0f6c6dff74
These functions first appeared in the First Edition of Unix (or earlier in the pdp-7 version). Just claim 1st Edition for all this. The pdp-7 code is too fragmented at this point to extend history that far back.
198 lines
5.0 KiB
Groff
198 lines
5.0 KiB
Groff
.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
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.\" $FreeBSD$
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.\"
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.Dd April 1, 2020
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.Dt EXP 3
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.Os
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.Sh NAME
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.Nm exp ,
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.Nm expf ,
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.Nm expl ,
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.\" The sorting error is intentional. exp, expf, and expl should be adjacent.
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.Nm exp2 ,
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.Nm exp2f ,
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.Nm exp2l ,
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.Nm expm1 ,
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.Nm expm1f ,
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.Nm expm1l ,
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.Nm pow ,
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.Nm powf ,
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.Nm powl
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.Nd exponential and power functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn exp "double x"
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.Ft float
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.Fn expf "float x"
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.Ft long double
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.Fn expl "long double x"
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.Ft double
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.Fn exp2 "double x"
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.Ft float
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.Fn exp2f "float x"
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.Ft long double
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.Fn exp2l "long double x"
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.Ft double
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.Fn expm1 "double x"
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.Ft float
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.Fn expm1f "float x"
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.Ft long double
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.Fn expm1l "long double x"
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.Ft double
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.Fn pow "double x" "double y"
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.Ft float
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.Fn powf "float x" "float y"
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.Ft long double
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.Fn powl "long double x" "long double y"
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.Sh DESCRIPTION
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The
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.Fn exp ,
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.Fn expf ,
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and
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.Fn expl
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functions compute the base
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.Ms e
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exponential value of the given argument
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.Fa x .
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.Pp
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The
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.Fn exp2 ,
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.Fn exp2f ,
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and
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.Fn exp2l
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functions compute the base 2 exponential of the given argument
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.Fa x .
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.Pp
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The
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.Fn expm1 ,
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.Fn expm1f ,
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and the
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.Fn expm1l
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functions compute the value exp(x)\-1 accurately even for tiny argument
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.Fa x .
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.Pp
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The
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.Fn pow ,
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.Fn powf ,
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and the
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.Fn powl
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functions compute the value
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of
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.Ar x
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to the exponent
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.Ar y .
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.Sh ERROR (due to Roundoff etc.)
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The values of
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.Fn exp 0 ,
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.Fn expm1 0 ,
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.Fn exp2 integer ,
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and
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.Fn pow integer integer
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are exact provided that they are representable.
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.\" XXX Is this really true for pow()?
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Otherwise the error in these functions is generally below one
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.Em ulp .
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.Sh RETURN VALUES
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These functions will return the appropriate computation unless an error
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occurs or an argument is out of range.
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The functions
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.Fn pow x y ,
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.Fn powf x y ,
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and
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.Fn powl x y
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raise an invalid exception and return an \*(Na if
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.Fa x
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< 0 and
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.Fa y
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is not an integer.
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.Sh NOTES
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The function
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.Fn pow x 0
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returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
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Previous implementations of pow may
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have defined x**0 to be undefined in some or all of these
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cases.
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Here are reasons for returning x**0 = 1 always:
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.Bl -enum -width indent
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.It
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Any program that already tests whether x is zero (or
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infinite or \*(Na) before computing x**0 cannot care
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whether 0**0 = 1 or not.
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Any program that depends
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upon 0**0 to be invalid is dubious anyway since that
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expression's meaning and, if invalid, its consequences
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vary from one computer system to another.
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.It
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Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
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all x, including x = 0.
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This is compatible with the convention that accepts a[0]
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as the value of polynomial
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.Bd -literal -offset indent
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p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
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.Ed
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.Pp
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at x = 0 rather than reject a[0]\(**0**0 as invalid.
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.It
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Analysts will accept 0**0 = 1 despite that x**y can
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approach anything or nothing as x and y approach 0
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independently.
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The reason for setting 0**0 = 1 anyway is this:
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.Bd -ragged -offset indent
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If x(z) and y(z) are
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.Em any
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functions analytic (expandable
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in power series) in z around z = 0, and if there
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x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
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.Ed
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.It
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If 0**0 = 1, then
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\*(If**0 = 1/0**0 = 1 too; and
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then \*(Na**0 = 1 too because x**0 = 1 for all finite
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and infinite x, i.e., independently of x.
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.El
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.Sh SEE ALSO
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.Xr clog 3
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.Xr cpow 3
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.Xr fenv 3 ,
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.Xr ldexp 3 ,
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.Xr log 3 ,
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.Xr math 3
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.Sh STANDARDS
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These functions conform to
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.St -isoC-99 .
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.Sh HISTORY
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The
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.Fn exp
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function appeared in
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.At v1 .
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