nsz
2786c7d216
Some code assumed ldexp(x, 1) is faster than 2.0*x, but ldexp is a wrapper around scalbn which uses multiplications inside, so this optimization is wrong. This commit also fixes fmal which accidentally used ldexp instead of ldexpl loosing precision. There are various additional changes from the work-in-progress const cleanups.
187 lines
4.6 KiB
C
187 lines
4.6 KiB
C
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log10l.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Common logarithm, long double precision
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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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* 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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* 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 9.0e-20 2.6e-20
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* IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
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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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* ERROR MESSAGES:
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*
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* log singularity: x = 0; returns MINLOG
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* log domain: x < 0; returns MINLOG
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*/
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double log10l(long double x)
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{
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return log10(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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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) <= x < sqrt(2)
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* Theoretical peak relative error = 6.2e-22
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*/
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static const long double P[] = {
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4.9962495940332550844739E-1L,
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1.0767376367209449010438E1L,
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7.7671073698359539859595E1L,
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2.5620629828144409632571E2L,
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4.2401812743503691187826E2L,
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3.4258224542413922935104E2L,
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1.0747524399916215149070E2L,
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};
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static const long double Q[] = {
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/* 1.0000000000000000000000E0,*/
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2.3479774160285863271658E1L,
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1.9444210022760132894510E2L,
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7.7952888181207260646090E2L,
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1.6911722418503949084863E3L,
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2.0307734695595183428202E3L,
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1.2695660352705325274404E3L,
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3.2242573199748645407652E2L,
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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 = 6.16e-22
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*/
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static const long double R[4] = {
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1.9757429581415468984296E-3L,
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-7.1990767473014147232598E-1L,
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1.0777257190312272158094E1L,
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-3.5717684488096787370998E1L,
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};
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static const long double S[4] = {
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/* 1.00000000000000000000E0L,*/
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-2.6201045551331104417768E1L,
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1.9361891836232102174846E2L,
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-4.2861221385716144629696E2L,
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};
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/* log10(2) */
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#define L102A 0.3125L
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#define L102B -1.1470004336018804786261e-2L
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/* log10(e) */
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#define L10EA 0.5L
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#define L10EB -6.5705518096748172348871e-2L
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#define SQRTH 0.70710678118654752440L
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long double log10l(long double x)
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{
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long double y;
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volatile long double z;
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int e;
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if (isnan(x))
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return x;
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if(x <= 0.0) {
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if(x == 0.0)
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return -1.0 / (x - x);
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return (x - x) / (x - x);
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}
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if (x == INFINITY)
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return INFINITY;
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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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if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
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e -= 1;
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z = x - 0.5;
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y = 0.5 * z + 0.5;
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} else { /* 2 (x-1)/(x+1) */
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z = x - 0.5;
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z -= 0.5;
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y = 0.5 * x + 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 * __polevll(z, R, 3) / __p1evll(z, S, 3));
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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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e -= 1;
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x = 2.0*x - 1.0;
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} else {
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x = x - 1.0;
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}
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z = x*x;
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y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
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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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* ***CAUTION***
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*
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* This sequence of operations is critical and it may
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* be horribly defeated by some compiler optimizers.
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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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#endif
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