expm1f man page on FreeBSD

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EXP(3)			 BSD Library Functions Manual			EXP(3)

     exp, expf, exp2, exp2f, exp2l, expm1, expm1f, pow, powf — exponential and
     power functions

     Math Library (libm, -lm)

     #include <math.h>

     exp(double x);

     expf(float x);

     exp2(double x);

     exp2f(float x);

     long double
     exp2l(long double x);

     expm1(double x);

     expm1f(float x);

     pow(double x, double y);

     powf(float x, float y);

     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

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.

     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.

     The function pow(x, 0) returns x**0 = 1 for all x including x = 0, ∞, and
     NaN .  Previous implementations of pow may have defined x**0 to be unde‐
     fined in some or all of these cases.  Here are reasons for returning 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 ∞**0 = 1/0**0 = 1 too; and then NaN**0 = 1 too
	     because x**0 = 1 for all finite and infinite x, i.e., indepen‐
	     dently of x.

     fenv(3), ldexp(3), log(3), math(3)

     These functions conform to ISO/IEC 9899:1999 (“ISO C99”).

BSD			       January 17, 2008				   BSD

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