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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>
7678 lines
222 KiB
ArmAsm
7678 lines
222 KiB
ArmAsm
.file "libm_lgammal.s"
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// Copyright (c) 2002 - 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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//*********************************************************************
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//
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// History:
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// 03/28/02 Original version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 08/21/02 Added support of SIGN(GAMMA(x)) calculation
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// 09/26/02 Algorithm description improved
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// 10/21/02 Now it returns SIGN(GAMMA(x))=-1 for negative zero
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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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//*********************************************************************
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//
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// Function: __libm_lgammal(long double x, int* signgam, int szsigngam)
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// computes the principal value of the logarithm of the GAMMA function
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// of x. Signum of GAMMA(x) is stored to memory starting at the address
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// specified by the signgam.
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//
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//*********************************************************************
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//
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// Resources Used:
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//
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// Floating-Point Registers: f8 (Input and Return Value)
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// f9-f15
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// f32-f127
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//
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// General Purpose Registers:
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// r2, r3, r8-r11, r14-r31
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// r32-r65
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// r66-r69 (Used to pass arguments to error handling routine)
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//
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// Predicate Registers: p6-p15
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//
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//*********************************************************************
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//
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// IEEE Special Conditions:
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//
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// __libm_lgammal(+inf) = +inf
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// __libm_lgammal(-inf) = QNaN
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// __libm_lgammal(+/-0) = +inf
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// __libm_lgammal(x<0, x - integer) = QNaN
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// __libm_lgammal(SNaN) = QNaN
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// __libm_lgammal(QNaN) = QNaN
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//
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//*********************************************************************
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//
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// ALGORITHM DESCRIPTION
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//
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// Below we suppose that there is log(z) function which takes an long
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// double argument and returns result as a pair of long double numbers
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// lnHi and lnLo (such that sum lnHi + lnLo provides ~80 correct bits
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// of significand). Algorithm description for such log(z) function
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// see below.
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// Also, it this algorithm description we use the following notational
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// conventions:
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// a) pair A = (Ahi, Alo) means number A represented as sum of Ahi and Alo
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// b) C = A + B = (Ahi, Alo) + (Bhi, Blo) means multi-precision addition.
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// The result would be C = (Chi, Clo). Notice, that Clo shouldn't be
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// equal to Alo + Blo
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// c) D = A*B = (Ahi, Alo)*(Bhi, Blo) = (Dhi, Dlo) multi-precisiion
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// multiplication.
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//
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// So, lgammal has the following computational paths:
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// 1) |x| < 0.5
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// P = A1*|x| + A2*|x|^2 + ... + A22*|x|^22
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// A1, A2, A3 represented as a sum of two double precision
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// numbers and multi-precision computations are used for 3 higher
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// terms of the polynomial. We get polynomial as a sum of two
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// double extended numbers: P = (Phi, Plo)
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// 1.1) x > 0
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// lgammal(x) = P - log(|x|) = (Phi, Plo) - (lnHi(|x|), lnLo(|x|))
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// 1.2) x < 0
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// lgammal(x) = -P - log(|x|) - log(sin(Pi*x)/(Pi*x))
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// P and log(|x|) are computed by the same way as in 1.1;
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// - log(sin(Pi*x)/(Pi*x)) is approximated by a polynomial Plnsin.
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// Plnsin:= fLnSin2*|x|^2 + fLnSin4*|x|^4 + ... + fLnSin36*|x|^36
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// The first coefficient of Plnsin is represented as sum of two
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// double precision numbers (fLnSin2, fLnSin2L). Multi-precision
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// computations for higher two terms of Plnsin are used.
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// So, the final result is reconstructed by the following formula
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// lgammal(x) = (-(Phi, Plo) - (lnHi(|x|), lnLo(|x|))) -
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// - (PlnsinHi,PlnsinLo)
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//
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// 2) 0.5 <= x < 0.75 -> t = x - 0.625
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// -0.75 < x <= -0.5 -> t = x + 0.625
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// 2.25 <= x < 4.0 -> t = x/2 - 1.5
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// 4.0 <= x < 8.0 -> t = x/4 - 1.5
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// -0.5 < x <= -0.40625 -> t = x + 0.5
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// -2.6005859375 < x <= -2.5 -> t = x + 2.5
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// 1.3125 <= x < 1.5625 -> t = x - LOC_MIN, where LOC_MIN is point in
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// which lgammal has local minimum. Exact
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// value can be found in the table below,
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// approximate value is ~1.46
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//
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// lgammal(x) is approximated by the polynomial of 25th degree: P25(t)
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// P25(t) = A0 + A1*t + ... + A25*t^25 = (Phi, Plo) + t^4*P21(t),
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// where
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// (Phi, Plo) is sum of four highest terms of the polynomial P25(t):
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// (Phi, Plo) = ((A0, A0L) + (A1, A1L)*t) + t^2 *((A2, A2L) + (A3, A3L)*t),
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// (Ai, AiL) - coefficients represented as pairs of DP numbers.
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//
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// P21(t) = (PolC(t)*t^8 + PolD(t))*t^8 + PolE(t),
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// where
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// PolC(t) = C21*t^5 + C20*t^4 + ... + C16,
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// C21 = A25, C20 = A24, ..., C16 = A20
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//
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// PolD(t) = D7*t^7 + D6*t^6 + ... + D0,
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// D7 = A19, D6 = A18, ..., D0 = A12
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//
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// PolE(t) = E7*t^7 + E6*t^6 + ... + E0,
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// E7 = A11, E6 = A10, ..., E0 = A4
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//
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// Cis and Dis are represented as double precision numbers,
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// Eis are represented as double extended numbers.
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//
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// 3) 0.75 <= x < 1.3125 -> t = x - 1.0
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// 1.5625 <= x < 2.25 -> t = x - 2.0
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// lgammal(x) is approximated by the polynomial of 25th degree: P25(t)
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// P25(t) = A1*t + ... + A25*t^25, and computations are carried out
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// by similar way as in the previous case
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//
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// 4) 10.0 < x <= Overflow Bound ("positive Sterling" range)
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// lgammal(x) is approximated using Sterling's formula:
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// lgammal(x) ~ ((x*(lnHi(x) - 1, lnLo(x))) - 0.5*(lnHi(x), lnLo(x))) +
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// + ((Chi, Clo) + S(1/x))
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// where
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// C = (Chi, Clo) - pair of double precision numbers representing constant
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// 0.5*ln(2*Pi);
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// S(1/x) = 1/x * (B2 + B4*(1/x)^2 + ... + B20*(1/x)^18), B2, ..., B20 are
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// Bernulli numbers. S is computed in native precision and then added to
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// Clo;
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// lnHi(x) - 1 is computed in native precision and the multiprecision
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// multiplication (x, 0) *(lnHi(x) - 1, lnLo(x)) is used.
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//
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// 5) -INF < x <= -2^63, any negative integer < 0
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// All numbers in this range are integers -> error handler is called
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//
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// 6) -2^63 < x <= -0.75 ("negative Sterling" range), x is "far" from root,
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// lgammal(-t) for positive t is approximated using the following formula:
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// lgammal(-t) = -lgammal(t)-log(t)-log(|dT|)+log(sin(Pi*|dT|)/(Pi*|dT|))
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// where dT = -t -round_to_nearest_integer(-t)
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// Last item is approximated by the same polynomial as described in 1.2.
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// We split the whole range into three subranges due to different ways of
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// approximation of the first terms.
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// 6.1) -2^63 < x < -6.0 ("negative Sterling" range)
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// lgammal(t) is approximated exactly as in #4. The only difference that
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// for -13.0 < x < -6.0 subrange instead of Bernulli numbers we use their
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// minimax approximation on this range.
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// log(t), log(|dT|) are approximated by the log routine mentioned above.
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// 6.2) -6.0 < x <= -0.75, |x + 1|> 2^(-7)
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// log(t), log(|dT|) are approximated by the log routine mentioned above,
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// lgammal(t) is approximated by polynomials of the 25th degree similar
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// to ones from #2. Arguments z of the polynomials are as follows
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// a) 0.75 <= t < 1.0 - 2^(-7), z = 2*t - 1.5
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// b) 1.0 - 2^(-7) < t < 2.0, z = t - 1.5
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// c) 2.0 < t < 3.0, z = t/2 - 1.5
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// d) 3.0 < t < 4.0, z = t/2 - 1.5. Notice, that range reduction is
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// the same as in case c) but the set of coefficients is different
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// e) 4.0 < t < 6.0, z = t/4 - 1.5
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// 6.3) |x + 1| <= 2^(-7)
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// log(1 + (x-1)) is approximated by Taylor series,
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// log(sin(Pi*|dT|)/(Pi*|dT|)) is still approximated by polynomial but
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// it has just 4th degree.
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// log(|dT|) is approximated by the log routine mentioned above.
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// lgammal(-x) is approximated by polynomial of 8th degree from (-x + 1).
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//
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// 7) -20.0 < x < -2.0, x falls in root "neighbourhood".
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// "Neighbourhood" means that |lgammal(x)| < epsilon, where epsilon is
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// different for every root (and it is stored in the table), but typically
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// it is ~ 0.15. There are 35 roots significant from "double extended"
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// point of view. We split all the roots into two subsets: "left" and "right"
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// roots. Considering [-(N+1), -N] range we call root as "left" one if it
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// lies closer to -(N+1) and "right" otherwise. There is no "left" root in
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// the [-20, -19] range (it exists, but is insignificant for double extended
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// precision). To determine if x falls in root "neighbourhood" we store
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// significands of all the 35 roots as well as epsilon values (expressed
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// by the left and right bound).
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// In these ranges we approximate lgammal(x) by polynomial series of 19th
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// degree:
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// lgammal(x) = P19(t) = A0 + A1*t + ...+ A19*t^19, where t = x - EDP_Root,
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// EDP_Root is the exact value of the corresponding root rounded to double
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// extended precision. So, we have 35 different polynomials which make our
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// table rather big. We may hope that x falls in root "neighbourhood"
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// quite rarely -> ther might be no need in frequent use of different
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// polynomials.
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// A0, A1, A2, A3 are represented as pairs of double precision numbers,
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// A4, A5 are long doubles, and to decrease the size of the table we
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// keep the rest of coefficients in just double precision
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//
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//*********************************************************************
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// Algorithm for log(X) = (lnHi(X), lnLo(X))
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//
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// ALGORITHM
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//
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// Here we use a table lookup method. The basic idea is that in
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// order to compute logl(Arg) for an argument Arg in [1,2), we
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// construct a value G such that G*Arg is close to 1 and that
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// logl(1/G) is obtainable easily from a table of values calculated
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// beforehand. Thus
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//
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// logl(Arg) = logl(1/G) + logl(G*Arg)
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// = logl(1/G) + logl(1 + (G*Arg - 1))
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//
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// Because |G*Arg - 1| is small, the second term on the right hand
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// side can be approximated by a short polynomial. We elaborate
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// this method in four steps.
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//
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// Step 0: Initialization
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//
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// We need to calculate logl( X ). Obtain N, S_hi such that
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//
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// X = 2^N * S_hi exactly
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//
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// where S_hi in [1,2)
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//
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// Step 1: Argument Reduction
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//
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// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
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//
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// G := G_1 * G_2 * G_3
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// r := (G * S_hi - 1)
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//
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// These G_j's have the property that the product is exactly
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// representable and that |r| < 2^(-12) as a result.
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//
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// Step 2: Approximation
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//
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//
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// logl(1 + r) is approximated by a short polynomial poly(r).
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//
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// Step 3: Reconstruction
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//
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//
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// Finally, logl( X ) is given by
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//
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// logl( X ) = logl( 2^N * S_hi )
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// ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
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// ~=~ N*logl(2) + logl(1/G) + poly(r).
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//
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// IMPLEMENTATION
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//
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// Step 0. Initialization
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// ----------------------
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//
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// Z := X
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// N := unbaised exponent of Z
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// S_hi := 2^(-N) * Z
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//
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// Step 1. Argument Reduction
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// --------------------------
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//
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// Let
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//
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// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63
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//
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// We obtain G_1, G_2, G_3 by the following steps.
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//
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//
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// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted
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// from S_hi.
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//
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// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated
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// to lsb = 2^(-4).
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//
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// Define index_1 := [ d_1 d_2 d_3 d_4 ].
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//
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// Fetch Z_1 := (1/A_1) rounded UP in fixed point with
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// fixed point lsb = 2^(-15).
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// Z_1 looks like z_0.z_1 z_2 ... z_15
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// Note that the fetching is done using index_1.
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// A_1 is actually not needed in the implementation
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// and is used here only to explain how is the value
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// Z_1 defined.
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//
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// Fetch G_1 := (1/A_1) truncated to 21 sig. bits.
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// floating pt. Again, fetching is done using index_1. A_1
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// explains how G_1 is defined.
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//
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// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14)
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// = 1.0 0 0 0 d_5 ... d_14
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// This is accomplished by integer multiplication.
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// It is proved that X_1 indeed always begin
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// with 1.0000 in fixed point.
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//
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//
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// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1
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// truncated to lsb = 2^(-8). Similar to A_1,
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// A_2 is not needed in actual implementation. It
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// helps explain how some of the values are defined.
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//
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// Define index_2 := [ d_5 d_6 d_7 d_8 ].
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//
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// Fetch Z_2 := (1/A_2) rounded UP in fixed point with
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// fixed point lsb = 2^(-15). Fetch done using index_2.
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// Z_2 looks like z_0.z_1 z_2 ... z_15
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//
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// Fetch G_2 := (1/A_2) truncated to 21 sig. bits.
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// floating pt.
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//
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// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14)
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// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14
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// This is accomplished by integer multiplication.
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// It is proved that X_2 indeed always begin
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// with 1.00000000 in fixed point.
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//
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//
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// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1.
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// This is 2^(-14) + X_2 truncated to lsb = 2^(-13).
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//
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// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ].
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//
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// Fetch G_3 := (1/A_3) truncated to 21 sig. bits.
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// floating pt. Fetch is done using index_3.
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//
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// Compute G := G_1 * G_2 * G_3.
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//
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// This is done exactly since each of G_j only has 21 sig. bits.
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//
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// Compute
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//
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// r := (G*S_hi - 1)
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//
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//
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// Step 2. Approximation
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// ---------------------
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//
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// This step computes an approximation to logl( 1 + r ) where r is the
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// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
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// thus logl(1+r) can be approximated by a short polynomial:
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//
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// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
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//
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//
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// Step 3. Reconstruction
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// ----------------------
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//
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// This step computes the desired result of logl(X):
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//
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// logl(X) = logl( 2^N * S_hi )
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// = N*logl(2) + logl( S_hi )
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// = N*logl(2) + logl(1/G) +
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// logl(1 + G*S_hi - 1 )
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//
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// logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers:
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// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are
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// single-precision numbers and the low parts are double precision
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|
// numbers. These have the property that
|
|
//
|
|
// N*log2_hi + SUM ( log1byGj_hi )
|
|
//
|
|
// is computable exactly in double-extended precision (64 sig. bits).
|
|
// Finally
|
|
//
|
|
// lnHi(X) := N*log2_hi + SUM ( log1byGj_hi )
|
|
// lnLo(X) := poly_hi + [ poly_lo +
|
|
// ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
|
|
//
|
|
//
|
|
//*********************************************************************
|
|
// General Purpose Registers
|
|
// scratch registers
|
|
rPolDataPtr = r2
|
|
rLnSinDataPtr = r3
|
|
rExpX = r8
|
|
rSignifX = r9
|
|
rDelta = r10
|
|
rSignExpX = r11
|
|
GR_ad_z_1 = r14
|
|
r17Ones = r15
|
|
GR_Index1 = r16
|
|
rSignif1andQ = r17
|
|
GR_X_0 = r18
|
|
GR_X_1 = r19
|
|
GR_X_2 = r20
|
|
GR_Z_1 = r21
|
|
GR_Z_2 = r22
|
|
GR_N = r23
|
|
rExpHalf = r24
|
|
rExp8 = r25
|
|
rX0Dx = r25
|
|
GR_ad_tbl_1 = r26
|
|
GR_ad_tbl_2 = r27
|
|
GR_ad_tbl_3 = r28
|
|
GR_ad_q = r29
|
|
GR_ad_z_1 = r30
|
|
GR_ad_z_2 = r31
|
|
// stacked registers
|
|
rPFS_SAVED = r32
|
|
GR_ad_z_3 = r33
|
|
rSgnGamAddr = r34
|
|
rSgnGamSize = r35
|
|
rLogDataPtr = r36
|
|
rZ1offsett = r37
|
|
rTmpPtr = r38
|
|
rTmpPtr2 = r39
|
|
rTmpPtr3 = r40
|
|
rExp2 = r41
|
|
rExp2tom7 = r42
|
|
rZ625 = r42
|
|
rExpOne = r43
|
|
rNegSingularity = r44
|
|
rXint = r45
|
|
rTbl1Addr = r46
|
|
rTbl2Addr = r47
|
|
rTbl3Addr = r48
|
|
rZ2Addr = r49
|
|
rRootsAddr = r50
|
|
rRootsBndAddr = r51
|
|
rRoot = r52
|
|
rRightBound = r53
|
|
rLeftBound = r54
|
|
rSignifDx = r55
|
|
rBernulliPtr = r56
|
|
rLnSinTmpPtr = r56
|
|
rIndex1Dx = r57
|
|
rIndexPol = r58
|
|
GR_Index3 = r59
|
|
GR_Index2 = r60
|
|
rSgnGam = r61
|
|
rXRnd = r62
|
|
|
|
GR_SAVE_B0 = r63
|
|
GR_SAVE_GP = r64
|
|
GR_SAVE_PFS = r65
|
|
// output parameters when calling error handling routine
|
|
GR_Parameter_X = r66
|
|
GR_Parameter_Y = r67
|
|
GR_Parameter_RESULT = r68
|
|
GR_Parameter_TAG = r69
|
|
|
|
//********************************************************************
|
|
// Floating Point Registers
|
|
// CAUTION: due to the lack of registers there exist (below in the code)
|
|
// sometimes "unconventional" use of declared registers
|
|
//
|
|
fAbsX = f6
|
|
fDelX4 = f6
|
|
fSignifX = f7
|
|
// macros for error handling routine
|
|
FR_X = f10 // first argument
|
|
FR_Y = f1 // second argument (lgammal has just one)
|
|
FR_RESULT = f8 // result
|
|
|
|
// First 7 Bernulli numbers
|
|
fB2 = f9
|
|
fLnDeltaL = f9
|
|
fXSqr = f9
|
|
fB4 = f10
|
|
fX4 = f10
|
|
fB6 = f11
|
|
fX6 = f11
|
|
fB8 = f12
|
|
fXSqrL = f12
|
|
fB10 = f13
|
|
fRes7H = f13
|
|
fB12 = f14
|
|
fRes7L = f14
|
|
fB14 = f15
|
|
|
|
// stack registers
|
|
// Polynomial coefficients: A0, ..., A25
|
|
fA0 = f32
|
|
fA0L = f33
|
|
fInvXL = f33
|
|
fA1 = f34
|
|
fA1L = f35
|
|
fA2 = f36
|
|
fA2L = f37
|
|
fA3 = f38
|
|
fA3L = f39
|
|
fA4 = f40
|
|
fA4L = f41
|
|
fRes6H = f41
|
|
fA5 = f42
|
|
fB2L = f42
|
|
fA5L = f43
|
|
fMinNegStir = f43
|
|
fRes6L = f43
|
|
fA6 = f44
|
|
fMaxNegStir = f44
|
|
fA7 = f45
|
|
fLnDeltaH = f45
|
|
fA8 = f46
|
|
fBrnL = f46
|
|
fA9 = f47
|
|
fBrnH = f47
|
|
fA10 = f48
|
|
fRes5L = f48
|
|
fA11 = f49
|
|
fRes5H = f49
|
|
fA12 = f50
|
|
fDx6 = f50
|
|
fA13 = f51
|
|
fDx8 = f51
|
|
fA14 = f52
|
|
fDx4 = f52
|
|
fA15 = f53
|
|
fYL = f53
|
|
fh3Dx = f53
|
|
fA16 = f54
|
|
fYH = f54
|
|
fH3Dx = f54
|
|
fA17 = f55
|
|
fResLnDxL = f55
|
|
fG3Dx = f55
|
|
fA18 = f56
|
|
fResLnDxH = f56
|
|
fh2Dx = f56
|
|
fA19 = f57
|
|
fFloatNDx = f57
|
|
fA20 = f58
|
|
fPolyHiDx = f58
|
|
fhDx = f58
|
|
fA21 = f59
|
|
fRDxCub = f59
|
|
fHDx = f59
|
|
fA22 = f60
|
|
fRDxSq = f60
|
|
fGDx = f60
|
|
fA23 = f61
|
|
fPolyLoDx = f61
|
|
fInvX3 = f61
|
|
fA24 = f62
|
|
fRDx = f62
|
|
fInvX8 = f62
|
|
fA25 = f63
|
|
fInvX4 = f63
|
|
fPol = f64
|
|
fPolL = f65
|
|
// Coefficients of ln(sin(Pi*x)/Pi*x)
|
|
fLnSin2 = f66
|
|
fLnSin2L = f67
|
|
fLnSin4 = f68
|
|
fLnSin6 = f69
|
|
fLnSin8 = f70
|
|
fLnSin10 = f71
|
|
fLnSin12 = f72
|
|
fLnSin14 = f73
|
|
fLnSin16 = f74
|
|
fLnSin18 = f75
|
|
fDelX8 = f75
|
|
fLnSin20 = f76
|
|
fLnSin22 = f77
|
|
fDelX6 = f77
|
|
fLnSin24 = f78
|
|
fLnSin26 = f79
|
|
fLnSin28 = f80
|
|
fLnSin30 = f81
|
|
fhDelX = f81
|
|
fLnSin32 = f82
|
|
fLnSin34 = f83
|
|
fLnSin36 = f84
|
|
fXint = f85
|
|
fDxSqr = f85
|
|
fRes3L = f86
|
|
fRes3H = f87
|
|
fRes4H = f88
|
|
fRes4L = f89
|
|
fResH = f90
|
|
fResL = f91
|
|
fDx = f92
|
|
FR_MHalf = f93
|
|
fRes1H = f94
|
|
fRes1L = f95
|
|
fRes2H = f96
|
|
fRes2L = f97
|
|
FR_FracX = f98
|
|
fRcpX = f99
|
|
fLnSinH = f99
|
|
fTwo = f100
|
|
fMOne = f100
|
|
FR_G = f101
|
|
FR_H = f102
|
|
FR_h = f103
|
|
FR_G2 = f104
|
|
FR_H2 = f105
|
|
FR_poly_lo = f106
|
|
FR_poly_hi = f107
|
|
FR_h2 = f108
|
|
FR_rsq = f109
|
|
FR_r = f110
|
|
FR_log2_hi = f111
|
|
FR_log2_lo = f112
|
|
fFloatN = f113
|
|
FR_Q4 = f114
|
|
FR_G3 = f115
|
|
FR_H3 = f116
|
|
FR_h3 = f117
|
|
FR_Q3 = f118
|
|
FR_Q2 = f119
|
|
FR_Q1 = f120
|
|
fThirteen = f121
|
|
fSix = f121
|
|
FR_rcub = f121
|
|
// Last three Bernulli numbers
|
|
fB16 = f122
|
|
fB18 = f123
|
|
fB20 = f124
|
|
fInvX = f125
|
|
fLnSinL = f125
|
|
fDxSqrL = f126
|
|
fFltIntX = f126
|
|
fRoot = f127
|
|
fNormDx = f127
|
|
|
|
// Data tables
|
|
//==============================================================
|
|
RODATA
|
|
// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
|
|
.align 16
|
|
LOCAL_OBJECT_START(lgammal_right_roots_data)
|
|
// List of all right roots themselves
|
|
data8 0x9D3FE4B007C360AB, 0x0000C000 // Range [-3, -2]
|
|
data8 0xC9306DE4F2CD7BEE, 0x0000C000 // Range [-4, -3]
|
|
data8 0x814273C2CCAC0618, 0x0000C001 // Range [-5, -4]
|
|
data8 0xA04352BF85B6C865, 0x0000C001 // Range [-6, -5]
|
|
data8 0xC00B592C4BE4676C, 0x0000C001 // Range [-7, -6]
|
|
data8 0xE0019FEF6FF0F5BF, 0x0000C001 // Range [-8, -7]
|
|
data8 0x80001A01459FC9F6, 0x0000C002 // Range [-9, -8]
|
|
data8 0x900002E3BB47D86D, 0x0000C002 // Range [-10, -9]
|
|
data8 0xA0000049F93BB992, 0x0000C002 // Range [-11, -10]
|
|
data8 0xB0000006B9915316, 0x0000C002 // Range [-12, -11]
|
|
data8 0xC00000008F76C773, 0x0000C002 // Range [-13, -12]
|
|
data8 0xD00000000B09230A, 0x0000C002 // Range [-14, -13]
|
|
data8 0xE000000000C9CBA5, 0x0000C002 // Range [-15, -14]
|
|
data8 0xF0000000000D73FA, 0x0000C002 // Range [-16, -15]
|
|
data8 0x8000000000006BA0, 0x0000C003 // Range [-17, -16]
|
|
data8 0x8800000000000655, 0x0000C003 // Range [-18, -17]
|
|
data8 0x900000000000005A, 0x0000C003 // Range [-19, -18]
|
|
data8 0x9800000000000005, 0x0000C003 // Range [-20, -19]
|
|
// List of bounds of ranges with special polynomial approximation near root
|
|
// Only significands of bounds are actually stored
|
|
data8 0xA000000000000000, 0x9800000000000000 // Bounds for root on [-3, -2]
|
|
data8 0xCAB88035C5EFBB41, 0xC7E05E31F4B02115 // Bounds for root on [-4, -3]
|
|
data8 0x817831B899735C72, 0x8114633941B8053A // Bounds for root on [-5, -4]
|
|
data8 0xA04E8B34C6AA9476, 0xA039B4A42978197B // Bounds for root on [-6, -5]
|
|
data8 0xC00D3D5E588A78A9, 0xC009BA25F7E858A6 // Bounds for root on [-7, -6]
|
|
data8 0xE001E54202991EB4, 0xE001648416CE897F // Bounds for root on [-8, -7]
|
|
data8 0x80001E56D13A6B9F, 0x8000164A3BAD888A // Bounds for root on [-9, -8]
|
|
data8 0x9000035F0529272A, 0x9000027A0E3D94F0 // Bounds for root on [-10, -9]
|
|
data8 0xA00000564D705880, 0xA000003F67EA0CC7 // Bounds for root on [-11, -10]
|
|
data8 0xB0000007D87EE0EF, 0xB0000005C3A122A5 // Bounds for root on [-12, -11]
|
|
data8 0xC0000000A75FE8B1, 0xC00000007AF818AC // Bounds for root on [-13, -12]
|
|
data8 0xD00000000CDFFE36, 0xD000000009758BBF // Bounds for root on [-14, -13]
|
|
data8 0xE000000000EB6D96, 0xE000000000ACF7B2 // Bounds for root on [-15, -14]
|
|
data8 0xF0000000000FB1F9, 0xF0000000000B87FB // Bounds for root on [-16, -15]
|
|
data8 0x8000000000007D90, 0x8000000000005C40 // Bounds for root on [-17, -16]
|
|
data8 0x8800000000000763, 0x880000000000056D // Bounds for root on [-18, -17]
|
|
data8 0x9000000000000069, 0x900000000000004D // Bounds for root on [-19, -18]
|
|
data8 0x9800000000000006, 0x9800000000000005 // Bounds for root on [-20, -19]
|
|
// List of all left roots themselves
|
|
data8 0xAFDA0850DEC8065E, 0x0000C000 // Range [-3, -2]
|
|
data8 0xFD238AA3E17F285C, 0x0000C000 // Range [-4, -3]
|
|
data8 0x9FBABBD37757E6A2, 0x0000C001 // Range [-5, -4]
|
|
data8 0xBFF497AC8FA06AFC, 0x0000C001 // Range [-6, -5]
|
|
data8 0xDFFE5FBB5C377FE8, 0x0000C001 // Range [-7, -6]
|
|
data8 0xFFFFCBFC0ACE7879, 0x0000C001 // Range [-8, -7]
|
|
data8 0x8FFFFD1C425E8100, 0x0000C002 // Range [-9, -8]
|
|
data8 0x9FFFFFB606BDFDCD, 0x0000C002 // Range [-10, -9]
|
|
data8 0xAFFFFFF9466E9F1B, 0x0000C002 // Range [-11, -10]
|
|
data8 0xBFFFFFFF70893874, 0x0000C002 // Range [-12, -11]
|
|
data8 0xCFFFFFFFF4F6DCF6, 0x0000C002 // Range [-13, -12]
|
|
data8 0xDFFFFFFFFF36345B, 0x0000C002 // Range [-14, -13]
|
|
data8 0xEFFFFFFFFFF28C06, 0x0000C002 // Range [-15, -14]
|
|
data8 0xFFFFFFFFFFFF28C0, 0x0000C002 // Range [-16, -15]
|
|
data8 0x87FFFFFFFFFFF9AB, 0x0000C003 // Range [-17, -16]
|
|
data8 0x8FFFFFFFFFFFFFA6, 0x0000C003 // Range [-18, -17]
|
|
data8 0x97FFFFFFFFFFFFFB, 0x0000C003 // Range [-19, -18]
|
|
data8 0x0000000000000000, 0x00000000 // pad to keep logic in the main path
|
|
// List of bounds of ranges with special polynomial approximation near root
|
|
// Only significands of bounds are actually stored
|
|
data8 0xB235880944CC758E, 0xADD2F1A9FBE76C8B // Bounds for root on [-3, -2]
|
|
data8 0xFD8E7844F307B07C, 0xFCA655C2152BDE4D // Bounds for root on [-4, -3]
|
|
data8 0x9FC4D876EE546967, 0x9FAEE4AF68BC4292 // Bounds for root on [-5, -4]
|
|
data8 0xBFF641FFBFCC44F1, 0xBFF2A47919F4BA89 // Bounds for root on [-6, -5]
|
|
data8 0xDFFE9C803DEFDD59, 0xDFFE18932EB723FE // Bounds for root on [-7, -6]
|
|
data8 0xFFFFD393FA47AFC3, 0xFFFFC317CF638AE1 // Bounds for root on [-8, -7]
|
|
data8 0x8FFFFD8840279925, 0x8FFFFC9DCECEEE92 // Bounds for root on [-9, -8]
|
|
data8 0x9FFFFFC0D34E2AF8, 0x9FFFFFA9619AA3B7 // Bounds for root on [-10, -9]
|
|
data8 0xAFFFFFFA41C18246, 0xAFFFFFF82025A23C // Bounds for root on [-11, -10]
|
|
data8 0xBFFFFFFF857ACB4E, 0xBFFFFFFF58032378 // Bounds for root on [-12, -11]
|
|
data8 0xCFFFFFFFF6934AB8, 0xCFFFFFFFF313EF0A // Bounds for root on [-13, -12]
|
|
data8 0xDFFFFFFFFF53A9E9, 0xDFFFFFFFFF13B5A5 // Bounds for root on [-14, -13]
|
|
data8 0xEFFFFFFFFFF482CB, 0xEFFFFFFFFFF03F4F // Bounds for root on [-15, -14]
|
|
data8 0xFFFFFFFFFFFF482D, 0xFFFFFFFFFFFF03F5 // Bounds for root on [-16, -15]
|
|
data8 0x87FFFFFFFFFFFA98, 0x87FFFFFFFFFFF896 // Bounds for root on [-17, -16]
|
|
data8 0x8FFFFFFFFFFFFFB3, 0x8FFFFFFFFFFFFF97 // Bounds for root on [-18, -17]
|
|
data8 0x97FFFFFFFFFFFFFC, 0x97FFFFFFFFFFFFFB // Bounds for root on [-19, -18]
|
|
LOCAL_OBJECT_END(lgammal_right_roots_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_0_Half_data)
|
|
// Polynomial coefficients for the lgammal(x), 0.0 < |x| < 0.5
|
|
data8 0xBFD9A4D55BEAB2D6, 0xBC8AA3C097746D1F //A3
|
|
data8 0x3FEA51A6625307D3, 0x3C7180E7BD2D0DCC //A2
|
|
data8 0xBFE2788CFC6FB618, 0xBC9E9346C4692BCC //A1
|
|
data8 0x8A8991563EC1BD13, 0x00003FFD //A4
|
|
data8 0xD45CE0BD52C27EF2, 0x0000BFFC //A5
|
|
data8 0xADA06587FA2BBD47, 0x00003FFC //A6
|
|
data8 0x9381D0ED2194902A, 0x0000BFFC //A7
|
|
data8 0x80859B3CF92D4192, 0x00003FFC //A8
|
|
data8 0xE4033517C622A946, 0x0000BFFB //A9
|
|
data8 0xCD00CE67A51FC82A, 0x00003FFB //A10
|
|
data8 0xBA44E2A96C3B5700, 0x0000BFFB //A11
|
|
data8 0xAAAD008FA46DBD99, 0x00003FFB //A12
|
|
data8 0x9D604AC65A41153D, 0x0000BFFB //A13
|
|
data8 0x917CECB864B5A861, 0x00003FFB //A14
|
|
data8 0x85A4810EB730FDE4, 0x0000BFFB //A15
|
|
data8 0xEF2761C38BD21F77, 0x00003FFA //A16
|
|
data8 0xC913043A128367DA, 0x0000BFFA //A17
|
|
data8 0x96A29B71FF7AFFAA, 0x00003FFA //A18
|
|
data8 0xBB9FFA1A5FE649BB, 0x0000BFF9 //A19
|
|
data8 0xB17982CD2DAA0EE3, 0x00003FF8 //A20
|
|
data8 0xDE1DDCBFFB9453F0, 0x0000BFF6 //A21
|
|
data8 0x87FBF5D7ACD9FA9D, 0x00003FF4 //A22
|
|
LOCAL_OBJECT_END(lgammal_0_Half_data)
|
|
|
|
LOCAL_OBJECT_START(Constants_Q)
|
|
// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1
|
|
data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
|
|
data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
|
|
data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
|
|
data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
|
|
data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
|
|
data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
|
|
LOCAL_OBJECT_END(Constants_Q)
|
|
|
|
LOCAL_OBJECT_START(Constants_Z_1)
|
|
// Z1 - 16 bit fixed
|
|
data4 0x00008000
|
|
data4 0x00007879
|
|
data4 0x000071C8
|
|
data4 0x00006BCB
|
|
data4 0x00006667
|
|
data4 0x00006187
|
|
data4 0x00005D18
|
|
data4 0x0000590C
|
|
data4 0x00005556
|
|
data4 0x000051EC
|
|
data4 0x00004EC5
|
|
data4 0x00004BDB
|
|
data4 0x00004925
|
|
data4 0x0000469F
|
|
data4 0x00004445
|
|
data4 0x00004211
|
|
LOCAL_OBJECT_END(Constants_Z_1)
|
|
|
|
LOCAL_OBJECT_START(Constants_G_H_h1)
|
|
// G1 and H1 - IEEE single and h1 - IEEE double
|
|
data4 0x3F800000,0x00000000,0x00000000,0x00000000
|
|
data4 0x3F70F0F0,0x3D785196,0x617D741C,0x3DA163A6
|
|
data4 0x3F638E38,0x3DF13843,0xCBD3D5BB,0x3E2C55E6
|
|
data4 0x3F579430,0x3E2FF9A0,0xD86EA5E7,0xBE3EB0BF
|
|
data4 0x3F4CCCC8,0x3E647FD6,0x86B12760,0x3E2E6A8C
|
|
data4 0x3F430C30,0x3E8B3AE7,0x5C0739BA,0x3E47574C
|
|
data4 0x3F3A2E88,0x3EA30C68,0x13E8AF2F,0x3E20E30F
|
|
data4 0x3F321640,0x3EB9CEC8,0xF2C630BD,0xBE42885B
|
|
data4 0x3F2AAAA8,0x3ECF9927,0x97E577C6,0x3E497F34
|
|
data4 0x3F23D708,0x3EE47FC5,0xA6B0A5AB,0x3E3E6A6E
|
|
data4 0x3F1D89D8,0x3EF8947D,0xD328D9BE,0xBDF43E3C
|
|
data4 0x3F17B420,0x3F05F3A1,0x0ADB090A,0x3E4094C3
|
|
data4 0x3F124920,0x3F0F4303,0xFC1FE510,0xBE28FBB2
|
|
data4 0x3F0D3DC8,0x3F183EBF,0x10FDE3FA,0x3E3A7895
|
|
data4 0x3F088888,0x3F20EC80,0x7CC8C98F,0x3E508CE5
|
|
data4 0x3F042108,0x3F29516A,0xA223106C,0xBE534874
|
|
LOCAL_OBJECT_END(Constants_G_H_h1)
|
|
|
|
LOCAL_OBJECT_START(Constants_Z_2)
|
|
// Z2 - 16 bit fixed
|
|
data4 0x00008000
|
|
data4 0x00007F81
|
|
data4 0x00007F02
|
|
data4 0x00007E85
|
|
data4 0x00007E08
|
|
data4 0x00007D8D
|
|
data4 0x00007D12
|
|
data4 0x00007C98
|
|
data4 0x00007C20
|
|
data4 0x00007BA8
|
|
data4 0x00007B31
|
|
data4 0x00007ABB
|
|
data4 0x00007A45
|
|
data4 0x000079D1
|
|
data4 0x0000795D
|
|
data4 0x000078EB
|
|
LOCAL_OBJECT_END(Constants_Z_2)
|
|
|
|
LOCAL_OBJECT_START(Constants_G_H_h2)
|
|
// G2 and H2 - IEEE single and h2 - IEEE double
|
|
data4 0x3F800000,0x00000000,0x00000000,0x00000000
|
|
data4 0x3F7F00F8,0x3B7F875D,0x22C42273,0x3DB5A116
|
|
data4 0x3F7E03F8,0x3BFF015B,0x21F86ED3,0x3DE620CF
|
|
data4 0x3F7D08E0,0x3C3EE393,0x484F34ED,0xBDAFA07E
|
|
data4 0x3F7C0FC0,0x3C7E0586,0x3860BCF6,0xBDFE07F0
|
|
data4 0x3F7B1880,0x3C9E75D2,0xA78093D6,0x3DEA370F
|
|
data4 0x3F7A2328,0x3CBDC97A,0x72A753D0,0x3DFF5791
|
|
data4 0x3F792FB0,0x3CDCFE47,0xA7EF896B,0x3DFEBE6C
|
|
data4 0x3F783E08,0x3CFC15D0,0x409ECB43,0x3E0CF156
|
|
data4 0x3F774E38,0x3D0D874D,0xFFEF71DF,0xBE0B6F97
|
|
data4 0x3F766038,0x3D1CF49B,0x5D59EEE8,0xBE080483
|
|
data4 0x3F757400,0x3D2C531D,0xA9192A74,0x3E1F91E9
|
|
data4 0x3F748988,0x3D3BA322,0xBF72A8CD,0xBE139A06
|
|
data4 0x3F73A0D0,0x3D4AE46F,0xF8FBA6CF,0x3E1D9202
|
|
data4 0x3F72B9D0,0x3D5A1756,0xBA796223,0xBE1DCCC4
|
|
data4 0x3F71D488,0x3D693B9D,0xB6B7C239,0xBE049391
|
|
LOCAL_OBJECT_END(Constants_G_H_h2)
|
|
|
|
LOCAL_OBJECT_START(Constants_G_H_h3)
|
|
// G3 and H3 - IEEE single and h3 - IEEE double
|
|
data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595
|
|
data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2
|
|
data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D
|
|
data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291
|
|
data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8
|
|
data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707
|
|
data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9
|
|
data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47
|
|
data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E
|
|
data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D
|
|
data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441
|
|
data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95
|
|
data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC
|
|
data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337
|
|
data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B
|
|
data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B
|
|
data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21
|
|
data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4
|
|
data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070
|
|
data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC
|
|
data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83
|
|
data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40
|
|
data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7
|
|
data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B
|
|
data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E
|
|
data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06
|
|
data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1
|
|
data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103
|
|
data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B
|
|
data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19
|
|
data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502
|
|
data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17
|
|
LOCAL_OBJECT_END(Constants_G_H_h3)
|
|
|
|
LOCAL_OBJECT_START(lgammal_data)
|
|
// Positive overflow value
|
|
data8 0xB8D54C8BFFFDEBF4, 0x00007FF1
|
|
LOCAL_OBJECT_END(lgammal_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_Stirling)
|
|
// Coefficients needed for Strirling's formula
|
|
data8 0x3FED67F1C864BEB4 // High part of 0.5*ln(2*Pi)
|
|
data8 0x3C94D252F2400510 // Low part of 0.5*ln(2*Pi)
|
|
//
|
|
// Bernulli numbers used in Striling's formula for -2^63 < |x| < -13.0
|
|
//(B1H, B1L) = 8.3333333333333333333262747254e-02
|
|
data8 0x3FB5555555555555, 0x3C55555555555555
|
|
data8 0xB60B60B60B60B60B, 0x0000BFF6 //B2 = -2.7777777777777777777777777778e-03
|
|
data8 0xD00D00D00D00D00D, 0x00003FF4 //B3 = 7.9365079365079365079365079365e-04
|
|
data8 0x9C09C09C09C09C0A, 0x0000BFF4 //B4 = -5.9523809523809523809523809524e-04
|
|
data8 0xDCA8F158C7F91AB8, 0x00003FF4 //B5 = 8.4175084175084175084175084175e-04
|
|
data8 0xFB5586CCC9E3E410, 0x0000BFF5 //B6 = -1.9175269175269175269175269175e-03
|
|
data8 0xD20D20D20D20D20D, 0x00003FF7 //B7 = 6.4102564102564102564102564103e-03
|
|
data8 0xF21436587A9CBEE1, 0x0000BFF9 //B8 = -2.9550653594771241830065359477e-02
|
|
data8 0xB7F4B1C0F033FFD1, 0x00003FFC //B9 = 1.7964437236883057316493849002e-01
|
|
data8 0xB23B3808C0F9CF6E, 0x0000BFFF //B10 = -1.3924322169059011164274322169e+00
|
|
// Polynomial coefficients for Stirling's formula, -13.0 < x < -6.0
|
|
data8 0x3FB5555555555555, 0x3C4D75060289C58B //A0
|
|
data8 0xB60B60B60B0F0876, 0x0000BFF6 //A1
|
|
data8 0xD00D00CE54B1256C, 0x00003FF4 //A2
|
|
data8 0x9C09BF46B58F75E1, 0x0000BFF4 //A3
|
|
data8 0xDCA8483BC91ACC6D, 0x00003FF4 //A4
|
|
data8 0xFB3965C939CC9FEE, 0x0000BFF5 //A5
|
|
data8 0xD0723ADE3F0BC401, 0x00003FF7 //A6
|
|
data8 0xE1ED7434E81F0B73, 0x0000BFF9 //A7
|
|
data8 0x8069C6982F993283, 0x00003FFC //A8
|
|
data8 0xC271F65BFA5BEE3F, 0x0000BFFD //A9
|
|
LOCAL_OBJECT_END(lgammal_Stirling)
|
|
|
|
LOCAL_OBJECT_START(lgammal_lnsin_data)
|
|
// polynomial approximation of -ln(sin(Pi*x)/(Pi*x)), 0 < x <= 0.5
|
|
data8 0x3FFA51A6625307D3, 0x3C81873332FAF94C //A2
|
|
data8 0x8A8991563EC241C3, 0x00003FFE //A4
|
|
data8 0xADA06588061805DF, 0x00003FFD //A6
|
|
data8 0x80859B57C338D0F7, 0x00003FFD //A8
|
|
data8 0xCD00F1C2D78754BD, 0x00003FFC //A10
|
|
data8 0xAAB56B1D3A1F4655, 0x00003FFC //A12
|
|
data8 0x924B6F2FBBED12B1, 0x00003FFC //A14
|
|
data8 0x80008E58765F43FC, 0x00003FFC //A16
|
|
data8 0x3FBC718EC115E429//A18
|
|
data8 0x3FB99CE544FE183E//A20
|
|
data8 0x3FB7251C09EAAD89//A22
|
|
data8 0x3FB64A970733628C//A24
|
|
data8 0x3FAC92D6802A3498//A26
|
|
data8 0x3FC47E1165261586//A28
|
|
data8 0xBFCA1BAA434750D4//A30
|
|
data8 0x3FE460001C4D5961//A32
|
|
data8 0xBFE6F06A3E4908AD//A34
|
|
data8 0x3FE300889EBB203A//A36
|
|
LOCAL_OBJECT_END(lgammal_lnsin_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_half_3Q_data)
|
|
// Polynomial coefficients for the lgammal(x), 0.5 <= x < 0.75
|
|
data8 0xBFF7A648EE90C62E, 0x3C713F326857E066 // A3, A0L
|
|
data8 0xBFF73E4B8BA780AE, 0xBCA953BC788877EF // A1, A1L
|
|
data8 0x403774DCD58D0291, 0xC0415254D5AE6623 // D0, D1
|
|
data8 0x40B07213855CBFB0, 0xC0B8855E25D2D229 // C20, C21
|
|
data8 0x3FFB359F85FF5000, 0x3C9BAECE6EF9EF3A // A2, A2L
|
|
data8 0x3FD717D498A3A8CC, 0xBC9088E101CFEDFA // A0, A3L
|
|
data8 0xAFEF36CC5AEC3FF0, 0x00004002 // E6
|
|
data8 0xABE2054E1C34E791, 0x00004001 // E4
|
|
data8 0xB39343637B2900D1, 0x00004000 // E2
|
|
data8 0xD74FB710D53F58F6, 0x00003FFF // E0
|
|
data8 0x4070655963BA4256, 0xC078DA9D263C4EA3 // D6, D7
|
|
data8 0x405CD2B6A9B90978, 0xC065B3B9F4F4F171 // D4, D5
|
|
data8 0x4049BC2204CF61FF, 0xC05337227E0BA152 // D2, D3
|
|
data8 0x4095509A50C07A96, 0xC0A0747949D2FB45 // C18, C19
|
|
data8 0x4082ECCBAD709414, 0xC08CD02FB088A702 // C16, C17
|
|
data8 0xFFE4B2A61B508DD5, 0x0000C002 // E7
|
|
data8 0xF461ADB8AE17E0A5, 0x0000C001 // E5
|
|
data8 0xF5BE8B0B90325F20, 0x0000C000 // E3
|
|
data8 0x877B275F3FB78DCA, 0x0000C000 // E1
|
|
LOCAL_OBJECT_END(lgammal_half_3Q_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_half_3Q_neg_data)
|
|
// Polynomial coefficients for the lgammal(x), -0.75 < x <= -0.5
|
|
data8 0xC014836EFD94899C, 0x3C9835679663B44F // A3, A0L
|
|
data8 0xBFF276C7B4FB1875, 0xBC92D3D9FA29A1C0 // A1, A1L
|
|
data8 0x40C5178F24E1A435, 0xC0D9DE84FBC5D76A // D0, D1
|
|
data8 0x41D4D1B236BF6E93, 0xC1EBB0445CE58550 // C20, C21
|
|
data8 0x4015718CD67F63D3, 0x3CC5354B6F04B59C // A2, A2L
|
|
data8 0x3FF554493087E1ED, 0xBCB72715E37B02B9 // A0, A3L
|
|
data8 0xE4AC7E915FA72229, 0x00004009 // E6
|
|
data8 0xA28244206395FCC6, 0x00004007 // E4
|
|
data8 0xFB045F19C07B2544, 0x00004004 // E2
|
|
data8 0xE5C8A6E6A9BA7D7B, 0x00004002 // E0
|
|
data8 0x4143943B55BF5118, 0xC158AC05EA675406 // D6, D7
|
|
data8 0x4118F6833D19717C, 0xC12F51A6F375CC80 // D4, D5
|
|
data8 0x40F00C209483481C, 0xC103F1DABF750259 // D2, D3
|
|
data8 0x4191038F2D8F9E40, 0xC1A413066DA8AE4A // C18, C19
|
|
data8 0x4170B537EDD833DE, 0xC1857E79424C61CE // C16, C17
|
|
data8 0x8941D8AB4855DB73, 0x0000C00B // E7
|
|
data8 0xBB822B131BD2E813, 0x0000C008 // E5
|
|
data8 0x852B4C03B83D2D4F, 0x0000C006 // E3
|
|
data8 0xC754CA7E2DDC0F1F, 0x0000C003 // E1
|
|
LOCAL_OBJECT_END(lgammal_half_3Q_neg_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_2Q_4_data)
|
|
// Polynomial coefficients for the lgammal(x), 2.25 <= |x| < 4.0
|
|
data8 0xBFCA4D55BEAB2D6F, 0x3C7ABC9DA14141F5 // A3, A0L
|
|
data8 0x3FFD8773039049E7, 0x3C66CB7957A95BA4 // A1, A1L
|
|
data8 0x3F45C3CC79E91E7D, 0xBF3A8E5005937E97 // D0, D1
|
|
data8 0x3EC951E35E1C9203, 0xBEB030A90026C5DF // C20, C21
|
|
data8 0x3FE94699894C1F4C, 0x3C91884D21D123F1 // A2, A2L
|
|
data8 0x3FE62E42FEFA39EF, 0xBC66480CEB70870F // A0, A3L
|
|
data8 0xF1C2EAFF0B3A7579, 0x00003FF5 // E6
|
|
data8 0xB36AF863926B55A3, 0x00003FF7 // E4
|
|
data8 0x9620656185BB44CA, 0x00003FF9 // E2
|
|
data8 0xA264558FB0906AFF, 0x00003FFB // E0
|
|
data8 0x3F03D59E9666C961, 0xBEF91115893D84A6 // D6, D7
|
|
data8 0x3F19333611C46225, 0xBF0F89EB7D029870 // D4, D5
|
|
data8 0x3F3055A96B347AFE, 0xBF243B5153E178A8 // D2, D3
|
|
data8 0x3ED9A4AEF30C4BB2, 0xBED388138B1CEFF2 // C18, C19
|
|
data8 0x3EEF7945A3C3A254, 0xBEE36F32A938EF11 // C16, C17
|
|
data8 0x9028923F47C82118, 0x0000BFF5 // E7
|
|
data8 0xCE0DAAFB6DC93B22, 0x0000BFF6 // E5
|
|
data8 0xA0D0983B34AC4C8D, 0x0000BFF8 // E3
|
|
data8 0x94D6C50FEB8B0CE7, 0x0000BFFA // E1
|
|
LOCAL_OBJECT_END(lgammal_2Q_4_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_4_8_data)
|
|
// Polynomial coefficients for the lgammal(x), 4.0 <= |x| < 8.0
|
|
data8 0xBFD6626BC9B31B54, 0x3CAA53C82493A92B // A3, A0L
|
|
data8 0x401B4C420A50AD7C, 0x3C8C6E9929F789A3 // A1, A1L
|
|
data8 0x3F49410427E928C2, 0xBF3E312678F8C146 // D0, D1
|
|
data8 0x3ED51065F7CD5848, 0xBED052782A03312F // C20, C21
|
|
data8 0x3FF735973273D5EC, 0x3C831DFC65BF8CCF // A2, A2L
|
|
data8 0x401326643C4479C9, 0xBC6FA0498C5548A6 // A0, A3L
|
|
data8 0x9382D8B3CD4EB7E3, 0x00003FF6 // E6
|
|
data8 0xE9F92CAD8A85CBCD, 0x00003FF7 // E4
|
|
data8 0xD58389FE38258CEC, 0x00003FF9 // E2
|
|
data8 0x81310136363AE8AA, 0x00003FFC // E0
|
|
data8 0x3F04F0AE38E78570, 0xBEF9E2144BB8F03C // D6, D7
|
|
data8 0x3F1B5E992A6CBC2A, 0xBF10F3F400113911 // D4, D5
|
|
data8 0x3F323EE00AAB7DEE, 0xBF2640FDFA9FB637 // D2, D3
|
|
data8 0x3ED2143EBAFF067A, 0xBEBBDEB92D6FF35D // C18, C19
|
|
data8 0x3EF173A42B69AAA4, 0xBEE78B9951A2EAA5 // C16, C17
|
|
data8 0xAB3CCAC6344E52AA, 0x0000BFF5 // E7
|
|
data8 0x81ACCB8915B16508, 0x0000BFF7 // E5
|
|
data8 0xDA62C7221102C426, 0x0000BFF8 // E3
|
|
data8 0xDF1BD44C4083580A, 0x0000BFFA // E1
|
|
LOCAL_OBJECT_END(lgammal_4_8_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_loc_min_data)
|
|
// Polynomial coefficients for the lgammal(x), 1.3125 <= x < 1.5625
|
|
data8 0xBB16C31AB5F1FB71, 0x00003FFF // xMin - point of local minimum
|
|
data8 0xBFC2E4278DC6BC23, 0xBC683DA8DDCA9650 // A3, A0L
|
|
data8 0x3BD4DB7D0CA61D5F, 0x386E719EDD01D801 // A1, A1L
|
|
data8 0x3F4CC72638E1D93F, 0xBF4228EC9953CCB9 // D0, D1
|
|
data8 0x3ED222F97A04613E,0xBED3DDD58095CB6C // C20, C21
|
|
data8 0x3FDEF72BC8EE38AB, 0x3C863AFF3FC48940 // A2, A2L
|
|
data8 0xBFBF19B9BCC38A41, 0xBC7425F1BFFC1442// A0, A3L
|
|
data8 0x941890032BEB34C3, 0x00003FF6 // E6
|
|
data8 0xC7E701591CE534BC, 0x00003FF7 // E4
|
|
data8 0x93373CBD05138DD4, 0x00003FF9 // E2
|
|
data8 0x845A14A6A81C05D6, 0x00003FFB // E0
|
|
data8 0x3F0F6C4DF6D47A13, 0xBF045DCDB5B49E19 // D6, D7
|
|
data8 0x3F22E23345DDE59C, 0xBF1851159AFB1735 // D4, D5
|
|
data8 0x3F37101EA4022B78, 0xBF2D721E6323AF13 // D2, D3
|
|
data8 0x3EE691EBE82DF09D, 0xBEDD42550961F730 // C18, C19
|
|
data8 0x3EFA793EDE99AD85, 0xBEF14000108E70BE // C16, C17
|
|
data8 0xB7CBC033ACE0C99C, 0x0000BFF5 // E7
|
|
data8 0xF178D1F7B1A45E27, 0x0000BFF6 // E5
|
|
data8 0xA8FCFCA8106F471C, 0x0000BFF8 // E3
|
|
data8 0x864D46FA898A9AD2, 0x0000BFFA // E1
|
|
LOCAL_OBJECT_END(lgammal_loc_min_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_03Q_1Q_data)
|
|
// Polynomial coefficients for the lgammal(x), 0.75 <= |x| < 1.3125
|
|
data8 0x3FD151322AC7D848, 0x3C7184DE0DB7B4EE // A4, A2L
|
|
data8 0x3FD9A4D55BEAB2D6, 0x3C9E934AAB10845F // A3, A1L
|
|
data8 0x3FB111289C381259, 0x3FAFFFCFB32AE18D // D2, D3
|
|
data8 0x3FB3B1D9E0E3E00D, 0x3FB2496F0D3768DF // D0, D1
|
|
data8 0xBA461972C057D439, 0x00003FFB // E6
|
|
data8 0x3FEA51A6625307D3, 0x3C76ABC886A72DA2 // A2, A4L
|
|
data8 0x3FA8EFE46B32A70E, 0x3F8F31B3559576B6 // C17, C20
|
|
data8 0xE403383700387D85, 0x00003FFB // E4
|
|
data8 0x9381D0EE74BF7251, 0x00003FFC // E2
|
|
data8 0x3FAA2177A6D28177, 0x3FA4895E65FBD995 // C18, C19
|
|
data8 0x3FAAED2C77DBEE5D, 0x3FA94CA59385512C // D6, D7
|
|
data8 0x3FAE1F522E8A5941, 0x3FAC785EF56DD87E // D4, D5
|
|
data8 0x3FB556AD5FA56F0A, 0x3FA81F416E87C783 // E7, C16
|
|
data8 0xCD00F1C2DC2C9F1E, 0x00003FFB // E5
|
|
data8 0x3FE2788CFC6FB618, 0x3C8E52519B5B17CB // A1, A3L
|
|
data8 0x80859B57C3E7F241, 0x00003FFC // E3
|
|
data8 0xADA065880615F401, 0x00003FFC // E1
|
|
data8 0xD45CE0BD530AB50E, 0x00003FFC // E0
|
|
LOCAL_OBJECT_END(lgammal_03Q_1Q_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_13Q_2Q_data)
|
|
// Polynomial coefficients for the lgammal(x), 1.5625 <= |x| < 2.25
|
|
data8 0x3F951322AC7D8483, 0x3C71873D88C6539D // A4, A2L
|
|
data8 0xBFB13E001A557606, 0x3C56CB907018A101 // A3, A1L
|
|
data8 0xBEC11B2EC1E7F6FC, 0x3EB0064ED9824CC7 // D2, D3
|
|
data8 0xBEE3CBC963EC103A, 0x3ED2597A330C107D // D0, D1
|
|
data8 0xBC6F2DEBDFE66F38, 0x0000BFF0 // E6
|
|
data8 0x3FD4A34CC4A60FA6, 0x3C3AFC9BF775E8A0 // A2, A4L
|
|
data8 0x3E48B0C542F85B32, 0xBE347F12EAF787AB // C17, C20
|
|
data8 0xE9FEA63B6984FA1E, 0x0000BFF2 // E4
|
|
data8 0x9C562E15FC703BBF, 0x0000BFF5 // E2
|
|
data8 0xBE3C12A50AB0355E, 0xBE1C941626AE4717 // C18, C19
|
|
data8 0xBE7AFA8714342BC4,0x3E69A12D2B7761CB // D6, D7
|
|
data8 0xBE9E25EF1D526730, 0x3E8C762291889B99 // D4, D5
|
|
data8 0x3EF580DCEE754733, 0xBE57C811D070549C // E7, C16
|
|
data8 0xD093D878BE209C98, 0x00003FF1 // E5
|
|
data8 0x3FDB0EE6072093CE, 0xBC6024B9E81281C4 // A1, A3L
|
|
data8 0x859B57C31CB77D96, 0x00003FF4 // E3
|
|
data8 0xBD6EB756DB617E8D, 0x00003FF6 // E1
|
|
data8 0xF2027E10C7AF8C38, 0x0000BFF7 // E0
|
|
LOCAL_OBJECT_END(lgammal_13Q_2Q_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_8_10_data)
|
|
// Polynomial coefficients for the lgammal(x), 8.0 <= |x| < 10.0
|
|
// Multi Precision terms
|
|
data8 0x40312008A3A23E5C, 0x3CE020B4F2E4083A //A1
|
|
data8 0x4025358E82FCB70C, 0x3CD4A5A74AF7B99C //A0
|
|
// Native precision terms
|
|
data8 0xF0AA239FFBC616D2, 0x00004000 //A2
|
|
data8 0x96A8EA798FE57D66, 0x0000BFFF //A3
|
|
data8 0x8D501B7E3B9B9BDB, 0x00003FFE //A4
|
|
data8 0x9EE062401F4B1DC2, 0x0000BFFD //A5
|
|
data8 0xC63FD8CD31E93431, 0x00003FFC //A6
|
|
data8 0x8461101709C23C30, 0x0000BFFC //A7
|
|
data8 0xB96D7EA7EF3648B2, 0x00003FFB //A8
|
|
data8 0x86886759D2ACC906, 0x0000BFFB //A9
|
|
data8 0xC894B6E28265B183, 0x00003FFA //A10
|
|
data8 0x98C4348CAD821662, 0x0000BFFA //A11
|
|
data8 0xEC9B092226A94DF2, 0x00003FF9 //A12
|
|
data8 0xB9F169FF9B98CDDC, 0x0000BFF9 //A13
|
|
data8 0x9A3A32BB040894D3, 0x00003FF9 //A14
|
|
data8 0xF9504CCC1003B3C3, 0x0000BFF8 //A15
|
|
LOCAL_OBJECT_END(lgammal_8_10_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_03Q_6_data)
|
|
// Polynomial coefficients for the lgammal(x), 0.75 <= |x| < 1.0
|
|
data8 0xBFBC47DCA479E295, 0xBC607E6C1A379D55 //A3
|
|
data8 0x3FCA051C372609ED, 0x3C7B02D73EB7D831 //A0
|
|
data8 0xBFE15FAFA86B04DB, 0xBC3F52EE4A8945B5 //A1
|
|
data8 0x3FD455C4FF28F0BF, 0x3C75F8C6C99F30BB //A2
|
|
data8 0xD2CF04CD934F03E1, 0x00003FFA //A4
|
|
data8 0xDB4ED667E29256E1, 0x0000BFF9 //A5
|
|
data8 0xF155A33A5B6021BF, 0x00003FF8 //A6
|
|
data8 0x895E9B9D386E0338, 0x0000BFF8 //A7
|
|
data8 0xA001BE94B937112E, 0x00003FF7 //A8
|
|
data8 0xBD82846E490ED048, 0x0000BFF6 //A9
|
|
data8 0xE358D24EC30DBB5D, 0x00003FF5 //A10
|
|
data8 0x89C4F3652446B78B, 0x0000BFF5 //A11
|
|
data8 0xA86043E10280193D, 0x00003FF4 //A12
|
|
data8 0xCF3A2FBA61EB7682, 0x0000BFF3 //A13
|
|
data8 0x3F300900CC9200EC //A14
|
|
data8 0xBF23F42264B94AE8 //A15
|
|
data8 0x3F18EEF29895FE73 //A16
|
|
data8 0xBF0F3C4563E3EDFB //A17
|
|
data8 0x3F0387DBBC385056 //A18
|
|
data8 0xBEF81B4004F92900 //A19
|
|
data8 0x3EECA6692A9A5B81 //A20
|
|
data8 0xBEDF61A0059C15D3 //A21
|
|
data8 0x3ECDA9F40DCA0111 //A22
|
|
data8 0xBEB60FE788217BAF //A23
|
|
data8 0x3E9661D795DFC8C6 //A24
|
|
data8 0xBE66C7756A4EDEE5 //A25
|
|
// Polynomial coefficients for the lgammal(x), 1.0 <= |x| < 2.0
|
|
data8 0xBFC1AE55B180726B, 0xBC7DE1BC478453F5 //A3
|
|
data8 0xBFBEEB95B094C191, 0xBC53456FF6F1C9D9 //A0
|
|
data8 0x3FA2AED059BD608A, 0x3C0B65CC647D557F //A1
|
|
data8 0x3FDDE9E64DF22EF2, 0x3C8993939A8BA8E4 //A2
|
|
data8 0xF07C206D6B100CFF, 0x00003FFA //A4
|
|
data8 0xED2CEA9BA52FE7FB, 0x0000BFF9 //A5
|
|
data8 0xFCE51CED52DF3602, 0x00003FF8 //A6
|
|
data8 0x8D45D27872326619, 0x0000BFF8 //A7
|
|
data8 0xA2B78D6BCEBE27F7, 0x00003FF7 //A8
|
|
data8 0xBF6DC0996A895B6F, 0x0000BFF6 //A9
|
|
data8 0xE4B9AD335AF82D79, 0x00003FF5 //A10
|
|
data8 0x8A451880195362A1, 0x0000BFF5 //A11
|
|
data8 0xA8BE35E63089A7A9, 0x00003FF4 //A12
|
|
data8 0xCF7FA175FA11C40C, 0x0000BFF3 //A13
|
|
data8 0x3F300C282FAA3B02 //A14
|
|
data8 0xBF23F6AEBDA68B80 //A15
|
|
data8 0x3F18F6860E2224DD //A16
|
|
data8 0xBF0F542B3CE32F28 //A17
|
|
data8 0x3F039436218C9BF8 //A18
|
|
data8 0xBEF8AE6307677AEC //A19
|
|
data8 0x3EF0B55527B3A211 //A20
|
|
data8 0xBEE576AC995E7605 //A21
|
|
data8 0x3ED102DDC1365D2D //A22
|
|
data8 0xBEC442184F97EA54 //A23
|
|
data8 0x3ED4D2283DFE5FC6 //A24
|
|
data8 0xBECB9219A9B46787 //A25
|
|
// Polynomial coefficients for the lgammal(x), 2.0 <= |x| < 3.0
|
|
data8 0xBFCA4D55BEAB2D6F, 0xBC66F80E5BFD5AF5 //A3
|
|
data8 0x3FE62E42FEFA39EF, 0x3C7ABC9E3B347E3D //A0
|
|
data8 0x3FFD8773039049E7, 0x3C66CB9007C426EA //A1
|
|
data8 0x3FE94699894C1F4C, 0x3C918726EB111663 //A2
|
|
data8 0xA264558FB0906209, 0x00003FFB //A4
|
|
data8 0x94D6C50FEB902ADC, 0x0000BFFA //A5
|
|
data8 0x9620656184243D17, 0x00003FF9 //A6
|
|
data8 0xA0D0983B8BCA910B, 0x0000BFF8 //A7
|
|
data8 0xB36AF8559B222BD3, 0x00003FF7 //A8
|
|
data8 0xCE0DACB3260AE6E5, 0x0000BFF6 //A9
|
|
data8 0xF1C2C0BF0437C7DB, 0x00003FF5 //A10
|
|
data8 0x902A2F2F3AB74A92, 0x0000BFF5 //A11
|
|
data8 0xAE05009B1B2C6E4C, 0x00003FF4 //A12
|
|
data8 0xD5B71F6456D7D4CB, 0x0000BFF3 //A13
|
|
data8 0x3F2F0351D71BC9C6 //A14
|
|
data8 0xBF2B53BC56A3B793 //A15
|
|
data8 0xBF18B12DC6F6B861 //A16
|
|
data8 0xBF43EE6EB5215C2F //A17
|
|
data8 0xBF5474787CDD455E //A18
|
|
data8 0xBF642B503C9C060A //A19
|
|
data8 0xBF6E07D1AA254AA3 //A20
|
|
data8 0xBF71C785443AAEE8 //A21
|
|
data8 0xBF6F67BF81B71052 //A22
|
|
data8 0xBF63E4BCCF4FFABF //A23
|
|
data8 0xBF50067F8C671D5A //A24
|
|
data8 0xBF29C770D680A5AC //A25
|
|
// Polynomial coefficients for the lgammal(x), 4.0 <= |x| < 6.0
|
|
data8 0xBFD6626BC9B31B54, 0xBC85AABE08680902 //A3
|
|
data8 0x401326643C4479C9, 0x3CAA53C26F31E364 //A0
|
|
data8 0x401B4C420A50AD7C, 0x3C8C76D55E57DD8D //A1
|
|
data8 0x3FF735973273D5EC, 0x3C83A0B78E09188A //A2
|
|
data8 0x81310136363AAB6D, 0x00003FFC //A4
|
|
data8 0xDF1BD44C4075C0E6, 0x0000BFFA //A5
|
|
data8 0xD58389FE38D8D664, 0x00003FF9 //A6
|
|
data8 0xDA62C7221D5B5F87, 0x0000BFF8 //A7
|
|
data8 0xE9F92CAD0263E157, 0x00003FF7 //A8
|
|
data8 0x81ACCB8606C165FE, 0x0000BFF7 //A9
|
|
data8 0x9382D8D263D1C2A3, 0x00003FF6 //A10
|
|
data8 0xAB3CCBA4C853B12C, 0x0000BFF5 //A11
|
|
data8 0xCA0818BBCCC59296, 0x00003FF4 //A12
|
|
data8 0xF18912691CBB5BD0, 0x0000BFF3 //A13
|
|
data8 0x3F323EF5D8330339 //A14
|
|
data8 0xBF2641132EA571F7 //A15
|
|
data8 0x3F1B5D9576175CA9 //A16
|
|
data8 0xBF10F56A689C623D //A17
|
|
data8 0x3F04CACA9141A18D //A18
|
|
data8 0xBEFA307AC9B4E85D //A19
|
|
data8 0x3EF4B625939FBE32 //A20
|
|
data8 0xBECEE6AC1420F86F //A21
|
|
data8 0xBE9A95AE2E485964 //A22
|
|
data8 0xBF039EF47F8C09BB //A23
|
|
data8 0xBF05345957F7B7A9 //A24
|
|
data8 0xBEF85AE6385D4CCC //A25
|
|
// Polynomial coefficients for the lgammal(x), 3.0 <= |x| < 4.0
|
|
data8 0xBFCA4D55BEAB2D6F, 0xBC667B20FF46C6A8 //A3
|
|
data8 0x3FE62E42FEFA39EF, 0x3C7ABC9E3B398012 //A0
|
|
data8 0x3FFD8773039049E7, 0x3C66CB9070238D77 //A1
|
|
data8 0x3FE94699894C1F4C, 0x3C91873D8839B1CD //A2
|
|
data8 0xA264558FB0906D7E, 0x00003FFB //A4
|
|
data8 0x94D6C50FEB8AFD72, 0x0000BFFA //A5
|
|
data8 0x9620656185B68F14, 0x00003FF9 //A6
|
|
data8 0xA0D0983B34B7088A, 0x0000BFF8 //A7
|
|
data8 0xB36AF863964AA440, 0x00003FF7 //A8
|
|
data8 0xCE0DAAFB5497AFB8, 0x0000BFF6 //A9
|
|
data8 0xF1C2EAFA79CC2864, 0x00003FF5 //A10
|
|
data8 0x9028922A839572B8, 0x0000BFF5 //A11
|
|
data8 0xAE1E62F870BA0278, 0x00003FF4 //A12
|
|
data8 0xD4726F681E2ABA29, 0x0000BFF3 //A13
|
|
data8 0x3F30559B9A02FADF //A14
|
|
data8 0xBF243ADEB1266CAE //A15
|
|
data8 0x3F19303B6F552603 //A16
|
|
data8 0xBF0F768C288EC643 //A17
|
|
data8 0x3F039D5356C21DE1 //A18
|
|
data8 0xBEF81BCA8168E6BE //A19
|
|
data8 0x3EEC74A53A06AD54 //A20
|
|
data8 0xBEDED52D1A5DACDF //A21
|
|
data8 0x3ECCB4C2C7087342 //A22
|
|
data8 0xBEB4F1FAFDFF5C2F //A23
|
|
data8 0x3E94C80B52D58904 //A24
|
|
data8 0xBE64A328CBE92A27 //A25
|
|
LOCAL_OBJECT_END(lgammal_03Q_6_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_1pEps_data)
|
|
// Polynomial coefficients for the lgammal(x), 1 - 2^(-7) <= |x| < 1 + 2^(-7)
|
|
data8 0x93C467E37DB0C7A5, 0x00003FFE //A1
|
|
data8 0xD28D3312983E9919, 0x00003FFE //A2
|
|
data8 0xCD26AADF559A47E3, 0x00003FFD //A3
|
|
data8 0x8A8991563EC22E81, 0x00003FFD //A4
|
|
data8 0x3FCA8B9C168D52FE //A5
|
|
data8 0x3FC5B40CB0696370 //A6
|
|
data8 0x3FC270AC2229A65D //A7
|
|
data8 0x3FC0110AF10FCBFC //A8
|
|
// Polynomial coefficients for the log1p(x), - 2^(-7) <= |x| < 2^(-7)
|
|
data8 0x3FBC71C71C71C71C //P8
|
|
data8 0xBFC0000000000000 //P7
|
|
data8 0x3FC2492492492492 //P6
|
|
data8 0xBFC5555555555555 //P5
|
|
data8 0x3FC999999999999A //P4
|
|
data8 0xBFD0000000000000 //P3
|
|
data8 0x3FD5555555555555 //P2
|
|
data8 0xBFE0000000000000 //P1
|
|
// short version of "lnsin" polynomial
|
|
data8 0xD28D3312983E9918, 0x00003FFF //A2
|
|
data8 0x8A8991563EC241B6, 0x00003FFE //A4
|
|
data8 0xADA06588061830A5, 0x00003FFD //A6
|
|
data8 0x80859B57C31CB746, 0x00003FFD //A8
|
|
LOCAL_OBJECT_END(lgammal_1pEps_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_neg2andHalf_data)
|
|
// Polynomial coefficients for the lgammal(x), -2.005859375 <= x < -2.5
|
|
data8 0xBF927781D4BB093A, 0xBC511D86D85B7045 // A3, A0L
|
|
data8 0x3FF1A68793DEFC15, 0x3C9852AE2DA7DEEF // A1, A1L
|
|
data8 0x408555562D45FAFD, 0xBF972CDAFE5FEFAD // D0, D1
|
|
data8 0xC18682331EF492A5, 0xC1845E3E0D29606B // C20, C21
|
|
data8 0x4013141822E16979, 0x3CCF8718B6E75F6C // A2, A2L
|
|
data8 0xBFACCBF9F5ED0F15, 0xBBDD1AEB73297401 // A0, A3L
|
|
data8 0xCCCDB17423046445, 0x00004006 // E6
|
|
data8 0x800514E230A3A452, 0x00004005 // E4
|
|
data8 0xAAE9A48EC162E76F, 0x00004003 // E2
|
|
data8 0x81D4F88B3F3EA0FC, 0x00004002 // E0
|
|
data8 0x40CF3F3E35238DA0, 0xC0F8B340945F1A7E // D6, D7
|
|
data8 0x40BF89EC0BD609C6, 0xC095897242AEFEE2 // D4, D5
|
|
data8 0x40A2482FF01DBC5C, 0xC02095E275FDCF62 // D2, D3
|
|
data8 0xC1641354F2312A6A, 0xC17B3657F85258E9 // C18, C19
|
|
data8 0xC11F964E9ECBE2C9, 0xC146D7A90F70696C // C16, C17
|
|
data8 0xE7AECDE6AF8EA816, 0x0000BFEF // E7
|
|
data8 0xD711252FEBBE1091, 0x0000BFEB // E5
|
|
data8 0xE648BD10F8C43391, 0x0000BFEF // E3
|
|
data8 0x948A1E78AA00A98D, 0x0000BFF4 // E1
|
|
LOCAL_OBJECT_END(lgammal_neg2andHalf_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_near_neg_half_data)
|
|
// Polynomial coefficients for the lgammal(x), -0.5 < x < -0.40625
|
|
data8 0xBFC1AE55B180726C, 0x3C8053CD734E6A1D // A3, A0L
|
|
data8 0x3FA2AED059BD608A, 0x3C0CD3D2CDBA17F4 // A1, A1L
|
|
data8 0x40855554DBCD1E1E, 0x3F96C51AC2BEE9E1 // D0, D1
|
|
data8 0xC18682331EF4927D, 0x41845E3E0D295DFC // C20, C21
|
|
data8 0x4011DE9E64DF22EF, 0x3CA692B70DAD6B7B // A2, A2L
|
|
data8 0x3FF43F89A3F0EDD6, 0xBC4955AED0FA087D // A0, A3L
|
|
data8 0xCCCD3F1DF4A2C1DD, 0x00004006 // E6
|
|
data8 0x80028ADE33C7FCD9, 0x00004005 // E4
|
|
data8 0xAACA474E485507EF, 0x00004003 // E2
|
|
data8 0x80F07C206D6B0ECD, 0x00004002 // E0
|
|
data8 0x40CF3F3E33E83056, 0x40F8B340944633D9 // D6, D7
|
|
data8 0x40BF89EC059931F0, 0x409589723307AD20 // D4, D5
|
|
data8 0x40A2482FD0054824, 0x402095CE7F19D011 // D2, D3
|
|
data8 0xC1641354F2313614, 0x417B3657F8525354 // C18, C19
|
|
data8 0xC11F964E9ECFD21C, 0x4146D7A90F701836 // C16, C17
|
|
data8 0x86A9C01F0EA11E5A, 0x0000BFF5 // E7
|
|
data8 0xBF6D8469142881C0, 0x0000BFF6 // E5
|
|
data8 0x8D45D277BA8255F1, 0x0000BFF8 // E3
|
|
data8 0xED2CEA9BA528BCC3, 0x0000BFF9 // E1
|
|
LOCAL_OBJECT_END(lgammal_near_neg_half_data)
|
|
|
|
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
////////////// POLYNOMIAL COEFFICIENTS FOR "NEAR ROOTS" RANGES /////////////
|
|
////////////// THIS PART OF TABLE SHOULD BE ADDRESSED REALLY RARE /////////////
|
|
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
LOCAL_OBJECT_START(lgammal_right_roots_polynomial_data)
|
|
// Polynomial coefficients for right root on [-3, -2]
|
|
// Lgammal is approximated by polynomial within [-.056244 ; .158208 ] range
|
|
data8 0xBBBD5E9DCD11030B, 0xB867411D9FF87DD4 //A0
|
|
data8 0x3FF83FE966AF535E, 0x3CAA21235B8A769A //A1
|
|
data8 0x40136EEBB002F55C, 0x3CC3959A6029838E //A2
|
|
data8 0xB4A5302C53C2BEDD, 0x00003FFF //A3
|
|
data8 0x8B8C6BE504F2DA1C, 0x00004002 //A4
|
|
data8 0xB99CFF02593B4D98, 0x00004001 //A5
|
|
data8 0x4038D32F682AA1CF //A6
|
|
data8 0x403809F04EE6C5B5 //A7
|
|
data8 0x40548EAA81634CEE //A8
|
|
data8 0x4059297ADB6BC03D //A9
|
|
data8 0x407286FB8EC5C9DA //A10
|
|
data8 0x407A92E05B744CFB //A11
|
|
data8 0x4091A9D4144258CD //A12
|
|
data8 0x409C4D01D24F367E //A13
|
|
data8 0x40B1871B9A426A83 //A14
|
|
data8 0x40BE51C48BD9A583 //A15
|
|
data8 0x40D2140D0C6153E7 //A16
|
|
data8 0x40E0FB2C989CE4A3 //A17
|
|
data8 0x40E52739AB005641 //A18
|
|
data8 0x41161E3E6DDF503A //A19
|
|
// Polynomial coefficients for right root on [-4, -3]
|
|
// Lgammal is approximated by polynomial within [-.172797 ; .171573 ] range
|
|
data8 0x3C172712B248E42E, 0x38CB8D17801A5D67 //A0
|
|
data8 0x401F20A65F2FAC54, 0x3CCB9EA1817A824E //A1
|
|
data8 0x4039D4D2977150EF, 0x3CDA42E149B6276A //A2
|
|
data8 0xE089B8926AE2D9CB, 0x00004005 //A3
|
|
data8 0x933901EBBB586C37, 0x00004008 //A4
|
|
data8 0xCCD319BED1CFA1CD, 0x0000400A //A5
|
|
data8 0x40D293C3F78D3C37 //A6
|
|
data8 0x40FBB97AA0B6DD02 //A7
|
|
data8 0x41251EA3345E5EB9 //A8
|
|
data8 0x415057F65C92E7B0 //A9
|
|
data8 0x41799C865241B505 //A10
|
|
data8 0x41A445209EFE896B //A11
|
|
data8 0x41D02D21880C953B //A12
|
|
data8 0x41F9FFDE8C63E16D //A13
|
|
data8 0x422504DC8302D2BE //A14
|
|
data8 0x425111BF18C95414 //A15
|
|
data8 0x427BCBE74A2B8EF7 //A16
|
|
data8 0x42A7256F59B286F7 //A17
|
|
data8 0x42D462D1586DE61F //A18
|
|
data8 0x42FBB1228D6C5118 //A19
|
|
// Polynomial coefficients for right root on [-5, -4]
|
|
// Lgammal is approximated by polynomial within [-.163171 ; .161988 ] range
|
|
data8 0x3C5840FBAFDEE5BB, 0x38CAC0336E8C490A //A0
|
|
data8 0x403ACA5CF4921642, 0x3CCEDCDDA5491E56 //A1
|
|
data8 0x40744415CD813F8E, 0x3CFBFEBC17E39146 //A2
|
|
data8 0xAACD88D954E3E1BD, 0x0000400B //A3
|
|
data8 0xCB68C710D75ED802, 0x0000400F //A4
|
|
data8 0x8130F5AB997277AC, 0x00004014 //A5
|
|
data8 0x41855E3DBF99EBA7 //A6
|
|
data8 0x41CD14FE49C49FC2 //A7
|
|
data8 0x421433DCE281F07D //A8
|
|
data8 0x425C8399C7A92B6F //A9
|
|
data8 0x42A45FBE67840F1A //A10
|
|
data8 0x42ED68D75F9E6C98 //A11
|
|
data8 0x433567291C27E5BE //A12
|
|
data8 0x437F5ED7A9D9FD28 //A13
|
|
data8 0x43C720A65C8AB711 //A14
|
|
data8 0x441120A6C1D40B9B //A15
|
|
data8 0x44596F561F2D1CBE //A16
|
|
data8 0x44A3507DA81D5C01 //A17
|
|
data8 0x44EF06A31E39EEDF //A18
|
|
data8 0x45333774C99F523F //A19
|
|
// Polynomial coefficients for right root on [-6, -5]
|
|
// Lgammal is approximated by polynomial within [-.156450 ; .156126 ] range
|
|
data8 0x3C71B82D6B2B3304, 0x3917186E3C0DC231 //A0
|
|
data8 0x405ED72E0829AE02, 0x3C960C25157980EB //A1
|
|
data8 0x40BCECC32EC22F9B, 0x3D5D8335A32F019C //A2
|
|
data8 0x929EC2B1FB931F17, 0x00004012 //A3
|
|
data8 0xD112EF96D37316DE, 0x00004018 //A4
|
|
data8 0x9F00BB9BB13416AB, 0x0000401F //A5
|
|
data8 0x425F7D8D5BDCB223 //A6
|
|
data8 0x42C9A8D00C776CC6 //A7
|
|
data8 0x433557FD8C481424 //A8
|
|
data8 0x43A209221A953EF0 //A9
|
|
data8 0x440EDC98D5618AB7 //A10
|
|
data8 0x447AABD25E367378 //A11
|
|
data8 0x44E73DE20CC3B288 //A12
|
|
data8 0x455465257B4E0BD8 //A13
|
|
data8 0x45C2011532085353 //A14
|
|
data8 0x462FEE4CC191945B //A15
|
|
data8 0x469C63AEEFEF0A7F //A16
|
|
data8 0x4709D045390A3810 //A17
|
|
data8 0x4778D360873C9F64 //A18
|
|
data8 0x47E26965BE9A682A //A19
|
|
// Polynomial coefficients for right root on [-7, -6]
|
|
// Lgammal is approximated by polynomial within [-.154582 ; .154521 ] range
|
|
data8 0x3C75F103A1B00A48, 0x391C041C190C726D //A0
|
|
data8 0x40869DE49E3AF2AA, 0x3D1C17E1F813063B //A1
|
|
data8 0x410FCE23484CFD10, 0x3DB6F38C2F11DAB9 //A2
|
|
data8 0xEF281D1E1BE2055A, 0x00004019 //A3
|
|
data8 0xFCE3DA92AC55DFF8, 0x00004022 //A4
|
|
data8 0x8E9EA838A20BD58E, 0x0000402C //A5
|
|
data8 0x4354F21E2FB9E0C9 //A6
|
|
data8 0x43E9500994CD4F09 //A7
|
|
data8 0x447F3A2C23C033DF //A8
|
|
data8 0x45139152656606D8 //A9
|
|
data8 0x45A8D45F8D3BF2E8 //A10
|
|
data8 0x463FD32110E5BFE5 //A11
|
|
data8 0x46D490B3BDBAE0BE //A12
|
|
data8 0x476AC3CAD905DD23 //A13
|
|
data8 0x48018558217AD473 //A14
|
|
data8 0x48970AF371D30585 //A15
|
|
data8 0x492E6273A8BEFFE3 //A16
|
|
data8 0x49C47CC9AE3F1073 //A17
|
|
data8 0x4A5D38E8C35EFF45 //A18
|
|
data8 0x4AF0123E89694CD8 //A19
|
|
// Polynomial coefficients for right root on [-8, -7]
|
|
// Lgammal is approximated by polynomial within [-.154217 ; .154208 ] range
|
|
data8 0xBCD2507D818DDD68, 0xB97F6940EA2871A0 //A0
|
|
data8 0x40B3B407AA387BCB, 0x3D6320238F2C43D1 //A1
|
|
data8 0x41683E85DAAFBAC7, 0x3E148D085958EA3A //A2
|
|
data8 0x9F2A95AF1E10A548, 0x00004022 //A3
|
|
data8 0x92F21522F482300E, 0x0000402E //A4
|
|
data8 0x90B51AB03A1F244D, 0x0000403A //A5
|
|
data8 0x44628E1C70EF534F //A6
|
|
data8 0x452393E2BC32D244 //A7
|
|
data8 0x45E5164141F4BA0B //A8
|
|
data8 0x46A712B3A8AF5808 //A9
|
|
data8 0x47698FD36CEDD0F2 //A10
|
|
data8 0x482C9AE6BBAA3637 //A11
|
|
data8 0x48F023821857C8E9 //A12
|
|
data8 0x49B2569053FC106F //A13
|
|
data8 0x4A74F646D5C1604B //A14
|
|
data8 0x4B3811CF5ABA4934 //A15
|
|
data8 0x4BFBB5DD6C84E233 //A16
|
|
data8 0x4CC05021086F637B //A17
|
|
data8 0x4D8450A345B0FB49 //A18
|
|
data8 0x4E43825848865DB2 //A19
|
|
// Polynomial coefficients for right root on [-9, -8]
|
|
// Lgammal is approximated by polynomial within [-.154160 ; .154158 ] range
|
|
data8 0x3CDF4358564F2B46, 0x397969BEE6042F81 //A0
|
|
data8 0x40E3B088FED67721, 0x3D82787BA937EE85 //A1
|
|
data8 0x41C83A3893550EF4, 0x3E542ED57E244DA8 //A2
|
|
data8 0x9F003C6DC56E0B8E, 0x0000402B //A3
|
|
data8 0x92BDF64A3213A699, 0x0000403A //A4
|
|
data8 0x9074F503AAD417AF, 0x00004049 //A5
|
|
data8 0x4582843E1313C8CD //A6
|
|
data8 0x467387BD6A7826C1 //A7
|
|
data8 0x4765074E788CF440 //A8
|
|
data8 0x4857004DD9D1E09D //A9
|
|
data8 0x4949792ED7530EAF //A10
|
|
data8 0x4A3C7F089A292ED3 //A11
|
|
data8 0x4B30125BF0AABB86 //A12
|
|
data8 0x4C224175195E307E //A13
|
|
data8 0x4D14DC4C8B32C08D //A14
|
|
data8 0x4E07F1DB2786197E //A15
|
|
data8 0x4EFB8EA1C336DACB //A16
|
|
data8 0x4FF03797EACD0F23 //A17
|
|
data8 0x50E4304A8E68A730 //A18
|
|
data8 0x51D3618FB2EC9F93 //A19
|
|
// Polynomial coefficients for right root on [-10, -9]
|
|
// Lgammal is approximated by polynomial within [-.154152 ; .154152 ] range
|
|
data8 0x3D42F34DA97ECF0C, 0x39FD1256F345B0D0 //A0
|
|
data8 0x4116261203919787, 0x3DC12D44055588EB //A1
|
|
data8 0x422EA8F32FB7FE99, 0x3ED849CE4E7B2D77 //A2
|
|
data8 0xE25BAF73477A57B5, 0x00004034 //A3
|
|
data8 0xEB021FD10060504A, 0x00004046 //A4
|
|
data8 0x8220A208EE206C5F, 0x00004059 //A5
|
|
data8 0x46B2C3903EC9DA14 //A6
|
|
data8 0x47D64393744B9C67 //A7
|
|
data8 0x48FAF79CCDC604DD //A8
|
|
data8 0x4A20975DB8061EBA //A9
|
|
data8 0x4B44AB9CBB38DB21 //A10
|
|
data8 0x4C6A032F60094FE9 //A11
|
|
data8 0x4D908103927634B4 //A12
|
|
data8 0x4EB516CA21D30861 //A13
|
|
data8 0x4FDB1BF12C58D318 //A14
|
|
data8 0x510180AAE094A553 //A15
|
|
data8 0x5226A8F2A2D45D57 //A16
|
|
data8 0x534E00B6B0C8B809 //A17
|
|
data8 0x5475022FE21215B2 //A18
|
|
data8 0x5596B02BF6C5E19B //A19
|
|
// Polynomial coefficients for right root on [-11, -10]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0x3D7AA9C2E2B1029C, 0x3A15FB37578544DB //A0
|
|
data8 0x414BAF825A0C91D4, 0x3DFB9DA2CE398747 //A1
|
|
data8 0x4297F3EC8AE0AF03, 0x3F34208B55FB8781 //A2
|
|
data8 0xDD0C97D3197F56DE, 0x0000403E //A3
|
|
data8 0x8F6F3AF7A5499674, 0x00004054 //A4
|
|
data8 0xC68DA1AF6D878EEB, 0x00004069 //A5
|
|
data8 0x47F1E4E1E2197CE0 //A6
|
|
data8 0x494A8A28E597C3EB //A7
|
|
data8 0x4AA4175D0D35D705 //A8
|
|
data8 0x4BFEE6F0AF69E814 //A9
|
|
data8 0x4D580FE7B3DBB3C6 //A10
|
|
data8 0x4EB2ECE60E4608AF //A11
|
|
data8 0x500E04BE3E2B4F24 //A12
|
|
data8 0x5167F9450F0FB8FD //A13
|
|
data8 0x52C342BDE747603F //A14
|
|
data8 0x541F1699D557268C //A15
|
|
data8 0x557927C5F079864E //A16
|
|
data8 0x56D4D10FEEDB030C //A17
|
|
data8 0x5832385DF86AD28A //A18
|
|
data8 0x598898914B4D6523 //A19
|
|
// Polynomial coefficients for right root on [-12, -11]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBD96F61647C58B03, 0xBA3ABB0C2A6C755B //A0
|
|
data8 0x418308A82714B70D, 0x3E1088FC6A104C39 //A1
|
|
data8 0x4306A493DD613C39, 0x3FB2341ECBF85741 //A2
|
|
data8 0x8FA8FE98339474AB, 0x00004049 //A3
|
|
data8 0x802CCDF570BA7942, 0x00004062 //A4
|
|
data8 0xF3F748AF11A32890, 0x0000407A //A5
|
|
data8 0x493E3B567EF178CF //A6
|
|
data8 0x4ACED38F651BA362 //A7
|
|
data8 0x4C600B357337F946 //A8
|
|
data8 0x4DF0F71A52B54CCF //A9
|
|
data8 0x4F8229F3B9FA2C70 //A10
|
|
data8 0x5113A4C4979B770E //A11
|
|
data8 0x52A56BC367F298D5 //A12
|
|
data8 0x543785CF31842DC0 //A13
|
|
data8 0x55C9FC37E3E40896 //A14
|
|
data8 0x575CD5D1BA556C82 //A15
|
|
data8 0x58F00A7AD99A9E08 //A16
|
|
data8 0x5A824088688B008D //A17
|
|
data8 0x5C15F75EF7E08EBD //A18
|
|
data8 0x5DA462EA902F0C90 //A19
|
|
// Polynomial coefficients for right root on [-13, -12]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0x3DC3191752ACFC9D, 0x3A26CB6629532DBF //A0
|
|
data8 0x41BC8CFC051191BD, 0x3E68A84DA4E62AF2 //A1
|
|
data8 0x43797926294A0148, 0x400F345FF3723CFF //A2
|
|
data8 0xF26D2AF700B82625, 0x00004053 //A3
|
|
data8 0xA238B24A4B1F7B15, 0x00004070 //A4
|
|
data8 0xE793B5C0A41A264F, 0x0000408C //A5
|
|
data8 0x4A9585BDDACE863D //A6
|
|
data8 0x4C6075953448088A //A7
|
|
data8 0x4E29B2F38D1FC670 //A8
|
|
data8 0x4FF4619B079C440F //A9
|
|
data8 0x51C05DAE118D8AD9 //A10
|
|
data8 0x538A8C7F87326AD4 //A11
|
|
data8 0x5555B6937588DAB3 //A12
|
|
data8 0x5721E1F8B6E6A7DB //A13
|
|
data8 0x58EDA1D7A77DD6E5 //A14
|
|
data8 0x5AB8A9616B7DC9ED //A15
|
|
data8 0x5C84942AA209ED17 //A16
|
|
data8 0x5E518FC34C6F54EF //A17
|
|
data8 0x601FB3F17BCCD9A0 //A18
|
|
data8 0x61E61128D512FE97 //A1
|
|
// Polynomial coefficients for right root on [-14, -13]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBE170D646421B3F5, 0xBAAD95F79FCB5097 //A0
|
|
data8 0x41F7328CBFCD9AC7, 0x3E743B8B1E8AEDB1 //A1
|
|
data8 0x43F0D0FA2DBDA237, 0x40A0422D6A227B55 //A2
|
|
data8 0x82082DF2D32686CC, 0x0000405F //A3
|
|
data8 0x8D64EE9B42E68B43, 0x0000407F //A4
|
|
data8 0xA3FFD82E08C5F1F1, 0x0000409F //A5
|
|
data8 0x4BF8C49D99123454 //A6
|
|
data8 0x4DFEC79DDF11342F //A7
|
|
data8 0x50038615A892F6BD //A8
|
|
data8 0x520929453DB32EF1 //A9
|
|
data8 0x54106A7808189A7F //A10
|
|
data8 0x5615A302D03C207B //A11
|
|
data8 0x581CC175AA736F5E //A12
|
|
data8 0x5A233E071147C017 //A13
|
|
data8 0x5C29E81917243F22 //A14
|
|
data8 0x5E3184B0B5AC4707 //A15
|
|
data8 0x6037C11DE62D8388 //A16
|
|
data8 0x6240787C4B1C9D6C //A17
|
|
data8 0x6448289235E80977 //A18
|
|
data8 0x664B5352C6C3449E //A19
|
|
// Polynomial coefficients for right root on [-15, -14]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0x3E562C2E34A9207D, 0x3ADC00DA3DFF7A83 //A0
|
|
data8 0x42344C3B2F0D90AB, 0x3EB8A2E979F24536 //A1
|
|
data8 0x4469BFFF28B50D07, 0x41181E3D05C1C294 //A2
|
|
data8 0xAE38F64DCB24D9F8, 0x0000406A //A3
|
|
data8 0xA5C3F52C1B350702, 0x0000408E //A4
|
|
data8 0xA83BC857BCD67A1B, 0x000040B2 //A5
|
|
data8 0x4D663B4727B4D80A //A6
|
|
data8 0x4FA82C965B0F7788 //A7
|
|
data8 0x51EAD58C02908D95 //A8
|
|
data8 0x542E427970E073D8 //A9
|
|
data8 0x56714644C558A818 //A10
|
|
data8 0x58B3EC2040C77BAE //A11
|
|
data8 0x5AF72AE6A83D45B1 //A12
|
|
data8 0x5D3B214F611F5D12 //A13
|
|
data8 0x5F7FF5E49C54E92A //A14
|
|
data8 0x61C2E917AB765FB2 //A15
|
|
data8 0x64066FD70907B4C1 //A16
|
|
data8 0x664B3998D60D0F9B //A17
|
|
data8 0x689178710782FA8B //A18
|
|
data8 0x6AD14A66C1C7BEC3 //A19
|
|
// Polynomial coefficients for right root on [-16, -15]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBE6D7E7192615BAE, 0xBB0137677D7CC719 //A0
|
|
data8 0x4273077763F6628C, 0x3F09250FB8FC8EC9 //A1
|
|
data8 0x44E6A1BF095B1AB3, 0x4178D5A74F6CB3B3 //A2
|
|
data8 0x8F8E0D5060FCC76E, 0x00004076 //A3
|
|
data8 0x800CC1DCFF092A63, 0x0000409E //A4
|
|
data8 0xF3AB0BA9D14CDA72, 0x000040C5 //A5
|
|
data8 0x4EDE3000A2F6D54F //A6
|
|
data8 0x515EC613B9C8E241 //A7
|
|
data8 0x53E003309FEEEA96 //A8
|
|
data8 0x5660ED908D7C9A90 //A9
|
|
data8 0x58E21E9B517B1A50 //A10
|
|
data8 0x5B639745E4374EE2 //A11
|
|
data8 0x5DE55BB626B2075D //A12
|
|
data8 0x606772B7506BA747 //A13
|
|
data8 0x62E9E581AB2E057B //A14
|
|
data8 0x656CBAD1CF85D396 //A15
|
|
data8 0x67EFF4EBD7989872 //A16
|
|
data8 0x6A722D2B19B7E2F9 //A17
|
|
data8 0x6CF5DEB3073B0743 //A18
|
|
data8 0x6F744AC11550B93A //A19
|
|
// Polynomial coefficients for right root on [-17, -16]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBEDCC6291188207E, 0xBB872E3FDD48F5B7 //A0
|
|
data8 0x42B3076EE7525EF9, 0x3F6687A5038CA81C //A1
|
|
data8 0x4566A1AAD96EBCB5, 0x421F0FEDFBF548D2 //A2
|
|
data8 0x8F8D4D3DE9850DBA, 0x00004082 //A3
|
|
data8 0x800BDD6DA2CE1859, 0x000040AE //A4
|
|
data8 0xF3A8EC4C9CDC1CE5, 0x000040D9 //A5
|
|
data8 0x505E2FAFDB812628 //A6
|
|
data8 0x531EC5B3A7508719 //A7
|
|
data8 0x55E002F77E99B628 //A8
|
|
data8 0x58A0ED4C9B4DAE54 //A9
|
|
data8 0x5B621E4A8240F90C //A10
|
|
data8 0x5E2396E5C8849814 //A11
|
|
data8 0x60E55B43D8C5CE71 //A12
|
|
data8 0x63A7722F5D45D01D //A13
|
|
data8 0x6669E4E010DCE45A //A14
|
|
data8 0x692CBA120D5E78F6 //A15
|
|
data8 0x6BEFF4045350B22E //A16
|
|
data8 0x6EB22C9807C21819 //A17
|
|
data8 0x7175DE20D04617C4 //A18
|
|
data8 0x74344AB87C6D655F //A19
|
|
// Polynomial coefficients for right root on [-18, -17]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBF28AEEE7B61D77C, 0xBBDBBB5FC57ABF79 //A0
|
|
data8 0x42F436F56B3B8A0C, 0x3FA43EE3C5C576E9 //A1
|
|
data8 0x45E98A22535D115D, 0x42984678BE78CC48 //A2
|
|
data8 0xAC176F3775E6FCFC, 0x0000408E //A3
|
|
data8 0xA3114F53A9FEB922, 0x000040BE //A4
|
|
data8 0xA4D168A8334ABF41, 0x000040EE //A5
|
|
data8 0x51E5B0E7EC7182BB //A6
|
|
data8 0x54E77D67B876EAB6 //A7
|
|
data8 0x57E9F7C30C09C4B6 //A8
|
|
data8 0x5AED29B0488614CA //A9
|
|
data8 0x5DF09486F87E79F9 //A10
|
|
data8 0x60F30B199979654E //A11
|
|
data8 0x63F60E02C7DCCC5F //A12
|
|
data8 0x66F9B8A00EB01684 //A13
|
|
data8 0x69FE2D3ED0700044 //A14
|
|
data8 0x6D01C8363C7DCC84 //A15
|
|
data8 0x700502B29C2F06E3 //A16
|
|
data8 0x730962B4500F4A61 //A17
|
|
data8 0x76103C6ED099192A //A18
|
|
data8 0x79100C7132CFD6E3 //A19
|
|
// Polynomial coefficients for right root on [-19, -18]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0x3F3C19A53328A0C3, 0x3BE04ADC3FBE1458 //A0
|
|
data8 0x4336C16C16C16C19, 0x3FE58CE3AC4A7C28 //A1
|
|
data8 0x46702E85C0898B70, 0x432C922E412CEC6E //A2
|
|
data8 0xF57B99A1C034335D, 0x0000409A //A3
|
|
data8 0x82EC9634223DF909, 0x000040CF //A4
|
|
data8 0x94F66D7557E2EA60, 0x00004103 //A5
|
|
data8 0x5376118B79AE34D0 //A6
|
|
data8 0x56BAE7106D52E548 //A7
|
|
data8 0x5A00BD48CC8E25AB //A8
|
|
data8 0x5D4529722821B493 //A9
|
|
data8 0x608B1654AF31BBC1 //A10
|
|
data8 0x63D182CC98AEA859 //A11
|
|
data8 0x6716D43D5EEB05E8 //A12
|
|
data8 0x6A5DF884FC172E1C //A13
|
|
data8 0x6DA3CA7EBB97976B //A14
|
|
data8 0x70EA416D0BE6D2EF //A15
|
|
data8 0x743176C31EBB65F2 //A16
|
|
data8 0x7777C401A8715CF9 //A17
|
|
data8 0x7AC1110C6D350440 //A18
|
|
data8 0x7E02D0971CF84865 //A19
|
|
// Polynomial coefficients for right root on [-20, -19]
|
|
// Lgammal is approximated by polynomial within [-.154151 ; .154151 ] range
|
|
data8 0xBFAB767F9BE21803, 0xBC5ACEF5BB1BD8B5 //A0
|
|
data8 0x4379999999999999, 0x4029241C7F5914C8 //A1
|
|
data8 0x46F47AE147AE147A, 0x43AC2979B64B9D7E //A2
|
|
data8 0xAEC33E1F67152993, 0x000040A7 //A3
|
|
data8 0xD1B71758E219616F, 0x000040DF //A4
|
|
data8 0x8637BD05AF6CF468, 0x00004118 //A5
|
|
data8 0x55065E9F80F293DE //A6
|
|
data8 0x588EADA78C44EE66 //A7
|
|
data8 0x5C15798EE22DEF09 //A8
|
|
data8 0x5F9E8ABFD644FA63 //A9
|
|
data8 0x6325FD7FE29BD7CD //A10
|
|
data8 0x66AFFC5C57E1F802 //A11
|
|
data8 0x6A3774CD7D5C0181 //A12
|
|
data8 0x6DC152724DE2A6FE //A13
|
|
data8 0x7149BB138EB3D0C2 //A14
|
|
data8 0x74D32FF8A70896C2 //A15
|
|
data8 0x785D3749F9C72BD7 //A16
|
|
data8 0x7BE5CCF65EBC4E40 //A17
|
|
data8 0x7F641A891B5FC652 //A18
|
|
data8 0x7FEFFFFFFFFFFFFF //A19
|
|
LOCAL_OBJECT_END(lgammal_right_roots_polynomial_data)
|
|
|
|
LOCAL_OBJECT_START(lgammal_left_roots_polynomial_data)
|
|
// Polynomial coefficients for left root on [-3, -2]
|
|
// Lgammal is approximated by polynomial within [.084641 ; -.059553 ] range
|
|
data8 0xBC0844590979B82E, 0xB8BC7CE8CE2ECC3B //A0
|
|
data8 0xBFFEA12DA904B18C, 0xBC91A6B2BAD5EF6E //A1
|
|
data8 0x4023267F3C265A51, 0x3CD7055481D03AED //A2
|
|
data8 0xA0C2D618645F8E00, 0x0000C003 //A3
|
|
data8 0xFA8256664F8CD2BE, 0x00004004 //A4
|
|
data8 0xC2C422C103F57158, 0x0000C006 //A5
|
|
data8 0x4084373F7CC70AF5 //A6
|
|
data8 0xC0A12239BDD6BB95 //A7
|
|
data8 0x40BDBA65E2709397 //A8
|
|
data8 0xC0DA2D2504DFB085 //A9
|
|
data8 0x40F758173CA5BF3C //A10
|
|
data8 0xC11506C65C267E72 //A11
|
|
data8 0x413318EE3A6B05FC //A12
|
|
data8 0xC1517767F247DA98 //A13
|
|
data8 0x41701237B4754D73 //A14
|
|
data8 0xC18DB8A03BC5C3D8 //A15
|
|
data8 0x41AB80953AC14A07 //A16
|
|
data8 0xC1C9B7B76638D0A4 //A17
|
|
data8 0x41EA727E3033E2D9 //A18
|
|
data8 0xC20812C297729142 //A19
|
|
//
|
|
// Polynomial coefficients for left root on [-4, -3]
|
|
// Lgammal is approximated by polynomial within [.147147 ; -.145158 ] range
|
|
data8 0xBC3130AE5C4F54DB, 0xB8ED23294C13398A //A0
|
|
data8 0xC034B99D966C5646, 0xBCE2E5FE3BC3DBB9 //A1
|
|
data8 0x406F76DEAE0436BD, 0x3D14974DDEC057BD //A2
|
|
data8 0xE929ACEA5979BE96, 0x0000C00A //A3
|
|
data8 0xF47C14F8A0D52771, 0x0000400E //A4
|
|
data8 0x88B7BC036937481C, 0x0000C013 //A5
|
|
data8 0x4173E8F3AB9FC266 //A6
|
|
data8 0xC1B7DBBE062FB11B //A7
|
|
data8 0x41FD2F76DE7A47A7 //A8
|
|
data8 0xC242225FE53B124D //A9
|
|
data8 0x4286D12AE2FBFA30 //A10
|
|
data8 0xC2CCFFC267A3C4C0 //A11
|
|
data8 0x431294E10008E014 //A12
|
|
data8 0xC357FAC8C9A2DF6A //A13
|
|
data8 0x439F2190AB9FAE01 //A14
|
|
data8 0xC3E44C1D8E8C67C3 //A15
|
|
data8 0x442A8901105D5A38 //A16
|
|
data8 0xC471C4421E908C3A //A17
|
|
data8 0x44B92CD4D59D6D17 //A18
|
|
data8 0xC4FB3A078B5247FA //A19
|
|
// Polynomial coefficients for left root on [-5, -4]
|
|
// Lgammal is approximated by polynomial within [.155671 ; -.155300 ] range
|
|
data8 0xBC57BF3C6E8A94C1, 0xB902FB666934AC9E //A0
|
|
data8 0xC05D224A3EF9E41F, 0xBCF6F5713913E440 //A1
|
|
data8 0x40BB533C678A3955, 0x3D688E53E3C72538 //A2
|
|
data8 0x869FBFF732E99B84, 0x0000C012 //A3
|
|
data8 0xBA9537AD61392DEC, 0x00004018 //A4
|
|
data8 0x89EAE8B1DEA06B05, 0x0000C01F //A5
|
|
data8 0x425A8C5C53458D3C //A6
|
|
data8 0xC2C5068B3ED6509B //A7
|
|
data8 0x4330FFA575E99B4E //A8
|
|
data8 0xC39BEC12DDDF7669 //A9
|
|
data8 0x44073825725F74F9 //A10
|
|
data8 0xC47380EBCA299047 //A11
|
|
data8 0x44E084DD9B666437 //A12
|
|
data8 0xC54C2DA6BF787ACF //A13
|
|
data8 0x45B82D65C8D6FA42 //A14
|
|
data8 0xC624D62113FE950A //A15
|
|
data8 0x469200CC19B45016 //A16
|
|
data8 0xC6FFDDC6DD938E2E //A17
|
|
data8 0x476DD7C07184B9F9 //A18
|
|
data8 0xC7D554A30085C052 //A19
|
|
// Polynomial coefficients for left root on [-6, -5]
|
|
// Lgammal is approximated by polynomial within [.157425 ; -.157360 ] range
|
|
data8 0x3C9E20A87C8B79F1, 0x39488BE34B2427DB //A0
|
|
data8 0xC08661F6A43A5E12, 0xBD3D912526D759CC //A1
|
|
data8 0x410F79DCB794F270, 0x3DB9BEE7CD3C1BF5 //A2
|
|
data8 0xEB7404450D0005DB, 0x0000C019 //A3
|
|
data8 0xF7AE9846DFE4D4AB, 0x00004022 //A4
|
|
data8 0x8AF535855A95B6DA, 0x0000C02C //A5
|
|
data8 0x43544D54E9FE240E //A6
|
|
data8 0xC3E8684E40CE6CFC //A7
|
|
data8 0x447DF44C1D803454 //A8
|
|
data8 0xC512AC305439B2BA //A9
|
|
data8 0x45A79226AF79211A //A10
|
|
data8 0xC63E0DFF7244893A //A11
|
|
data8 0x46D35216C3A83AF3 //A12
|
|
data8 0xC76903BE0C390E28 //A13
|
|
data8 0x48004A4DECFA4FD5 //A14
|
|
data8 0xC8954FBD243DB8BE //A15
|
|
data8 0x492BF3A31EB18DDA //A16
|
|
data8 0xC9C2C6A864521F3A //A17
|
|
data8 0x4A5AB127C62E8DA1 //A18
|
|
data8 0xCAECF60EF3183C57 //A19
|
|
// Polynomial coefficients for left root on [-7, -6]
|
|
// Lgammal is approximated by polynomial within [.157749 ; -.157739 ] range
|
|
data8 0x3CC9B9E8B8D551D6, 0x3961813C8E1E10DB //A0
|
|
data8 0xC0B3ABF7A5CEA91F, 0xBD55638D4BCB4CC4 //A1
|
|
data8 0x4168349A25504236, 0x3E0287ECE50CCF76 //A2
|
|
data8 0x9EC8ED6E4C219E67, 0x0000C022 //A3
|
|
data8 0x9279EB1B799A3FF3, 0x0000402E //A4
|
|
data8 0x90213EF8D9A5DBCF, 0x0000C03A //A5
|
|
data8 0x4462775E857FB71C //A6
|
|
data8 0xC52377E70B45FDBF //A7
|
|
data8 0x45E4F3D28EDA8C28 //A8
|
|
data8 0xC6A6E85571BD2D0B //A9
|
|
data8 0x47695BB17E74DF74 //A10
|
|
data8 0xC82C5AC0ED6A662F //A11
|
|
data8 0x48EFF8159441C2E3 //A12
|
|
data8 0xC9B22602C1B68AE5 //A13
|
|
data8 0x4A74BA8CE7B34100 //A14
|
|
data8 0xCB37C7E208482E4B //A15
|
|
data8 0x4BFB5A1D57352265 //A16
|
|
data8 0xCCC01CB3021212FF //A17
|
|
data8 0x4D841613AC3431D1 //A18
|
|
data8 0xCE431C9E9EE43AD9 //A19
|
|
// Polynomial coefficients for left root on [-8, -7]
|
|
// Lgammal is approximated by polynomial within [.157799 ; -.157798 ] range
|
|
data8 0xBCF9C7A33AD9478C, 0xB995B0470F11E5ED //A0
|
|
data8 0xC0E3AF76FE4C2F8B, 0xBD8DBCD503250511 //A1
|
|
data8 0x41C838E76CAAF0D5, 0x3E5D79F5E2E069C3 //A2
|
|
data8 0x9EF345992B262CE0, 0x0000C02B //A3
|
|
data8 0x92AE0292985FD559, 0x0000403A //A4
|
|
data8 0x90615420C08F7D8C, 0x0000C049 //A5
|
|
data8 0x45828139342CEEB7 //A6
|
|
data8 0xC67384066C31E2D3 //A7
|
|
data8 0x476502BC4DAC2C35 //A8
|
|
data8 0xC856FAADFF22ADC6 //A9
|
|
data8 0x49497243255AB3CE //A10
|
|
data8 0xCA3C768489520F6B //A11
|
|
data8 0x4B300D1EA47AF838 //A12
|
|
data8 0xCC223B0508AC620E //A13
|
|
data8 0x4D14D46583338CD8 //A14
|
|
data8 0xCE07E7A87AA068E4 //A15
|
|
data8 0x4EFB811AD2F8BEAB //A16
|
|
data8 0xCFF0351B51508523 //A17
|
|
data8 0x50E4364CCBF53100 //A18
|
|
data8 0xD1D33CFD0BF96FA6 //A19
|
|
// Polynomial coefficients for left root on [-9, -8]
|
|
// Lgammal is approximated by polynomial within [.157806 ; -.157806 ] range
|
|
data8 0x3D333E4438B1B9D4, 0x39E7B956B83964C1 //A0
|
|
data8 0xC11625EDFC63DCD8, 0xBDCF39625709EFAC //A1
|
|
data8 0x422EA8C150480F16, 0x3EC16ED908AB7EDD //A2
|
|
data8 0xE2598725E2E11646, 0x0000C034 //A3
|
|
data8 0xEAFF2346DE3EBC98, 0x00004046 //A4
|
|
data8 0x821E90DE12A0F05F, 0x0000C059 //A5
|
|
data8 0x46B2C334AE5366FE //A6
|
|
data8 0xC7D64314B43191B6 //A7
|
|
data8 0x48FAF6ED5899E01B //A8
|
|
data8 0xCA2096E4472AF37D //A9
|
|
data8 0x4B44AAF49FB7E4C8 //A10
|
|
data8 0xCC6A02469F2BD920 //A11
|
|
data8 0x4D9080626D2EFC07 //A12
|
|
data8 0xCEB515EDCF0695F7 //A13
|
|
data8 0x4FDB1AC69BF36960 //A14
|
|
data8 0xD1017F8274339270 //A15
|
|
data8 0x5226A684961BAE2F //A16
|
|
data8 0xD34E085C088404A5 //A17
|
|
data8 0x547511892FF8960E //A18
|
|
data8 0xD5968FA3B1ED67A9 //A19
|
|
// Polynomial coefficients for left root on [-10, -9]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBD355818A2B42BA2, 0xB9B7320B6A0D61EA //A0
|
|
data8 0xC14BAF7DA5F3770E, 0xBDE64AF9A868F719 //A1
|
|
data8 0x4297F3E8791F9CD3, 0x3F2A553E59B4835E //A2
|
|
data8 0xDD0C5F7E551BD13C, 0x0000C03E //A3
|
|
data8 0x8F6F0A3B2EB08BBB, 0x00004054 //A4
|
|
data8 0xC68D4D5AD230BA08, 0x0000C069 //A5
|
|
data8 0x47F1E4D8C35D1A3E //A6
|
|
data8 0xC94A8A191DB0A466 //A7
|
|
data8 0x4AA4174F65FE6AE8 //A8
|
|
data8 0xCBFEE6D90F94E9DD //A9
|
|
data8 0x4D580FD3438BE16C //A10
|
|
data8 0xCEB2ECD456D50224 //A11
|
|
data8 0x500E049F7FE64546 //A12
|
|
data8 0xD167F92D9600F378 //A13
|
|
data8 0x52C342AE2B43261A //A14
|
|
data8 0xD41F15DEEDA4B67E //A15
|
|
data8 0x55792638748AFB7D //A16
|
|
data8 0xD6D4D760074F6E6B //A17
|
|
data8 0x5832469D58ED3FA9 //A18
|
|
data8 0xD988769F3DC76642 //A19
|
|
// Polynomial coefficients for left root on [-11, -10]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBDA050601F39778A, 0xBA0D4D1CE53E8241 //A0
|
|
data8 0xC18308A7D8EA4039, 0xBE370C379D3EAD41 //A1
|
|
data8 0x4306A49380644E6C, 0x3FBBB143C0E7B5C8 //A2
|
|
data8 0x8FA8FB233E4AA6D2, 0x0000C049 //A3
|
|
data8 0x802CC9D8AEAC207D, 0x00004062 //A4
|
|
data8 0xF3F73EE651A37A13, 0x0000C07A //A5
|
|
data8 0x493E3B550A7B9568 //A6
|
|
data8 0xCACED38DAA060929 //A7
|
|
data8 0x4C600B346BAB3BC6 //A8
|
|
data8 0xCDF0F719193E3D26 //A9
|
|
data8 0x4F8229F24528B151 //A10
|
|
data8 0xD113A4C2D32FBBE2 //A11
|
|
data8 0x52A56BC13DC4474D //A12
|
|
data8 0xD43785CFAF5E3CE3 //A13
|
|
data8 0x55C9FC3EA5941202 //A14
|
|
data8 0xD75CD545A3341AF5 //A15
|
|
data8 0x58F009911F77C282 //A16
|
|
data8 0xDA8246294D210BEC //A17
|
|
data8 0x5C1608AAC32C3A8E //A18
|
|
data8 0xDDA446E570A397D5 //A19
|
|
// Polynomial coefficients for left root on [-12, -11]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0x3DEACBB3081C502E, 0x3A8AA6F01DEDF745 //A0
|
|
data8 0xC1BC8CFBFB0A9912, 0xBE6556B6504A2AE6 //A1
|
|
data8 0x43797926206941D7, 0x40289A9644C2A216 //A2
|
|
data8 0xF26D2A78446D0839, 0x0000C053 //A3
|
|
data8 0xA238B1D937FFED38, 0x00004070 //A4
|
|
data8 0xE793B4F6DE470538, 0x0000C08C //A5
|
|
data8 0x4A9585BDC44DC45D //A6
|
|
data8 0xCC60759520342C47 //A7
|
|
data8 0x4E29B2F3694C0404 //A8
|
|
data8 0xCFF4619AE7B6BBAB //A9
|
|
data8 0x51C05DADF52B89E8 //A10
|
|
data8 0xD38A8C7F48819A4A //A11
|
|
data8 0x5555B6932D687860 //A12
|
|
data8 0xD721E1FACB6C1B5B //A13
|
|
data8 0x58EDA1E2677C8F91 //A14
|
|
data8 0xDAB8A8EC523C1F71 //A15
|
|
data8 0x5C84930133F30411 //A16
|
|
data8 0xDE51952FDFD1EC49 //A17
|
|
data8 0x601FCCEC1BBD25F1 //A18
|
|
data8 0xE1E5F2D76B610920 //A19
|
|
// Polynomial coefficients for left root on [-13, -12]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBE01612F373268ED, 0xBA97B7A18CDF103B //A0
|
|
data8 0xC1F7328CBF7A4FAC, 0xBE89A25A6952F481 //A1
|
|
data8 0x43F0D0FA2DBDA237, 0x40A0422EC1CE6084 //A2
|
|
data8 0x82082DF2D32686C5, 0x0000C05F //A3
|
|
data8 0x8D64EE9B42E68B36, 0x0000407F //A4
|
|
data8 0xA3FFD82E08C630C9, 0x0000C09F //A5
|
|
data8 0x4BF8C49D99123466 //A6
|
|
data8 0xCDFEC79DDF1119ED //A7
|
|
data8 0x50038615A892D242 //A8
|
|
data8 0xD20929453DC8B537 //A9
|
|
data8 0x54106A78083BA1EE //A10
|
|
data8 0xD615A302C69E27B2 //A11
|
|
data8 0x581CC175870FF16F //A12
|
|
data8 0xDA233E0979E12B74 //A13
|
|
data8 0x5C29E822BC568C80 //A14
|
|
data8 0xDE31845DB5340FBC //A15
|
|
data8 0x6037BFC6D498D5F9 //A16
|
|
data8 0xE2407D92CD613E82 //A17
|
|
data8 0x64483B9B62367EB7 //A18
|
|
data8 0xE64B2DC830E8A799 //A1
|
|
// Polynomial coefficients for left root on [-14, -13]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0x3E563D0B930B371F, 0x3AE779957E14F012 //A0
|
|
data8 0xC2344C3B2F083767, 0xBEC0B7769AA3DD66 //A1
|
|
data8 0x4469BFFF28B50D07, 0x41181E3F13ED2401 //A2
|
|
data8 0xAE38F64DCB24D9EE, 0x0000C06A //A3
|
|
data8 0xA5C3F52C1B3506F2, 0x0000408E //A4
|
|
data8 0xA83BC857BCD6BA92, 0x0000C0B2 //A5
|
|
data8 0x4D663B4727B4D81A //A6
|
|
data8 0xCFA82C965B0F62E9 //A7
|
|
data8 0x51EAD58C02905B71 //A8
|
|
data8 0xD42E427970FA56AD //A9
|
|
data8 0x56714644C57D8476 //A10
|
|
data8 0xD8B3EC2037EC95F2 //A11
|
|
data8 0x5AF72AE68BBA5B3D //A12
|
|
data8 0xDD3B2152C67AA6B7 //A13
|
|
data8 0x5F7FF5F082861B8B //A14
|
|
data8 0xE1C2E8BE125A5B7A //A15
|
|
data8 0x64066E92FE9EBE7D //A16
|
|
data8 0xE64B4201CDF9F138 //A17
|
|
data8 0x689186351E58AA88 //A18
|
|
data8 0xEAD132A585DFC60A //A19
|
|
// Polynomial coefficients for left root on [-15, -14]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBE6D7DDE12700AC1, 0xBB1E025BF1667FB5 //A0
|
|
data8 0xC273077763F60AD5, 0xBF2A1698184C7A9A //A1
|
|
data8 0x44E6A1BF095B1AB3, 0x4178D5AE8A4A2874 //A2
|
|
data8 0x8F8E0D5060FCC767, 0x0000C076 //A3
|
|
data8 0x800CC1DCFF092A57, 0x0000409E //A4
|
|
data8 0xF3AB0BA9D14D37D1, 0x0000C0C5 //A5
|
|
data8 0x4EDE3000A2F6D565 //A6
|
|
data8 0xD15EC613B9C8C800 //A7
|
|
data8 0x53E003309FEECCAA //A8
|
|
data8 0xD660ED908D8B15C4 //A9
|
|
data8 0x58E21E9B51A1C4AE //A10
|
|
data8 0xDB639745DB82210D //A11
|
|
data8 0x5DE55BB60C68FCF6 //A12
|
|
data8 0xE06772BA3FCA23C6 //A13
|
|
data8 0x62E9E58B4F702C31 //A14
|
|
data8 0xE56CBA49B071ABE2 //A15
|
|
data8 0x67EFF31E4F2BA36A //A16
|
|
data8 0xEA7232C8804F32C3 //A17
|
|
data8 0x6CF5EFEE929A0928 //A18
|
|
data8 0xEF742EE03EC3E8FF //A19
|
|
// Polynomial coefficients for left root on [-16, -15]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBEDCC628FEAC7A1B, 0xBB80582C8BEBB198 //A0
|
|
data8 0xC2B3076EE752595E, 0xBF5388F55AFAE53E //A1
|
|
data8 0x4566A1AAD96EBCB5, 0x421F0FEFE2444293 //A2
|
|
data8 0x8F8D4D3DE9850DB2, 0x0000C082 //A3
|
|
data8 0x800BDD6DA2CE184C, 0x000040AE //A4
|
|
data8 0xF3A8EC4C9CDC7A43, 0x0000C0D9 //A5
|
|
data8 0x505E2FAFDB81263F //A6
|
|
data8 0xD31EC5B3A7506CD9 //A7
|
|
data8 0x55E002F77E999810 //A8
|
|
data8 0xD8A0ED4C9B5C2900 //A9
|
|
data8 0x5B621E4A8267C401 //A10
|
|
data8 0xDE2396E5BFCFDA7A //A11
|
|
data8 0x60E55B43BE6F9A79 //A12
|
|
data8 0xE3A772324C7405FA //A13
|
|
data8 0x6669E4E9B7E57A2D //A14
|
|
data8 0xE92CB989F8A8FB37 //A15
|
|
data8 0x6BEFF2368849A36E //A16
|
|
data8 0xEEB23234FE191D55 //A17
|
|
data8 0x7175EF5D1080B105 //A18
|
|
data8 0xF4342ED7B1B7BE31 //A19
|
|
// Polynomial coefficients for left root on [-17, -16]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBF28AEEE7B58C790, 0xBBC4448DE371FA0A //A0
|
|
data8 0xC2F436F56B3B89B1, 0xBF636755245AC63A //A1
|
|
data8 0x45E98A22535D115D, 0x4298467DA93DB784 //A2
|
|
data8 0xAC176F3775E6FCF2, 0x0000C08E //A3
|
|
data8 0xA3114F53A9FEB908, 0x000040BE //A4
|
|
data8 0xA4D168A8334AFE5A, 0x0000C0EE //A5
|
|
data8 0x51E5B0E7EC7182CF //A6
|
|
data8 0xD4E77D67B876D6B4 //A7
|
|
data8 0x57E9F7C30C098C83 //A8
|
|
data8 0xDAED29B0489EF7A7 //A9
|
|
data8 0x5DF09486F8A524B8 //A10
|
|
data8 0xE0F30B19910A2393 //A11
|
|
data8 0x63F60E02AB3109F4 //A12
|
|
data8 0xE6F9B8A3431854D5 //A13
|
|
data8 0x69FE2D4A6D94218E //A14
|
|
data8 0xED01C7E272A73560 //A15
|
|
data8 0x7005017D82B186B6 //A16
|
|
data8 0xF3096A81A69BD8AE //A17
|
|
data8 0x76104951BAD67D5C //A18
|
|
data8 0xF90FECC99786FD5B //A19
|
|
// Polynomial coefficients for left root on [-18, -17]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0x3F3C19A53328E26A, 0x3BE238D7BA036B3B //A0
|
|
data8 0xC336C16C16C16C13, 0xBFEACE245DEC56F3 //A1
|
|
data8 0x46702E85C0898B70, 0x432C922B64FD1DA4 //A2
|
|
data8 0xF57B99A1C0343350, 0x0000C09A //A3
|
|
data8 0x82EC9634223DF90D, 0x000040CF //A4
|
|
data8 0x94F66D7557E3237D, 0x0000C103 //A5
|
|
data8 0x5376118B79AE34D6 //A6
|
|
data8 0xD6BAE7106D52CE49 //A7
|
|
data8 0x5A00BD48CC8E11AB //A8
|
|
data8 0xDD4529722833E2DF //A9
|
|
data8 0x608B1654AF5F46AF //A10
|
|
data8 0xE3D182CC90D8723F //A11
|
|
data8 0x6716D43D46706AA0 //A12
|
|
data8 0xEA5DF888C5B428D3 //A13
|
|
data8 0x6DA3CA85888931A6 //A14
|
|
data8 0xF0EA40EF2AC7E070 //A15
|
|
data8 0x743175D1A251AFCD //A16
|
|
data8 0xF777CB6E2B550D73 //A17
|
|
data8 0x7AC11E468A134A51 //A18
|
|
data8 0xFE02B6BDD0FC40AA //A19
|
|
// Polynomial coefficients for left root on [-19, -18]
|
|
// Lgammal is approximated by polynomial within [.157807 ; -.157807 ] range
|
|
data8 0xBFAB767F9BE217FC, 0xBC4A5541CE0D8D0D //A0
|
|
data8 0xC379999999999999, 0xC01A84981B490BE8 //A1
|
|
data8 0x46F47AE147AE147A, 0x43AC2987BBC466EB //A2
|
|
data8 0xAEC33E1F67152987, 0x0000C0A7 //A3
|
|
data8 0xD1B71758E2196153, 0x000040DF //A4
|
|
data8 0x8637BD05AF6D420E, 0x0000C118 //A5
|
|
data8 0x55065E9F80F293B2 //A6
|
|
data8 0xD88EADA78C44BFA7 //A7
|
|
data8 0x5C15798EE22EC6CD //A8
|
|
data8 0xDF9E8ABFD67895CF //A9
|
|
data8 0x6325FD7FE13B0DE0 //A10
|
|
data8 0xE6AFFC5C3DE70858 //A11
|
|
data8 0x6A3774CE81C70D43 //A12
|
|
data8 0xEDC1527412D8129F //A13
|
|
data8 0x7149BABCDA8B7A72 //A14
|
|
data8 0xF4D330AD49071BB5 //A15
|
|
data8 0x785D4046F4C5F1FD //A16
|
|
data8 0xFBE59BFEDBA73FAF //A17
|
|
data8 0x7F64BEF2B2EC8DA1 //A18
|
|
data8 0xFFEFFFFFFFFFFFFF //A19
|
|
LOCAL_OBJECT_END(lgammal_left_roots_polynomial_data)
|
|
|
|
|
|
//==============================================================
|
|
// Code
|
|
//==============================================================
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(__libm_lgammal)
|
|
{ .mfi
|
|
getf.exp rSignExpX = f8
|
|
// Test x for NaTVal, NaN, +/-0, +/-INF, denormals
|
|
fclass.m p6,p0 = f8,0x1EF
|
|
addl r17Ones = 0x1FFFF, r0 // exponent mask
|
|
}
|
|
{ .mfi
|
|
addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
|
|
fcvt.fx.s1 fXint = f8 // Convert arg to int (int repres. in FR)
|
|
adds rDelta = 0x3FC, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.sig rSignifX = f8
|
|
fcmp.lt.s1 p15, p14 = f8, f0
|
|
shl rDelta = rDelta, 20 // single precision 1.5
|
|
}
|
|
{ .mfi
|
|
ld8 GR_ad_z_1 = [GR_ad_z_1]// get pointer to Constants_Z_1
|
|
fma.s1 fTwo = f1, f1, f1 // 2.0
|
|
addl rExp8 = 0x10002, r0 // exponent of 8.0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
alloc rPFS_SAVED = ar.pfs, 0, 34, 4, 0 // get some registers
|
|
fmerge.s fAbsX = f1, f8 // |x|
|
|
and rExpX = rSignExpX, r17Ones // mask sign bit
|
|
}
|
|
{ .mib
|
|
addl rExpHalf = 0xFFFE, r0 // exponent of 0.5
|
|
addl rExp2 = 0x10000, r0 // exponent of 2.0
|
|
// branch out if x is NaTVal, NaN, +/-0, +/-INF, or denormalized number
|
|
(p6) br.cond.spnt lgammal_spec
|
|
}
|
|
;;
|
|
_deno_back_to_main_path:
|
|
{ .mfi
|
|
// Point to Constants_G_H_h1
|
|
add rTbl1Addr = 0x040, GR_ad_z_1
|
|
frcpa.s1 fRcpX, p0 = f1, f8 // initial approximation of 1/x
|
|
extr.u GR_Index1 = rSignifX, 59, 4
|
|
}
|
|
{ .mib
|
|
(p14) cmp.ge.unc p8, p0 = rExpX, rExp8 // p8 = 1 if x >= 8.0
|
|
adds rZ625 = 0x3F2, r0
|
|
(p8) br.cond.spnt lgammal_big_positive // branch out if x >= 8.0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd rZ1offsett = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
fmerge.se fSignifX = f1, f8 // sifnificand of x
|
|
// Get high 15 bits of significand
|
|
extr.u GR_X_0 = rSignifX, 49, 15
|
|
}
|
|
{ .mib
|
|
cmp.lt.unc p9, p0 = rExpX, rExpHalf // p9 = 1 if |x| < 0.5
|
|
// set p11 if 2 <= x < 4
|
|
(p14) cmp.eq.unc p11, p0 = rExpX, rExp2
|
|
(p9) br.cond.spnt lgammal_0_half // branch out if |x| < 0.5
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [rZ1offsett] // Load Z_1
|
|
fms.s1 fA5L = f1, f1, f8 // for 0.75 <= x < 1.3125 path
|
|
shl rZ625 = rZ625, 20 // sinfle precision 0.625
|
|
}
|
|
{ .mib
|
|
setf.s FR_MHalf = rDelta
|
|
// set p10 if x >= 4.0
|
|
(p14) cmp.gt.unc p10, p0 = rExpX, rExp2
|
|
// branch to special path for 4.0 <= x < 8
|
|
(p10) br.cond.spnt lgammal_4_8
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// for 1.3125 <= x < 1.5625 path
|
|
addl rPolDataPtr= @ltoff(lgammal_loc_min_data),gp
|
|
// argument of polynomial approximation for 1.5625 <= x < 2.25
|
|
fms.s1 fB4 = f8, f1, fTwo
|
|
cmp.eq p12, p0 = rExpX, rExpHalf
|
|
}
|
|
{ .mib
|
|
addl rExpOne = 0xFFFF, r0 // exponent of 1.0
|
|
// set p10 if significand of x >= 1.125
|
|
(p11) cmp.le p11, p0 = 2, GR_Index1
|
|
(p11) br.cond.spnt lgammal_2Q_4
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// point to xMin for 1.3125 <= x < 1.5625 path
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
fcvt.xf fFltIntX = fXint // RTN(x)
|
|
(p14) cmp.eq.unc p13, p7 = rExpX, rExpOne // p13 set if 1.0 <= x < 2.0
|
|
}
|
|
{ .mib
|
|
setf.s FR_FracX = rZ625
|
|
// set p12 if |x| < 0.75
|
|
(p12) cmp.gt.unc p12, p0 = 8, GR_Index1
|
|
// branch out to special path for |x| < 0.75
|
|
(p12) br.cond.spnt lgammal_half_3Q
|
|
}
|
|
;;
|
|
.pred.rel "mutex", p7, p13
|
|
{ .mfi
|
|
getf.sig rXRnd = fXint // integer part of the input value
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 1st NR iteration
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
|
|
}
|
|
{ .mib
|
|
(p7) cmp.eq p6, p0 = rExpX, rExp2 // p6 set if 2.0 <= x < 2.25
|
|
(p13) cmp.le p6, p0 = 9, GR_Index1
|
|
// branch to special path 1.5625 <= x < 2.25
|
|
(p6) br.cond.spnt lgammal_13Q_2Q
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr // Point to G_1
|
|
fma.s1 fSix = fTwo, fTwo, fTwo // 6.0
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q
|
|
}
|
|
{ .mib
|
|
add rTmpPtr3 = -0x50, GR_ad_z_1
|
|
(p13) cmp.gt p7, p0 = 5, GR_Index1
|
|
// branch to special path 0.75 <= x < 1.3125
|
|
(p7) br.cond.spnt lgammal_03Q_1Q
|
|
}
|
|
;;
|
|
{ .mfi
|
|
add rTmpPtr = 8, GR_ad_tbl_1
|
|
fma.s1 fRoot = f8, f1, f1 // x + 1
|
|
// Absolute value of int arg. Will be used as index in table with roots
|
|
sub rXRnd = r0, rXRnd
|
|
}
|
|
{ .mib
|
|
ldfe fA5L = [rPolDataPtr], 16 // xMin
|
|
addl rNegSingularity = 0x3003E, r0
|
|
(p14) br.cond.spnt lgammal_loc_min
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1], 8 // Load G_1, H_1
|
|
nop.f 0
|
|
add rZ2Addr = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
}
|
|
{ .mib
|
|
ldfd FR_h = [rTmpPtr] // Load h_1
|
|
// If arg is less or equal to -2^63
|
|
cmp.geu.unc p8,p0 = rSignExpX, rNegSingularity
|
|
// Singularity for x < -2^63 since all such arguments are integers
|
|
// branch to special code which deals with singularity
|
|
(p8) br.cond.spnt lgammal_singularity
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q], 32 // Load log2_hi
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [rTmpPtr3], 32 // Load log2_lo
|
|
fms.s1 fDx = f8, f1, fFltIntX // x - RTN(x)
|
|
// index in table with roots and bounds
|
|
adds rXint = -2, rXRnd
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q], 32 // Load Q4
|
|
nop.f 0
|
|
// set p12 if x may be close to negative root: -19.5 < x < -2.0
|
|
cmp.gtu p12, p0 = 18, rXint
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2
|
|
fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 1st NR iteration
|
|
// Point to Constants_G_H_h2
|
|
add rTbl2Addr = 0x180, GR_ad_z_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2
|
|
// set p9 if x is integer and negative
|
|
fcmp.eq.s1 p9, p0 = f8,fFltIntX
|
|
// Point to Constants_G_H_h3
|
|
add rTbl3Addr = 0x280, GR_ad_z_1
|
|
}
|
|
{ .mfi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
nop.f 0
|
|
sub GR_N = rExpX, rExpHalf, 1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q3 = [rTmpPtr3], 32 // Load Q3
|
|
nop.f 0
|
|
// Point to lnsin polynomial coefficients
|
|
adds rLnSinDataPtr = 864, rTbl3Addr
|
|
}
|
|
{ .mfi
|
|
ldfe FR_Q2 = [GR_ad_q],32 // Load Q2
|
|
nop.f 0
|
|
add rTmpPtr = 8, GR_ad_tbl_2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q1 = [rTmpPtr3] // Load Q1
|
|
fcmp.lt.s1 p0, p15 = fAbsX, fSix // p15 is set when x < -6.0
|
|
// point to table with roots and bounds
|
|
adds rRootsBndAddr = -1296, GR_ad_z_1
|
|
}
|
|
{ .mfb
|
|
// Put integer N into rightmost significand
|
|
setf.sig fFloatN = GR_N
|
|
fma.s1 fThirteen = fSix, fTwo, f1 // 13.0
|
|
// Singularity if -2^63 < x < 0 and x is integer
|
|
// branch to special code which deals with singularity
|
|
(p9) br.cond.spnt lgammal_singularity
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2] // Load G_2, H_2
|
|
// y = |x|/2^(exponent(x)) - 1.5
|
|
fms.s1 FR_FracX = fSignifX, f1, FR_MHalf
|
|
// Get bits 30-15 of X_1 * Z_2
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h2 = [rTmpPtr] // Load h_2
|
|
fma.s1 fDxSqr = fDx, fDx, f0 // deltaX^2
|
|
adds rTmpPtr3 = 128, rLnSinDataPtr
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
getf.exp rRoot = fRoot // sign and biased exponent of (x + 1)
|
|
nop.f 0
|
|
// set p6 if -4 < x <= -2
|
|
cmp.eq p6, p0 = rExpX, rExp2
|
|
}
|
|
{ .mfi
|
|
ldfpd fLnSin2, fLnSin2L = [rLnSinDataPtr], 16
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 2nd NR iteration
|
|
sub rIndexPol = rExpX, rExpHalf // index of polynom
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin4 = [rLnSinDataPtr], 96
|
|
// p10 is set if x is potential "right" root
|
|
// p11 set for possible "left" root
|
|
fcmp.lt.s1 p10, p11 = fDx, f0
|
|
shl rIndexPol = rIndexPol, 6 // (i*16)*4
|
|
}
|
|
{ .mfi
|
|
ldfpd fLnSin18, fLnSin20 = [rTmpPtr3], 16
|
|
nop.f 0
|
|
mov rExp2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.sig rSignifDx = fDx // Get significand of RTN(x)
|
|
nop.f 0
|
|
// set p6 if -4 < x <= -3.0
|
|
(p6) cmp.le.unc p6, p0 = 0x8, GR_Index1
|
|
}
|
|
{ .mfi
|
|
ldfpd fLnSin22, fLnSin24 = [rTmpPtr3], 16
|
|
nop.f 0
|
|
// mask sign bit in the exponent of (x + 1)
|
|
and rRoot = rRoot, r17Ones
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin16 = [rLnSinDataPtr], -80
|
|
nop.f 0
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
{ .mfi
|
|
ldfpd fLnSin26, fLnSin28 = [rTmpPtr3], 16
|
|
nop.f 0
|
|
and rXRnd = 1, rXRnd
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3
|
|
fms.s1 fDxSqrL = fDx, fDx, fDxSqr // low part of deltaX^2
|
|
// potential "left" root
|
|
(p11) adds rRootsBndAddr = 560, rRootsBndAddr
|
|
}
|
|
{ .mib
|
|
ldfpd fLnSin30, fLnSin32 = [rTmpPtr3], 16
|
|
// set p7 if |x+1| < 2^-7
|
|
cmp.lt p7, p0 = rRoot, rExp2tom7
|
|
// branch to special path for |x+1| < 2^-7
|
|
(p7) br.cond.spnt _closeToNegOne
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3
|
|
fcmp.lt.s1 p14, p0 = fAbsX, fThirteen // set p14 if x > -13.0
|
|
// base address of polynomial on range [-6.0, -0.75]
|
|
adds rPolDataPtr = 3440, rTbl3Addr
|
|
}
|
|
{ .mfi
|
|
// (i*16)*4 + (i*16)*8 - offsett of polynomial on range [-6.0, -0.75]
|
|
shladd rTmpPtr = rIndexPol, 2, rIndexPol
|
|
fma.s1 fXSqr = FR_FracX, FR_FracX, f0 // y^2
|
|
// point to left "near root" bound
|
|
(p12) shladd rRootsBndAddr = rXint, 4, rRootsBndAddr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fLnSin34, fLnSin36 = [rTmpPtr3], 16
|
|
fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 2nd NR iteration
|
|
// add special offsett if -4 < x <= -3.0
|
|
(p6) adds rPolDataPtr = 640, rPolDataPtr
|
|
}
|
|
{ .mfi
|
|
// point to right "near root" bound
|
|
adds rTmpPtr2 = 8, rRootsBndAddr
|
|
fnma.s1 fMOne = f1, f1, f0 // -1.0
|
|
// Point to Bernulli numbers
|
|
adds rBernulliPtr = 544, rTbl3Addr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// left bound of "near root" range
|
|
(p12) ld8 rLeftBound = [rRootsBndAddr]
|
|
fmerge.se fNormDx = f1, fDx // significand of DeltaX
|
|
// base address + offsett for polynomial coeff. on range [-6.0, -0.75]
|
|
add rPolDataPtr = rPolDataPtr, rTmpPtr
|
|
}
|
|
{ .mfi
|
|
// right bound of "near root" range
|
|
(p12) ld8 rRightBound = [rTmpPtr2]
|
|
fcvt.xf fFloatN = fFloatN
|
|
// special "Bernulli" numbers for Stirling's formula for -13 < x < -6
|
|
(p14) adds rBernulliPtr = 160, rBernulliPtr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
adds rTmpPtr3 = -160, rTmpPtr3
|
|
}
|
|
{ .mfb
|
|
adds rTmpPtr = 80, rPolDataPtr
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
// p15 is set if -2^63 < x < 6.0 and x is not an integer
|
|
// branch to path with implementation using Stirling's formula for neg. x
|
|
(p15) br.cond.spnt _negStirling
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA3, fA3L = [rPolDataPtr], 16 // A3
|
|
fma.s1 fDelX4 = fDxSqr, fDxSqr, f0 // deltaX^4
|
|
// Get high 4 bits of signif
|
|
extr.u rIndex1Dx = rSignifDx, 59, 4
|
|
}
|
|
{ .mfi
|
|
ldfe fA5 = [rTmpPtr], -16 // A5
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
adds rLnSinTmpPtr = 16, rLnSinDataPtr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0
|
|
fma.s1 fLnSin20 = fLnSin20, fDxSqr, fLnSin18
|
|
// Get high 15 bits of significand
|
|
extr.u rX0Dx = rSignifDx, 49, 15
|
|
}
|
|
{ .mfi
|
|
ldfe fA4 = [rTmpPtr], 192 // A4
|
|
fms.s1 fXSqrL = FR_FracX, FR_FracX, fXSqr // low part of y^2
|
|
shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1
|
|
fma.s1 fX4 = fXSqr, fXSqr, f0 // y^4
|
|
adds rTmpPtr2 = 32, rTmpPtr
|
|
}
|
|
{ .mfi
|
|
ldfpd fA18, fA19 = [rTmpPtr], 16 // A18, A19
|
|
fma.s1 fLnSin24 = fLnSin24, fDxSqr, fLnSin22
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin6 = [rLnSinDataPtr], 32
|
|
fma.s1 fLnSin28 = fLnSin28, fDxSqr, fLnSin26
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin8 = [rLnSinTmpPtr], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA20, fA21 = [rTmpPtr], 16 // A20, A21
|
|
fma.s1 fLnSin32 = fLnSin32, fDxSqr, fLnSin30
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA22, fA23 = [rTmpPtr2], 16 // A22, A23
|
|
fma.s1 fB20 = f1, f1, FR_MHalf // 2.5
|
|
(p12) cmp.ltu.unc p6, p0 = rSignifX, rLeftBound
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
// set p6 if x falls in "near root" range
|
|
(p6) cmp.geu.unc p6, p0 = rSignifX, rRightBound
|
|
}
|
|
{ .mfb
|
|
adds rTmpPtr3 = -64, rTmpPtr
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
// branch to special path if x falls in "near root" range
|
|
(p6) br.cond.spnt _negRoots
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA24, fA25 = [rTmpPtr2], 16 // A24, A25
|
|
fma.s1 fLnSin36 = fLnSin36, fDxSqr, fLnSin34
|
|
(p11) cmp.eq.unc p7, p0 = 1,rXint // p7 set if -3.0 < x < -2.5
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr = -48, rTmpPtr
|
|
fma.s1 fLnSin20 = fLnSin20, fDxSqr, fLnSin16
|
|
addl rDelta = 0x5338, r0 // significand of -2.605859375
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.exp GR_N = fDx // Get N = exponent of DeltaX
|
|
fma.s1 fX6 = fX4, fXSqr, f0 // y^6
|
|
// p7 set if -2.605859375 <= x < -2.5
|
|
(p7) cmp.gt.unc p7, p0 = rDelta, GR_X_0
|
|
}
|
|
{ .mfb
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
fma.s1 fDelX8 = fDelX4, fDelX4, f0 // deltaX^8
|
|
// branch to special path for -2.605859375 <= x < -2.5
|
|
(p7) br.cond.spnt _neg2andHalf
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA14, fA15 = [rTmpPtr3], 16 // A14, A15
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
adds rTmpPtr2 = 128 , rPolDataPtr
|
|
}
|
|
{ .mfi
|
|
ldfpd fA16, fA17 = [rTmpPtr], 16 // A16, A17
|
|
fma.s1 fLnSin28 = fLnSin28, fDelX4, fLnSin24
|
|
adds rPolDataPtr = 144 , rPolDataPtr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin10 = [rLnSinDataPtr], 32
|
|
fma.s1 fRes1H = fA3, FR_FracX, f0 // (A3*y)hi
|
|
and GR_N = GR_N, r17Ones // mask sign bit
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin12 = [rLnSinTmpPtr]
|
|
fma.s1 fDelX6 = fDxSqr, fDelX4, f0 // DeltaX^6
|
|
shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA13 = [rPolDataPtr], -32 // A13
|
|
fma.s1 fA4 = fA5, FR_FracX, fA4 // A5*y + A4
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = rX0Dx, GR_Z_1, 15
|
|
}
|
|
{ .mfi
|
|
ldfe fA12 = [rTmpPtr2], -32 // A12
|
|
fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1
|
|
sub GR_N = GR_N, rExpHalf, 1 // unbisaed exponent of DeltaX
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
.pred.rel "mutex",p10,p11
|
|
{ .mfi
|
|
ldfe fA11 = [rPolDataPtr], -32 // A11
|
|
// High part of log(|x|) = Y_hi = N * log2_hi + H
|
|
fma.s1 fResH = fFloatN, FR_log2_hi, FR_H
|
|
(p10) cmp.eq p8, p9 = rXRnd, r0
|
|
}
|
|
{ .mfi
|
|
ldfe fA10 = [rTmpPtr2], -32 // A10
|
|
fma.s1 fRes6H = fA1, FR_FracX, f0 // (A1*y)hi
|
|
(p11) cmp.eq p9, p8 = rXRnd, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA9 = [rPolDataPtr], -32 // A9
|
|
fma.s1 fB14 = fLnSin6, fDxSqr, f0 // (LnSin6*deltaX^2)hi
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
{ .mfi
|
|
ldfe fA8 = [rTmpPtr2], -32 // A8
|
|
fma.s1 fA18 = fA19, FR_FracX, fA18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA7 = [rPolDataPtr] // A7
|
|
fma.s1 fA23 = fA23, FR_FracX, fA22
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA6 = [rTmpPtr2] // A6
|
|
fma.s1 fA21 = fA21, FR_FracX, fA20
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin14 = [rLnSinDataPtr]
|
|
fms.s1 fRes1L = fA3, FR_FracX, fRes1H // delta((A3*y)hi)
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
setf.sig fFloatNDx = GR_N
|
|
fadd.s1 fPol = fRes1H, fA2 // (A3*y + A2)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1], 8 // Load G_1, H_1
|
|
fma.s1 fRes2H = fA4, fXSqr, f0 // ((A5 + A4*y)*y^2)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2
|
|
fma.s1 fA25 = fA25, FR_FracX, fA24
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p8,p9
|
|
{ .mfi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
fms.s1 fRes6L = fA1, FR_FracX, fRes6H // delta((A1*y)hi)
|
|
// sign of GAMMA(x) is negative
|
|
(p8) adds rSgnGam = -1, r0
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr = 8, GR_ad_tbl_2
|
|
fadd.s1 fRes3H = fRes6H, fA0 // (A1*y + A0)hi
|
|
// sign of GAMMA(x) is positive
|
|
(p9) adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2] // Load G_2, H_2
|
|
// (LnSin6*deltaX^2 + LnSin4)hi
|
|
fadd.s1 fLnSinH = fB14, fLnSin4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h2 = [rTmpPtr] // Load h_2
|
|
fms.s1 fB16 = fLnSin6, fDxSqr, fB14 // delta(LnSin6*deltaX^2)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fhDelX = [GR_ad_tbl_1] // Load h_1
|
|
fma.s1 fA21 = fA21, fXSqr, fA18
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDelX4, fLnSin32
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1L = fA3L, FR_FracX, fRes1L // (A3*y)lo
|
|
// Get bits 30-15 of X_1 * Z_
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fPolL = fA2, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
nop.m 0
|
|
// delta(((A5 + A4*y)*y^2)hi)
|
|
fms.s1 fRes2L = fA4, fXSqr, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (((A5 + A4*y)*y^2) + A3*y + A2)hi
|
|
fadd.s1 fRes4H = fRes2H, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fRes6L = fA1L, FR_FracX, fRes6L // (A1*y)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fsub.s1 fRes3L = fA0, fRes3H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fLnSinL = fLnSin4, fLnSinH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)hi
|
|
fma.s1 fB18 = fLnSinH, fDxSqr, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
adds rTmpPtr = 8, rTbl3Addr
|
|
fma.s1 fB16 = fLnSin6, fDxSqrL, fB16 // (LnSin6*deltaX^2)lo
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fXSqr, fA23
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3
|
|
fadd.s1 fPolL = fPolL, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
shladd rTmpPtr = GR_Index3, 4, rTmpPtr // Point to G_3
|
|
fadd.s1 fRes1L = fRes1L, fA2L // (A3*y)lo + A2lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3] // Load G_3, H_3
|
|
fma.s1 fRes2L = fA4, fXSqrL, fRes2L // ((A5 + A4*y)*y^2)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h3 = [rTmpPtr] // Load h_3
|
|
fsub.s1 fRes4L = fPol, fRes4H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)hi
|
|
fma.s1 fRes7H = fRes4H, fXSqr, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, FR_FracX, fA14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fRes6H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes6L = fRes6L, fA0L // (A1*y)lo + A0lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSinL = fLnSinL, fB14
|
|
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// delta((LnSin6*deltaX^2 + LnSin4)*deltaX^2)
|
|
fms.s1 fB20 = fLnSinH, fDxSqr, fB18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fPolL = fPolL, fRes1L // (A3*y + A2)lo
|
|
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)hi
|
|
fadd.s1 fLnSin6 = fB18, fLnSin2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, FR_FracX, fA16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// delta(((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)
|
|
fms.s1 fRes7L = fRes4H, fXSqr, fRes7H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fPol = fRes7H, fRes3H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fRes6L // (A1*y + A0)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fX4, fA21
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (LnSin6*deltaX^2 + LnSin4)lo
|
|
fadd.s1 fLnSinL = fLnSinL, fB16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB20 = fLnSinH, fDxSqrL, fB20
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fLnSin4 = fLnSin2, fLnSin6
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)*DeltaX^2)hi
|
|
fma.s1 fLnSinH = fLnSin6, fDxSqr, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((A5 + A4*y)*y^2)lo + (A3*y + A2)lo
|
|
fadd.s1 fRes2L = fRes2L, fPolL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fXSqr, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)lo
|
|
fma.s1 fRes7L = fRes4H, fXSqrL, fRes7L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fPolL = fRes3H, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, FR_FracX, fA12
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, FR_FracX, fA10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)lo
|
|
fma.s1 fB20 = fLnSinL, fDxSqr, fB20
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSin4 = fLnSin4, fB18
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fLnSinL = fLnSin6, fDxSqr, fLnSinH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (((A5 + A4*y)*y^2) + A3*y + A2)lo
|
|
fadd.s1 fRes4L = fRes4L, fRes2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fhDelX = fhDelX, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes7L = fRes7L, fRes3L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fPolL = fPolL, fRes7H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fcvt.xf fFloatNDx = fFloatNDx
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((LnSin6*deltaX^2 + LnSin4)*deltaX^2)lo + (LnSin2)lo
|
|
fadd.s1 fLnSin2L = fLnSin2L, fB20
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fX4, fA17
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, fXSqr, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_FracX, fA8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, FR_FracX, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDelX8, fLnSin28
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin14, fDxSqr, fLnSin12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin10 = fLnSin10, fDxSqr, fLnSin8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRDx = FR_G, fNormDx, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((((A5 + A4*y)*y^2) + A3*y + A2)*y^2)lo + (A1*y + A0)lo
|
|
fma.s1 fRes7L = fRes4L, fXSqr, fRes7L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fX4, fA13
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, fXSqr, fA7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fhDelX = fhDelX, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDelX6, fLnSin20
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin14, fDelX4, fLnSin10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 fPolyLoDx = fRDx, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 fRDxSq = fRDx, fRDx // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_hi = N * log2_hi + H
|
|
fma.s1 fResLnDxH = fFloatNDx, FR_log2_hi, FR_H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA25, fX4, fA9
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fPolL = fPolL, fRes7L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSin4 = fLnSin4, fLnSin2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fma.s1 fhDelX = fFloatNDx, FR_log2_lo, fhDelX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDelX8, fLnSin14
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)lo
|
|
fma.s1 fLnSinL = fLnSin6, fDxSqrL, fLnSinL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 fPolyLoDx = fPolyLoDx, fRDx, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRDxCub = fRDxSq, fRDx, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
famax.s0 fRes5H = fPol, fResH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of (lgammal(|x|) + log(|x|))
|
|
fadd.s1 fRes1H = fPol, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fA9, fX6, fPolL // P25lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
famin.s0 fRes5L = fPol, fResH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of -(LnSin + log(|DeltaX|))
|
|
fnma.s1 fRes2H = fResLnDxH, f1, fLnSinH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// (((LnSin6*deltaX^2 + LnSin4)*deltaX^2 + LnSin2)*DeltaX^2)lo
|
|
fma.s1 fLnSinL = fLnSin4, fDxSqr, fLnSinL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDelX6, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 fPolyHiDx = FR_Q1, fRDxSq, fRDx
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 fPolyLoDx = fPolyLoDx, fRDxCub, fhDelX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes1L = fRes5H, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// -(lgammal(|x|) + log(|x|))hi
|
|
fnma.s1 fRes1H = fRes1H, f1, f0
|
|
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes2L = fResLnDxH, fMOne, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSinL = fLnSin36, fDxSqr, fLnSinL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fResLnDxL = fPolyHiDx, fPolyLoDx
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fRes5L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// high part of the final result
|
|
fadd.s1 fYH = fRes2H, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fResL = FR_poly_hi, FR_poly_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
famax.s0 fRes4H = fRes2H, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
famin.s0 fRes4L = fRes2H, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (LnSin)lo + (log(|DeltaX|))lo
|
|
fsub.s1 fLnSinL = fLnSinL, fResLnDxL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fLnSinH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
//(lgammal(|x|))lo + (log(|x|))lo
|
|
fadd.s1 fPolL = fResL, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fYL = fRes4H, fYH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Low part of -(LnSin + log(|DeltaX|))
|
|
fadd.s1 fRes2L = fRes2L, fLnSinL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of (lgammal(|x|) + log(|x|))
|
|
fadd.s1 fRes1L = fRes1L, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fYL = fYL, fRes4L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes2L = fRes2L, fRes1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// low part of the final result
|
|
fadd.s1 fYL = fYL, fRes2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for -6.0 < x <= -0.75, non-integer, "far" from roots
|
|
fma.s0 f8 = fYH, f1, fYL
|
|
// exit here for -6.0 < x <= -0.75, non-integer, "far" from roots
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x+1| < 2^(-7)
|
|
.align 32
|
|
_closeToNegOne:
|
|
{ .mfi
|
|
getf.exp GR_N = fDx // Get N = exponent of x
|
|
fmerge.se fAbsX = f1, fDx // Form |deltaX|
|
|
// Get high 4 bits of significand of deltaX
|
|
extr.u rIndex1Dx = rSignifDx, 59, 4
|
|
}
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_1pEps_data),gp
|
|
fma.s1 fA0L = fDxSqr, fDxSqr, f0 // deltaX^4
|
|
// sign of GAMMA is positive if p10 is set to 1
|
|
(p10) adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1
|
|
fnma.s1 fResL = fDx, f1, f0 // -(x+1)
|
|
// Get high 15 bits of significand
|
|
extr.u GR_X_0 = rSignifDx, 49, 15
|
|
}
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.f 0
|
|
and GR_N = GR_N, r17Ones // mask sign bit
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr = 8, GR_ad_tbl_1
|
|
nop.f 0
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
nop.f 0
|
|
adds rTmpPtr2 = 96, rPolDataPtr
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h = [rTmpPtr] // Load h_1
|
|
nop.f 0
|
|
// unbiased exponent of deltaX
|
|
sub GR_N = GR_N, rExpHalf, 1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
adds rTmpPtr3 = 192, rPolDataPtr
|
|
nop.f 0
|
|
// sign of GAMMA is negative if p11 is set to 1
|
|
(p11) adds rSgnGam = -1, r0
|
|
}
|
|
{ .mfi
|
|
ldfe fA1 = [rPolDataPtr], 16 // A1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA2 = [rPolDataPtr], 16 // A2
|
|
nop.f 0
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
|
|
}
|
|
{ .mfi
|
|
ldfpd fA20, fA19 = [rTmpPtr2], 16 // P8, P7
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe fA3 = [rPolDataPtr], 16 // A3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA18, fA17 = [rTmpPtr2], 16 // P6, P5
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA4 = [rPolDataPtr], 16 // A4
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA16, fA15 = [rTmpPtr2], 16 // P4, p3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA5L, fA6 = [rPolDataPtr], 16 // A5, A6
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA14, fA13 = [rTmpPtr2], 16 // P2, P1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA7, fA8 = [rPolDataPtr], 16 // A7, A8
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin2 = [rTmpPtr2], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2
|
|
nop.f 0
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin4 = [rTmpPtr2], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
nop.f 0
|
|
adds rTmpPtr = 8, GR_ad_tbl_2
|
|
}
|
|
{ .mfi
|
|
// Put integer N into rightmost significand
|
|
setf.sig fFloatN = GR_N
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin6 = [rTmpPtr3]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin8 = [rTmpPtr2]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h2 = [rTmpPtr] // Load h_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fResH = fA20, fResL, fA19 //polynomial for log(|x|)
|
|
// Get bits 30-15 of X_1 * Z_2
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA2 = fA2, fDx, fA1 // polynomial for lgammal(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA18 = fA18, fResL, fA17 //polynomial for log(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA16 = fA16, fResL, fA15 //polynomial for log(|x|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4 = fA4, fDx, fA3 // polynomial for lgammal(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA14 = fA14, fResL, fA13 //polynomial for log(|x|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA6 = fA6, fDx, fA5L // polynomial for lgammal(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA8, fDx, fA7 // polynomial for lgammal(|x|)
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3
|
|
// loqw part of lnsin polynomial
|
|
fma.s1 fRes3L = fLnSin4, fDxSqr, fLnSin2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3
|
|
fcvt.xf fFloatN = fFloatN // N as FP number
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fResH, fDxSqr, fA18 // High part of log(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fma.s1 fA4 = fA4, fDxSqr, fA2 // Low part of lgammal(|x|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// high part of lnsin polynomial
|
|
fma.s1 fRes3H = fLnSin8, fDxSqr, fLnSin6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA16 = fA16, fDxSqr, fA14 // Low part of log(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fDxSqr, fA6 // High part of lgammal(|x|)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fResH, fA0L, fA16 // log(|x|)/deltaX^2 - deltaX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fResH, fDxSqr, fResL // log(|x|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fA0L, fA4 // lgammal(|x|)/|x|
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, fAbsX, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// high part of log(deltaX)= Y_hi = N * log2_hi + H
|
|
fma.s1 fRes4H = fFloatN, FR_log2_hi, FR_H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fPol, fDx, fResH // lgammal(|x|) + log(|x|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// lnsin/deltaX^2
|
|
fma.s1 fRes3H = fRes3H, fA0L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// lnSin - log(|x|) - lgammal(|x|)
|
|
fms.s1 fResH = fRes3H, fDxSqr, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// low part of log(|deltaX|) = Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fRes4L = FR_poly_hi, FR_poly_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fResH = fResH, fRes4L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for |x+1|< 2^(-7) path
|
|
fsub.s0 f8 = fResH, fRes4H
|
|
// exit for |x+1|< 2^(-7) path
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
|
|
// here if -2^63 < x < -6.0 and x is not an integer
|
|
// Also we are going to filter out cases when x falls in
|
|
// range which is "close enough" to negative root. Rhis case
|
|
// may occur only for -19.5 < x since other roots of lgamma are
|
|
// insignificant from double extended point of view (they are closer
|
|
// to RTN(x) than one ulp(x).
|
|
.align 32
|
|
_negStirling:
|
|
{ .mfi
|
|
ldfe fLnSin6 = [rLnSinDataPtr], 32
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 3rd NR iteration
|
|
// Get high 4 bits of significand of deltaX
|
|
extr.u rIndex1Dx = rSignifDx, 59, 4
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin8 = [rTmpPtr3], 32
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
(p12) cmp.ltu.unc p6, p0 = rSignifX, rLeftBound
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin10 = [rLnSinDataPtr], 32
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
// Get high 15 bits of significand
|
|
extr.u GR_X_0 = rSignifDx, 49, 15
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_1 = rIndex1Dx, 2, GR_ad_z_1 // Point to Z_1
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
// set p6 if x falls in "near root" range
|
|
(p6) cmp.geu.unc p6, p0 = rSignifX, rRightBound
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.exp GR_N = fDx // Get N = exponent of x
|
|
fma.s1 fDx4 = fDxSqr, fDxSqr, f0 // deltaX^4
|
|
adds rTmpPtr = 96, rBernulliPtr
|
|
}
|
|
{ .mfb
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
fma.s1 fLnSin34 = fLnSin34, fDxSqr, fLnSin32
|
|
// branch to special path if x falls in "near root" range
|
|
(p6) br.cond.spnt _negRoots
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p10,p11
|
|
{ .mfi
|
|
ldfe fLnSin12 = [rTmpPtr3]
|
|
fma.s1 fLnSin26 = fLnSin26, fDxSqr, fLnSin24
|
|
(p10) cmp.eq p8, p9 = rXRnd, r0
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin14 = [rLnSinDataPtr]
|
|
fma.s1 fLnSin30 = fLnSin30, fDxSqr, fLnSin28
|
|
(p11) cmp.eq p9, p8 = rXRnd, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fB2, fB2L = [rBernulliPtr], 16
|
|
fma.s1 fLnSin18 = fLnSin18, fDxSqr, fLnSin16
|
|
shladd GR_ad_tbl_1 = rIndex1Dx, 4, rTbl1Addr // Point to G_1
|
|
|
|
}
|
|
{ .mfi
|
|
ldfe fB14 = [rTmpPtr], 16
|
|
fma.s1 fLnSin22 = fLnSin22, fDxSqr, fLnSin20
|
|
and GR_N = GR_N, r17Ones // mask sign bit
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB4 = [rBernulliPtr], 16
|
|
fma.s1 fInvX = fInvX, fRcpX, fRcpX // end of 3rd NR iteration
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
|
|
}
|
|
{ .mfi
|
|
ldfe fB16 = [rTmpPtr], 16
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
adds rTmpPtr2 = 8, GR_ad_tbl_1
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe fB6 = [rBernulliPtr], 16
|
|
fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1
|
|
adds rTmpPtr3 = -48, rTmpPtr
|
|
}
|
|
{ .mfi
|
|
ldfe fB18 = [rTmpPtr], 16
|
|
// High part of the log(|x|) = Y_hi = N * log2_hi + H
|
|
fma.s1 fResH = fFloatN, FR_log2_hi, FR_H
|
|
sub GR_N = GR_N, rExpHalf, 1 // unbiased exponent of deltaX
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p8,p9
|
|
{ .mfi
|
|
ldfe fB8 = [rBernulliPtr], 16
|
|
fma.s1 fLnSin36 = fLnSin36, fDx4, fLnSin34
|
|
// sign of GAMMA(x) is negative
|
|
(p8) adds rSgnGam = -1, r0
|
|
}
|
|
{ .mfi
|
|
ldfe fB20 = [rTmpPtr], -160
|
|
fma.s1 fRes5H = fLnSin4, fDxSqr, f0
|
|
// sign of GAMMA(x) is positive
|
|
(p9) adds rSgnGam = 1, r0
|
|
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB10 = [rBernulliPtr], 16
|
|
fma.s1 fLnSin30 = fLnSin30, fDx4, fLnSin26
|
|
(p14) adds rTmpPtr = -160, rTmpPtr
|
|
}
|
|
{ .mfi
|
|
ldfe fB12 = [rTmpPtr3], 16
|
|
fma.s1 fDx8 = fDx4, fDx4, f0 // deltaX^8
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps fGDx, fHDx = [GR_ad_tbl_1], 8 // Load G_1, H_1
|
|
fma.s1 fDx6 = fDx4, fDxSqr, f0 // deltaX^6
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
ldfd fhDx = [rTmpPtr2] // Load h_1
|
|
fma.s1 fLnSin22 = fLnSin22, fDx4, fLnSin18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// Load two parts of C
|
|
ldfpd fRes1H, fRes1L = [rTmpPtr], 16
|
|
fma.s1 fRcpX = fInvX, fInvX, f0 // (1/x)^2
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, rTbl2Addr // Point to G_2
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, rZ2Addr // Point to Z_2
|
|
fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h// h = N * log2_lo + h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
fnma.s1 fInvXL = f8, fInvX, f1 // relative error of 1/x
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr2 = 8, GR_ad_tbl_2
|
|
fma.s1 fLnSin8 = fLnSin8, fDxSqr, fLnSin6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fh2Dx = [rTmpPtr2] // Load h_2
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA1L = fB2, fInvX, f0 // (B2*(1/x))hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// Put integer N into rightmost significand
|
|
setf.sig fFloatNDx = GR_N
|
|
fms.s1 fRes4H = fResH, f1, f1 // ln(|x|)hi - 1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2H = fRes5H, fLnSin2//(lnSin4*DeltaX^2 + lnSin2)hi
|
|
// Get bits 30-15 of X_1 * Z_2
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes5L = fLnSin4, fDxSqr, fRes5H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fInvX4 = fRcpX, fRcpX, f0 // (1/x)^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB6 = fB6, fRcpX, fB4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fB18 = fB18, fRcpX, fB16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fInvXL = fInvXL, fInvX, f0 // low part of 1/x
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3H = fRes4H, f8, f0 // (-|x|*(ln(|x|)-1))hi
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, rTbl3Addr // Point to G_3
|
|
fms.s1 fA2L = fB2, fInvX, fA1L // delta(B2*(1/x))
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fBrnH = fRes1H, f1, fA1L // (-C - S(1/x))hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps fG3Dx, fH3Dx = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
fma.s1 fInvX8 = fInvX4, fInvX4, f0 // (1/x)^8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB10 = fB10, fRcpX, fB8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfd fh3Dx = [GR_ad_tbl_3] // Load h_3
|
|
fma.s1 fB20 = fB20, fInvX4, fB18
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB14 = fB14, fRcpX, fB12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDx8, fLnSin30
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin12 = fLnSin12, fDxSqr, fLnSin10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes2L = fLnSin2, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fRes2H, fDxSqr, f0 // high part of LnSin
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fResH = fResH, FR_MHalf, fResH // -0.5*ln(|x|)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 fGDx = fGDx, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// B2lo*(1/x)hi+ delta(B2*(1/x))
|
|
fma.s1 fA2L = fB2L, fInvX, fA2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB20 = fB20, fInvX4, fB14
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB10 = fB10, fInvX4, fB6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fcvt.xf fFloatNDx = fFloatNDx
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin14, fDx4, fLnSin12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDx8, fLnSin22
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes3L = fRes4H, f8, fRes3H // delta(-|x|*(ln(|x|)-1))
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 fGDx = fGDx, fG3Dx // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1) - 0.5ln(|x|))hi
|
|
fadd.s1 fRes4H = fRes3H, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2L = fInvXL, fB2, fA2L //(B2*(1/x))lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// low part of log(|x|) = Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fResL = FR_poly_hi, FR_poly_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB20 = fB20, fInvX8, fB10
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fInvX3 = fInvX, fRcpX, f0 // (1/x)^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fHDx = fHDx, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes5L = fRes5L, fLnSin2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes5H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fhDx = fhDx, fh2Dx // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fBrnL = fRes1H, fMOne, fBrnH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = fGDx, fNormDx, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3L = fResL, f8 , fRes3L // (-|x|*(ln(|x|)-1))lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes4L = fRes3H, fRes4H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// low part of "Bernulli" polynomial
|
|
fma.s1 fB20 = fB20, fInvX3, fA2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fResL = fResL, FR_MHalf, fResL // -0.5*ln(|x|)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fHDx = fHDx, fH3Dx // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fPolL = fRes2H, fDxSqr, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fhDx = fhDx, fh3Dx // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1) - 0.5ln(|x|) - C - S(1/x))hi
|
|
fadd.s1 fB14 = fRes4H, fBrnH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fResH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fBrnL = fBrnL, fA1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1))lo + (-0.5ln(|x|))lo
|
|
fadd.s1 fRes3L = fRes3L, fResL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fB20 = fRes1L, f1, fB20 // -Clo - S(1/x)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes5L // (lnSin4*DeltaX^2 + lnSin2)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fDxSqrL, fRes2H, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin14, fDx4, fLnSin8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin36, fDx8, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fB12 = fRes4H, fB14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1) - 0.5ln(|x|))lo
|
|
fadd.s1 fRes4L = fRes4L, fRes3L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fBrnL = fBrnL, fB20 // (-C - S(1/x))lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// high part of log(|DeltaX|) = Y_hi = N * log2_hi + H
|
|
fma.s1 fLnDeltaH = fFloatNDx, FR_log2_hi, fHDx
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fma.s1 fhDx = fFloatNDx, FR_log2_lo, fhDx
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fRes2L, fDxSqr, fPolL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin36, fDxSqr, fLnSin14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1) - 0.5ln(|x|))lo + (- C - S(1/x))lo
|
|
fadd.s1 fBrnL = fBrnL, fRes4L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB12 = fB12, fBrnH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, fhDx
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fRes1H = fLnDeltaH, f1, fPol//(-ln(|DeltaX|) + LnSin)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fDxSqrL, fRes2L, fPolL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin36 = fLnSin14, fDx6, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-|x|*(ln(|x|)-1) - 0.5ln(|x|) - C - S(1/x))lo
|
|
fadd.s1 fB12 = fB12, fBrnL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// low part of log(|DeltaX|) = Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fLnDeltaL= FR_poly_hi, FR_poly_lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes1L = fLnDeltaH, fMOne, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fPolL = fPolL, fLnSin36
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
//(-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi + (-ln(|DeltaX|) + LnSin)hi
|
|
fadd.s1 f8 = fRes1H, fB14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
//max((-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi,
|
|
// (-ln(|DeltaX|) + LnSin)hi)
|
|
famax.s1 fMaxNegStir = fRes1H, fB14
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
//min((-|x|*(ln(|x|)-1)-0.5ln(|x|) - C - S(1/x))hi,
|
|
// (-ln(|DeltaX|) + LnSin)hi)
|
|
famin.s1 fMinNegStir = fRes1H, fB14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fPol
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (-ln(|DeltaX|))lo + (LnSin)lo
|
|
fnma.s1 fPolL = fLnDeltaL, f1, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 f9 = fMaxNegStir, f8 // delta1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fPolL // (-ln(|DeltaX|) + LnSin)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 f9 = f9, fMinNegStir
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fB12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// low part of the result
|
|
fadd.s1 f9 = f9, fRes1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for -2^63 < x < -6.0 path
|
|
fma.s0 f8 = f8, f1, f9
|
|
// exit here for -2^63 < x < -6.0 path
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x falls in neighbourhood of any negative root
|
|
// "neighbourhood" typically means that |lgammal(x)| < 0.17
|
|
// on the [-3.0,-2.0] range |lgammal(x)| has even less
|
|
// magnitude
|
|
// rXint contains index of the root
|
|
// p10 is set if root belongs to "right" ones
|
|
// p11 is set if root belongs to "left" ones
|
|
// lgammal(x) is approximated by polynomial of
|
|
// 19th degree from (x - root) argument
|
|
.align 32
|
|
_negRoots:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_right_roots_polynomial_data),gp
|
|
nop.f 0
|
|
shl rTmpPtr2 = rXint, 7 // (i*16)*8
|
|
}
|
|
{ .mfi
|
|
adds rRootsAddr = -288, rRootsBndAddr
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fRoot = [rRootsAddr] // FP representation of root
|
|
nop.f 0
|
|
shl rTmpPtr = rXint, 6 // (i*16)*4
|
|
}
|
|
{ .mfi
|
|
(p11) adds rTmpPtr2 = 3536, rTmpPtr2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
shladd rTmpPtr = rXint, 4, rTmpPtr // (i*16) + (i*16)*4
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr3 = 32, rTmpPtr2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p10,p11
|
|
{ .mfi
|
|
add rTmpPtr3 = rTmpPtr, rTmpPtr3
|
|
nop.f 0
|
|
(p10) cmp.eq p8, p9 = rXRnd, r0
|
|
}
|
|
{ .mfi
|
|
// (i*16) + (i*16)*4 + (i*16)*8
|
|
add rTmpPtr = rTmpPtr, rTmpPtr2
|
|
nop.f 0
|
|
(p11) cmp.eq p9, p8 = rXRnd, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
add rTmpPtr2 = rPolDataPtr, rTmpPtr3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
add rPolDataPtr = rPolDataPtr, rTmpPtr // begin + offsett
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0
|
|
nop.f 0
|
|
adds rTmpPtr = 112, rTmpPtr2
|
|
}
|
|
{ .mfi
|
|
ldfpd fA2, fA2L = [rTmpPtr2], 16 // A2
|
|
nop.f 0
|
|
cmp.eq p12, p13 = 4, rSgnGamSize
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA3 = [rTmpPtr2], 128 // A4
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA12, fA13 = [rTmpPtr], 16 // A12, A13
|
|
nop.f 0
|
|
adds rTmpPtr3 = 64, rPolDataPtr
|
|
}
|
|
{ .mfi
|
|
ldfpd fA16, fA17 = [rTmpPtr2], 16 // A16, A17
|
|
nop.f 0
|
|
adds rPolDataPtr = 32, rPolDataPtr
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p8,p9
|
|
{ .mfi
|
|
ldfpd fA14, fA15 = [rTmpPtr], 16 // A14, A15
|
|
nop.f 0
|
|
// sign of GAMMA(x) is negative
|
|
(p8) adds rSgnGam = -1, r0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA18, fA19 = [rTmpPtr2], 16 // A18, A19
|
|
nop.f 0
|
|
// sign of GAMMA(x) is positive
|
|
(p9) adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA4 = [rPolDataPtr], 16 // A4
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA6, fA7 = [rTmpPtr3], 16 // A6, A7
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA5 = [rPolDataPtr], 16 // A5
|
|
// if x equals to (rounded) root exactly
|
|
fcmp.eq.s1 p6, p0 = f8, fRoot
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA8, fA9 = [rTmpPtr3], 16 // A8, A9
|
|
fms.s1 FR_FracX = f8, f1, fRoot
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p12) st4 [rSgnGamAddr] = rSgnGam
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
// store signgam if size of variable is 8 bytes
|
|
(p13) st8 [rSgnGamAddr] = rSgnGam
|
|
// answer if x equals to (rounded) root exactly
|
|
(p6) fadd.s0 f8 = fA0, fA0L
|
|
// exit if x equals to (rounded) root exactly
|
|
(p6) br.ret.spnt b0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfpd fA10, fA11 = [rTmpPtr3], 16 // A10, A11
|
|
nop.m 0
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fA2, FR_FracX, f0 // (A2*x)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4L = FR_FracX, FR_FracX, f0 // x^2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, FR_FracX, fA16
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, FR_FracX, fA12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, FR_FracX, fA18
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, FR_FracX, fA14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA7, FR_FracX, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_FracX, fA8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fResL = fA2, FR_FracX, fResH // delta(A2*x)
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1H = fResH, fA1 // (A2*x + A1)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, FR_FracX, fA10
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA5L = fA4L, fA4L, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA4L, fA17
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fA4L, fA13
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, FR_FracX, fA5
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA3L = fA4L, FR_FracX, f0 // x^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// delta(A2*x) + A2L*x = (A2*x)lo
|
|
fma.s1 fResL = fA2L, FR_FracX, fResL
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fsub.s1 fRes1L = fA1, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fA4L, fA9
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA5L, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, FR_FracX, fA4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fResL = fResL, fA1L // (A2*x)lo + A1
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2H = fRes1H, FR_FracX, f0 // ((A2*x + A1)*x)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA5L, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, FR_FracX, fA3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fResL // (A2*x + A1)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// delta((A2*x + A1)*x)
|
|
fms.s1 fRes2L = fRes1H, FR_FracX, fRes2H
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3H = fRes2H, fA0 // ((A2*x + A1)*x + A0)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA5L, f0
|
|
nop.i 0
|
|
}
|
|
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2L = fRes1L, FR_FracX, fRes2L // ((A2*x + A1)*x)lo
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fsub.s1 fRes3L = fRes2H, fRes3H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA19, FR_FracX, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fA0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fA0L // ((A2*x + A1)*x)lo + A0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fRes2L // (((A2*x + A1)*x) + A0)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fRes3L = fPol, fA3L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for arguments which are close to negative roots
|
|
fma.s0 f8 = fRes3H, f1, fRes3L
|
|
// exit here for arguments which are close to negative roots
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x| < 0.5
|
|
.align 32
|
|
lgammal_0_half:
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [rZ1offsett] // Load Z_1
|
|
fma.s1 fA4L = f8, f8, f0 // x^2
|
|
addl rPolDataPtr = @ltoff(lgammal_0_Half_data), gp
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr// Point to G_1
|
|
nop.f 0
|
|
addl rLnSinDataPtr = @ltoff(lgammal_lnsin_data), gp
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
nop.f 0
|
|
// Point to Constants_Z_2
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1
|
|
}
|
|
{ .mfi
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q
|
|
nop.f 0
|
|
// Point to Constants_G_H_h2
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
// Point to Constants_G_H_h3
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.f 0
|
|
sub GR_N = rExpX, rExpHalf, 1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rLnSinDataPtr = [rLnSinDataPtr]
|
|
nop.f 0
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
|
|
}
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
nop.f 0
|
|
sub GR_N = r0, GR_N
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [GR_ad_q], 16 // Load log2_lo
|
|
nop.f 0
|
|
add rTmpPtr2 = 320, rPolDataPtr
|
|
}
|
|
{ .mfi
|
|
add rTmpPtr = 32, rPolDataPtr
|
|
nop.f 0
|
|
// exponent of 0.25
|
|
adds rExp2 = -1, rExpHalf
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA3, fA3L = [rPolDataPtr], 16 // A3
|
|
fma.s1 fA5L = fA4L, fA4L, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA1, fA1L = [rTmpPtr], 16 // A1
|
|
fms.s1 fB8 = f8, f8, fA4L // x^2 - <x^2>
|
|
// set p6 if -0.5 < x <= -0.25
|
|
(p15) cmp.eq.unc p6, p0 = rExpX, rExp2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2
|
|
nop.f 0
|
|
// set p6 if -0.5 < x <= -0.40625
|
|
(p6) cmp.le.unc p6, p0 = 10, GR_Index1
|
|
}
|
|
{ .mfi
|
|
ldfe fA21 = [rTmpPtr2], -16 // A21
|
|
// Put integer N into rightmost significand
|
|
nop.f 0
|
|
adds rTmpPtr = 240, rTmpPtr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
setf.sig fFloatN = GR_N
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q], 16 // Load Q4
|
|
nop.f 0
|
|
adds rPolDataPtr = 304, rPolDataPtr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA20 = [rTmpPtr2], -32 // A20
|
|
nop.f 0
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
}
|
|
{ .mfi
|
|
ldfe fA19 = [rTmpPtr], -32 // A19
|
|
nop.f 0
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2// Point to G_2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA17 = [rTmpPtr], -32 // A17
|
|
nop.f 0
|
|
adds rTmpPtr3 = 8, GR_ad_tbl_2
|
|
}
|
|
{ .mfb
|
|
ldfe fA18 = [rTmpPtr2], -32 // A18
|
|
nop.f 0
|
|
// branch to special path for -0.5 < x <= 0.40625
|
|
(p6) br.cond.spnt lgammal_near_neg_half
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
ldfe fA15 = [rTmpPtr], -32 // A15
|
|
fma.s1 fB20 = fA5L, fA5L, f0 // x^8
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA16 = [rTmpPtr2], -32 // A16
|
|
ldfe fA13 = [rTmpPtr], -32 // A13
|
|
fms.s1 fB16 = fA4L, fA4L, fA5L
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2], 8 // Load G_2, H_2
|
|
ldfd FR_h2 = [rTmpPtr3] // Load h_2
|
|
fmerge.s fB10 = f8, fA5L // sign(x) * x^4
|
|
}
|
|
;;
|
|
{ .mmi
|
|
ldfe fA14 = [rTmpPtr2], -32 // A14
|
|
ldfe fA11 = [rTmpPtr], -32 // A11
|
|
// Get bits 30-15 of X_1 * Z_2
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe fA12 = [rTmpPtr2], -32 // A12
|
|
fma.s1 fRes4H = fA3, fAbsX, f0
|
|
adds rTmpPtr3 = 16, GR_ad_q
|
|
}
|
|
{ .mfi
|
|
ldfe fA9 = [rTmpPtr], -32 // A9
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA10 = [rTmpPtr2], -32 // A10
|
|
ldfe fA7 = [rTmpPtr], -32 // A7
|
|
fma.s1 fB18 = fB20, fB20, f0 // x^16
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA8 = [rTmpPtr2], -32 // A8
|
|
ldfe fA22 = [rPolDataPtr], 16 // A22
|
|
fcvt.xf fFloatN = fFloatN
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA5 = [rTmpPtr], -32 // A5
|
|
fma.s1 fA21 = fA21, fAbsX, fA20 // v16
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
{ .mfi
|
|
ldfe fA6 = [rTmpPtr2], -32 // A6
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
// Point to G_3
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3
|
|
ldfe fA4 = [rTmpPtr2], -32 // A4
|
|
fma.s1 fA19 = fA19, fAbsX, fA18 // v13
|
|
}
|
|
;;
|
|
.pred.rel "mutex",p14,p15
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
fms.s1 fRes4L = fA3, fAbsX, fRes4H
|
|
(p14) adds rSgnGam = 1, r0
|
|
}
|
|
{ .mfi
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
fadd.s1 fRes2H = fRes4H, fA2
|
|
(p15) adds rSgnGam = -1, r0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fma.s1 fA17 = fA17, fAbsX, fA16 // v12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q3 = [GR_ad_q], 32 // Load Q3
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe FR_Q2 = [rTmpPtr3], 16 // Load Q2
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
fma.s1 fA15 = fA15, fAbsX, fA14 // v8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr3 = 32, rLnSinDataPtr
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfpd fLnSin2, fLnSin2L = [rLnSinDataPtr], 16
|
|
ldfe fLnSin6 = [rTmpPtr3], 32
|
|
fma.s1 fA13 = fA13, fAbsX, fA12 // v7
|
|
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin4 = [rLnSinDataPtr], 32
|
|
fma.s1 fRes4L = fA3L, fAbsX, fRes4L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin10 = [rTmpPtr3], 32
|
|
fsub.s1 fRes2L = fA2, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin8 = [rLnSinDataPtr], 32
|
|
fma.s1 fResH = fRes2H, fAbsX, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fLnSin14 = [rTmpPtr3], 32
|
|
fma.s1 fA22 = fA22, fA4L, fA21 // v15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin12 = [rLnSinDataPtr], 32
|
|
fma.s1 fA9 = fA9, fAbsX, fA8 // v4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin18 = [rTmpPtr3], 16
|
|
fma.s1 fA11 = fA11, fAbsX, fA10 // v5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fLnSin16 = [rLnSinDataPtr], 24
|
|
fma.s1 fA19 = fA19, fA4L, fA17 // v11
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin22 = [rTmpPtr3], 16
|
|
fma.s1 fPolL = fA7, fAbsX, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fLnSin20 = [rLnSinDataPtr], 16
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin26 = [rTmpPtr3], 16
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fLnSin24 = [rLnSinDataPtr], 16
|
|
fadd.s1 fRes2L = fRes2L, fRes4H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin30 = [rTmpPtr3], 16
|
|
fadd.s1 fA2L = fA2L, fRes4L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fLnSin28 = [rLnSinDataPtr], 16
|
|
fms.s1 fResL = fRes2H, fAbsX, fResH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin34 = [rTmpPtr3], 8
|
|
fadd.s1 fRes2H = fResH, fA1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fLnSin32 = [rLnSinDataPtr]
|
|
fma.s1 fA11 = fA11, fA4L, fA9 // v3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd fLnSin36 = [rTmpPtr3]
|
|
fma.s1 fA15 = fA15, fA4L, fA13 // v6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA5 = fA5, fAbsX, fA4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, fSignifX, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of the log(|x|): Y_hi = N * log2_hi + H
|
|
fms.s1 FR_log2_hi = fFloatN, FR_log2_hi, FR_H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fA3L = fRes2L, fA2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA22 = fA22, fA5L, fA19
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes2L = fA1, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3H = fRes2H, f8, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fA5L, fA11 // v2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin18 = fLnSin18, fA4L, fLnSin16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fms.s1 FR_h = fFloatN, FR_log2_lo, FR_h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fPolL, fA4L, fA5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResL = fA3L, fAbsX, fResL
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin30 = fLnSin30, fA4L, fLnSin28
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fResH
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes3L = fRes2H, f8, fRes3H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1H = fRes3H, FR_log2_hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fB20, fA22, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin34 = fLnSin34, fA4L, fLnSin32
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin14 = fLnSin14, fA4L, fLnSin12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fA1L = fA1L, fResL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin22 = fLnSin22, fA4L, fLnSin20
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin26 = fLnSin26, fA4L, fLnSin24
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes1L = FR_log2_hi, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fA5L, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin34 = fLnSin36, fA5L, fLnSin34
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin18 = fLnSin18, fA5L, fLnSin14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin6 = fLnSin6, fA4L, fLnSin4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin10 = fLnSin10, fA4L, fLnSin8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fA1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB2 = fLnSin2, fA4L, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fRes3H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fB10, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin26 = fLnSin26, fA5L, fLnSin22
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin34 = fLnSin34, fA5L, fLnSin30
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin10 = fLnSin10, fA5L, fLnSin6
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin2L = fLnSin2L, fA4L, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3L = fRes2L, f8, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_lo = poly_hi + poly_lo
|
|
fsub.s1 FR_log2_lo = FR_poly_lo, FR_poly_hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fB4 = fLnSin2, fA4L, fB2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2H = fRes1H, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin34 = fLnSin34, fB20, fLnSin26
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin18 = fLnSin18, fB20, fLnSin10
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fLnSin2L = fB8, fLnSin2, fLnSin2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_log2_lo = FR_log2_lo, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes2L = fRes1H, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB6 = fLnSin34, fB18, fLnSin18
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB4 = fLnSin2L, fB4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, FR_log2_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB12 = fB6, fA5L, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fB14 = fB6, fA5L, fB12
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
fadd.s1 fLnSin30 = fB2, fB12
|
|
// branch out if x is negative
|
|
(p15) br.cond.spnt _O_Half_neg
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// sign(x)*Pol(|x|) - log(|x|)
|
|
fma.s0 f8 = fRes2H, f1, fRes2L
|
|
// it's an answer already for positive x
|
|
// exit if 0 < x < 0.5
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x is negative and |x| < 0.5
|
|
.align 32
|
|
_O_Half_neg:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB14 = fB16, fB6, fB14
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fLnSin16 = fB2, fLnSin30
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fResH = fLnSin30, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSin16 = fLnSin16, fB12
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB4 = fB14, fB4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSin16 = fB4, fLnSin16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fResL = fRes2H, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fResL = fResL, fLnSin30
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fLnSin16 = fLnSin16, fRes2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fResL = fResL, fLnSin16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for -0.5 < x < 0
|
|
fma.s0 f8 = fResH, f1, fResL
|
|
// exit for -0.5 < x < 0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x >= 8.0
|
|
// there are two computational paths:
|
|
// 1) For x >10.0 Stirling's formula is used
|
|
// 2) Polynomial approximation for 8.0 <= x <= 10.0
|
|
.align 32
|
|
lgammal_big_positive:
|
|
{ .mfi
|
|
addl rPolDataPtr = @ltoff(lgammal_data), gp
|
|
fmerge.se fSignifX = f1, f8
|
|
// Get high 15 bits of significand
|
|
extr.u GR_X_0 = rSignifX, 49, 15
|
|
}
|
|
{.mfi
|
|
shladd rZ1offsett = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 1st NR iteration
|
|
adds rSignif1andQ = 0x5, r0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ld4 GR_Z_1 = [rZ1offsett] // Load Z_1
|
|
nop.f 0
|
|
shl rSignif1andQ = rSignif1andQ, 61 // significand of 1.25
|
|
}
|
|
{ .mfi
|
|
cmp.eq p8, p0 = rExpX, rExp8 // p8 = 1 if 8.0 <= x < 16
|
|
nop.f 0
|
|
adds rSgnGam = 1, r0 // gamma is positive at this range
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, rTbl1Addr// Point to G_1
|
|
nop.f 0
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_Q
|
|
}
|
|
{ .mlx
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
movl rDelta = 0x3FF2000000000000
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
nop.f 0
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
}
|
|
{ .mfi
|
|
// Point to Constants_G_H_h2
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1
|
|
nop.f 0
|
|
// p8 = 1 if 8.0 <= x <= 10.0
|
|
(p8) cmp.leu.unc p8, p0 = rSignifX, rSignif1andQ
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.f 0
|
|
// Get bits 30-15 of X_0 * Z_1
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
|
|
}
|
|
{ .mfb
|
|
(p8) setf.d FR_MHalf = rDelta
|
|
nop.f 0
|
|
(p8) br.cond.spnt lgammal_8_10 // branch out if 8.0 <= x <= 10.0
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe fA1 = [rPolDataPtr], 16 // Load overflow threshold
|
|
fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 1st NR iteration
|
|
// Point to Constants_G_H_h3
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
movl rDelta = 0xBFE0000000000000 // -0.5 in DP
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
nop.f 0
|
|
sub GR_N = rExpX, rExpHalf, 1 // unbiased exponent of x
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
setf.d FR_MHalf = rDelta
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// Put integer N into rightmost significand
|
|
setf.sig fFloatN = GR_N
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
}
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q], 16 // Load Q4
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
nop.f 0
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2// Point to G_2
|
|
}
|
|
{ .mfi
|
|
ldfe FR_Q3 = [GR_ad_q], 16 // Load Q3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 2nd NR iteration
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2], 8 // Load G_2, H_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
nop.f 0
|
|
// Get bits 30-15 of X_1 * Z_2
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15
|
|
}
|
|
;;
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
fcmp.gt.s1 p7,p0 = f8, fA1 // check if x > overflow threshold
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfpd fA0, fA0L = [rPolDataPtr], 16 // Load two parts of C
|
|
fma.s1 fRcpX = fInvX, fRcpX, fRcpX // end of 2nd NR iteration
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
ldfpd fB2, fA1 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
(p7) br.cond.spnt lgammal_overflow // branch if x > overflow threshold
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fB4 = [rPolDataPtr], 16
|
|
fcvt.xf fFloatN = fFloatN
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3// Point to G_3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fB6 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3], 8 // Load G_3, H_3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe fB8 = [rPolDataPtr], 16
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fInvX = f8, fRcpX, f1 // start of 3rd NR iteration
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB10 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB12 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB14 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe fB16 = [rPolDataPtr], 16
|
|
// get double extended coefficients from two doubles
|
|
// two doubles are needed in Stitling's formula for negative x
|
|
fadd.s1 fB2 = fB2, fA1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB18 = [rPolDataPtr], 16
|
|
fma.s1 fInvX = fInvX, fRcpX, fRcpX // end of 3rd NR iteration
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB20 = [rPolDataPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRcpX = fInvX, fInvX, f0 // 1/x^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA0L = fB2, fInvX, fA0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = fSignifX, FR_G, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of the log(x): Y_hi = N * log2_hi + H
|
|
fma.s1 fRes2H = fFloatN, FR_log2_hi, FR_H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// h = N * log2_lo + h
|
|
fma.s1 FR_h = fFloatN, FR_log2_lo, FR_h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// High part of the log(x): Y_hi = N * log2_hi + H
|
|
fma.s1 fRes1H = fFloatN, FR_log2_hi, FR_H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fB18, fRcpX, fB16 // v9
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2L = fRcpX, fRcpX, f0 // v10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fA3 = fB6, fRcpX, fB4 // v3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4 = fB10, fRcpX, fB8 // v4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes2H =fRes2H, f1, f1 // log_Hi(x) -1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = r * Q4 + Q3
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1H = fRes1H, FR_MHalf, f0 // -0.5*log_Hi(x)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fB14, fRcpX, fB12 // v7
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA8 = fA2L, fB20, fPol // v8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2 = fA4, fA2L, fA3 // v2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4L = fA2L, fA2L, f0 // v5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fRes2H, f8, f0 // (x*(ln(x)-1))hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = Q1 * rsq + r
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fRcpX, fInvX, f0 // 1/x^3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA6 = fA8, fA2L, fA7 // v6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fResL = fRes2H, f8, fResH // d(x*(ln(x)-1))
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3H = fResH, fRes1H // (x*(ln(x)-1) -0.5ln(x))hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA4L, fA6, fA2 // v1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// raise inexact exception
|
|
fma.s0 FR_log2_lo = FR_log2_lo, FR_log2_lo, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4H = fRes3H, fA0 // (x*(ln(x)-1) -0.5ln(x))hi + Chi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes3L = fResH, fRes3H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_lo = poly_hi + poly_lo
|
|
fadd.s1 fRes2L = FR_poly_hi, FR_poly_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA0L = fPol, fA11, fA0L // S(1/x) + Clo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes4L = fRes3H, fRes4H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResL = fRes2L, f8 , fResL // lo part of x*(ln(x)-1)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Clo + S(1/x) - 0.5*logLo(x)
|
|
fma.s1 fA0L = fRes2L, FR_MHalf, fA0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fA0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Clo + S(1/x) - 0.5*logLo(x) + (x*(ln(x)-1))lo
|
|
fadd.s1 fA0L = fA0L, fResL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fA0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 f8 = fRes4H, f1, fRes4L
|
|
// exit for x > 10.0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
// here if 8.0 <= x <= 10.0
|
|
// Result = P15(y), where y = x/8.0 - 1.5
|
|
.align 32
|
|
lgammal_8_10:
|
|
{ .mfi
|
|
addl rPolDataPtr = @ltoff(lgammal_8_10_data), gp
|
|
fms.s1 FR_FracX = fSignifX, f1, FR_MHalf // y = x/8.0 - 1.5
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rLnSinDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
adds rZ1offsett = 32, rLnSinDataPtr
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
adds rLnSinDataPtr = 48, rLnSinDataPtr
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA2 = [rZ1offsett], 32 // A5
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA0, fA0L = [rPolDataPtr], 16 // A0
|
|
fma.s1 FR_rsq = FR_FracX, FR_FracX, f0 // y^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA3 = [rLnSinDataPtr],32 // A5
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA4 = [rZ1offsett], 32 // A4
|
|
ldfe fA5 = [rLnSinDataPtr], 32 // A5
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA6 = [rZ1offsett], 32 // A6
|
|
ldfe fA7 = [rLnSinDataPtr], 32 // A7
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA8 = [rZ1offsett], 32 // A8
|
|
ldfe fA9 = [rLnSinDataPtr], 32 // A9
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA10 = [rZ1offsett], 32 // A10
|
|
ldfe fA11 = [rLnSinDataPtr], 32 // A11
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA12 = [rZ1offsett], 32 // A12
|
|
ldfe fA13 = [rLnSinDataPtr], 32 // A13
|
|
fma.s1 FR_Q4 = FR_rsq, FR_rsq, f0 // y^4
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA14 = [rZ1offsett], 32 // A14
|
|
ldfe fA15 = [rLnSinDataPtr], 32 // A15
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1H = FR_FracX, fA1, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA3 = fA3, FR_FracX, fA2 // v4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, FR_FracX, fA4 // v5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store sign of GAMMA(x) if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA3L = FR_Q4, FR_Q4, f0 // v9 = y^8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store sign of GAMMA(x) if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA7 = fA7, FR_FracX, fA6 // v7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_FracX, fA8 // v8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes1L = FR_FracX, fA1, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, FR_FracX, fA10 // v12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, FR_FracX, fA12 // v13
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2H = fRes1H, f1, fA0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, FR_FracX, fA14 // v16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, FR_rsq, fA3 // v3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_rsq, fA7 // v6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1L = FR_FracX, fA1L, fRes1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes2L = fA0, f1, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, FR_rsq, fA11 // v11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_Q4, fA5 // v2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1L = fRes1L, f1, fA0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2L = fRes2L, f1, fRes1H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, FR_Q4, fA13 // v10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2L = fRes1L, f1, fRes2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA3L, fA15, fA9
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f8 = FR_rsq , fPol, fRes2H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, FR_rsq, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes1L = fRes2H, f1, f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes1L = fRes1L, f1, fPol
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fRes1L = fRes1L, f1, fRes2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 f8 = f8, f1, fRes1L
|
|
// exit for 8.0 <= x <= 10.0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if 4.0 <=x < 8.0
|
|
.align 32
|
|
lgammal_4_8:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_4_8_data),gp
|
|
fms.s1 FR_FracX = fSignifX, f1, FR_MHalf
|
|
adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
nop.f 0
|
|
// branch to special path which computes polynomial of 25th degree
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
|
|
// here if 2.25 <=x < 4.0
|
|
.align 32
|
|
lgammal_2Q_4:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_2Q_4_data),gp
|
|
fms.s1 FR_FracX = fSignifX, f1, FR_MHalf
|
|
adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
nop.f 0
|
|
// branch to special path which computes polynomial of 25th degree
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
|
|
// here if 0.5 <= |x| < 0.75
|
|
.align 32
|
|
lgammal_half_3Q:
|
|
.pred.rel "mutex", p14, p15
|
|
{ .mfi
|
|
(p14) addl rPolDataPtr= @ltoff(lgammal_half_3Q_data),gp
|
|
// FR_FracX = x - 0.625 for positive x
|
|
(p14) fms.s1 FR_FracX = f8, f1, FR_FracX
|
|
(p14) adds rSgnGam = 1, r0
|
|
}
|
|
{ .mfi
|
|
(p15) addl rPolDataPtr= @ltoff(lgammal_half_3Q_neg_data),gp
|
|
// FR_FracX = x + 0.625 for negative x
|
|
(p15) fma.s1 FR_FracX = f8, f1, FR_FracX
|
|
(p15) adds rSgnGam = -1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
nop.f 0
|
|
// branch to special path which computes polynomial of 25th degree
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
// here if 1.3125 <= x < 1.5625
|
|
.align 32
|
|
lgammal_loc_min:
|
|
{ .mfi
|
|
adds rSgnGam = 1, r0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
fms.s1 FR_FracX = f8, f1, fA5L
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
// here if -2.605859375 <= x < -2.5
|
|
// special polynomial approximation used since neither "near root"
|
|
// approximation nor reflection formula give satisfactory accuracy on
|
|
// this range
|
|
.align 32
|
|
_neg2andHalf:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_neg2andHalf_data),gp
|
|
fma.s1 FR_FracX = fB20, f1, f8 // 2.5 + x
|
|
adds rSgnGam = -1, r0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
nop.f 0
|
|
// branch to special path which computes polynomial of 25th degree
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
|
|
// here if -0.5 < x <= -0.40625
|
|
.align 32
|
|
lgammal_near_neg_half:
|
|
{ .mmf
|
|
addl rPolDataPtr= @ltoff(lgammal_near_neg_half_data),gp
|
|
setf.exp FR_FracX = rExpHalf
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
adds rSgnGam = -1, r0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
adds rTmpPtr = 160, rPolDataPtr
|
|
fma.s1 FR_FracX = FR_FracX, f1, f8
|
|
// branch to special path which computes polynomial of 25th degree
|
|
br.sptk lgamma_polynom25
|
|
}
|
|
;;
|
|
|
|
// here if there an answer is P25(x)
|
|
// rPolDataPtr, rTmpPtr point to coefficients
|
|
// x is in FR_FracX register
|
|
.align 32
|
|
lgamma_polynom25:
|
|
{ .mfi
|
|
ldfpd fA3, fA0L = [rPolDataPtr], 16 // A3
|
|
nop.f 0
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
{ .mfi
|
|
ldfpd fA18, fA19 = [rTmpPtr], 16 // D7, D6
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA1, fA1L = [rPolDataPtr], 16 // A1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA16, fA17 = [rTmpPtr], 16 // D4, D5
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA12, fA13 = [rPolDataPtr], 16 // D0, D1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA14, fA15 = [rTmpPtr], 16 // D2, D3
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA24, fA25 = [rPolDataPtr], 16 // C21, C20
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA22, fA23 = [rTmpPtr], 16 // C19, C18
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA2, fA2L = [rPolDataPtr], 16 // A2
|
|
fma.s1 fA4L = FR_FracX, FR_FracX, f0 // x^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA20, fA21 = [rTmpPtr], 16 // C17, C16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA11 = [rTmpPtr], 16 // E7
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA0, fA3L = [rPolDataPtr], 16 // A0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
ldfe fA10 = [rPolDataPtr], 16 // E6
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA9 = [rTmpPtr], 16 // E5
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA8 = [rPolDataPtr], 16 // E4
|
|
ldfe fA7 = [rTmpPtr], 16 // E3
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA6 = [rPolDataPtr], 16 // E2
|
|
ldfe fA5 = [rTmpPtr], 16 // E1
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA4 = [rPolDataPtr], 16 // E0
|
|
fma.s1 fA5L = fA4L, fA4L, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fB2 = FR_FracX, FR_FracX, fA4L // x^2 - <x^2>
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fRes4H = fA3, FR_FracX, f0 // (A3*x)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA19 = fA19, FR_FracX, fA18 // D7*x + D6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fA1, FR_FracX, f0 // (A1*x)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB6 = fA1L, FR_FracX, fA0L // A1L*x + A0L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, FR_FracX, fA16 // D5*x + D4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, FR_FracX, fA14 // D3*x + D2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, FR_FracX, fA24 // C21*x + C20
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, FR_FracX, fA12 // D1*x + D0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA23 = fA23, FR_FracX, fA22 // C19*x + C18
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA21 = fA21, FR_FracX, fA20 // C17*x + C16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes4L = fA3, FR_FracX, fRes4H // delta((A3*x)hi)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2H = fRes4H, fA2 // (A3*x + A2)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fResL = fA1, FR_FracX, fResH // d(A1*x)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1H = fResH, fA0 // (A1*x + A0)hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA4L, fA17 // Dhi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, FR_FracX, fA10 // E7*x + E6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Doing this to raise inexact flag
|
|
fma.s0 fA10 = fA0, fA0, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fA4L, fA13 // Dlo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (C21*x + C20)*x^2 + C19*x + C18
|
|
fma.s1 fA25 = fA25, fA4L, fA23
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, FR_FracX, fA8 // E5*x + E4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, FR_FracX, fA6 // E3*x + E2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes4L = fA3L, FR_FracX, fRes4L // (A3*x)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes2L = fA2, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fResL = fResL, fB6 // (A1L*x + A0L) + d(A1*x)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes1L = fA0, fRes1H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, FR_FracX, fA4 // E1*x + E0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB8 = fA5L, fA5L, f0 // x^8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((C21*x + C20)*x^2 + C19*x + C18)*x^2 + C17*x + C16
|
|
fma.s1 fA25 = fA25, fA4L, fA21
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA19 = fA19, fA5L, fA15 // D
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fA4L, fA9 // Ehi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes4H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fA2L // (A3*x)lo + A2L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3H = fRes2H, fA4L, f0 // ((A3*x + A2)*x^2)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3L = fRes2H, fB2, f0 // (A3*x + A2)hi*d(x^2)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, fA4L, fA5 // Elo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fB8, fA19 // C*x^8 + D
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes4L // (A3*x + A2)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fB4 = fRes2H, fA4L, fRes3H // d((A3*x + A2)*x^2))
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fResL // (A1*x + A0)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB20 = fRes3H, fRes1H // Phi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fA5L, fA7 // E
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ( (A3*x + A2)lo*<x^2> + (A3*x + A2)hi*d(x^2))
|
|
fma.s1 fRes3L = fRes2L, fA4L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// d((A3*x + A2)*x^2)) + (A1*x + A0)lo
|
|
fadd.s1 fRes1L = fRes1L, fB4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fB18 = fRes1H, fB20
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA25, fB8, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB18 = fB18, fRes3H
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes4H = fPol, fA5L, fB20
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fPol, fA5L, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB18 = fB18, fRes1L // Plo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes4L = fB20, fRes4H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB18 = fB18, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fB18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 f8 = fRes4H, f1, fRes4L
|
|
// P25(x) computed, exit here
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
|
|
// here if 0.75 <= x < 1.3125
|
|
.align 32
|
|
lgammal_03Q_1Q:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_03Q_1Q_data),gp
|
|
fma.s1 FR_FracX = fA5L, f1, f0 // x
|
|
adds rSgnGam = 1, r0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB4 = fA5L, fA5L, f0 // x^2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
adds rTmpPtr = 144, rPolDataPtr
|
|
nop.f 0
|
|
br.sptk lgamma_polynom24x
|
|
}
|
|
;;
|
|
|
|
// here if 1.5625 <= x < 2.25
|
|
.align 32
|
|
lgammal_13Q_2Q:
|
|
{ .mfi
|
|
addl rPolDataPtr= @ltoff(lgammal_13Q_2Q_data),gp
|
|
fma.s1 FR_FracX = fB4, f1, f0 // x
|
|
adds rSgnGam = 1, r0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB4 = fB4, fB4, f0 // x^2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ld8 rPolDataPtr = [rPolDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
adds rTmpPtr = 144, rPolDataPtr
|
|
nop.f 0
|
|
br.sptk lgamma_polynom24x
|
|
}
|
|
;;
|
|
|
|
// here if result is Pol24(x)
|
|
// x is in FR_FracX,
|
|
// rPolDataPtr, rTmpPtr point to coefficients
|
|
.align 32
|
|
lgamma_polynom24x:
|
|
{ .mfi
|
|
ldfpd fA4, fA2L = [rPolDataPtr], 16
|
|
nop.f 0
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
{ .mfi
|
|
ldfpd fA23, fA24 = [rTmpPtr], 16 // C18, C19
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA3, fA1L = [rPolDataPtr], 16
|
|
fma.s1 fA5L = fB4, fB4, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA19, fA20 = [rTmpPtr], 16 // D6, D7
|
|
fms.s1 fB2 = FR_FracX, FR_FracX, fB4 // x^2 - <x^2>
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfpd fA15, fA16 = [rPolDataPtr], 16 // D2, D3
|
|
ldfpd fA17, fA18 = [rTmpPtr], 16 // D4, D5
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfpd fA13, fA14 = [rPolDataPtr], 16 // D0, D1
|
|
ldfpd fA12, fA21 = [rTmpPtr], 16 // E7, C16
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA11 = [rPolDataPtr], 16 // E6
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA10 = [rTmpPtr], 16 // E5
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA2, fA4L = [rPolDataPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA1, fA3L = [rTmpPtr], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA22, fA25 = [rPolDataPtr], 16 // C17, C20
|
|
fma.s1 fA0 = fA5L, fA5L, f0 // x^8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA0L = fA5L, FR_FracX, f0 // x^5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA9 = [rPolDataPtr], 16 // E4
|
|
ldfe fA8 = [rTmpPtr], 16 // E3
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mmf
|
|
ldfe fA7 = [rPolDataPtr], 16 // E2
|
|
ldfe fA6 = [rTmpPtr], 16 // E1
|
|
nop.f 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA5 = [rTmpPtr], 16 // E0
|
|
fma.s1 fRes4H = fA4, fB4, f0 // A4*<x^2>
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA24, FR_FracX, fA23 // C19*x + C18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fRes1H = fA3, fB4, f0 // A3*<x^2>
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s1 fA1L = fA3, fB2,fA1L // A3*d(x^2) + A1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA20 = fA20, FR_FracX, fA19 // D7*x + D6
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA18 = fA18, FR_FracX, fA17 // D5*x + D4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA16 = fA16, FR_FracX, fA15 // D3*x + D2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA14 = fA14, FR_FracX, fA13 // D1*x + D0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2L = fA4, fB2,fA2L // A4*d(x^2) + A2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA12 = fA12, FR_FracX, fA11 // E7*x + E6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes2L = fA4, fB4, fRes4H // delta(A4*<x^2>)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2H = fRes4H, fA2 // A4*<x^2> + A2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fRes3L = fA3, fB4, fRes1H // delta(A3*<x^2>)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3H = fRes1H, fA1 // A3*<x^2> + A1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA20 = fA20, fB4, fA18 // (D7*x + D6)*x^2 + D5*x + D4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA22 = fA22, FR_FracX, fA21 // C17*x + C16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA16 = fA16, fB4, fA14 // (D3*x + D2)*x^2 + D1*x + D0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fA25, fB4, fPol // C20*x^2 + C19*x + C18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2L = fA4L, fB4, fA2L // A4L*<x^2> + A4*d(x^2) + A2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA1L = fA3L, fB4, fA1L // A3L*<x^2> + A3*d(x^2) + A1L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes4L = fA2, fRes2H // d1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResH = fRes2H, fB4, f0 // (A4*<x^2> + A2)*x^2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes1L = fA1, fRes3H // d1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB6 = fRes3H, FR_FracX, f0 // (A3*<x^2> + A1)*x
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA10 = fA10, FR_FracX, fA9 // E5*x + E4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA8 = fA8, FR_FracX, fA7 // E3*x + E2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// (C20*x^2 + C19*x + C18)*x^2 + C17*x + C16
|
|
fma.s1 fPol = fPol, fB4, fA22
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA6 = fA6, FR_FracX, fA5 // E1*x + E0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// A4L*<x^2> + A4*d(x^2) + A2L + delta(A4*<x^2>)
|
|
fadd.s1 fRes2L = fA2L, fRes2L
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// A3L*<x^2> + A3*d(x^2) + A1L + delta(A3*<x^2>)
|
|
fadd.s1 fRes3L = fA1L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fRes4H // d2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fResL = fRes2H, fB4, fResH // d(A4*<x^2> + A2)*x^2)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes1L = fRes1L, fRes1H // d2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fB8 = fRes3H, FR_FracX, fB6 // d((A3*<x^2> + A1)*x)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB10 = fResH, fB6 // (A4*x^4 + .. + A1*x)hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA12 = fA12, fB4, fA10 // Ehi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// ((D7*x + D6)*x^2 + D5*x + D4)*x^4 + (D3*x + D2)*x^2 + D1*x + D0
|
|
fma.s1 fA20 = fA20, fA5L, fA16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA8 = fA8, fB4, fA6 // Elo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes2L = fRes2L, fRes4L // (A4*<x^2> + A2)lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// d(A4*<x^2> + A2)*x^2) + A4*<x^2> + A2)*d(x^2)
|
|
fma.s1 fResL = fRes2H, fB2, fResL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fRes1L // (A4*<x^2> + A2)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fB12 = fB6, fB10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fA0, fA20 // PolC*x^8 + PolD
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolL = fA12, fA5L, fA8 // E
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fResL = fB4, fRes2L, fResL // ((A4*<x^2> + A2)*x^2)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes3L = fRes3L, FR_FracX, fB8 // ((A3*<x^2> + A1)*x)lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fB12 = fB12, fResH
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPol = fPol, fA0, fPolL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fRes3L, fResL
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes2H = fPol, fA0L, fB10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes3L = fB12, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fsub.s1 fRes4L = fB10, fRes2H
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes4L = fPol, fA0L, fRes4L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 fRes4L = fRes4L, fRes3L
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for all paths for which the result is Pol24(x)
|
|
fma.s0 f8 = fRes2H, f1, fRes4L
|
|
// here is the exit for all paths for which the result is Pol24(x)
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
|
|
// here if x is natval, nan, +/-inf, +/-0, or denormal
|
|
.align 32
|
|
lgammal_spec:
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m p9, p0 = f8, 0xB // +/-denormals
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m p6, p0 = f8, 0x1E1 // Test x for natval, nan, +inf
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
fclass.m p7, p0 = f8, 0x7 // +/-0
|
|
(p9) br.cond.sptk lgammal_denormal_input
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
// branch out if x is natval, nan, +inf
|
|
(p6) br.cond.spnt lgammal_nan_pinf
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
(p7) br.cond.spnt lgammal_singularity
|
|
};;
|
|
// if we are still here then x = -inf
|
|
{ .mfi
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
nop.f 0
|
|
adds rSgnGam = 1, r0
|
|
};;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s0 f8 = f8,f8,f0 // return +inf, no call to error support
|
|
br.ret.spnt b0
|
|
};;
|
|
|
|
// here if x is NaN, NatVal or +INF
|
|
.align 32
|
|
lgammal_nan_pinf:
|
|
{ .mfi
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
nop.f 0
|
|
adds rSgnGam = 1, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
fma.s0 f8 = f8,f1,f8 // return x+x if x is natval, nan, +inf
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
nop.f 0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x denormal or unnormal
|
|
.align 32
|
|
lgammal_denormal_input:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s0 fResH = f1, f1, f8 // raise denormal exception
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnorm.s1 f8 = f8 // normalize input value
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.sig rSignifX = f8
|
|
fmerge.se fSignifX = f1, f8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
getf.exp rSignExpX = f8
|
|
fcvt.fx.s1 fXint = f8 // Convert arg to int (int repres. in FR)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.exp rSignExpX = f8
|
|
fcmp.lt.s1 p15, p14 = f8, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
and rExpX = rSignExpX, r17Ones
|
|
fmerge.s fAbsX = f1, f8 // |x|
|
|
br.cond.sptk _deno_back_to_main_path
|
|
}
|
|
;;
|
|
|
|
|
|
// here if overflow (x > overflow_bound)
|
|
.align 32
|
|
lgammal_overflow:
|
|
{ .mfi
|
|
addl r8 = 0x1FFFE, r0
|
|
nop.f 0
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
}
|
|
{ .mfi
|
|
adds rSgnGam = 1, r0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
setf.exp f9 = r8
|
|
fmerge.s FR_X = f8,f8
|
|
mov GR_Parameter_TAG = 102 // overflow
|
|
};;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
fma.s0 FR_RESULT = f9,f9,f0 // Set I,O and +INF result
|
|
br.cond.sptk __libm_error_region
|
|
};;
|
|
|
|
// here if x is negative integer or +/-0 (SINGULARITY)
|
|
.align 32
|
|
lgammal_singularity:
|
|
{ .mfi
|
|
adds rSgnGam = 1, r0
|
|
fclass.m p8,p0 = f8,0x6 // is x -0?
|
|
mov GR_Parameter_TAG = 103 // negative
|
|
}
|
|
{ .mfi
|
|
cmp.eq p6, p7 = 4, rSgnGamSize
|
|
fma.s1 FR_X = f0,f0,f8
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
(p8) sub rSgnGam = r0, rSgnGam
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
// store signgam if size of variable is 4 bytes
|
|
(p6) st4 [rSgnGamAddr] = rSgnGam
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
// store signgam if size of variable is 8 bytes
|
|
(p7) st8 [rSgnGamAddr] = rSgnGam
|
|
frcpa.s0 FR_RESULT, p0 = f1, f0
|
|
br.cond.sptk __libm_error_region
|
|
};;
|
|
|
|
GLOBAL_LIBM_END(__libm_lgammal)
|
|
|
|
|
|
|
|
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
|
|
stfe [GR_Parameter_Y] = FR_Y,16 // Save 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
|
|
stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .mib
|
|
stfe [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 999
|
|
nop.i 999
|
|
};;
|
|
{ .mmi
|
|
ldfe 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#
|