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Manual Pages  — EXP


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



Math Library (libm, -lm)


#include <math.h>

exp(double x);

expf(float x);

long double
expl(long double x);

exp2(double x);

exp2f(float x);

long double
exp2l(long double x);

expm1(double x);

expm1f(float x);

long double
expm1l(long double x);

pow(double x, double y);

powf(float x, float y);

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


The exp(), expf(), and expl() functions compute the base
.Ms 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(), expm1(), 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), powf(x, y), and powl(x, y) raise an invalid exception and return an NaN if x < 0 and y is not an integer.


The function pow(x) returns x**0 = 1 for all x including x = 0, ∞, 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 ∞**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.


To conform with newer C/C++ standards, a stub implementation for powl was committed to the math library, where powl is mapped to pow. Thus, the numerical accuracy is at most that of the 53-bit double precision implementation.


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


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

EXP (3) December 8, 2017

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