# FreeBSD Manual Pages

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

NAME
exp, expf,	expl, exp2, exp2f, exp2l, expm1, expm1f, expm1l, pow, powf,
powl -- exponential and power functions

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <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);

long double
powl(long double x, long double y);

DESCRIPTION
The exp(),	expf(),	and expl() 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(), expm1f(), and	the expm1l() functions compute the value
exp(x)-1 accurately even for tiny argument	x.

The pow(),	powf(),	and the	powl() 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), powf(x,
y), and powl(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,	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, in-
cluding x = 0.  This is compatible	with the convention that ac-
cepts 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.

clog(3) cpow(3) fenv(3), ldexp(3),	log(3),	math(3)

STANDARDS
These functions conform to	ISO/IEC	9899:1999 ("ISO	C99").

HISTORY
The exp() function	appeared in Version 1 AT&T UNIX.

FreeBSD	13.0			 April 1, 2020			  FreeBSD 13.0
```

NAME | LIBRARY | SYNOPSIS | DESCRIPTION | ERROR (due to Roundoff etc.) | RETURN VALUES | NOTES | SEE ALSO | STANDARDS | HISTORY

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