

 
Manual Reference Pages  POWF (3)
NAME
exp,
expf,
expl,
exp2,
exp2f,
exp2l,
expm1,
expm1f,
expm1l,
pow,
powf
 exponential and power functions
CONTENTS
Library
Synopsis
Description
ERROR (due to Roundoff etc.)
Return Values
Notes
See Also
Standards
LIBRARY
.Lb libm
SYNOPSIS
.In 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
pow double x double y
float
powf float x float y
DESCRIPTION
The
exp,
expf,
and
expl
functions compute the base
.Ms 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,
expm1f,
and the
expm1l
functions compute the value exp(x)1 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 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, 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.
SEE ALSO
fenv(3),
ldexp(3),
log(3),
math(3)
STANDARDS
These functions conform to
isoC99.
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