DragonFly On-Line Manual Pages

EXP(3)		      DragonFly Library Functions Manual		EXP(3)

NAME
     exp, expf, exp2, exp2f, exp2l, expm1, expm1f, pow, powf -- exponential
     and 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);

     long double
     exp2l(long double x);

     double
     expm1(double x);

     float
     expm1f(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(), exp2f(), and exp2l() 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 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.

NOTES
     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), ldexp(3), log(3), math(3)

STANDARDS
     These functions conform to ISO/IEC 9899:1999 (``ISO C99'').

DragonFly 3.5		       December 21, 2011		 DragonFly 3.5