EXP(3)                 FreeBSD Library Functions Manual                 EXP(3)

NAME
     exp, expf, expl, exp2, exp2f, exp2l, expm1, expm1f, expm1l, pow, powf,
     powl - exponential and power functions

LIBRARY
     Math Library (libm, -lm)

SYNOPSIS
     #include <math.h>

     double
     exp(double x);

     float
     expf(float x);

     long double
     expl(long double x);

     double
     exp2(double x);

     float
     exp2f(float x);

     long double
     exp2l(long double x);

     double
     expm1(double x);

     float
     expm1f(float x);

     long double
     expm1l(long double x);

     double
     pow(double x, double y);

     float
     powf(float x, float y);

     long double
     powl(long double x, long double y);

DESCRIPTION
     The exp(), expf(), and expl() 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(), expm1f(), and the expm1l() functions compute the value
     exp(x)-1 accurately even for tiny argument x.

     The pow(), powf(), and the powl() 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), powf(x,
     y), and powl(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,
     infinity, 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
     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
             anyway since that expression's meaning and, if invalid, its
             consequences 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
             anything 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.,
             independently of x.

SEE ALSO
     clog(3), cpow(3), fenv(3), ldexp(3), log(3), math(3)

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

HISTORY
     The exp() function appeared in Version 1 AT&T UNIX.

FreeBSD 13.1-RELEASE-p6          April 1, 2020         FreeBSD 13.1-RELEASE-p6