Manual Reference Pages - EXP (3)
- exponential, logarithm, power functions
ERROR (due to Roundoff etc.)
exp double x
expf float x
exp2 double x
exp2f float x
expm1 double x
expm1f float x
log double x
logf float x
log10 double x
log10f float x
log1p double x
log1pf float x
pow double x double y
powf float x float y
functions compute the base
exponential value of the given argument
functions compute the base 2 exponential of the given argument
functions compute the value exp(x)-1 accurately even for tiny argument
functions compute the value of the natural logarithm of argument
functions compute the value of the logarithm of argument
to base 10.
the value of log(1+x) accurately even for tiny argument
functions compute the value
to the exponent
ERROR (due to Roundoff etc.)
The values of
pow integer integer
are exact provided that they are representable.
Otherwise the error in these functions is generally below one
These functions will return the appropriate computation unless an error
occurs or an argument is out of range.
pow x y
powf x y
raise an invalid exception and return an NaN if
< 0 and
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 NaN will be generated.
The functions exp(x)-1 and log(1+x) are called
expm1 and logp1 in
on the Hewlett-Packard
in Pascal, exp1 and log1 in C
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.
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
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
expressions meaning and, if invalid, its consequences
vary from one computer system to another.
- Some Algebra texts (e.g. Siglers) define x**0 = 1 for
all x, including x = 0.
This is compatible with the convention that accepts a
as the value of polynomial
p(x) = a*x**0 + a*x**1 + a*x**2 +...+ a[n]*x**n
at x = 0 rather than reject a*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
The reason for setting 0**0 = 1 anyway is this:
If x(z) and y(z) are
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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