std::pow

 

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Defined in header <cmath>
float       pow( float base, float exp );	(1)
double      pow( double base, double exp );	(2)
long double pow( long double base, long double exp );	(3)
float       pow( float base, int iexp );	(4)	(until C++11)
double      pow( double base, int iexp );	(5)	(until C++11)
long double pow( long double base, int iexp );	(6)	(until C++11)
Promoted    pow( Arithmetic1 base, Arithmetic2 exp );	(7)	(since C++11)

1-6) Computes the value of base raised to the power exp or iexp.

7) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has integral type, it is cast to double. If any argument is long double, then the return type Promoted is also long double, otherwise the return type is always double.

Parameters

base	-	base as a value of floating-point or integral type
exp	-	exponent as a value of floating-point or integral type
iexp	-	exponent as integer value

Return value

If no errors occur, base raised to the power of exp (or iexp) (baseexp
), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported)

If a pole error or a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling

If base is finite and negative and exp is finite and non-integer, a domain error occurs and a range error may occur.

If base is zero and exp is zero, a domain error may occur.

If base is zero and exp is negative, a domain error or a pole error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• pow(+0, exp), where exp is a negative odd integer, returns +∞ and raises FE_DIVBYZERO
• pow(-0, exp), where exp is a negative odd integer, returns -∞ and raises FE_DIVBYZERO
• pow(±0, exp), where exp is negative, finite, and is an even integer or a non-integer, returns +∞ and raises FE_DIVBYZERO
• pow(±0, -∞) returns +∞ and may raise FE_DIVBYZERO
• pow(+0, exp), where exp is a positive odd integer, returns +0
• pow(-0, exp), where exp is a positive odd integer, returns -0
• pow(±0, exp), where exp is positive non-integer or a positive even integer, returns +0
• pow(-1, ±∞) returns 1
• pow(+1, exp) returns 1 for any exp, even when exp is NaN
• pow(base, ±0) returns 1 for any base, even when base is NaN
• pow(base, exp) returns NaN and raises FE_INVALID if base is finite and negative and exp is finite and non-integer.
• pow(base, -∞) returns +∞ for any |base|<1
• pow(base, -∞) returns +0 for any |base|>1
• pow(base, +∞) returns +0 for any |base|<1
• pow(base, +∞) returns +∞ for any |base|>1
• pow(-∞, exp) returns -0 if exp is a negative odd integer
• pow(-∞, exp) returns +0 if exp is a negative non-integer or even integer
• pow(-∞, exp) returns -∞ if exp is a positive odd integer
• pow(-∞, exp) returns +∞ if exp is a positive non-integer or even integer
• pow(+∞, exp) returns +0 for any negative exp
• pow(+∞, exp) returns +∞ for any positive exp
• except where specified above, if any argument is NaN, NaN is returned

Notes

pow(float, int) returns float until C++11 (per overload 4) but returns double since C++11 (per overload 7)

Although std::pow cannot be used to obtain a root of a negative number, std::cbrt is provided for the common case where exp is 1/3

Example

Run this code

#include <iostream>
#include <cmath>
#include <cerrno>
#include <cfenv>
#include <cstring>
 
#pragma STDC FENV_ACCESS ON
int main()
{
    // typical usage
    std::cout << "pow(2, 10) = " << std::pow(2,10) << '\n'
              << "pow(2, 0.5) = " << std::pow(2,0.5) << '\n'
              << "pow(-2, -3) = " << std::pow(-2,-3) << '\n';
    // special values
    std::cout << "pow(-1, NAN) = " << std::pow(-1,NAN) << '\n'
              << "pow(+1, NAN) = " << std::pow(+1,NAN) << '\n'
              << "pow(INFINITY, 2) = " << std::pow(INFINITY, 2) << '\n'
              << "pow(INFINITY, -1) = " << std::pow(INFINITY, -1) << '\n';
    // error handling 
    errno = 0; std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "pow(-1, 1/3) = " << std::pow(-1, 1.0/3) << '\n';
    if(errno == EDOM) std::cout << "    errno == EDOM " << std::strerror(errno) << '\n';
    if(std::fetestexcept(FE_INVALID)) std::cout << "    FE_INVALID raised\n";
 
    std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "pow(-0, -3) = " << std::pow(-0.0, -3) << '\n';
    if(std::fetestexcept(FE_DIVBYZERO)) std::cout << "    FE_DIVBYZERO raised\n";
}

Possible output:

pow(2, 10) = 1024
pow(2, 0.5) = 1.41421
pow(-2, -3) = -0.125
pow(-1, NAN) = nan
pow(+1, NAN) = 1
pow(INFINITY, 2) = inf
pow(INFINITY, -1) = 0
pow(-1, 1/3) = -nan
    errno == EDOM Numerical argument out of domain
    FE_INVALID raised
pow(-0, -3) = -inf
    FE_DIVBYZERO raised

See also

sqrt	computes square root (√x) (function)
cbrt (C++11)	computes cubic root (3√x) (function)
hypot (C++11)	computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function)
pow(std::complex)	complex power, one or both arguments may be a complex number (function template)
pow(std::valarray)	applies the function std::pow to two valarrays or a valarray and a value (function template)
C documentation for pow