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0b7a5f9201
Similar to various other bugs in this area, some log1p implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. (The ldbl-128ibm implementation doesn't currently need any change as it already generates this exception, albeit through code that would generate spurious exceptions in other cases; special code for this issue will only be needed there when fixing the spurious exceptions.) Tested for x86_64, x86, powerpc and mips64. [BZ #16339] * sysdeps/i386/fpu/s_log1p.S (dbl_min): New object. (__log1p): Force underflow exception for results with small absolute value. * sysdeps/i386/fpu/s_log1pf.S (flt_min): New object. (__log1pf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/s_log1p.c: Include <float.h>. (__log1p): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/s_log1pf.c: Include <float.h>. (__log1pf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/s_log1pl.c: Include <float.h>. (__log1pl): Force underflow exception for results with small absolute value. * math/auto-libm-test-in: Do not allow missing underflow exceptions from log1p. * math/auto-libm-test-out: Regenerated.
262 lines
6.7 KiB
C
262 lines
6.7 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 <float.h>
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#include <math.h>
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#include <math_private.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 maxlog = 1.1356523406294143949491931077970764891253E4L;
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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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ieee854_long_double_shape_type u;
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int32_t hx;
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int e;
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/* Test for NaN or infinity input. */
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u.value = xm1;
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hx = u.parts32.w0;
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if (hx >= 0x7fff0000)
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return xm1;
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/* log1p(+- 0) = +- 0. */
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if (((hx & 0x7fffffff) == 0)
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&& (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
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return xm1;
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if ((hx & 0x7fffffff) < 0x3f8e0000)
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{
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if (fabsl (xm1) < LDBL_MIN)
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{
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long double force_underflow = xm1 * xm1;
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math_force_eval (force_underflow);
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}
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if ((int) xm1 == 0)
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return xm1;
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}
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if (xm1 >= 0x1p113L)
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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 / zero); /* log1p(-1) = -inf */
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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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