8 + nop.m 999 + nop.i 999 +} +;; +{ .mmb + getf.sig log_GR_significand_f8 = log_NORM_f8 + and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones + br.cond.sptk L(LOG_COMMON) +} +;; + +L(LOG_ZERO_NEG): + +// qnan snan inf norm unorm 0 -+ +// 0 0 0 0 0 1 11 0x7 +// 0 0 1 1 1 0 10 0x3a + +// Save x (f8) in f10 { .mfi - getf.sig GR_Sig = f8 // recompute significand - nop.f 0 - nop.i 0 -};; -{ .mib - sub GR_N = GR_Exp,GR_05,1 // unbiased exponent N - nop.i 0 - br.cond.sptk logf_core // return into main path -};; + nop.m 999 + fmerge.s f10 = f8,f8 + nop.i 999 ;; +} + +// p8 p9 means ln(+-0) = -inf +// p7 p10 means log(+-0) = -inf + +// p13 means ln(-) +// p14 means log(-) + -.align 32 -logf_nan_nat_pinf: { .mfi - nop.m 0 - fma.s.s0 f8 = f8,f1,f0 // set V-flag - nop.i 0 + nop.m 999 + fmerge.ns f6 = f1,f1 // Form -1.0 + nop.i 999 ;; } -{ .mfb - nop.m 0 - nop.f 0 - br.ret.sptk b0 // exit for NaN, NaT or +Inf -};; -.align 32 -logf_zeroes: +// p9 means ln(+-0) = -inf +// p10 means log(+-0) = -inf +// Log(+-0) = -inf + { .mfi - nop.m 0 - fmerge.s FR_X = f8,f8 // keep input argument for subsequent - // call of __libm_error_support# - nop.i 0 + nop.m 999 +(p8) fclass.m.unc p9,p0 = f10, 0x07 + nop.i 999 } { .mfi -(p13) mov GR_TAG = 4 // set libm error in case of logf - fms.s1 FR_tmp = f0,f0,f1 // -1.0 - nop.i 0 -};; + nop.m 999 +(p7) fclass.m.unc p10,p0 = f10, 0x07 + nop.i 999 ;; +} + + +// p13 ln(-) +// p14 log(-) + +// Log(-inf, -normal, -unnormal) = QNAN indefinite { .mfi - nop.m 0 - 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 + nop.m 999 +(p8) fclass.m.unc p13,p0 = f10, 0x3a + nop.i 999 +} +{ .mfi + nop.m 999 +(p7) fclass.m.unc p14,p0 = f10, 0x3a + nop.i 999 ;; } -{ .mib -(p14) mov GR_TAG = 10 // set libm error in case of log10f - nop.i 0 - br.cond.sptk logf_libm_err -};; -.align 32 -logf_negatives: + +.pred.rel "mutex",p9,p10 { .mfi -(p13) mov GR_TAG = 5 // set libm error in case of logf - fmerge.s FR_X = f8,f8 // keep input argument for subsequent - // call of __libm_error_support# - nop.i 0 -};; +(p9) mov log_GR_tag = 4 +(p9) frcpa f8,p11 = f6,f0 + nop.i 999 +} { .mfi -(p14) mov GR_TAG = 11 // set libm error in case of log10f - 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. - nop.i 0 -};; +(p10) mov log_GR_tag = 10 +(p10) frcpa f8,p12 = f6,f0 + nop.i 999 ;; +} + +.pred.rel "mutex",p13,p14 +{ .mfi +(p13) mov log_GR_tag = 5 +(p13) frcpa f8,p11 = f0,f0 + nop.i 999 +} +{ .mfb +(p14) mov log_GR_tag = 11 +(p14) frcpa f8,p12 = f0,f0 + br.cond.sptk __libm_error_region ;; +} +.endp logf +ASM_SIZE_DIRECTIVE(logf) +ASM_SIZE_DIRECTIVE(__ieee754_logf) -.align 32 -logf_libm_err: -{ .mmi - alloc r32 = ar.pfs,1,4,4,0 - mov GR_Parameter_TAG = GR_TAG - nop.i 0 -};; -GLOBAL_IEEE754_END(logf) // Stack operations when calling error support. // (1) (2) (3) (call) (4) @@ -1101,56 +890,70 @@ GLOBAL_IEEE754_END(logf) // save ar.pfs save b0 restore gp // save gp restore ar.pfs -LOCAL_LIBM_ENTRY(__libm_error_region) + + +.proc __libm_error_region +__libm_error_region: .prologue + +// (1) { .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 + 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 + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp };; + + +// (2) { .mmi - stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfs [GR_Parameter_Y] = f1,16 // 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 + mov GR_SAVE_B0=b0 // Save b0 };; + .body +// (3) { .mib - stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 } { .mib - stfs [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 + stfs [GR_Parameter_Y] = f8 // 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 - nop.m 0 - nop.m 0 - add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp };; + +// (4) { .mmi - ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack + ldfs 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 + 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 + 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) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) + .type __libm_error_support#,@function .global __libm_error_support# - |