183 lines
4.5 KiB
C
183 lines
4.5 KiB
C
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log2l.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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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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* Base 2 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, log2l();
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*
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* y = log2l( 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 2 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 (natural)
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* logarithm 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 9.8e-20 2.7e-20
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* IEEE exp(+-10000) 70000 5.4e-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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#include "libc/math/libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double log2l(long double x)
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{
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return log2(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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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 = 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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/* log2(e) - 1 */
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#define LOG2EA 4.4269504088896340735992e-1L
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#define SQRTH 0.70710678118654752440L
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long double log2l(long double x)
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{
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long double y, 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 == INFINITY)
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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/(x*x); /* -inf with divbyzero */
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return 0/0.0f; /* nan with invalid */
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}
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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 log2(e)
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* and base 2 exponent by 1
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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 * LOG2EA;
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z += x * LOG2EA;
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z += y;
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z += x;
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z += e;
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return z;
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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// TODO: broken implementation to make things compile
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long double log2l(long double x)
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{
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return log2(x);
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}
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#endif
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