diff options
Diffstat (limited to 'libm/man/exp.3')
| -rw-r--r-- | libm/man/exp.3 | 236 |
1 files changed, 236 insertions, 0 deletions
diff --git a/libm/man/exp.3 b/libm/man/exp.3 new file mode 100644 index 0000000..f6aed8f --- /dev/null +++ b/libm/man/exp.3 @@ -0,0 +1,236 @@ +.\" Copyright (c) 1985, 1991 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. +.\" +.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91 +.\" $FreeBSD: src/lib/msun/man/exp.3,v 1.22 2005/04/05 02:57:28 das Exp $ +.\" +.Dd April 5, 2005 +.Dt EXP 3 +.Os +.Sh NAME +.Nm exp , +.Nm expf , +.\" The sorting error is intentional. exp and expf should be adjacent. +.Nm exp2 , +.Nm exp2f , +.Nm expm1 , +.Nm expm1f , +.Nm log , +.Nm logf , +.Nm log10 , +.Nm log10f , +.Nm log1p , +.Nm log1pf , +.Nm pow , +.Nm powf +.Nd exponential, logarithm, power functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn exp "double x" +.Ft float +.Fn expf "float x" +.Ft double +.Fn exp2 "double x" +.Ft float +.Fn exp2f "float x" +.Ft double +.Fn expm1 "double x" +.Ft float +.Fn expm1f "float x" +.Ft double +.Fn log "double x" +.Ft float +.Fn logf "float x" +.Ft double +.Fn log10 "double x" +.Ft float +.Fn log10f "float x" +.Ft double +.Fn log1p "double x" +.Ft float +.Fn log1pf "float x" +.Ft double +.Fn pow "double x" "double y" +.Ft float +.Fn powf "float x" "float y" +.Sh DESCRIPTION +The +.Fn exp +and the +.Fn expf +functions compute the base +.Ms e +exponential value of the given argument +.Fa x . +.Pp +The +.Fn exp2 +and the +.Fn exp2f +functions compute the base 2 exponential of the given argument +.Fa x . +.Pp +The +.Fn expm1 +and the +.Fn expm1f +functions compute the value exp(x)\-1 accurately even for tiny argument +.Fa x . +.Pp +The +.Fn log +and the +.Fn logf +functions compute the value of the natural logarithm of argument +.Fa x . +.Pp +The +.Fn log10 +and the +.Fn log10f +functions compute the value of the logarithm of argument +.Fa x +to base 10. +.Pp +The +.Fn log1p +and the +.Fn log1pf +functions compute +the value of log(1+x) 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. +An attempt to take the logarithm of \*(Pm0 will result in +a divide-by-zero exception, and an infinity will be returned. +An attempt to take the logarithm of a negative number will +result in an invalid exception, and an \*(Na will be generated. +.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, 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 math 3 |