diff options
| author | Jakub Jelinek <jakub@redhat.com> | 2007-07-12 18:26:36 +0000 |
|---|---|---|
| committer | Jakub Jelinek <jakub@redhat.com> | 2007-07-12 18:26:36 +0000 |
| commit | 0ecb606cb6cf65de1d9fc8a919bceb4be476c602 (patch) | |
| tree | 2ea1f8305970753e4a657acb2ccc15ca3eec8e2c /sysdeps/ia64/fpu/e_logf.S | |
| parent | 7d58530341304d403a6626d7f7a1913165fe2f32 (diff) | |
| download | glibc-0ecb606cb6cf65de1d9fc8a919bceb4be476c602.tar.gz glibc-0ecb606cb6cf65de1d9fc8a919bceb4be476c602.tar.xz glibc-0ecb606cb6cf65de1d9fc8a919bceb4be476c602.zip | |
2.5-18.1
Diffstat (limited to 'sysdeps/ia64/fpu/e_logf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_logf.S | 1786 |
1 files changed, 993 insertions, 793 deletions
diff --git a/sysdeps/ia64/fpu/e_logf.S b/sysdeps/ia64/fpu/e_logf.S index 829d0abed0..3d11a296cc 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, 2001, Intel Corporation + +// Copyright (c) 2000 - 2005, Intel Corporation // All rights reserved. -// -// 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. +// +// 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 @@ -20,860 +20,1074 @@ // * 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://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // History //============================================================== -// 3/01/00 Initial version -// 8/15/00 Bundle added after call to __libm_error_support to properly +// 03/01/00 Initial version +// 08/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. -// 1/10/01 Improved speed, fixed flags for neg denormals -// +// 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 +// 03/31/05 Reformatted delimiters between data tables // // API //============================================================== // float logf(float) // float log10f(float) // +// // Overview of operation //============================================================== // Background +// ---------- // -// 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) +// This algorithm is based on fact that +// log(a b) = log(a) + log(b). // -// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63) +// 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) // -// -log(frcpa(x)) = -log(C) -// = -log(2^-N) - log(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) -// = +Nlog2 - 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 +// +// 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) // -// 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) // -// Log(x) = +Nlog2 + T + log(C x) +// To compute log10(x) we just use identity: // -// Cx = 1 + r +// log10(x) = log(x)/log(10) // -// Log(x) = +Nlog2 + T + log(1+r) -// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....) +// 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) // -// 1.f1 f2 ... f8 has 256 entries. -// They are 1 + k/2^8, k = 0 ... 255 -// These 256 values are the table entries. // // Implementation -//=============== -// CASE 1: |x-1| >= 2^-8 -// C = frcpa(x) -// r = C * x - 1 +// -------------- +// 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) // -// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 +// 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. // -// 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 +// Note that both log and log10 use common approximation polynomial +// it means we need only one set of coefficients of approximation. // -// result = (T + Nfloat * log(2)) + rseries +// 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. // -// 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 +// N = float(n) where n is true unbiased exponent of x // -// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4 +// 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 // -// result = wseries - -// Special values +// 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. +// +// 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 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. +// +// 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 - +// +// 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 +// // Registers used //============================================================== -// Floating Point registers used: +// Floating Point registers used: // f8, input -// f9 -> f15, f32 -> f47 - -// General registers used: -// r32 -> r51 - +// f12 -> f14, f33 -> f39 +// +// General registers used: +// r8 -> r11 +// r14 -> r19 +// // Predicate registers used: -// 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 +// p6 -> p12 -// 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 //============================================================== -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 +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 // Data tables //============================================================== - -#ifdef _LIBC -.rodata -#else -.data -#endif - +RODATA .align 16 - -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 - +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 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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 +//============================================================== .section .text -.proc log10f# -.align 32 -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) +// logf has p13 true, p14 false +// log10f has p14 true, p13 false - - -.section .text -.proc logf# -.align 32 -logf: -#ifdef _LIBC -.global __ieee754_logf -.type __ieee754_logf,@function -__ieee754_logf: -#endif - -{ .mfi - alloc r32=ar.pfs,1,15,4,0 - frcpa.s1 log_C,p9 = f1,f8 - cmp.eq.unc p8,p7 = r0, r0 -} +GLOBAL_IEEE754_ENTRY(log10f) { .mfi - addl log_AD_1 = @ltoff(log_table_1), gp - fnorm.s1 log_NORM_f8 = f8 - nop.i 999 + 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 } -;; - -L(LOG_LOG10_X): - +{ .mlx + addl GR_ad_T = @ltoff(log10f_data),gp + movl GR_A3 = 0x3FD5555555555555 // double precision memory + // representation of A3 +};; { .mfi - 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 + 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 } +{ .mlx + ld8 GR_ad_T = [GR_ad_T] + movl GR_Ln2 = 0x3FD34413509F79FF // double precision memory + // representation of + // log(2)/ln(10) +};; { .mfi - ld8 log_AD_1 = [log_AD_1] - fms.s1 log_w = f8,f1,f1 - mov log_GR_exp_17_ones = 0x1ffff -} -;; - -{ .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 + 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 } -;; +{ .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 - 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 + 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_T = @ltoff(logf_data),gp + movl GR_A3 = 0x3FD5555555555555 // double precision memory + // representation of A3 +};; { .mfi - setf.sig log_int_Nfloat = log_GR_true_exp_f8 - nop.f 999 - nop.i 999 + 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 } -;; - - { .mfi - ldfd log_log2 = [log_AD_2],16 - fma.s1 log_wsq = log_w, log_w, f0 - nop.i 999 -} -{ .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 -} -;; - - + ld8 GR_ad_T = [GR_ad_T] + nop.f 0 + sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25 +};; { .mfi - 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 -} -{ .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 -;; + 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 } - +{ .mlx + setf.exp FR_A2 = GR_05 // create A2 + movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory + // representation of log(2) +};; +logf_log10f_common: { .mfi - 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 -;; + 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] } - - +{ .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: { .mfi - and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w - nop.f 999 - nop.i 999 + 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 } -{ .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 - nop.m 999 - fma.s1 log_rp_p32 = log_P3, log_r, log_P2 - nop.i 999 -} + nop.m 0 + nop.f 0 + sub GR_x = GR_x,GR_xorg // difference between representations + // of x and 255/256 +};; { .mfi - nop.m 999 - fma.s1 log_rp_q32 = log_P3, log_w, log_P2 - nop.i 999 -;; + 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 } - +{ .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 - nop.m 999 - fcvt.xf log_Nfloat = log_int_Nfloat - nop.i 999 ;; + 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 } - +{ .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 999 - fma.s1 log_rp_p10 = log_P1, log_r, f1 - nop.i 999 + nop.m 0 + fnma.s1 FR_A2 = FR_A2,FR_r,f1 // A2*r+1 + nop.i 0 } { .mfi - nop.m 999 - fma.s1 log_rp_q10 = log_P1, log_w, f1 - nop.i 999 -;; -} - -// p13 <== large w log -// p14 <== small w log + nop.m 0 + fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 + nop.i 0 +};; { .mfi -(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 -;; + nop.m 0 + fcvt.xf FR_N = FR_N // convert integer N in significand of FR_N + // to floating-point representation + nop.i 0 } - -// p10 <== large w log10 -// p11 <== small w log10 { .mfi -(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7 - nop.f 999 - nop.i 999 ;; -} - + nop.m 0 + fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3 + nop.i 0 +};; { .mfi - nop.m 999 - fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T - nop.i 999 ;; + nop.m 0 + fma.s1 FR_r = FR_r,FR_InvLn10,f0 // For log10f we have r/log(10) + nop.i 0 } - - { .mfi - nop.m 999 - fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 - nop.i 999 -} + nop.m 0 + nop.f 0 + nop.i 0 +};; { .mfi - nop.m 999 - fma.s1 log_rp_q2 = log_rp_q32, log_wsq, log_rp_q10 - nop.i 999 -;; + nop.m 0 + fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1) + nop.i 0 } - - -// small w, log <== p14 { .mfi - nop.m 999 -(p14) fma.s f8 = log_rp_q2, log_w, f0 - nop.i 999 -} + nop.m 0 + fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T // N*Ln2+T + nop.i 0 +};; +.pred.rel "mutex",p6,p7 { .mfi - nop.m 999 -(p11) fma.s1 log_Q = log_rp_q2, log_w, f0 - nop.i 999 ;; + nop.m 0 +(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result for |x-1|>=1/256 + nop.i 0 } +{ .mfb + nop.m 0 +(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result for |x-1|<1/256 + br.ret.sptk b0 +};; - -// large w, log <== p13 -.pred.rel "mutex",p13,p10 +.align 32 +logf_positive_unorm: { .mfi - nop.m 999 -(p13) fma.s f8 = log_rp_p2, log_r, log_T_plus_Nlog2 - nop.i 999 -} + nop.m 0 +(p8) fma.s0 f8 = f8,f1,f0 // Normalize & set D-flag + nop.i 0 +};; { .mfi - 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 + 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] +};; { .mfi - 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(-) - + 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 +};; +.align 32 +logf_nan_nat_pinf: { .mfi - nop.m 999 - fmerge.ns f6 = f1,f1 // Form -1.0 - nop.i 999 ;; + nop.m 0 + fma.s.s0 f8 = f8,f1,f0 // set V-flag + nop.i 0 } +{ .mfb + nop.m 0 + nop.f 0 + br.ret.sptk b0 // exit for NaN, NaT or +Inf +};; -// p9 means ln(+-0) = -inf -// p10 means log(+-0) = -inf -// Log(+-0) = -inf - -{ .mfi - nop.m 999 -(p8) fclass.m.unc p9,p0 = f10, 0x07 - nop.i 999 -} +.align 32 +logf_zeroes: { .mfi - nop.m 999 -(p7) fclass.m.unc p10,p0 = f10, 0x07 - nop.i 999 ;; + nop.m 0 + fmerge.s FR_X = f8,f8 // keep input argument for subsequent + // call of __libm_error_support# + nop.i 0 } - - -// p13 ln(-) -// p14 log(-) - -// Log(-inf, -normal, -unnormal) = QNAN indefinite { .mfi - nop.m 999 -(p8) fclass.m.unc p13,p0 = f10, 0x3a - nop.i 999 -} +(p13) mov GR_TAG = 4 // set libm error in case of logf + fms.s1 FR_tmp = f0,f0,f1 // -1.0 + nop.i 0 +};; { .mfi - nop.m 999 -(p7) fclass.m.unc p14,p0 = f10, 0x3a - nop.i 999 ;; + 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 } +{ .mib +(p14) mov GR_TAG = 10 // set libm error in case of log10f + nop.i 0 + br.cond.sptk logf_libm_err +};; - -.pred.rel "mutex",p9,p10 +.align 32 +logf_negatives: { .mfi -(p9) mov log_GR_tag = 4 -(p9) frcpa f8,p11 = f6,f0 - nop.i 999 -} +(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 +};; { .mfi -(p10) mov log_GR_tag = 10 -(p10) frcpa f8,p12 = f6,f0 - nop.i 999 ;; -} +(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 +};; -.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. @@ -890,70 +1104,56 @@ ASM_SIZE_DIRECTIVE(__ieee754_logf) // save ar.pfs save b0 restore gp // save gp restore ar.pfs - - -.proc __libm_error_region -__libm_error_region: +LOCAL_LIBM_ENTRY(__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] = f1,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfs [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 + mov GR_SAVE_B0=b0 // Save b0 };; - .body -// (3) { .mib - stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + 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 } { .mib - 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 + 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 };; - { .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 };; -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) - +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# + |