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b303185df9
The ldbl-128ibm implementation of log1pl does ordered comparisons on a negative qNaN argument, so resulting in spurious "invalid" exceptions (for soft-float powerpc; hard-float only avoids this because of GCC bug 58684 meaning ordered comparison instructions never get generated). This patch fixes this by arranging for the test for NaN or infinity arguments to handle negative arguments as well. Tested for powerpc (soft float). [BZ #22693] * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Handle negative arguments in test for NaN or infinity argument.
250 lines
6.4 KiB
C
250 lines
6.4 KiB
C
/* log1pl.c
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*
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* Relative error logarithm
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* Natural logarithm of 1+x, 128-bit long double precision
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*
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, log1pl();
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*
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* y = log1pl( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the base e (2.718...) logarithm of 1+x.
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*
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* The argument 1+x is separated into its exponent and fractional
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* parts. If the exponent is between -1 and +1, the logarithm
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* of the fraction is approximated by
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*
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* log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
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*
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* Otherwise, setting z = 2(w-1)/(w+1),
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*
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* log(w) = z + z^3 P(z)/Q(z).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -1, 8 100000 1.9e-34 4.3e-35
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*/
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/* Copyright 2001 by Stephen L. Moshier
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include <math_ldbl_opt.h>
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/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
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* 1/sqrt(2) <= 1+x < sqrt(2)
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* Theoretical peak relative error = 5.3e-37,
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* relative peak error spread = 2.3e-14
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*/
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static const long double
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P12 = 1.538612243596254322971797716843006400388E-6L,
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P11 = 4.998469661968096229986658302195402690910E-1L,
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P10 = 2.321125933898420063925789532045674660756E1L,
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P9 = 4.114517881637811823002128927449878962058E2L,
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P8 = 3.824952356185897735160588078446136783779E3L,
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P7 = 2.128857716871515081352991964243375186031E4L,
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P6 = 7.594356839258970405033155585486712125861E4L,
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P5 = 1.797628303815655343403735250238293741397E5L,
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P4 = 2.854829159639697837788887080758954924001E5L,
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P3 = 3.007007295140399532324943111654767187848E5L,
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P2 = 2.014652742082537582487669938141683759923E5L,
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P1 = 7.771154681358524243729929227226708890930E4L,
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P0 = 1.313572404063446165910279910527789794488E4L,
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/* Q12 = 1.000000000000000000000000000000000000000E0L, */
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Q11 = 4.839208193348159620282142911143429644326E1L,
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Q10 = 9.104928120962988414618126155557301584078E2L,
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Q9 = 9.147150349299596453976674231612674085381E3L,
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Q8 = 5.605842085972455027590989944010492125825E4L,
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Q7 = 2.248234257620569139969141618556349415120E5L,
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Q6 = 6.132189329546557743179177159925690841200E5L,
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Q5 = 1.158019977462989115839826904108208787040E6L,
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Q4 = 1.514882452993549494932585972882995548426E6L,
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Q3 = 1.347518538384329112529391120390701166528E6L,
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Q2 = 7.777690340007566932935753241556479363645E5L,
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Q1 = 2.626900195321832660448791748036714883242E5L,
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Q0 = 3.940717212190338497730839731583397586124E4L;
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/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
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* where z = 2(x-1)/(x+1)
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* 1/sqrt(2) <= x < sqrt(2)
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* Theoretical peak relative error = 1.1e-35,
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* relative peak error spread 1.1e-9
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*/
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static const long double
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R5 = -8.828896441624934385266096344596648080902E-1L,
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R4 = 8.057002716646055371965756206836056074715E1L,
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R3 = -2.024301798136027039250415126250455056397E3L,
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R2 = 2.048819892795278657810231591630928516206E4L,
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R1 = -8.977257995689735303686582344659576526998E4L,
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R0 = 1.418134209872192732479751274970992665513E5L,
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/* S6 = 1.000000000000000000000000000000000000000E0L, */
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S5 = -1.186359407982897997337150403816839480438E2L,
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S4 = 3.998526750980007367835804959888064681098E3L,
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S3 = -5.748542087379434595104154610899551484314E4L,
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S2 = 4.001557694070773974936904547424676279307E5L,
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S1 = -1.332535117259762928288745111081235577029E6L,
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S0 = 1.701761051846631278975701529965589676574E6L;
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/* C1 + C2 = ln 2 */
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static const long double C1 = 6.93145751953125E-1L;
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static const long double C2 = 1.428606820309417232121458176568075500134E-6L;
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static const long double sqrth = 0.7071067811865475244008443621048490392848L;
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/* ln (2^16384 * (1 - 2^-113)) */
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static const long double zero = 0.0L;
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long double
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__log1pl (long double xm1)
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{
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long double x, y, z, r, s;
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double xhi;
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int32_t hx, lx;
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int e;
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/* Test for NaN or infinity input. */
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xhi = ldbl_high (xm1);
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EXTRACT_WORDS (hx, lx, xhi);
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if ((hx & 0x7fffffff) >= 0x7ff00000)
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return xm1 + xm1 * xm1;
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/* log1p(+- 0) = +- 0. */
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if (((hx & 0x7fffffff) | lx) == 0)
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return xm1;
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if (xm1 >= 0x1p107L)
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x = xm1;
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else
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x = xm1 + 1.0L;
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/* log1p(-1) = -inf */
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if (x <= 0.0L)
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{
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if (x == 0.0L)
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return (-1.0L / 0.0L);
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else
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return (zero / (x - x));
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}
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/* Separate mantissa from exponent. */
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/* Use frexp used so that denormal numbers will be handled properly. */
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x = __frexpl (x, &e);
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/* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
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where z = 2(x-1)/x+1). */
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if ((e > 2) || (e < -2))
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{
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if (x < sqrth)
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{ /* 2( 2x-1 )/( 2x+1 ) */
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e -= 1;
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z = x - 0.5L;
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y = 0.5L * z + 0.5L;
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}
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else
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{ /* 2 (x-1)/(x+1) */
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z = x - 0.5L;
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z -= 0.5L;
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y = 0.5L * x + 0.5L;
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}
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x = z / y;
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z = x * x;
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r = ((((R5 * z
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+ R4) * z
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+ R3) * z
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+ R2) * z
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+ R1) * z
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+ R0;
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s = (((((z
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+ S5) * z
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+ S4) * z
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+ S3) * z
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+ S2) * z
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+ S1) * z
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+ S0;
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z = x * (z * r / s);
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z = z + e * C2;
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z = z + x;
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z = z + e * C1;
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return (z);
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}
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/* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */
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if (x < sqrth)
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{
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e -= 1;
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if (e != 0)
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x = 2.0L * x - 1.0L; /* 2x - 1 */
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else
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x = xm1;
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}
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else
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{
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if (e != 0)
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x = x - 1.0L;
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else
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x = xm1;
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}
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z = x * x;
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r = (((((((((((P12 * x
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+ P11) * x
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+ P10) * x
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+ P9) * x
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+ P8) * x
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+ P7) * x
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+ P6) * x
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+ P5) * x
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+ P4) * x
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+ P3) * x
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+ P2) * x
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+ P1) * x
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+ P0;
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s = (((((((((((x
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+ Q11) * x
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+ Q10) * x
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+ Q9) * x
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+ Q8) * x
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+ Q7) * x
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+ Q6) * x
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+ Q5) * x
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+ Q4) * x
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+ Q3) * x
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+ Q2) * x
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+ Q1) * x
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+ Q0;
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y = x * (z * r / s);
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y = y + e * C2;
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z = y - 0.5L * z;
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z = z + x;
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z = z + e * C1;
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return (z);
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}
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