1.\" Copyright (c) 1985, 1991 Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 4. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91 29.\" $FreeBSD$ 30.\" 31.Dd January 17, 2008 32.Dt EXP 3 33.Os 34.Sh NAME 35.Nm exp , 36.Nm expf , 37.\" The sorting error is intentional. exp and expf should be adjacent. 38.Nm exp2 , 39.Nm exp2f , 40.Nm exp2l , 41.Nm expm1 , 42.Nm expm1f , 43.Nm pow , 44.Nm powf 45.Nd exponential and power functions 46.Sh LIBRARY 47.Lb libm 48.Sh SYNOPSIS 49.In math.h 50.Ft double 51.Fn exp "double x" 52.Ft float 53.Fn expf "float x" 54.Ft double 55.Fn exp2 "double x" 56.Ft float 57.Fn exp2f "float x" 58.Ft long double 59.Fn exp2l "long double x" 60.Ft double 61.Fn expm1 "double x" 62.Ft float 63.Fn expm1f "float x" 64.Ft double 65.Fn pow "double x" "double y" 66.Ft float 67.Fn powf "float x" "float y" 68.Sh DESCRIPTION 69The 70.Fn exp 71and the 72.Fn expf 73functions compute the base 74.Ms e 75exponential value of the given argument 76.Fa x . 77.Pp 78The 79.Fn exp2 , 80.Fn exp2f , 81and 82.Fn exp2l 83functions compute the base 2 exponential of the given argument 84.Fa x . 85.Pp 86The 87.Fn expm1 88and the 89.Fn expm1f 90functions compute the value exp(x)\-1 accurately even for tiny argument 91.Fa x . 92.Pp 93The 94.Fn pow 95and the 96.Fn powf 97functions compute the value 98of 99.Ar x 100to the exponent 101.Ar y . 102.Sh ERROR (due to Roundoff etc.) 103The values of 104.Fn exp 0 , 105.Fn expm1 0 , 106.Fn exp2 integer , 107and 108.Fn pow integer integer 109are exact provided that they are representable. 110.\" XXX Is this really true for pow()? 111Otherwise the error in these functions is generally below one 112.Em ulp . 113.Sh RETURN VALUES 114These functions will return the appropriate computation unless an error 115occurs or an argument is out of range. 116The functions 117.Fn pow x y 118and 119.Fn powf x y 120raise an invalid exception and return an \*(Na if 121.Fa x 122< 0 and 123.Fa y 124is not an integer. 125.Sh NOTES 126The function 127.Fn pow x 0 128returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na . 129Previous implementations of pow may 130have defined x**0 to be undefined in some or all of these 131cases. 132Here are reasons for returning x**0 = 1 always: 133.Bl -enum -width indent 134.It 135Any program that already tests whether x is zero (or 136infinite or \*(Na) before computing x**0 cannot care 137whether 0**0 = 1 or not. 138Any program that depends 139upon 0**0 to be invalid is dubious anyway since that 140expression's meaning and, if invalid, its consequences 141vary from one computer system to another. 142.It 143Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for 144all x, including x = 0. 145This is compatible with the convention that accepts a[0] 146as the value of polynomial 147.Bd -literal -offset indent 148p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n 149.Ed 150.Pp 151at x = 0 rather than reject a[0]\(**0**0 as invalid. 152.It 153Analysts will accept 0**0 = 1 despite that x**y can 154approach anything or nothing as x and y approach 0 155independently. 156The reason for setting 0**0 = 1 anyway is this: 157.Bd -ragged -offset indent 158If x(z) and y(z) are 159.Em any 160functions analytic (expandable 161in power series) in z around z = 0, and if there 162x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. 163.Ed 164.It 165If 0**0 = 1, then 166\*(If**0 = 1/0**0 = 1 too; and 167then \*(Na**0 = 1 too because x**0 = 1 for all finite 168and infinite x, i.e., independently of x. 169.El 170.Sh SEE ALSO 171.Xr fenv 3 , 172.Xr ldexp 3 , 173.Xr log 3 , 174.Xr math 3 175.Sh STANDARDS 176These functions conform to 177.St -isoC-99 . 178