exp

Name

exp, expf, expl,exp2, exp2f, exp2l, expm1, expm1f, expm1f, expm1l
log, logf, logl, log10, log10f, log10l, log1p, log1pf, log1pl

pow, powf, powl,

- exponential, logarithm, power functions

Library

libm.lib

Synopsis

#include <math.h>

double exp (double x);

float expf (float x);

long double expl (long double x);

double exp2 (double x);

float exp2f (float x);

long double exp2l (long double x);

double expm1 (double x);

float expm1f (float x);

long double expm1l (long double x);

double log (double x);

float logf (float x);

long double logl (long double x);

double log10 (double x);

float log10f (float x);

long double log10l (long double x);

double log1p (double x);

float log1pf (float x);

long double log1pl (long double x);

double pow (double x, double y);

float powf (float x, float y);

long double powl (long double x, long double y);

Return values

These functions will return the appropriate computation unless an error occurs or an argument is out of range. The functions pow (x, y);
and powf (x, y);
return an NaN if x < 0 and y is not an integer. An attempt to take the logarithm of ±0 will return infinity. An attempt to take the logarithm of a negative number will return a NaN.

Detailed description

The exp and expf functions compute the base e exponential value of the given argument x.

The exp2 and exp2f functions compute the base 2 exponential of the given argument x.

The expm1 and expm1f functions compute the value exp(x)-1 accurately even for tiny argument x.

The log and logf functions compute the value of the natural logarithm of argument x.

The log10 and log10f functions compute the value of the logarithm of argument x to base 10.

The log1p and log1pf functions compute the value of log(1+x) accurately even for tiny argument x.

The pow and powf functions compute the value of x to the exponent y.

Here the long double version APIs are aliases to the double version APIs. All apis <function>l behaves similiar to that <function>.

Examples

#include <math.h>
int main( void )
{
   double x, y;
   x = 1.0;
   y = exp( x );
   printf( "exp( %f ) = %f\n", x, y );
   y = expf( x );
   printf( "expf( %f ) = %f\n",x, y );
   y = expl( x );
   printf( "expl( %f ) = %f\n",x, y );
   x = 0.0;
   y = exp2( x );
   printf( "exp2( %f ) = %f\n", x, y );
   y = exp2f( x );
   printf( "exp2f( %f ) = %f\n",x, y );
   y = exp2l( x );
   printf( "exp2l( %f ) = %f\n",x, y );
   x = 1.0 ;
   y = expm1( x );
   printf( "expm1( %f ) = %f\n", x, y );
   y = expm1f( x );
   printf( "expm1f( %f ) = %f\n",x, y );
   y = expm1l( x );
   printf( "expm1l( %f ) = %f\n",x, y );
}

Output

exp   ( 1.0 ) = 2.718282
expf  ( 1.0 ) = 2.718282
expl  ( 1.0 ) = 2.718282
exp2  ( 0.0 ) = 1.000000
exp2f ( 0.0 ) = 1.000000
exp2l ( 0.0 ) = 1.000000
expm1 ( 1.0 ) = 1.718281        
expm1f( 1.0 ) = 1.718281
expm1l( 1.0 ) = 1.718281

Notes

The functions exp(x)-1 and log(1+x) are called expm1 and logp1 in BASIC on the Hewlett-Packard HP -71B and APPLE Macintosh, EXP1 and LN1 in Pascal, exp1 and log1 in C on APPLE Macintoshes, where they have been provided to make sure financial calculations of ((1+x)**n-1)/x, namely expm1(n*log1p(x))/x, will be accurate when x is tiny. They also provide accurate inverse hyperbolic functions.

The function pow (x, 0);
returns x**0 = 1 for all x including x = 0, oo, and NaN . Previous implementations of pow may have defined x**0 to be undefined in some or all of these cases. Here are reasons for returning x**0 = 1 always:

Any program that already tests whether x is zero (or infinite or NaN) before computing x**0 cannot care whether 0**0 = 1 or not. Any program that depends upon 0**0 to be invalid is dubious anyway since that expression’s meaning and, if invalid, its consequences vary from one computer system to another.
Some Algebra texts (e.g. Sigler’s) define x**0 = 1 for all x, including x = 0. This is compatible with the convention that accepts a[0] as the value of polynomial
```
p(x) = a[0]*x**0 + a[1]*x**1 + a[2]*x**2 +...+ a[n]*x**n

               
```
at x = 0 rather than reject a[0]*0**0 as invalid.

Analysts will accept 0**0 = 1 despite that x**y can approach anything or nothing as x and y approach 0 independently. The reason for setting 0**0 = 1 anyway is this:

If x(z) and y(z) are

               
 any
functions analytic (expandable
in power series) in z around z = 0, and if there
x(0) = y(0) = 0, then x(z)**y(z) -> 1 as z -> 0.

If 0**0 = 1, then oo**0 = 1/0**0 = 1 too; and then NaN**0 = 1 too because x**0 = 1 for all finite and infinite x, i.e., independently of x.

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