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```EXP(3)		       FreeBSD Library Functions Manual			EXP(3)

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

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 accu-
rately even for tiny argument x.

The log() and the logf() functions	compute	the value of the natural loga-
rithm 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
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.

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	Pas-
cal, exp1 and log1	in C on	APPLE Macintoshes, where they have been	pro-
vided 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,	infin-
ity, 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 return-
ing 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 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.

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 infinity**0 = 1/0**0 = 1	too; and then NaN**0 =
1 too because x**0	= 1 for	all finite and infinite	x, i.e., inde-
pendently of x.