freebsd-dev/lib/msun/man/exp.3
Steve Kargl 3ffff4bad5 ld80 and ld128 implementations of expm1l(). This code started life
as a fairly faithful implementation of the algorithm found in

PTP Tang, "Table-driven implementation of the Expm1 function
in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 18,
211-222 (1992).

Over the last 18-24 months, the code has under gone significant
optimization and testing.

Reviewed by:	bde
Obtained from:	bde (most of the optimizations)
2013-06-03 19:51:32 +00:00

186 lines
4.8 KiB
Groff

.\" Copyright (c) 1985, 1991 Regents of the University of California.
.\" All rights reserved.
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.\" modification, are permitted provided that the following conditions
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" 4. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
.\" $FreeBSD$
.\"
.Dd June 3, 2013
.Dt EXP 3
.Os
.Sh NAME
.Nm exp ,
.Nm expf ,
.Nm expl ,
.\" The sorting error is intentional. exp, expf, and expl should be adjacent.
.Nm exp2 ,
.Nm exp2f ,
.Nm exp2l ,
.Nm expm1 ,
.Nm expm1f ,
.Nm expm1l ,
.Nm pow ,
.Nm powf
.Nd exponential and power functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn exp "double x"
.Ft float
.Fn expf "float x"
.Ft long double
.Fn expl "long double x"
.Ft double
.Fn exp2 "double x"
.Ft float
.Fn exp2f "float x"
.Ft long double
.Fn exp2l "long double x"
.Ft double
.Fn expm1 "double x"
.Ft float
.Fn expm1f "float x"
.Ft long double
.Fn expm1l "long double x"
.Ft double
.Fn pow "double x" "double y"
.Ft float
.Fn powf "float x" "float y"
.Sh DESCRIPTION
The
.Fn exp ,
.Fn expf ,
and
.Fn expl
functions compute the base
.Ms e
exponential value of the given argument
.Fa x .
.Pp
The
.Fn exp2 ,
.Fn exp2f ,
and
.Fn exp2l
functions compute the base 2 exponential of the given argument
.Fa x .
.Pp
The
.Fn expm1 ,
.Fn expm1f ,
and the
.Fn expm1l
functions compute the value exp(x)\-1 accurately even for tiny argument
.Fa x .
.Pp
The
.Fn pow
and the
.Fn powf
functions compute the value
of
.Ar x
to the exponent
.Ar y .
.Sh ERROR (due to Roundoff etc.)
The values of
.Fn exp 0 ,
.Fn expm1 0 ,
.Fn exp2 integer ,
and
.Fn pow integer integer
are exact provided that they are representable.
.\" XXX Is this really true for pow()?
Otherwise the error in these functions is generally below one
.Em ulp .
.Sh RETURN VALUES
These functions will return the appropriate computation unless an error
occurs or an argument is out of range.
The functions
.Fn pow x y
and
.Fn powf x y
raise an invalid exception and return an \*(Na if
.Fa x
< 0 and
.Fa y
is not an integer.
.Sh NOTES
The function
.Fn pow x 0
returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
Previous implementations of pow may
have defined x**0 to be undefined in some or all of these
cases.
Here are reasons for returning x**0 = 1 always:
.Bl -enum -width indent
.It
Any program that already tests whether x is zero (or
infinite or \*(Na) before computing x**0 cannot care
whether 0**0 = 1 or not.
Any program that depends
upon 0**0 to be invalid is dubious anyway since that
expression's meaning and, if invalid, its consequences
vary from one computer system to another.
.It
Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
all x, including x = 0.
This is compatible with the convention that accepts a[0]
as the value of polynomial
.Bd -literal -offset indent
p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
.Ed
.Pp
at x = 0 rather than reject a[0]\(**0**0 as invalid.
.It
Analysts will accept 0**0 = 1 despite that x**y can
approach anything or nothing as x and y approach 0
independently.
The reason for setting 0**0 = 1 anyway is this:
.Bd -ragged -offset indent
If x(z) and y(z) are
.Em any
functions analytic (expandable
in power series) in z around z = 0, and if there
x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
.Ed
.It
If 0**0 = 1, then
\*(If**0 = 1/0**0 = 1 too; and
then \*(Na**0 = 1 too because x**0 = 1 for all finite
and infinite x, i.e., independently of x.
.El
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr ldexp 3 ,
.Xr log 3 ,
.Xr math 3
.Sh STANDARDS
These functions conform to
.St -isoC-99 .