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-.\" Copyright (c) 1985, 1991, 1993
-.\"	The Regents of the University of California.  All rights reserved.
-.\"
-.\" Redistribution and use in source and binary forms, with or without
-.\" modification, are permitted provided that the following conditions
-.\" are met:
-.\" 1. Redistributions of source code must retain the above copyright
-.\"    notice, this list of conditions and the following disclaimer.
-.\" 2. Redistributions in binary form must reproduce the above copyright
-.\"    notice, this list of conditions and the following disclaimer in the
-.\"    documentation and/or other materials provided with the distribution.
-.\" 3. All advertising materials mentioning features or use of this software
-.\"    must display the following acknowledgement:
-.\"	This product includes software developed by the University of
-.\"	California, Berkeley and its contributors.
-.\" 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.
-.\"
-.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
-.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
-.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-.\" SUCH DAMAGE.
-.\"
-.\"     @(#)exp.3	8.2 (Berkeley) 4/19/94
-.\" $FreeBSD$
-.\"
-.Dd April 19, 1994
-.Dt EXP 3
-.Os
-.Sh NAME
-.Nm exp ,
-.Nm expm1 ,
-.Nm log ,
-.Nm log10 ,
-.Nm log1p ,
-.Nm pow
-.Nd exponential, logarithm, power functions
-.Sh LIBRARY
-.Lb libm
-.Sh SYNOPSIS
-.In math.h
-.Ft double
-.Fn exp "double x"
-.Ft double
-.Fn expm1 "double x"
-.Ft double
-.Fn log "double x"
-.Ft double
-.Fn log10 "double x"
-.Ft double
-.Fn log1p "double x"
-.Ft double
-.Fn pow "double x" "double y"
-.Sh DESCRIPTION
-The
-.Fn exp
-function computes the exponential value of the given argument
-.Fa x .
-.Pp
-The
-.Fn expm1
-function computes the value exp(x)\-1 accurately even for tiny argument
-.Fa x .
-.Pp
-The
-.Fn log
-function computes the value for the natural logarithm of
-the argument x.
-.Pp
-The
-.Fn log10
-function computes the value for the logarithm of
-argument
-.Fa x
-to base 10.
-.Pp
-The
-.Fn log1p
-function computes
-the value of log(1+x) accurately even for tiny argument
-.Fa x .
-.Pp
-The
-.Fn pow
-computes the value
-of
-.Ar x
-to the exponent
-.Ar y .
-.Sh ERROR (due to Roundoff etc.)
-exp(x), log(x), expm1(x) and log1p(x) are accurate to within
-an
-.Em up ,
-and log10(x) to within about 2
-.Em ups ;
-an
-.Em up
-is one
-.Em Unit
-in the
-.Em Last
-.Em Place .
-The error in
-.Fn pow x y
-is below about 2
-.Em ups
-when its
-magnitude is moderate, but increases as
-.Fn pow x y
-approaches
-the over/underflow thresholds until almost as many bits could be
-lost as are occupied by the floating\-point format's exponent
-field; that is 8 bits for
-.Tn "VAX D"
-and 11 bits for IEEE 754 Double.
-No such drastic loss has been exposed by testing; the worst
-errors observed have been below 20
-.Em ups
-for
-.Tn "VAX D" ,
-300
-.Em ups
-for
-.Tn IEEE
-754 Double.
-Moderate values of
-.Fn pow
-are accurate enough that
-.Fn pow integer integer
-is exact until it is bigger than 2**56 on a
-.Tn VAX ,
-2**53 for
-.Tn IEEE
-754.
-.Sh RETURN VALUES
-These functions will return the appropriate computation unless an error
-occurs or an argument is out of range.
-The functions
-.Fn exp ,
-.Fn expm1
-and
-.Fn pow
-detect if the computed value will overflow,
-set the global variable
-.Va errno
-to
-.Er ERANGE
-and cause a reserved operand fault on a
-.Tn VAX
-or
-.Tn Tahoe .
-The function
-.Fn pow x y
-checks to see if
-.Fa x
-< 0 and
-.Fa y
-is not an integer, in the event this is true,
-the global variable
-.Va errno
-is set to
-.Er EDOM
-and on the
-.Tn VAX
-and
-.Tn Tahoe
-generate a reserved operand fault.
-On a
-.Tn VAX
-and
-.Tn Tahoe ,
-.Va errno
-is set to
-.Er EDOM
-and the reserved operand is returned
-by log unless
-.Fa x
-> 0, by
-.Fn log1p
-unless
-.Fa x
-> \-1.
-.Sh NOTES
-The functions exp(x)\-1 and log(1+x) are called
-expm1 and logp1 in
-.Tn BASIC
-on the Hewlett\-Packard
-.Tn HP Ns \-71B
-and
-.Tn APPLE
-Macintosh,
-.Tn EXP1
-and
-.Tn LN1
-in Pascal, exp1 and log1 in C
-on
-.Tn APPLE
-Macintoshes, where they have been provided to make
-sure financial calculations of ((1+x)**n\-1)/x, namely
-expm1(n\(**log1p(x))/x, will be accurate when x is tiny.
-They also provide accurate inverse hyperbolic functions.
-.Pp
-The function
-.Fn pow x 0
-returns x**0 = 1 for all x including x = 0,
-.if n \
-Infinity
-.if t \
-\(if
-(not found on a
-.Tn VAX ) ,
-and
-.Em NaN
-(the reserved
-operand on a
-.Tn VAX ) .
-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 n \
-infinity**0 = 1/0**0 = 1 too; and
-.if t \
-\(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 infnan 3 ,
-.Xr math 3
-.Sh HISTORY
-A
-.Fn exp ,
-.Fn log
-and
-.Fn pow
-function
-appeared in
-.At v6 .
-A
-.Fn log10
-function
-appeared in
-.At v7 .
-The
-.Fn log1p
-and
-.Fn expm1
-functions appeared in
-.Bx 4.3 .