logl

Logarithm functions

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Contents

Interface
Description
Special Values
See Also
Standards
Page Comments

Interface

#include <math.h>double  log (double x)
long  logl (long double x)
float  logf (float x)
double  log2 (double x)
long  log2l (long double x)
float  log2f (float x)
double  log10 (double x)
long  log10l (long double x)
float  log10f (float x)
double  log1p (double x)
long  log1pl (long double x)
float  log1pf (float x)

Description

The log function computes the value of the natural logarithm of argument x.

The log2 function computes the value of the logarithm of argument x to base 2.

The log10 function computes the value of the logarithm of argument x to base 10.

The log1p function computes the value of $\inline \log(1+x)$ accurately even for very small values of x.

Example:

Example - Logarithm functions

Workings

#include <math.h>
#include <stdio.h>
int main()
{
  printf("\n   x    \t   log   \t   log2   \t   log10   \t   log1p");  
  for(double x=0; x<=10; x+=0.5)
    printf("\n%lf\t%lf\t%lf\t%lf\t%lf", x, log(x), log2(x), log10(x), log1p(x));   
  return 0;
}

Solution

Output

x    	   log   	   log2   	   log10   	   log1p
0.000000	-inf	        -inf	        -inf	        0.000000
0.500000	-0.693147	-1.000000	-0.301030	0.405465
1.000000	0.000000	0.000000	0.000000	0.693147
1.500000	0.405465	0.584963	0.176091	0.916291
2.000000	0.693147	1.000000	0.301030	1.098612
2.500000	0.916291	1.321928	0.397940	1.252763
3.000000	1.098612	1.584963	0.477121	1.386294
3.500000	1.252763	1.807355	0.544068	1.504077
4.000000	1.386294	2.000000	0.602060	1.609438
4.500000	1.504077	2.169925	0.653213	1.704748
5.000000	1.609438	2.321928	0.698970	1.791759
5.500000	1.704748	2.459432	0.740363	1.871802
6.000000	1.791759	2.584963	0.778151	1.945910
6.500000	1.871802	2.700440	0.812913	2.014903
7.000000	1.945910	2.807355	0.845098	2.079442
7.500000	2.014903	2.906891	0.875061	2.140066
8.000000	2.079442	3.000000	0.903090	2.197225
8.500000	2.140066	3.087463	0.929419	2.251292
9.000000	2.197225	3.169925	0.954243	2.302585
9.500000	2.251292	3.247928	0.977724	2.351375
10.000000	2.302585	3.321928	1.000000	2.397895

Special Values

log ( ±0 ), log2 ( ±0 ), and log10( ±0 ) return -∞ and raise the divide-by-zero floating-point exception.

log ( 1 ), log2 ( 1 ), and log10 ( 1 ) return +0.

log ( x ), log2 ( x ), and log10 ( x ) return a NaN and raise the invalid floating-point exception for x < 0.

log ( +∞ ), log2 ( +∞ ), and log10 ( +∞ ) return +∞.

log1p ( ±0 ) returns ±0.

log1p ( -1 ) returns -∞ and raises the divide-by-zero floating-point exception.

log1p ( x ) returns a NaN and raises the invalid floating-point exception for x < -1.

log1p ( +∞ ) returns +∞.

Standards

The log, log2, log10 and log1p functions conform to ISO/IEC 9899:1999(E).

double	`log` (double x)
long	`logl` (long double x)
float	`logf` (float x)
double	`log2` (double x)
long	`log2l` (long double x)
float	`log2f` (float x)
double	`log10` (double x)
long	`log10l` (long double x)
float	`log10f` (float x)
double	`log1p` (double x)
long	`log1pl` (long double x)
float	`log1pf` (float x)