EXP(3)

NAME
exp, expf, exp2, exp2f, expm1, expm1f, log, logf, log10, log10f, log1p, log1pf, pow, powf - exponential, logarithm, power functions

LIBRARY
libm

SYNOPSIS
#include <math.h>
double
exp(double x);
float
expf(float x);
double
exp2(double x);
float
exp2f(float x);
double
expm1(double x);
float
expm1f(float x);
double
log(double x);
float
logf(float x);
double
log10(double x);
float
log10f(float x);
double
log1p(double x);
float
log1pf(float x);
double
pow(double x, double y);
float
powf(float x, float y);

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

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

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

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

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

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

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

ERROR (due to Roundoff etc.)
The values of exp(0), expm1(0), exp2(integer), and pow(integer, integer) are exact provided that they are representable. Otherwise the error in these functions is generally below one ulp.

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) raise an invalid exception and return an if x < 0 and y is not an integer. An attempt to take the logarithm of 0 will result in a divide-by-zero exception, and an infinity will be returned. An attempt to take the logarithm of a negative number will result in an invalid exception, and an will be generated.

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, , and . 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:

1.  Any program that already tests whether x is zero (or infinite or ) 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.

2.  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.

3.  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.

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

SEE ALSO
fenv(3), math(3)