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.\" 3. 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.Dd April 1, 2020 29.Dt EXP 3 30.Os 31.Sh NAME 32.Nm exp , 33.Nm expf , 34.Nm expl , 35.\" The sorting error is intentional. exp, expf, and expl should be adjacent. 36.Nm exp2 , 37.Nm exp2f , 38.Nm exp2l , 39.Nm expm1 , 40.Nm expm1f , 41.Nm expm1l , 42.Nm pow , 43.Nm powf , 44.Nm powl 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 long double 55.Fn expl "long double x" 56.Ft double 57.Fn exp2 "double x" 58.Ft float 59.Fn exp2f "float x" 60.Ft long double 61.Fn exp2l "long double x" 62.Ft double 63.Fn expm1 "double x" 64.Ft float 65.Fn expm1f "float x" 66.Ft long double 67.Fn expm1l "long double x" 68.Ft double 69.Fn pow "double x" "double y" 70.Ft float 71.Fn powf "float x" "float y" 72.Ft long double 73.Fn powl "long double x" "long double 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 , 103.Fn powf , 104and the 105.Fn powl 106functions compute the value 107of 108.Fa x 109to the exponent 110.Fa y . 111.Sh ERROR (due to Roundoff etc.) 112The values of 113.Fn exp 0 , 114.Fn expm1 0 , 115.Fn exp2 integer , 116and 117.Fn pow integer integer 118are exact provided that they are representable. 119.\" XXX Is this really true for pow()? 120Otherwise the error in these functions is generally below one 121.Em ulp . 122.Sh RETURN VALUES 123These functions will return the appropriate computation unless an error 124occurs or an argument is out of range. 125The functions 126.Fn pow x y , 127.Fn powf x y , 128and 129.Fn powl x y 130raise an invalid exception and return an \*(Na if 131.Fa x 132< 0 and 133.Fa y 134is not an integer. 135.Sh NOTES 136The function 137.Fn pow x 0 138returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na . 139Previous implementations of pow may 140have defined x**0 to be undefined in some or all of these 141cases. 142Here are reasons for returning x**0 = 1 always: 143.Bl -enum -width indent 144.It 145Any program that already tests whether x is zero (or 146infinite or \*(Na) before computing x**0 cannot care 147whether 0**0 = 1 or not. 148Any program that depends 149upon 0**0 to be invalid is dubious anyway since that 150expression's meaning and, if invalid, its consequences 151vary from one computer system to another. 152.It 153Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for 154all x, including x = 0. 155This is compatible with the convention that accepts a[0] 156as the value of polynomial 157.Bd -literal -offset indent 158p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n 159.Ed 160.Pp 161at x = 0 rather than reject a[0]\(**0**0 as invalid. 162.It 163Analysts will accept 0**0 = 1 despite that x**y can 164approach anything or nothing as x and y approach 0 165independently. 166The reason for setting 0**0 = 1 anyway is this: 167.Bd -ragged -offset indent 168If x(z) and y(z) are 169.Em any 170functions analytic (expandable 171in power series) in z around z = 0, and if there 172x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. 173.Ed 174.It 175If 0**0 = 1, then 176\*(If**0 = 1/0**0 = 1 too; and 177then \*(Na**0 = 1 too because x**0 = 1 for all finite 178and infinite x, i.e., independently of x. 179.El 180.Sh SEE ALSO 181.Xr clog 3 , 182.Xr cpow 3 , 183.Xr fenv 3 , 184.Xr ldexp 3 , 185.Xr log 3 , 186.Xr math 3 187.Sh STANDARDS 188These functions conform to 189.St -isoC-99 . 190.Sh HISTORY 191The 192.Fn exp 193function appeared in 194.At v1 . 195