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 June 3, 2013 32.Dt EXP 3 33.Os 34.Sh NAME 35.Nm exp , 36.Nm expf , 37.Nm expl , 38.\" The sorting error is intentional. exp, expf, and expl should be adjacent. 39.Nm exp2 , 40.Nm exp2f , 41.Nm exp2l , 42.Nm expm1 , 43.Nm expm1f , 44.Nm expm1l , 45.Nm pow , 46.Nm powf 47.Nd exponential and power functions 48.Sh LIBRARY 49.Lb libm 50.Sh SYNOPSIS 51.In math.h 52.Ft double 53.Fn exp "double x" 54.Ft float 55.Fn expf "float x" 56.Ft long double 57.Fn expl "long double x" 58.Ft double 59.Fn exp2 "double x" 60.Ft float 61.Fn exp2f "float x" 62.Ft long double 63.Fn exp2l "long double x" 64.Ft double 65.Fn expm1 "double x" 66.Ft float 67.Fn expm1f "float x" 68.Ft long double 69.Fn expm1l "long double x" 70.Ft double 71.Fn pow "double x" "double y" 72.Ft float 73.Fn powf "float x" "float y" 74.Sh DESCRIPTION 75The 76.Fn exp , 77.Fn expf , 78and 79.Fn expl 80functions compute the base 81.Ms e 82exponential value of the given argument 83.Fa x . 84.Pp 85The 86.Fn exp2 , 87.Fn exp2f , 88and 89.Fn exp2l 90functions compute the base 2 exponential of the given argument 91.Fa x . 92.Pp 93The 94.Fn expm1 , 95.Fn expm1f , 96and the 97.Fn expm1l 98functions compute the value exp(x)\-1 accurately even for tiny argument 99.Fa x . 100.Pp 101The 102.Fn pow 103and the 104.Fn powf 105functions compute the value 106of 107.Ar x 108to the exponent 109.Ar y . 110.Sh ERROR (due to Roundoff etc.) 111The values of 112.Fn exp 0 , 113.Fn expm1 0 , 114.Fn exp2 integer , 115and 116.Fn pow integer integer 117are exact provided that they are representable. 118.\" XXX Is this really true for pow()? 119Otherwise the error in these functions is generally below one 120.Em ulp . 121.Sh RETURN VALUES 122These functions will return the appropriate computation unless an error 123occurs or an argument is out of range. 124The functions 125.Fn pow x y 126and 127.Fn powf x y 128raise an invalid exception and return an \*(Na if 129.Fa x 130< 0 and 131.Fa y 132is not an integer. 133.Sh NOTES 134The function 135.Fn pow x 0 136returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na . 137Previous implementations of pow may 138have defined x**0 to be undefined in some or all of these 139cases. 140Here are reasons for returning x**0 = 1 always: 141.Bl -enum -width indent 142.It 143Any program that already tests whether x is zero (or 144infinite or \*(Na) before computing x**0 cannot care 145whether 0**0 = 1 or not. 146Any program that depends 147upon 0**0 to be invalid is dubious anyway since that 148expression's meaning and, if invalid, its consequences 149vary from one computer system to another. 150.It 151Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for 152all x, including x = 0. 153This is compatible with the convention that accepts a[0] 154as the value of polynomial 155.Bd -literal -offset indent 156p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n 157.Ed 158.Pp 159at x = 0 rather than reject a[0]\(**0**0 as invalid. 160.It 161Analysts will accept 0**0 = 1 despite that x**y can 162approach anything or nothing as x and y approach 0 163independently. 164The reason for setting 0**0 = 1 anyway is this: 165.Bd -ragged -offset indent 166If x(z) and y(z) are 167.Em any 168functions analytic (expandable 169in power series) in z around z = 0, and if there 170x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. 171.Ed 172.It 173If 0**0 = 1, then 174\*(If**0 = 1/0**0 = 1 too; and 175then \*(Na**0 = 1 too because x**0 = 1 for all finite 176and infinite x, i.e., independently of x. 177.El 178.Sh SEE ALSO 179.Xr fenv 3 , 180.Xr ldexp 3 , 181.Xr log 3 , 182.Xr math 3 183.Sh STANDARDS 184These functions conform to 185.St -isoC-99 . 186