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02bbfb414f
This runs the attached sed script against these files using a regex which aggressively matches long double literals when not obviously part of a comment. Likewise, 5 digit or less integral constants are replaced with integer constants, excepting the two cases of 0 used in large tables, which are also the only integral values of the form x.0*E0L encountered within these converted files. Likewise, -L(x) is transformed into L(-x). Naturally, the script has a few minor hiccups which are more clearly remedied via the attached fixup patch. Such hiccups include, context-sensitive promotion to a real type, and munging constants inside harder to detect comment blocks.
260 lines
6.4 KiB
C
260 lines
6.4 KiB
C
/* log10l.c
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*
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* Common logarithm, 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, log10l();
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*
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* y = log10l( 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 10 logarithm of x.
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*
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* The argument 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(x-1)/x+1),
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*
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* log(x) = 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 0.5, 2.0 30000 2.3e-34 4.9e-35
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* IEEE exp(+-10000) 30000 1.0e-34 4.1e-35
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*
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* In the tests over the interval exp(+-10000), the logarithms
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* of the random arguments were uniformly distributed over
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* [-10000, +10000].
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*
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*/
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/*
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Cephes Math Library Release 2.2: January, 1991
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Copyright 1984, 1991 by Stephen L. Moshier
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Adapted for glibc November, 2001
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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 <http://www.gnu.org/licenses/>.
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*/
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#include <math.h>
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#include <math_private.h>
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/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
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* 1/sqrt(2) <= 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 _Float128 P[13] =
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{
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L(1.313572404063446165910279910527789794488E4),
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L(7.771154681358524243729929227226708890930E4),
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L(2.014652742082537582487669938141683759923E5),
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L(3.007007295140399532324943111654767187848E5),
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L(2.854829159639697837788887080758954924001E5),
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L(1.797628303815655343403735250238293741397E5),
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L(7.594356839258970405033155585486712125861E4),
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L(2.128857716871515081352991964243375186031E4),
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L(3.824952356185897735160588078446136783779E3),
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L(4.114517881637811823002128927449878962058E2),
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L(2.321125933898420063925789532045674660756E1),
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L(4.998469661968096229986658302195402690910E-1),
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L(1.538612243596254322971797716843006400388E-6)
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};
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static const _Float128 Q[12] =
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{
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L(3.940717212190338497730839731583397586124E4),
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L(2.626900195321832660448791748036714883242E5),
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L(7.777690340007566932935753241556479363645E5),
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L(1.347518538384329112529391120390701166528E6),
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L(1.514882452993549494932585972882995548426E6),
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L(1.158019977462989115839826904108208787040E6),
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L(6.132189329546557743179177159925690841200E5),
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L(2.248234257620569139969141618556349415120E5),
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L(5.605842085972455027590989944010492125825E4),
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L(9.147150349299596453976674231612674085381E3),
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L(9.104928120962988414618126155557301584078E2),
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L(4.839208193348159620282142911143429644326E1)
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/* 1.000000000000000000000000000000000000000E0L, */
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};
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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 _Float128 R[6] =
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{
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L(1.418134209872192732479751274970992665513E5),
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L(-8.977257995689735303686582344659576526998E4),
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L(2.048819892795278657810231591630928516206E4),
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L(-2.024301798136027039250415126250455056397E3),
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L(8.057002716646055371965756206836056074715E1),
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L(-8.828896441624934385266096344596648080902E-1)
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};
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static const _Float128 S[6] =
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{
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L(1.701761051846631278975701529965589676574E6),
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L(-1.332535117259762928288745111081235577029E6),
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L(4.001557694070773974936904547424676279307E5),
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L(-5.748542087379434595104154610899551484314E4),
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L(3.998526750980007367835804959888064681098E3),
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L(-1.186359407982897997337150403816839480438E2)
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/* 1.000000000000000000000000000000000000000E0L, */
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};
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static const _Float128
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/* log10(2) */
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L102A = L(0.3125),
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L102B = L(-1.14700043360188047862611052755069732318101185E-2),
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/* log10(e) */
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L10EA = L(0.5),
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L10EB = L(-6.570551809674817234887108108339491770560299E-2),
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/* sqrt(2)/2 */
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SQRTH = L(7.071067811865475244008443621048490392848359E-1);
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/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
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static _Float128
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neval (_Float128 x, const _Float128 *p, int n)
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{
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_Float128 y;
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p += n;
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y = *p--;
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do
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{
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y = y * x + *p--;
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}
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while (--n > 0);
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return y;
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}
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/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
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static _Float128
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deval (_Float128 x, const _Float128 *p, int n)
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{
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_Float128 y;
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p += n;
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y = x + *p--;
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do
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{
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y = y * x + *p--;
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}
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while (--n > 0);
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return y;
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}
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_Float128
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__ieee754_log10l (_Float128 x)
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{
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_Float128 z;
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_Float128 y;
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int e;
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int64_t hx, lx;
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/* Test for domain */
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GET_LDOUBLE_WORDS64 (hx, lx, x);
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if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
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return (-1 / (x - x));
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if (hx < 0)
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return (x - x) / (x - x);
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if (hx >= 0x7fff000000000000LL)
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return (x + x);
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if (x == 1)
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return 0;
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/* separate mantissa from exponent */
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/* Note, frexp is used so that denormal numbers
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* will be handled properly.
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*/
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x = __frexpl (x, &e);
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/* logarithm using log(x) = z + z**3 P(z)/Q(z),
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* where z = 2(x-1)/x+1)
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*/
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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 - L(0.5);
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y = L(0.5) * z + L(0.5);
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}
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else
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{ /* 2 (x-1)/(x+1) */
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z = x - L(0.5);
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z -= L(0.5);
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y = L(0.5) * x + L(0.5);
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}
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x = z / y;
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z = x * x;
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y = x * (z * neval (z, R, 5) / deval (z, S, 5));
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goto done;
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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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x = 2.0 * x - 1; /* 2x - 1 */
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}
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else
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{
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x = x - 1;
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}
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z = x * x;
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y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
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y = y - 0.5 * z;
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done:
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/* Multiply log of fraction by log10(e)
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* and base 2 exponent by log10(2).
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*/
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z = y * L10EB;
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z += x * L10EB;
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z += e * L102B;
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z += y * L10EA;
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z += x * L10EA;
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z += e * L102A;
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return (z);
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}
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strong_alias (__ieee754_log10l, __log10l_finite)
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