---
name: "exp2"
section: "3"
platform: "freebsd"
package: "base"
version: "16.0-CURRENT-20261027-61c70dc16a79"
release: "FreeBSD 16.0-CURRENT (2026-10-27)"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/exp/3"
---

# exp2(3)

exponential and power functions

Part of [exp(3)](/exp/3.md).

## 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  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, , and  . 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:

1. Any program that already tests whether x is zero (or infinite or ) 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.

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\[0\] 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.

3. 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.

4. If 0\*\*0 = 1, then \*\*0 = 1/0\*\*0 = 1 too; and then \*\*0 = 1 too because x\*\*0 = 1 for all finite and infinite x, i.e., independently of x.

## SEE ALSO

[clog(3)](/clog/3.md), [cpow(3)](/cpow/3.md), [fenv(3)](/fenv/3.md), [ldexp(3)](/ldexp/3.md), [log(3)](/log/3.md), [math(3)](/math/3.md)

## STANDARDS

These functions conform to ISO/IEC 9899:1999 (“ISO C99”).

## HISTORY

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