

 
Manual Reference Pages  EXP (3)
NAME
exp,
expf,
exp2,
exp2f,
expm1,
expm1f,
log,
logf,
log10,
log10f,
log1p,
log1pf,
pow,
powf
 exponential, logarithm, power functions
CONTENTS
Library
Synopsis
Description
ERROR (due to Roundoff etc.)
Return Values
Notes
See Also
LIBRARY
.Lb libm
SYNOPSIS
.In 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
.Ms 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 NaN if
x
< 0 and
y
is not an integer.
An attempt to take the logarithm of ±0 will result in
a dividebyzero 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 NaN will be generated.
NOTES
The functions exp(x)1 and log(1+x) are called
expm1 and logp1 in
BASIC
on the HewlettPackard
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)**n1)/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.
SEE ALSO
fenv(3),
math(3)
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