# FreeBSD Manual Pages

EXP(3) FreeBSD Library Functions Manual EXP(3)NAMEexp,expf,exp2,exp2f,expm1,expm1f,log,logf,log10,log10f,log1p,log1pf,pow,powf-- exponential, logarithm, power functionsLIBRARYMath Library (libm, -lm)SYNOPSIS#include<math.h>doubleexp(doublex);floatexpf(floatx);doubleexp2(doublex);floatexp2f(floatx);doubleexpm1(doublex);floatexpm1f(floatx);doublelog(doublex);floatlogf(floatx);doublelog10(doublex);floatlog10f(floatx);doublelog1p(doublex);floatlog1pf(floatx);doublepow(doublex,doubley);floatpowf(floatx,floaty);DESCRIPTIONTheexp() and theexpf() functions compute the baseeexponential value of the given argumentx. Theexp2() and theexp2f() functions compute the base 2 exponential of the given argumentx. Theexpm1() and theexpm1f() functions compute the value exp(x)-1 accu- rately even for tiny argumentx. Thelog() and thelogf() functions compute the value of the natural loga- rithm of argumentx. Thelog10() and thelog10f() functions compute the value of the logarithm of argumentxto base 10. Thelog1p() and thelog1pf() functions compute the value of log(1+x) accurately even for tiny argumentx. Thepow() and thepowf() functions compute the value ofxto the exponenty.ERROR (due to Roundoff etc.)The values ofexp(0),expm1(0),exp2(integer), andpow(integer,integer) are exact provided that they are representable. Otherwise the error in these functions is generally below oneulp.RETURN VALUESThese functions will return the appropriate computation unless an error occurs or an argument is out of range. The functionspow(x,y) andpowf(x,y) raise an invalid exception and return anNaNifx< 0 andyis not an integer. An attempt to take the logarithm of +-0 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 anNaNwill be generated.NOTESThe functions exp(x)-1 and log(1+x) are called expm1 and logp1 in BASIC on the Hewlett-Packard HP-71B and APPLE Macintosh, EXP1 and LN1 in Pas- cal, exp1 and log1 in C on APPLE Macintoshes, where they have been pro- vided 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. The functionpow(x,0) returns x**0 = 1 for all x including x = 0, infin- ity, andNaN. Previous implementations of pow may have defined x**0 to be undefined in some or all of these cases. Here are reasons for return- ing x**0 = 1 always: 1. Any program that already tests whether x is zero (or infinite orNaN) before computing x**0 cannot care whether 0**0 = 1 or not. Any program that depends upon 0**0 to be invalid is dubious any- way since that expression's meaning and, if invalid, its conse- quences vary from one computer system to another. 2. 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 p(x) = a[0]*x**0 + a[1]*x**1 + a[2]*x**2 +...+ a[n]*x**n at x = 0 rather than reject a[0]*0**0 as invalid. 3. Analysts will accept 0**0 = 1 despite that x**y can approach any- thing or nothing as x and y approach 0 independently. The reason for setting 0**0 = 1 anyway is this: If x(z) and y(z) areanyfunctions 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. 4. If 0**0 = 1, then infinity**0 = 1/0**0 = 1 too; and thenNaN**0 = 1 too because x**0 = 1 for all finite and infinite x, i.e., inde- pendently of x.SEE ALSOfenv(3), math(3) FreeBSD 7.1 April 5, 2005 FreeBSD 7.1

NAME | LIBRARY | SYNOPSIS | DESCRIPTION | ERROR (due to Roundoff etc.) | RETURN VALUES | NOTES | SEE ALSO

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