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# std::pow

From cppreference.com
< cpp‎ | numeric‎ | math

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.

### [edit] 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

### [edit] 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.

### [edit] 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

### [edit] 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

### [edit] 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

### [edit] See also

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

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