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 November 9, 2015 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.Nm powl 48.Nd exponential and power functions 49.Sh LIBRARY 50.Lb libm 51.Sh SYNOPSIS 52.In math.h 53.Ft double 54.Fn exp "double x" 55.Ft float 56.Fn expf "float x" 57.Ft long double 58.Fn expl "long double x" 59.Ft double 60.Fn exp2 "double x" 61.Ft float 62.Fn exp2f "float x" 63.Ft long double 64.Fn exp2l "long double x" 65.Ft double 66.Fn expm1 "double x" 67.Ft float 68.Fn expm1f "float x" 69.Ft long double 70.Fn expm1l "long double x" 71.Ft double 72.Fn pow "double x" "double y" 73.Ft float 74.Fn powf "float x" "float y" 75.Ft long double 76.Fn powl "long double x" "long double y" 77.Sh DESCRIPTION 78The 79.Fn exp , 80.Fn expf , 81and 82.Fn expl 83functions compute the base 84.Ms e 85exponential value of the given argument 86.Fa x . 87.Pp 88The 89.Fn exp2 , 90.Fn exp2f , 91and 92.Fn exp2l 93functions compute the base 2 exponential of the given argument 94.Fa x . 95.Pp 96The 97.Fn expm1 , 98.Fn expm1f , 99and the 100.Fn expm1l 101functions compute the value exp(x)\-1 accurately even for tiny argument 102.Fa x . 103.Pp 104The 105.Fn pow , 106.Fn powf , 107and the 108.Fn powl 109functions compute the value 110of 111.Ar x 112to the exponent 113.Ar y . 114.Sh ERROR (due to Roundoff etc.) 115The values of 116.Fn exp 0 , 117.Fn expm1 0 , 118.Fn exp2 integer , 119and 120.Fn pow integer integer 121are exact provided that they are representable. 122.\" XXX Is this really true for pow()? 123Otherwise the error in these functions is generally below one 124.Em ulp . 125.Sh RETURN VALUES 126These functions will return the appropriate computation unless an error 127occurs or an argument is out of range. 128The functions 129.Fn pow x y , 130.Fn powf x y , 131and 132.Fn powl x y 133raise an invalid exception and return an \*(Na if 134.Fa x 135< 0 and 136.Fa y 137is not an integer. 138.Sh NOTES 139The function 140.Fn pow x 0 141returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na . 142Previous implementations of pow may 143have defined x**0 to be undefined in some or all of these 144cases. 145Here are reasons for returning x**0 = 1 always: 146.Bl -enum -width indent 147.It 148Any program that already tests whether x is zero (or 149infinite or \*(Na) before computing x**0 cannot care 150whether 0**0 = 1 or not. 151Any program that depends 152upon 0**0 to be invalid is dubious anyway since that 153expression's meaning and, if invalid, its consequences 154vary from one computer system to another. 155.It 156Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for 157all x, including x = 0. 158This is compatible with the convention that accepts a[0] 159as the value of polynomial 160.Bd -literal -offset indent 161p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n 162.Ed 163.Pp 164at x = 0 rather than reject a[0]\(**0**0 as invalid. 165.It 166Analysts will accept 0**0 = 1 despite that x**y can 167approach anything or nothing as x and y approach 0 168independently. 169The reason for setting 0**0 = 1 anyway is this: 170.Bd -ragged -offset indent 171If x(z) and y(z) are 172.Em any 173functions analytic (expandable 174in power series) in z around z = 0, and if there 175x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. 176.Ed 177.It 178If 0**0 = 1, then 179\*(If**0 = 1/0**0 = 1 too; and 180then \*(Na**0 = 1 too because x**0 = 1 for all finite 181and infinite x, i.e., independently of x. 182.El 183.Sh SEE ALSO 184.Xr fenv 3 , 185.Xr ldexp 3 , 186.Xr log 3 , 187.Xr math 3 188.Sh STANDARDS 189These functions conform to 190.St -isoC-99 . 191