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 July 10, 2012 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 pow , 45.Nm powf 46.Nd exponential and power functions 47.Sh LIBRARY 48.Lb libm 49.Sh SYNOPSIS 50.In math.h 51.Ft double 52.Fn exp "double x" 53.Ft float 54.Fn expf "float x" 55.Ft long double 56.Fn expl "long double x" 57.Ft double 58.Fn exp2 "double x" 59.Ft float 60.Fn exp2f "float x" 61.Ft long double 62.Fn exp2l "long double x" 63.Ft double 64.Fn expm1 "double x" 65.Ft float 66.Fn expm1f "float x" 67.Ft double 68.Fn pow "double x" "double y" 69.Ft float 70.Fn powf "float x" "float y" 71.Sh DESCRIPTION 72The 73.Fn exp , 74.Fn expf , 75and 76.Fn expl 77functions compute the base 78.Ms e 79exponential value of the given argument 80.Fa x . 81.Pp 82The 83.Fn exp2 , 84.Fn exp2f , 85and 86.Fn exp2l 87functions compute the base 2 exponential of the given argument 88.Fa x . 89.Pp 90The 91.Fn expm1 92and the 93.Fn expm1f 94functions compute the value exp(x)\-1 accurately even for tiny argument 95.Fa x . 96.Pp 97The 98.Fn pow 99and the 100.Fn powf 101functions compute the value 102of 103.Ar x 104to the exponent 105.Ar y . 106.Sh ERROR (due to Roundoff etc.) 107The values of 108.Fn exp 0 , 109.Fn expm1 0 , 110.Fn exp2 integer , 111and 112.Fn pow integer integer 113are exact provided that they are representable. 114.\" XXX Is this really true for pow()? 115Otherwise the error in these functions is generally below one 116.Em ulp . 117.Sh RETURN VALUES 118These functions will return the appropriate computation unless an error 119occurs or an argument is out of range. 120The functions 121.Fn pow x y 122and 123.Fn powf x y 124raise an invalid exception and return an \*(Na if 125.Fa x 126< 0 and 127.Fa y 128is not an integer. 129.Sh NOTES 130The function 131.Fn pow x 0 132returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na . 133Previous implementations of pow may 134have defined x**0 to be undefined in some or all of these 135cases. 136Here are reasons for returning x**0 = 1 always: 137.Bl -enum -width indent 138.It 139Any program that already tests whether x is zero (or 140infinite or \*(Na) before computing x**0 cannot care 141whether 0**0 = 1 or not. 142Any program that depends 143upon 0**0 to be invalid is dubious anyway since that 144expression's meaning and, if invalid, its consequences 145vary from one computer system to another. 146.It 147Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for 148all x, including x = 0. 149This is compatible with the convention that accepts a[0] 150as the value of polynomial 151.Bd -literal -offset indent 152p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n 153.Ed 154.Pp 155at x = 0 rather than reject a[0]\(**0**0 as invalid. 156.It 157Analysts will accept 0**0 = 1 despite that x**y can 158approach anything or nothing as x and y approach 0 159independently. 160The reason for setting 0**0 = 1 anyway is this: 161.Bd -ragged -offset indent 162If x(z) and y(z) are 163.Em any 164functions analytic (expandable 165in power series) in z around z = 0, and if there 166x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. 167.Ed 168.It 169If 0**0 = 1, then 170\*(If**0 = 1/0**0 = 1 too; and 171then \*(Na**0 = 1 too because x**0 = 1 for all finite 172and infinite x, i.e., independently of x. 173.El 174.Sh SEE ALSO 175.Xr fenv 3 , 176.Xr ldexp 3 , 177.Xr log 3 , 178.Xr math 3 179.Sh STANDARDS 180These functions conform to 181.St -isoC-99 . 182