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We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
1166 lines
38 KiB
ArmAsm
1166 lines
38 KiB
ArmAsm
.file "logf.s"
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// Copyright (c) 2000 - 2005, Intel Corporation
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// All rights reserved.
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//
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 03/01/00 Initial version
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// 08/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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// 01/10/01 Improved speed, fixed flags for neg denormals
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 05/23/02 Modified algorithm. Now only one polynomial is used
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// for |x-1| >= 1/256 and for |x-1| < 1/256
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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// 03/31/05 Reformatted delimiters between data tables
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//
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// API
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//==============================================================
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// float logf(float)
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// float log10f(float)
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//
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//
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// Overview of operation
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//==============================================================
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// Background
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// ----------
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//
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// This algorithm is based on fact that
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// log(a b) = log(a) + log(b).
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//
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// In our case we have x = 2^N f, where 1 <= f < 2.
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// So
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// log(x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
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//
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// To calculate log(f) we do following
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// log(f) = log(f * frcpa(f) / frcpa(f)) =
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// = log(f * frcpa(f)) + log(1/frcpa(f))
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//
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// According to definition of IA-64's frcpa instruction it's a
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// floating point that approximates 1/f using a lookup on the
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// top of 8 bits of the input number's significand with relative
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// error < 2^(-8.886). So we have following
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//
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// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
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//
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// and
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//
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// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
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// = log(1 + r) + T
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//
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// The first value can be computed by polynomial P(r) approximating
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// log(1 + r) on |r| < 1/256 and the second is precomputed tabular
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// value defined by top 8 bit of f.
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//
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// Finally we have that log(x) ~ (N*log(2) + T) + P(r)
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//
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// Note that if input argument is close to 1.0 (in our case it means
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// that |1 - x| < 1/256) we can use just polynomial approximation
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// because x = 2^0 * f = f = 1 + r and
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// log(x) = log(1 + r) ~ P(r)
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//
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//
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// To compute log10(x) we just use identity:
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//
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// log10(x) = log(x)/log(10)
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//
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// so we have that
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//
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// log10(x) = (N*log(2) + T + log(1+r)) / log(10) =
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// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10)
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//
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//
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// Implementation
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// --------------
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// It can be seen that formulas for log and log10 differ from one another
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// only by coefficients and tabular values. Namely as log as log10 are
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// calculated as (N*L1 + T) + L2*Series(r) where in case of log
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// L1 = log(2)
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// T = log(1/frcpa(x))
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// L2 = 1.0
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// and in case of log10
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// L1 = log(2)/log(10)
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// T = log(1/frcpa(x))/log(10)
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// L2 = 1.0/log(10)
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//
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// So common code with two different entry points those set pointers
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// to the base address of coresponding data sets containing values
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// of L2,T and prepare integer representation of L1 needed for following
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// setf instruction can be used.
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//
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// Note that both log and log10 use common approximation polynomial
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// it means we need only one set of coefficients of approximation.
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//
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// 1. Computation of log(x) for |x-1| >= 1/256
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// InvX = frcpa(x)
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// r = InvX*x - 1
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// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are created with setf inctruction.
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// We use Taylor series and so A4 = 1/4, A3 = 1/3,
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// A2 = 1/2 rounded to double.
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//
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// N = float(n) where n is true unbiased exponent of x
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//
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// T is tabular value of log(1/frcpa(x)) calculated in quad precision
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// and rounded to double. To T we get bits from 55 to 62 of register
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// format significand of x and calculate address
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// ad_T = table_base_addr + 8 * index
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//
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// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad
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// precision and rounded to double; it's loaded from memory
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//
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// L1 (log(2) or log10(2) depending on function) is calculated in quad
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// precision and rounded to double; it's created with setf.
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//
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// And final result = P2(r)*(r*L2) + (T + N*L1)
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//
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//
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// 2. Computation of log(x) for |x-1| < 1/256
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// r = x - 1
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// P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are the same as in case |x-1| >= 1/256
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//
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// And final result = P2(r)*(r*L2)
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//
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// 3. How we define is input argument such that |x-1| < 1/256 or not.
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//
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// To do it we analyze biased exponent and significand of input argument.
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//
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// a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e.
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// we test is 0.5 <= x < 2). This comparison can be performed using
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// unsigned version of cmp instruction in such a way
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// biased_exponent_of_x - 0xFFFE < 2
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//
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//
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// b) Second (in case when result of a) is true) we need to compare x
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// with 1-1/256 and 1+1/256 or in register format representation with
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// 0xFFFEFF00000000000000 and 0xFFFF8080000000000000 correspondingly.
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// As far as biased exponent of x here can be equal only to 0xFFFE or
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// 0xFFFF we need to test only last bit of it. Also signifigand always
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// has implicit bit set to 1 that can be exluded from comparison.
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// Thus it's quite enough to generate 64-bit integer bits of that are
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// ix[63] = biased_exponent_of_x[0] and ix[62-0] = significand_of_x[62-0]
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// and compare it with 0x7F00000000000000 and 0x80800000000000000 (those
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// obtained like ix from register representatinos of 255/256 and
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// 257/256). This comparison can be made like in a), using unsigned
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// version of cmp i.e. ix - 0x7F00000000000000 < 0x0180000000000000.
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// 0x0180000000000000 is difference between 0x80800000000000000 and
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// 0x7F00000000000000.
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//
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// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
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// filtered and processed on special branches.
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//
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//
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// Special values
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//==============================================================
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//
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// logf(+0) = -inf
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// logf(-0) = -inf
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//
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// logf(+qnan) = +qnan
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// logf(-qnan) = -qnan
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// logf(+snan) = +qnan
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// logf(-snan) = -qnan
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//
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// logf(-n) = QNAN Indefinite
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// logf(-inf) = QNAN Indefinite
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//
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// logf(+inf) = +inf
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input
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// f12 -> f14, f33 -> f39
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//
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// General registers used:
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// r8 -> r11
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// r14 -> r19
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//
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// Predicate registers used:
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// p6 -> p12
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// Assembly macros
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//==============================================================
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GR_TAG = r8
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GR_ad_T = r8
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GR_N = r9
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GR_Exp = r10
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GR_Sig = r11
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GR_025 = r14
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GR_05 = r15
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GR_A3 = r16
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GR_Ind = r17
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GR_dx = r15
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GR_Ln2 = r19
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GR_de = r20
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GR_x = r21
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GR_xorg = r22
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35
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GR_SAVE_SP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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FR_A2 = f12
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FR_A3 = f13
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FR_A4 = f14
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FR_RcpX = f33
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FR_r = f34
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FR_r2 = f35
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FR_tmp = f35
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FR_Ln2 = f36
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FR_T = f37
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FR_N = f38
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FR_NxLn2pT = f38
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FR_NormX = f39
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FR_InvLn10 = f40
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FR_Y = f1
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FR_X = f10
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FR_RESULT = f8
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// Data tables
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(logf_data)
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data8 0x3FF0000000000000 // 1.0
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//
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// ln(1/frcpa(1+i/256)), i=0...255
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data8 0x3F60040155D5889E // 0
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data8 0x3F78121214586B54 // 1
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data8 0x3F841929F96832F0 // 2
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data8 0x3F8C317384C75F06 // 3
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data8 0x3F91A6B91AC73386 // 4
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data8 0x3F95BA9A5D9AC039 // 5
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data8 0x3F99D2A8074325F4 // 6
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data8 0x3F9D6B2725979802 // 7
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data8 0x3FA0C58FA19DFAAA // 8
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data8 0x3FA2954C78CBCE1B // 9
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data8 0x3FA4A94D2DA96C56 // 10
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data8 0x3FA67C94F2D4BB58 // 11
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data8 0x3FA85188B630F068 // 12
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data8 0x3FAA6B8ABE73AF4C // 13
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data8 0x3FAC441E06F72A9E // 14
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data8 0x3FAE1E6713606D07 // 15
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data8 0x3FAFFA6911AB9301 // 16
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data8 0x3FB0EC139C5DA601 // 17
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data8 0x3FB1DBD2643D190B // 18
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data8 0x3FB2CC7284FE5F1C // 19
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data8 0x3FB3BDF5A7D1EE64 // 20
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data8 0x3FB4B05D7AA012E0 // 21
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data8 0x3FB580DB7CEB5702 // 22
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data8 0x3FB674F089365A7A // 23
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data8 0x3FB769EF2C6B568D // 24
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data8 0x3FB85FD927506A48 // 25
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data8 0x3FB9335E5D594989 // 26
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data8 0x3FBA2B0220C8E5F5 // 27
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data8 0x3FBB0004AC1A86AC // 28
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data8 0x3FBBF968769FCA11 // 29
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data8 0x3FBCCFEDBFEE13A8 // 30
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data8 0x3FBDA727638446A2 // 31
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data8 0x3FBEA3257FE10F7A // 32
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data8 0x3FBF7BE9FEDBFDE6 // 33
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data8 0x3FC02AB352FF25F4 // 34
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data8 0x3FC097CE579D204D // 35
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data8 0x3FC1178E8227E47C // 36
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data8 0x3FC185747DBECF34 // 37
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data8 0x3FC1F3B925F25D41 // 38
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data8 0x3FC2625D1E6DDF57 // 39
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data8 0x3FC2D1610C86813A // 40
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data8 0x3FC340C59741142E // 41
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data8 0x3FC3B08B6757F2A9 // 42
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data8 0x3FC40DFB08378003 // 43
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data8 0x3FC47E74E8CA5F7C // 44
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data8 0x3FC4EF51F6466DE4 // 45
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data8 0x3FC56092E02BA516 // 46
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data8 0x3FC5D23857CD74D5 // 47
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data8 0x3FC6313A37335D76 // 48
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data8 0x3FC6A399DABBD383 // 49
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data8 0x3FC70337DD3CE41B // 50
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data8 0x3FC77654128F6127 // 51
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data8 0x3FC7E9D82A0B022D // 52
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data8 0x3FC84A6B759F512F // 53
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data8 0x3FC8AB47D5F5A310 // 54
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data8 0x3FC91FE49096581B // 55
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data8 0x3FC981634011AA75 // 56
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data8 0x3FC9F6C407089664 // 57
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data8 0x3FCA58E729348F43 // 58
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data8 0x3FCABB55C31693AD // 59
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data8 0x3FCB1E104919EFD0 // 60
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data8 0x3FCB94EE93E367CB // 61
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data8 0x3FCBF851C067555F // 62
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data8 0x3FCC5C0254BF23A6 // 63
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data8 0x3FCCC000C9DB3C52 // 64
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data8 0x3FCD244D99C85674 // 65
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data8 0x3FCD88E93FB2F450 // 66
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data8 0x3FCDEDD437EAEF01 // 67
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data8 0x3FCE530EFFE71012 // 68
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data8 0x3FCEB89A1648B971 // 69
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data8 0x3FCF1E75FADF9BDE // 70
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data8 0x3FCF84A32EAD7C35 // 71
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data8 0x3FCFEB2233EA07CD // 72
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data8 0x3FD028F9C7035C1C // 73
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data8 0x3FD05C8BE0D9635A // 74
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data8 0x3FD085EB8F8AE797 // 75
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data8 0x3FD0B9C8E32D1911 // 76
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data8 0x3FD0EDD060B78081 // 77
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data8 0x3FD122024CF0063F // 78
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data8 0x3FD14BE2927AECD4 // 79
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data8 0x3FD180618EF18ADF // 80
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data8 0x3FD1B50BBE2FC63B // 81
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data8 0x3FD1DF4CC7CF242D // 82
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data8 0x3FD214456D0EB8D4 // 83
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data8 0x3FD23EC5991EBA49 // 84
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data8 0x3FD2740D9F870AFB // 85
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data8 0x3FD29ECDABCDFA04 // 86
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data8 0x3FD2D46602ADCCEE // 87
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data8 0x3FD2FF66B04EA9D4 // 88
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data8 0x3FD335504B355A37 // 89
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data8 0x3FD360925EC44F5D // 90
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data8 0x3FD38BF1C3337E75 // 91
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data8 0x3FD3C25277333184 // 92
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data8 0x3FD3EDF463C1683E // 93
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data8 0x3FD419B423D5E8C7 // 94
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data8 0x3FD44591E0539F49 // 95
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data8 0x3FD47C9175B6F0AD // 96
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data8 0x3FD4A8B341552B09 // 97
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data8 0x3FD4D4F3908901A0 // 98
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data8 0x3FD501528DA1F968 // 99
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data8 0x3FD52DD06347D4F6 // 100
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data8 0x3FD55A6D3C7B8A8A // 101
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data8 0x3FD5925D2B112A59 // 102
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data8 0x3FD5BF406B543DB2 // 103
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data8 0x3FD5EC433D5C35AE // 104
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data8 0x3FD61965CDB02C1F // 105
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data8 0x3FD646A84935B2A2 // 106
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data8 0x3FD6740ADD31DE94 // 107
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data8 0x3FD6A18DB74A58C5 // 108
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data8 0x3FD6CF31058670EC // 109
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data8 0x3FD6F180E852F0BA // 110
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data8 0x3FD71F5D71B894F0 // 111
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data8 0x3FD74D5AEFD66D5C // 112
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data8 0x3FD77B79922BD37E // 113
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data8 0x3FD7A9B9889F19E2 // 114
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data8 0x3FD7D81B037EB6A6 // 115
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data8 0x3FD8069E33827231 // 116
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data8 0x3FD82996D3EF8BCB // 117
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data8 0x3FD85855776DCBFB // 118
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data8 0x3FD8873658327CCF // 119
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data8 0x3FD8AA75973AB8CF // 120
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data8 0x3FD8D992DC8824E5 // 121
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data8 0x3FD908D2EA7D9512 // 122
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data8 0x3FD92C59E79C0E56 // 123
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data8 0x3FD95BD750EE3ED3 // 124
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data8 0x3FD98B7811A3EE5B // 125
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data8 0x3FD9AF47F33D406C // 126
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data8 0x3FD9DF270C1914A8 // 127
|
|
data8 0x3FDA0325ED14FDA4 // 128
|
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data8 0x3FDA33440224FA79 // 129
|
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data8 0x3FDA57725E80C383 // 130
|
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data8 0x3FDA87D0165DD199 // 131
|
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data8 0x3FDAAC2E6C03F896 // 132
|
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data8 0x3FDADCCC6FDF6A81 // 133
|
|
data8 0x3FDB015B3EB1E790 // 134
|
|
data8 0x3FDB323A3A635948 // 135
|
|
data8 0x3FDB56FA04462909 // 136
|
|
data8 0x3FDB881AA659BC93 // 137
|
|
data8 0x3FDBAD0BEF3DB165 // 138
|
|
data8 0x3FDBD21297781C2F // 139
|
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data8 0x3FDC039236F08819 // 140
|
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data8 0x3FDC28CB1E4D32FD // 141
|
|
data8 0x3FDC4E19B84723C2 // 142
|
|
data8 0x3FDC7FF9C74554C9 // 143
|
|
data8 0x3FDCA57B64E9DB05 // 144
|
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data8 0x3FDCCB130A5CEBB0 // 145
|
|
data8 0x3FDCF0C0D18F326F // 146
|
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data8 0x3FDD232075B5A201 // 147
|
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data8 0x3FDD490246DEFA6B // 148
|
|
data8 0x3FDD6EFA918D25CD // 149
|
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data8 0x3FDD9509707AE52F // 150
|
|
data8 0x3FDDBB2EFE92C554 // 151
|
|
data8 0x3FDDEE2F3445E4AF // 152
|
|
data8 0x3FDE148A1A2726CE // 153
|
|
data8 0x3FDE3AFC0A49FF40 // 154
|
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data8 0x3FDE6185206D516E // 155
|
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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
|
|
//==============================================================
|
|
.section .text
|
|
|
|
// logf has p13 true, p14 false
|
|
// log10f has p14 true, p13 false
|
|
|
|
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
|
|
}
|
|
{ .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
|
|
}
|
|
{ .mlx
|
|
ld8 GR_ad_T = [GR_ad_T]
|
|
movl GR_Ln2 = 0x3FD34413509F79FF // double precision memory
|
|
// representation of
|
|
// log(2)/ln(10)
|
|
};;
|
|
{ .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
|
|
}
|
|
{ .mib
|
|
setf.exp FR_A2 = GR_05 // create A2
|
|
sub GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE
|
|
// needed for comparison with 0.5 and 2.0
|
|
br.cond.sptk logf_log10f_common
|
|
};;
|
|
GLOBAL_IEEE754_END(log10f)
|
|
libm_alias_float_other (__log10, log10)
|
|
|
|
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
|
|
}
|
|
{ .mlx
|
|
addl GR_ad_T = @ltoff(logf_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?
|
|
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
|
|
ld8 GR_ad_T = [GR_ad_T]
|
|
nop.f 0
|
|
sub GR_025 = GR_05,r0,1 // biased exponent of A4=0.25
|
|
};;
|
|
{ .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 for comparison 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
|
|
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
|
|
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
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
sub GR_x = GR_x,GR_xorg // difference between representations
|
|
// of x and 255/256
|
|
};;
|
|
{ .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
|
|
}
|
|
{ .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
|
|
}
|
|
{ .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
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
|
|
nop.i 0
|
|
};;
|
|
{ .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
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
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 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .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
|
|
}
|
|
{ .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
|
|
{ .mfi
|
|
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
|
|
};;
|
|
|
|
.align 32
|
|
logf_positive_unorm:
|
|
{ .mfi
|
|
nop.m 0
|
|
(p8) fma.s0 f8 = f8,f1,f0 // Normalize & set D-flag
|
|
nop.i 0
|
|
};;
|
|
{ .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]
|
|
};;
|
|
{ .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
|
|
};;
|
|
|
|
.align 32
|
|
logf_nan_nat_pinf:
|
|
{ .mfi
|
|
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
|
|
};;
|
|
|
|
.align 32
|
|
logf_zeroes:
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8 // keep input argument for subsequent
|
|
// call of __libm_error_support#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
(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 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
|
|
};;
|
|
|
|
.align 32
|
|
logf_negatives:
|
|
{ .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
|
|
};;
|
|
{ .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
|
|
};;
|
|
|
|
.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)
|
|
libm_alias_float_other (__log, log)
|
|
#ifdef SHARED
|
|
.symver logf,logf@@GLIBC_2.27
|
|
.weak __logf_compat
|
|
.set __logf_compat,__logf
|
|
.symver __logf_compat,logf@GLIBC_2.2
|
|
#endif
|
|
|
|
|
|
// Stack operations when calling error support.
|
|
// (1) (2) (3) (call) (4)
|
|
// sp -> + psp -> + psp -> + sp -> +
|
|
// | | | |
|
|
// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8
|
|
// | | | |
|
|
// | <-GR_Y Y2->| Y2 ->| <- GR_Y |
|
|
// | | | |
|
|
// | | <- GR_X X1 ->| |
|
|
// | | | |
|
|
// sp-64 -> + sp -> + sp -> + +
|
|
// save ar.pfs save b0 restore gp
|
|
// save gp restore ar.pfs
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
{ .mfi
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
nop.f 0
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
{ .mmi
|
|
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
|
|
};;
|
|
.body
|
|
{ .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
|
|
}
|
|
{ .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
|
|
};;
|
|
{ .mmi
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
{ .mmi
|
|
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
|
|
};;
|
|
{ .mib
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
br.ret.sptk b0 // Return
|
|
};;
|
|
|
|
LOCAL_LIBM_END(__libm_error_region)
|
|
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|