Skip site navigation (1)Skip section navigation (2)

FreeBSD Manual Pages

  
 
  

home | help
EXP(3)		       FreeBSD Library Functions Manual			EXP(3)

NAME
     exp, expf,	exp2, exp2f, expm1, expm1f, log, logf, log10, log10f, log1p,
     log1pf, pow, powf -- exponential, logarithm, power	functions

LIBRARY
     Math Library (libm, -lm)

SYNOPSIS
     #include <math.h>

     double
     exp(double	x);

     float
     expf(float	x);

     double
     exp2(double x);

     float
     exp2f(float x);

     double
     expm1(double x);

     float
     expm1f(float x);

     double
     log(double	x);

     float
     logf(float	x);

     double
     log10(double x);

     float
     log10f(float x);

     double
     log1p(double x);

     float
     log1pf(float x);

     double
     pow(double	x, double y);

     float
     powf(float	x, float y);

DESCRIPTION
     The exp() and the expf() functions	compute	the base e exponential value
     of	the given argument x.

     The exp2()	and the	exp2f()	functions compute the base 2 exponential of
     the given argument	x.

     The expm1() and the expm1f() functions compute the	value exp(x)-1 accu-
     rately even for tiny argument x.

     The log() and the logf() functions	compute	the value of the natural loga-
     rithm of argument x.

     The log10() and the log10f() functions compute the	value of the logarithm
     of	argument x to base 10.

     The log1p() and the log1pf() functions compute the	value of log(1+x)
     accurately	even for tiny argument x.

     The pow() and the powf() functions	compute	the value of x to the exponent
     y.

ERROR (due to Roundoff etc.)
     The values	of exp(0), expm1(0), exp2(integer), and	pow(integer, integer)
     are exact provided	that they are representable.  Otherwise	the error in
     these functions is	generally below	one ulp.

RETURN VALUES
     These functions will return the appropriate computation unless an error
     occurs or an argument is out of range.  The functions pow(x, y) and
     powf(x, y)	raise an invalid exception and return an NaN if	x < 0 and y is
     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 an NaN will	be generated.

NOTES
     The 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 function pow(x, 0) returns x**0 = 1 for all x including x = 0,	infin-
     ity, and NaN .  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 or
	     NaN) 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) are	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.

     4.	     If	0**0 = 1, then infinity**0 = 1/0**0 = 1	too; and then NaN**0 =
	     1 too because x**0	= 1 for	all finite and infinite	x, i.e., inde-
	     pendently of x.

SEE ALSO
     fenv(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

Want to link to this manual page? Use this URL:
<https://www.freebsd.org/cgi/man.cgi?query=pow&manpath=FreeBSD+7.1-RELEASE>

home | help