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# Manual Reference Pages  -  EXP2L (3)

### NAME

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

### CONTENTS

Library
Synopsis
Description
ERROR (due to Roundoff etc.)
Return Values
Notes
Standards

.Lb libm

### SYNOPSIS

.In 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

### DESCRIPTION

The exp, expf, and expl functions compute the base
.Ms 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 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.

### NOTES

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:
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 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 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.