EXP(3) BSD Library Functions Manual EXP(3)NAME
exp, expf, exp2, exp2f, exp2l, expm1, expm1f, pow, powf — exponential and
power functions
LIBRARY
Math Library (libm, -lm)
SYNOPSIS
#include <math.h>
double
exp(double x);
float
expf(float x);
double
exp2(double x);
float
exp2f(float x);
long double
exp2l(long double x);
double
expm1(double x);
float
expm1f(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(), exp2f(), and exp2l() functions compute the base 2 exponential
of the given argument x.
The expm1() and the expm1f() functions compute the value exp(x)-1 accu‐
rately 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 NaN if x < 0 and y is
not an integer.
NOTES
The function pow(x, 0) returns x**0 = 1 for all x including x = 0, ∞, and
NaN . Previous implementations of pow may have defined x**0 to be unde‐
fined 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
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 any‐
way since that expression's meaning and, if invalid, its conse‐
quences 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 any‐
thing 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 NaN**0 = 1 too
because x**0 = 1 for all finite and infinite x, i.e., indepen‐
dently of x.
SEE ALSOfenv(3), ldexp(3), log(3), math(3)STANDARDS
These functions conform to ISO/IEC 9899:1999 (“ISO C99”).
BSD January 17, 2008 BSD