EXP(3) BSD Library Functions Manual EXP(3)NAME
exp, expf, exp2, exp2f, expm1, expm1f, -- exponential 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);
DESCRIPTION
The exp() and the expf() functions compute the base e exponential value of the given argument x.
The exp2(), and exp2f() functions compute the base 2 exponential of the given argument x.
The expm1() and the expm1f() functions computes the value exp(x)-1 accurately even for tiny argument x.
RETURN VALUES
These functions will return the appropriate computation unless an error occurs or an argument is out of range. The functions exp() and
expm1() detect if the computed value will overflow, set the global variable errno to ERANGE and cause a reserved operand fault on a VAX.
SEE ALSO math(3)STANDARDS
The exp() functions conform to ANSI X3.159-1989 (``ANSI C89''). The exp2(), exp2f(), expf(), expm1(), and expm1f() functions conform to
ISO/IEC 9899:1999 (``ISO C99'').
HISTORY
The exp() functions appeared in Version 6 AT&T UNIX. The expm1() function appeared in 4.3BSD.
BSD September 13, 2011 BSD
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EXP(3) BSD Library Functions Manual EXP(3)NAME
exp, expf, expl, exp2, exp2f, exp2l, expm1, expm1f, expm1l, pow, powf -- 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);
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() 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, 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., 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'').
BSD June 3, 2013 BSD