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authorUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
committerUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
commita334319f6530564d22e775935d9c91663623a1b4 (patch)
treeb5877475619e4c938e98757d518bb1e9cbead751 /sysdeps/ieee754/ldbl-128ibm/e_log10l.c
parent0ecb606cb6cf65de1d9fc8a919bceb4be476c602 (diff)
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(CFLAGS-tst-align.c): Add -mpreferred-stack-boundary=4.
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_log10l.c')
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diff --git a/sysdeps/ieee754/ldbl-128ibm/e_log10l.c b/sysdeps/ieee754/ldbl-128ibm/e_log10l.c
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-/* log10l.c
- *
- * Common logarithm, 128-bit long double precision
- *
- *
- *
- * SYNOPSIS:
- *
- * long double x, y, log10l();
- *
- * y = log10l( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the base 10 logarithm of x.
- *
- * The argument is separated into its exponent and fractional
- * parts. If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
- *
- * Otherwise, setting z = 2(x-1)/x+1),
- *
- * log(x) = z + z^3 P(z)/Q(z).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35
- * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35
- *
- * In the tests over the interval exp(+-10000), the logarithms
- * of the random arguments were uniformly distributed over
- * [-10000, +10000].
- *
- */
-
-/*
- Cephes Math Library Release 2.2: January, 1991
- Copyright 1984, 1991 by Stephen L. Moshier
- Adapted for glibc November, 2001
-
- This library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- This library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with this library; if not, write to the Free Software
- Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-
- */
-
-#include "math.h"
-#include "math_private.h"
-
-/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 5.3e-37,
- * relative peak error spread = 2.3e-14
- */
-static const long double P[13] =
-{
- 1.313572404063446165910279910527789794488E4L,
- 7.771154681358524243729929227226708890930E4L,
- 2.014652742082537582487669938141683759923E5L,
- 3.007007295140399532324943111654767187848E5L,
- 2.854829159639697837788887080758954924001E5L,
- 1.797628303815655343403735250238293741397E5L,
- 7.594356839258970405033155585486712125861E4L,
- 2.128857716871515081352991964243375186031E4L,
- 3.824952356185897735160588078446136783779E3L,
- 4.114517881637811823002128927449878962058E2L,
- 2.321125933898420063925789532045674660756E1L,
- 4.998469661968096229986658302195402690910E-1L,
- 1.538612243596254322971797716843006400388E-6L
-};
-static const long double Q[12] =
-{
- 3.940717212190338497730839731583397586124E4L,
- 2.626900195321832660448791748036714883242E5L,
- 7.777690340007566932935753241556479363645E5L,
- 1.347518538384329112529391120390701166528E6L,
- 1.514882452993549494932585972882995548426E6L,
- 1.158019977462989115839826904108208787040E6L,
- 6.132189329546557743179177159925690841200E5L,
- 2.248234257620569139969141618556349415120E5L,
- 5.605842085972455027590989944010492125825E4L,
- 9.147150349299596453976674231612674085381E3L,
- 9.104928120962988414618126155557301584078E2L,
- 4.839208193348159620282142911143429644326E1L
-/* 1.000000000000000000000000000000000000000E0L, */
-};
-
-/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
- * where z = 2(x-1)/(x+1)
- * 1/sqrt(2) <= x < sqrt(2)
- * Theoretical peak relative error = 1.1e-35,
- * relative peak error spread 1.1e-9
- */
-static const long double R[6] =
-{
- 1.418134209872192732479751274970992665513E5L,
- -8.977257995689735303686582344659576526998E4L,
- 2.048819892795278657810231591630928516206E4L,
- -2.024301798136027039250415126250455056397E3L,
- 8.057002716646055371965756206836056074715E1L,
- -8.828896441624934385266096344596648080902E-1L
-};
-static const long double S[6] =
-{
- 1.701761051846631278975701529965589676574E6L,
- -1.332535117259762928288745111081235577029E6L,
- 4.001557694070773974936904547424676279307E5L,
- -5.748542087379434595104154610899551484314E4L,
- 3.998526750980007367835804959888064681098E3L,
- -1.186359407982897997337150403816839480438E2L
-/* 1.000000000000000000000000000000000000000E0L, */
-};
-
-static const long double
-/* log10(2) */
-L102A = 0.3125L,
-L102B = -1.14700043360188047862611052755069732318101185E-2L,
-/* log10(e) */
-L10EA = 0.5L,
-L10EB = -6.570551809674817234887108108339491770560299E-2L,
-/* sqrt(2)/2 */
-SQRTH = 7.071067811865475244008443621048490392848359E-1L;
-
-
-
-/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
-
-static long double
-neval (long double x, const long double *p, int n)
-{
- long double y;
-
- p += n;
- y = *p--;
- do
- {
- y = y * x + *p--;
- }
- while (--n > 0);
- return y;
-}
-
-
-/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
-
-static long double
-deval (long double x, const long double *p, int n)
-{
- long double y;
-
- p += n;
- y = x + *p--;
- do
- {
- y = y * x + *p--;
- }
- while (--n > 0);
- return y;
-}
-
-
-
-long double
-__ieee754_log10l (x)
- long double x;
-{
- long double z;
- long double y;
- int e;
- int64_t hx, lx;
-
-/* Test for domain */
- GET_LDOUBLE_WORDS64 (hx, lx, x);
- if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0)
- return (-1.0L / (x - x));
- if (hx < 0)
- return (x - x) / (x - x);
- if (hx >= 0x7ff0000000000000LL)
- return (x + x);
-
-/* separate mantissa from exponent */
-
-/* Note, frexp is used so that denormal numbers
- * will be handled properly.
- */
- x = __frexpl (x, &e);
-
-
-/* logarithm using log(x) = z + z**3 P(z)/Q(z),
- * where z = 2(x-1)/x+1)
- */
- if ((e > 2) || (e < -2))
- {
- if (x < SQRTH)
- { /* 2( 2x-1 )/( 2x+1 ) */
- e -= 1;
- z = x - 0.5L;
- y = 0.5L * z + 0.5L;
- }
- else
- { /* 2 (x-1)/(x+1) */
- z = x - 0.5L;
- z -= 0.5L;
- y = 0.5L * x + 0.5L;
- }
- x = z / y;
- z = x * x;
- y = x * (z * neval (z, R, 5) / deval (z, S, 5));
- goto done;
- }
-
-
-/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
-
- if (x < SQRTH)
- {
- e -= 1;
- x = 2.0 * x - 1.0L; /* 2x - 1 */
- }
- else
- {
- x = x - 1.0L;
- }
- z = x * x;
- y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
- y = y - 0.5 * z;
-
-done:
-
- /* Multiply log of fraction by log10(e)
- * and base 2 exponent by log10(2).
- */
- z = y * L10EB;
- z += x * L10EB;
- z += e * L102B;
- z += y * L10EA;
- z += x * L10EA;
- z += e * L102A;
- return (z);
-}