# std::pow, std::powf, std::powl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float pow ( float base, float exp ); double pow ( double base, double exp ); long double pow ( long double base, long double exp ); |  | (until C++23)
/* floating-point-type */ pow ( /* floating-point-type */ base, /* floating-point-type */ exp ) |  | (since C++23) (constexpr since C++26)
float pow ( float base, int exp ); double pow ( double base, int exp ); long double pow ( long double base, int exp ); | (2) | (until C++11)
float powf( float base, float exp ); | (3) | (since C++11) (constexpr since C++26)
long double powl( long double base, long double exp ); | (4) | (since C++11) (constexpr since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Arithmetic1, class Arithmetic2 > /* common-floating-point-type */ pow ( Arithmetic1 base, Arithmetic2 exp ); | (A) | (constexpr since C++26)

1-4) Computes the value of base raised to the power exp. The library provides overloads of `std::pow` for all cv-unqualified floating-point types as the type of the parameters base and exp. (since C++23)

A) Additional overloads are provided for all other combinations of arithmetic types. | (since C++11)

### Parameters

base | - | base as a floating-point or integer value
exp | - | exponent as a floating-point or integer value

### Return value

If no errors occur, base raised to the power of exp (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 negative even integer
- pow(-∞, exp) returns -∞ if exp is a positive odd integer
- pow(-∞, exp) returns +∞ if exp is a positive non-integer or positive 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

C++98 added overloads where exp has type int on top of C `pow()`, and the return type of std::pow(float, int) was float. However, the additional overloads introduced in C++11 specify that std::pow(float, int) should return double. LWG issue 550 was raised to target this conflict, and the resolution is to removed the extra int exp overloads.

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.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:

If num1 or num2 has type long double, then std::pow(num1, num2) has the same effect as std::pow(static_cast<long double>(num1), static_cast<long double>(num2)). Otherwise, if num1 and/or num2 has type double or an integer type, then std::pow(num1, num2) has the same effect as std::pow(static_cast<double>(num1), static_cast<double>(num2)). Otherwise, if num1 or num2 has type float, then std::pow(num1, num2) has the same effect as std::pow(static_cast<float>(num1), static_cast<float>(num2)). | (until C++23)
If num1 and num2 have arithmetic types, then std::pow(num1, num2) has the same effect as std::pow(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2, arguments of integer type are considered to have the same floating-point conversion rank as double. If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided. | (since C++23)

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cmath>
    #include <cstring>
    #include <iostream>

    // #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 sqrtf sqrtl (C++11)(C++11) | computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrt cbrtf cbrtl (C++11)(C++11)(C++11) | computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypot hypotf hypotl (C++11)(C++11)(C++11) | computes square root of the sum of the squares of two or three (since C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√x2 +y2 +z2 ) (since C++17) (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)

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