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/* log2f.c
*
* Base 2 logarithm
*
*
*
* SYNOPSIS:
*
* float x, y, log2f();
*
* y = log2f( x );
*
*
*
* DESCRIPTION:
*
* Returns the base 2 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the base e
* 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 exp(+-88) 100000 1.1e-7 2.4e-8
* IEEE 0.5, 2.0 100000 1.1e-7 3.0e-8
*
* In the tests over the interval [exp(+-88)], the logarithms
* of the random arguments were uniformly distributed.
*
* ERROR MESSAGES:
*
* log singularity: x = 0; returns MINLOGF/log(2)
* log domain: x < 0; returns MINLOGF/log(2)
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
static char fname[] = {"log2"};
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)
* 1/sqrt(2) <= x < sqrt(2)
*/
static float P[] = {
7.0376836292E-2,
-1.1514610310E-1,
1.1676998740E-1,
-1.2420140846E-1,
1.4249322787E-1,
-1.6668057665E-1,
2.0000714765E-1,
-2.4999993993E-1,
3.3333331174E-1
};
#define LOG2EA 0.44269504088896340735992
#define SQRTH 0.70710678118654752440
extern float MINLOGF, LOGE2F;
float frexpf(float, int *), polevlf(float, float *, int);
float log2f(float xx)
{
float x, y, z;
int e;
x = xx;
/* Test for domain */
if( x <= 0.0 )
{
if( x == 0.0 )
mtherr( fname, SING );
else
mtherr( fname, DOMAIN );
return( MINLOGF/LOGE2F );
}
/* separate mantissa from exponent */
x = frexpf( x, &e );
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if( x < SQRTH )
{
e -= 1;
x = 2.0*x - 1.0;
}
else
{
x = x - 1.0;
}
z = x*x;
y = x * ( z * polevlf( x, P, 8 ) );
y = y - 0.5 * z; /* y - 0.5 * x**2 */
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*
* ***CAUTION***
*
* This sequence of operations is critical and it may
* be horribly defeated by some compiler optimizers.
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += (float )e;
return( z );
}
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