.\" Copyright (c) 1985 Regents of the University of California.
.\" All rights reserved.  The Berkeley software License Agreement
.\" specifies the terms and conditions for redistribution.
.\"
.\"	@(#)exp.3m	6.9 (Berkeley) 5/27/86
.\"
.TH EXP 3  "May 27, 1986"
.UC 4
.ds up \fIulp\fR
.SH NAME
exp, expm1, log, log10, log1p, pow \- exponential, logarithm, power
.SH SYNOPSIS
.nf
.ft B
#include <math.h>

double exp(double \fIx\fP)
double expm1(double \fIx\fP)
double log(double \fIx\fP)
double log10(double \fIx\fP)
double log1p(double \fIx\fP)
double pow(double \fIx\fP, double \fIy\fP)
.ft R
.fi
.SH DESCRIPTION
.PP
Exp returns the exponential function of x.
.PP
Expm1 returns exp(x)\-1 accurately even for tiny x.
.PP
Log returns the natural logarithm of x.
.PP
Log10 returns the logarithm of x to base 10.
.PP
Log1p returns log(1+x) accurately even for tiny x.
.PP
Pow(x,y) returns
.if n x**y.
.if t x\u\s8y\s10\d.
.SH "ERROR (due to Roundoff etc.)"
exp(x), log(x), expm1(x), log(x) and log1p(x) are accurate to within 
an \*(up, and log10(x) to within about 2 \*(ups;
an \*(up is one \fIU\fRnit in the \fIL\fRast \fIP\fRlace.
Pow(x,y) returns
.if n x**y
.if t x\u\s8y\s10\d
nearly rounded.  In particular pow(integer,integer) always returns the
correct integer provided it is representable.
.SH DIAGNOSTICS
exp(Inf) = Inf, exp(NaN) = NaN.
.br
For a finite argument, only exp(0) = 1 is exact.
.br
Overflow of exp(x) if x > 7.09782712893383973096e+02.
.br
Underflow of exp(x) if x < \-7.45133219101941108420e+02.
.PP
expm1(Inf) = Inf, expm1(NaN) = NaN, expm1(\-Inf) = \-1.
.br
For a finite argument, only expm1(0) = 0 is exact.
.br
Overflow of expm1(x) if x > 7.09782712893383973096e+02.
.PP
log(x) = NaN with signal if x < 0 (including \-Inf).
.br
log(NaN) = that NaN with no signal.
.br
log(+Inf) = +Inf.
.br
log(0) = \-Inf with signal.
.PP
log10(x) = NaN with signal if x < 0.
.br
log10(NaN) = that NaN with no signal.
.br
log10(+Inf) = +Inf.
.br
log10(0) = \-Inf with signal.
.br
.if n log10(10**n)
.if t log10(10\u\s8n\s10\d)
= n for n = 0, 1, ..., 22.
.PP
log1p(x) = NaN with signal if x < \-1 (including \-Inf).
.br
log1p(NaN) = that NaN with no signal.
.br
log1p(+Inf) = +Inf.
.br
log1p(\-1) = \-Inf with signal.
.PP
pow([anything], 0) = 1
.br
pow([anything], 1) = [that anything]
.br
pow([anything], NaN) = NaN
.br
pow(NaN, [anything except 0]) = NaN
.br
pow(\(+-[|x| > 1], +Inf) = +Inf
.br
pow(\(+-[|x| > 1], \-Inf) = +0
.br
pow(\(+-[|x| < 1], +Inf) = +0
.br
pow(\(+-[|x| < 1], \-Inf) = +Inf
.br
pow(\(+-1 , \(+-Inf) = NaN
.br
pow(+0, [+anything except 0, NaN]) = +0
.br
pow(\-0, [+anything except 0, NaN, odd integer]) = +0
.br
pow(+0, [\-anything except 0, NaN]) = +Inf
.br
pow(\-0, [\-anything except 0, NaN, odd integer]) = +Inf
.br
pow(\-0, [odd integer]) = \-( +0 ** [odd integer] )
.br
pow(+Inf, [+anything except 0, NaN]) = +Inf
.br
pow(+Inf, [\-anything except 0, NaN]) = +0
.br
pow(\-Inf, [anything]) = \-0 ** [\-anything])
.br
pow([\-anything], [integer]) = (\-1)**integer*(+anything**integer)
.br
pow([\-anything except 0 and Inf], [non-integer]) = NaN
.SH NOTES
To guarantee
.if n log10(10**n)
.if t log10(10\u\s8n\s10\d)
= n, where
.if n 10**n
.if t 10\u\s8n\s10\d
is normal, the rounding mode must set to Round-to-Nearest.
Log10 is monotonic on all binary break points.
.SH SEE ALSO
.BR math (3).
.SH AUTHOR
Kwok\-Choi Ng, W. Kahan