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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>
789 lines
22 KiB
ArmAsm
789 lines
22 KiB
ArmAsm
.file "log1pf.s"
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// Copyright (c) 2000 - 2003, 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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// 02/02/00 Initial version
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// 04/04/00 Unwind support added
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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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// 06/29/01 Improved speed of all paths
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 10/02/02 Improved performance by basing on log algorithm
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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// 04/18/03 Eliminate possible WAW dependency warning
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// 12/16/03 Fixed parameter passing to/from error handling routine
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//
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// API
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//==============================================================
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// float log1pf(float)
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//
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// log1p(x) = log(x+1)
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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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// log1p(x) = log(1+x) and
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// log(a b) = log(a) + log(b).
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// In our case we have 1+x = 2^N f, where 1 <= f < 2.
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// So
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// log(1+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 + 1 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(1+x) ~ (N*log(2) + T) + P(r)
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//
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// Note that if input argument is close to 0.0 (in our case it means
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// that |x| < 1/256) we can use just polynomial approximation
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// because 1+x = 2^0 * f = f = 1 + r and
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// log(1+x) = log(1 + r) ~ P(r)
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//
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//
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// Implementation
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// --------------
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//
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// 1. |x| >= 2^(-8), and x > -1
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// InvX = frcpa(x+1)
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// r = InvX*(x+1) - 1
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// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are created with setf instruction.
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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 load T we get bits from 55 to 62 of register
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// format significand as index and calculate address
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// ad_T = table_base_addr + 8 * index
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//
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// L1 (log(2)) is calculated in quad precision and rounded to double;
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// it's created with setf
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//
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// And final result = P2(r)*r + (T + N*L1)
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//
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//
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// 2. 2^(-40) <= |x| < 2^(-8)
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// r = x
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// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are the same as in case |x| >= 1/256
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//
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// And final result = P2(r)*r
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//
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// 3. 0 < |x| < 2^(-40)
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// Although log1p(x) is basically x, we would like to preserve the inexactness
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// nature as well as consistent behavior under different rounding modes.
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// We can do this by computing the result as
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//
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// log1p(x) = x - x*x
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//
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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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// log1p(-1) = -inf // Call error support
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//
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// log1p(+qnan) = +qnan
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// log1p(-qnan) = -qnan
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// log1p(+snan) = +qnan
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// log1p(-snan) = -qnan
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//
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// log1p(x),x<-1= QNAN Indefinite // Call error support
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// log1p(-inf) = QNAN Indefinite
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// log1p(+inf) = +inf
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// log1p(+/-0) = +/-0
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//
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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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// f7 -> f15, f32 -> f36
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//
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// General registers used:
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// r8 -> r11
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// r14 -> r22
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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 = r9
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GR_Exp = r10
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GR_N = r11
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GR_signexp_x = r14
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GR_exp_mask = r15
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GR_exp_bias = r16
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GR_05 = r17
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GR_A3 = r18
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GR_Sig = r19
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GR_Ind = r19
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GR_exp_x = r20
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GR_Ln2 = r21
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GR_025 = 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_NormX = f7
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FR_RcpX = f9
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FR_r = f10
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FR_r2 = f11
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FR_r4 = f12
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FR_N = f13
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FR_Ln2 = f14
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FR_Xp1 = f15
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FR_A4 = f33
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FR_A3 = f34
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FR_A2 = f35
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FR_T = f36
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FR_NxLn2pT = f36
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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
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(log_data)
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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
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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
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data8 0x3FDB015B3EB1E790 // 134
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data8 0x3FDB323A3A635948 // 135
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data8 0x3FDB56FA04462909 // 136
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data8 0x3FDB881AA659BC93 // 137
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data8 0x3FDBAD0BEF3DB165 // 138
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data8 0x3FDBD21297781C2F // 139
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data8 0x3FDC039236F08819 // 140
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data8 0x3FDC28CB1E4D32FD // 141
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data8 0x3FDC4E19B84723C2 // 142
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data8 0x3FDC7FF9C74554C9 // 143
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data8 0x3FDCA57B64E9DB05 // 144
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data8 0x3FDCCB130A5CEBB0 // 145
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data8 0x3FDCF0C0D18F326F // 146
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data8 0x3FDD232075B5A201 // 147
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data8 0x3FDD490246DEFA6B // 148
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data8 0x3FDD6EFA918D25CD // 149
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data8 0x3FDD9509707AE52F // 150
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data8 0x3FDDBB2EFE92C554 // 151
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data8 0x3FDDEE2F3445E4AF // 152
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data8 0x3FDE148A1A2726CE // 153
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data8 0x3FDE3AFC0A49FF40 // 154
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data8 0x3FDE6185206D516E // 155
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data8 0x3FDE882578823D52 // 156
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data8 0x3FDEAEDD2EAC990C // 157
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data8 0x3FDED5AC5F436BE3 // 158
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data8 0x3FDEFC9326D16AB9 // 159
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data8 0x3FDF2391A2157600 // 160
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data8 0x3FDF4AA7EE03192D // 161
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data8 0x3FDF71D627C30BB0 // 162
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data8 0x3FDF991C6CB3B379 // 163
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data8 0x3FDFC07ADA69A910 // 164
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data8 0x3FDFE7F18EB03D3E // 165
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data8 0x3FE007C053C5002E // 166
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data8 0x3FE01B942198A5A1 // 167
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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(log_data)
|
|
|
|
|
|
// Code
|
|
//==============================================================
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(log1pf)
|
|
{ .mfi
|
|
getf.exp GR_signexp_x = f8 // if x is unorm then must recompute
|
|
fadd.s1 FR_Xp1 = f8, f1 // Form 1+x
|
|
mov GR_05 = 0xfffe
|
|
}
|
|
{ .mlx
|
|
addl GR_ad_T = @ltoff(log_data),gp
|
|
movl GR_A3 = 0x3fd5555555555555 // double precision memory
|
|
// representation of A3
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ld8 GR_ad_T = [GR_ad_T]
|
|
fclass.m p8,p0 = f8,0xb // Is x unorm?
|
|
mov GR_exp_mask = 0x1ffff
|
|
}
|
|
{ .mfi
|
|
mov GR_025 = 0xfffd // Exponent of 0.25
|
|
fnorm.s1 FR_NormX = f8 // Normalize x
|
|
mov GR_exp_bias = 0xffff
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.exp FR_A2 = GR_05 // create A2 = 0.5
|
|
fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
setf.d FR_A3 = GR_A3 // create A3
|
|
nop.i 0
|
|
(p8) br.cond.spnt log1p_unorm // Branch if x=unorm
|
|
}
|
|
;;
|
|
|
|
log1p_common:
|
|
{ .mfi
|
|
setf.exp FR_A4 = GR_025 // create A4 = 0.25
|
|
frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p9) fma.s.s0 f8 = f8,f1,f0 // set V-flag
|
|
(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.exp GR_Exp = FR_Xp1 // signexp of x+1
|
|
fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
|
|
and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory
|
|
// representation of log(2)
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig GR_Sig = FR_Xp1 // get significand to calculate index
|
|
// for T if |x| >= 2^-8
|
|
fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0?
|
|
sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
|
|
fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1?
|
|
cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1
|
|
}
|
|
;;
|
|
|
|
// p6 is true if |x| < 1/256
|
|
// p7 is true if |x| >= 1/256
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256
|
|
(p6) cmp.gt.unc p10,p0 = -40, GR_exp_x // Is |x| < 2^-40
|
|
}
|
|
{ .mfb
|
|
(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the
|
|
// significand field of FR_N
|
|
(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
|
|
(p12) br.ret.spnt b0 // exit for x=0, return x
|
|
}
|
|
;;
|
|
|
|
{ .mib
|
|
setf.d FR_Ln2 = GR_Ln2 // create log(2)
|
|
(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
|
|
(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
(p7) shladd GR_ad_T = GR_Ind,3,GR_ad_T // address of T
|
|
nop.m 0
|
|
(p10) fnma.s.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x
|
|
}
|
|
;;
|
|
|
|
{ .mmb
|
|
(p7) ldfd FR_T = [GR_ad_T]
|
|
nop.m 0
|
|
(p10) br.ret.spnt b0 // Exit if |x| < 2^-40
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A2 = FR_A2,FR_r,f1 // 1.0 - A2*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A3 - A4*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fcvt.xf FR_N = FR_N
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// (A3*r+A2)*r^2+r
|
|
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
|
|
// N*Ln2hi+T
|
|
(p7) fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result if 2^(-40) <= |x| < 1/256
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result if |x| >= 1/256
|
|
br.ret.sptk b0 // Exit if |x| >= 2^(-40)
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_unorm:
|
|
// Here if x=unorm
|
|
{ .mfb
|
|
getf.exp GR_signexp_x = FR_NormX // recompute biased exponent
|
|
nop.f 0
|
|
br.cond.sptk log1p_common
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_eq_minus_1:
|
|
// Here if x=-1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8 // keep input argument for subsequent
|
|
// call of __libm_error_support#
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 142 // set libm error in case of log1p(-1).
|
|
frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
|
|
// We can get it using frcpa because it
|
|
// sets result to the IEEE-754 mandated
|
|
// quotient of f8/f0.
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
nop.m 0
|
|
nop.i 0
|
|
br.cond.sptk log_libm_err
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_lt_minus_1:
|
|
// Here if x < -1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 143 // set libm error in case of x < -1.
|
|
frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 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
|
|
log_libm_err:
|
|
{ .mmi
|
|
alloc r32 = ar.pfs,1,4,4,0
|
|
mov GR_Parameter_TAG = GR_TAG
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
GLOBAL_IEEE754_END(log1pf)
|
|
libm_alias_float_other (__log1p, log1p)
|
|
|
|
|
|
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
|
|
add GR_Parameter_RESULT = 48,sp
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
{ .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#
|