mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2024-12-29 13:03:42 +01:00
255 lines
6.3 KiB
C
255 lines
6.3 KiB
C
/* $OpenBSD: e_log10l.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */
|
|
|
|
/*
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose with or without fee is hereby granted, provided that the above
|
|
* copyright notice and this permission notice appear in all copies.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
|
|
*/
|
|
|
|
/* 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].
|
|
*
|
|
*/
|
|
|
|
#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
|
|
log10l(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) == 0)
|
|
return (-1.0L / (x - x));
|
|
if (hx < 0)
|
|
return (x - x) / (x - x);
|
|
if (hx >= 0x7fff000000000000LL)
|
|
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);
|
|
}
|