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author | rgrimes <rgrimes@FreeBSD.org> | 1994-05-27 05:00:24 +0000 |
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committer | rgrimes <rgrimes@FreeBSD.org> | 1994-05-27 05:00:24 +0000 |
commit | be22b15ae2ff8d7fe06b6e14fddf0c5b444a95da (patch) | |
tree | a18a706dffa5baf86a3b12bbfb4f81caa097f349 /lib/libm/common_source/exp.3 | |
parent | 2a27bd86e6002c871e3b5561a5334653bb222a77 (diff) | |
download | FreeBSD-src-be22b15ae2ff8d7fe06b6e14fddf0c5b444a95da.zip FreeBSD-src-be22b15ae2ff8d7fe06b6e14fddf0c5b444a95da.tar.gz |
BSD 4.4 Lite Lib Sources
Diffstat (limited to 'lib/libm/common_source/exp.3')
-rw-r--r-- | lib/libm/common_source/exp.3 | 284 |
1 files changed, 284 insertions, 0 deletions
diff --git a/lib/libm/common_source/exp.3 b/lib/libm/common_source/exp.3 new file mode 100644 index 0000000..1bdf060 --- /dev/null +++ b/lib/libm/common_source/exp.3 @@ -0,0 +1,284 @@ +.\" 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 +.\" +.Dd April 19, 1994 +.Dt EXP 3 +.Os BSD 4 +.Sh NAME +.Nm exp , +.Nm expm1 , +.Nm log , +.Nm log10 , +.Nm log1p , +.Nm pow +.Nd exponential, logarithm, power functions +.Sh SYNOPSIS +.Fd #include <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 RANGE +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 -filled -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 math 3 , +.Xr infnan 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 . |