# pow, powf, powl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float powf( float base, float exponent ); | (1) | (since C99)
double pow( double base, double exponent ); | (2) |
long double powl( long double base, long double exponent ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define pow( base, exponent ) | (4) | (since C99)

1-3) Computes the value of `base` raised to the power `exponent`.
4) Type-generic macro: If any argument has type long double, `powl` is called. Otherwise, if any argument has integer type or has type double, `pow` is called. Otherwise, `powf` is called. If at least one argument is complex or imaginary, then the macro invokes the corresponding complex function (cpowf, cpow, cpowl).

### Parameters

base | - | base as floating point value
exponent | - | exponent as floating point value

### Return value

If no errors occur, `base` raised to the power of `exponent` (baseexponent
) 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 `exponent` is finite and non-integer, a domain error occurs and a range error may occur.

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

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

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

- pow(+0, exponent), where `exponent` is a negative odd integer, returns `+∞` and raises FE_DIVBYZERO
- pow(-0, exponent), where `exponent` is a negative odd integer, returns `-∞` and raises FE_DIVBYZERO
- pow(±0, exponent), where `exponent` 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, exponent), where `exponent` is a positive odd integer, returns +0
- pow(-0, exponent), where `exponent` is a positive odd integer, returns -0
- pow(±0, exponent), where `exponent` is positive non-integer or a positive even integer, returns +0
- pow(-1, ±∞) returns `1`
- pow(+1, exponent) returns `1` for any `exponent`, even when `exponent` is `NaN`
- pow(base, ±0) returns `1` for any `base`, even when `base` is `NaN`
- pow(base, exponent) returns `NaN` and raises FE_INVALID if `base` is finite and negative and `exponent` 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(-∞, exponent) returns -0 if `exponent` is a negative odd integer
- pow(-∞, exponent) returns +0 if `exponent` is a negative non-integer or even integer
- pow(-∞, exponent) returns -∞ if `exponent` is a positive odd integer
- pow(-∞, exponent) returns +∞ if `exponent` is a positive non-integer or even integer
- pow(+∞, exponent) returns +0 for any negative `exponent`
- pow(+∞, exponent) returns +∞ for any positive `exponent`
- except where specified above, if any argument is NaN, NaN is returned

### Notes

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

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <errno.h>
    #include <fenv.h>

    #pragma STDC FENV_ACCESS ON
    int main(void)
    {
        // typical usage
        printf("pow(2, 10) = %f\n", pow(2,10));
        printf("pow(2, 0.5) = %f\n", pow(2,0.5));
        printf("pow(-2, -3) = %f\n", pow(-2,-3));
        // special values
        printf("pow(-1, NAN) = %f\n", pow(-1,NAN));
        printf("pow(+1, NAN) = %f\n", pow(+1,NAN));
        printf("pow(INFINITY, 2) = %f\n", pow(INFINITY, 2));
        printf("pow(INFINITY, -1) = %f\n", pow(INFINITY, -1));
        // error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("pow(-1, 1/3) = %f\n", pow(-1, 1.0/3));
        if(errno == EDOM)         perror("    errno == EDOM");
        if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");

        feclearexcept(FE_ALL_EXCEPT);
        printf("pow(-0, -3) = %f\n", pow(-0.0, -3));
        if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
    }

Possible output:

    pow(2, 10) = 1024.000000
    pow(2, 0.5) = 1.414214
    pow(-2, -3) = -0.125000
    pow(-1, NAN) = nan
    pow(+1, NAN) = 1.000000
    pow(INFINITY, 2) = inf
    pow(INFINITY, -1) = 0.000000
    pow(-1, 1/3) = -nan
        errno == EDOM: Numerical argument out of domain
        FE_INVALID raised
    pow(-0, -3) = -inf
        FE_DIVBYZERO raised

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.7.4 The pow functions (p: 248-249)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.4.4 The pow functions (p: 524-525)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.7.4 The pow functions (p: 229)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.4.4 The pow functions (p: 461)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.5.1 The pow function

### See also

sqrt sqrtf sqrtl (C99)(C99) | computes square root (√x) (function)
cbrt cbrtf cbrtl (C99)(C99)(C99) | computes cubic root (3√x) (function)
hypot hypotf hypotl (C99)(C99)(C99) | computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function)
cpow cpowf cpowl (C99)(C99)(C99) | computes the complex power function (function)
C++ documentation for pow

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