cbrt, cbrtf, cbrtl

Defined in header `<math.h>`
float cbrtf( float arg );	(1)	(since C99)
double cbrt( double arg );	(2)	(since C99)
long double cbrtl( long double arg );	(3)	(since C99)
Defined in header `<tgmath.h>`
#define cbrt( arg )	(4)	(since C99)

1-3) Computes the cube root of arg.

4) Type-generic macro: If arg has type long double, cbrtl is called. Otherwise, if arg has integer type or the type double, cbrt is called. Otherwise, cbrtf is called.

Parameters

arg

floating point value

Return value

If no errors occur, the cube root of arg (\(\small{\sqrt[3]{arg} }\)3√arg), 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 the implementation supports IEEE floating-point arithmetic (IEC 60559),

if the argument is ±0 or ±∞, it is returned, unchanged
if the argument is NaN, NaN is returned.

Notes

cbrt(arg) is not equivalent to pow(arg, 1.0/3) because the rational number \(\small{\frac1{3} }\)1/3 is typically not equal to 1.0/3 and std::pow cannot raise a negative base to a fractional exponent. Moreover, cbrt(arg) usually gives more accurate results than pow(arg, 1.0/3) (see example).

Example

#include <stdio.h>
#include <float.h>
#include <math.h>
 
int main(void)
{
    printf("Normal use:\n"
           "cbrt(729)      = %f\n", cbrt(729));
    printf("cbrt(-0.125)   = %f\n", cbrt(-0.125));
    printf("Special values:\n"
           "cbrt(-0)       = %f\n", cbrt(-0.0));
    printf("cbrt(+inf)     = %f\n", cbrt(INFINITY));
    printf("Accuracy:\n"
           "cbrt(343)      = %.*f\n", DBL_DECIMAL_DIG, cbrt(343));
    printf("pow(343,1.0/3) = %.*f\n", DBL_DECIMAL_DIG, pow(343, 1.0/3));
}

Possible output:

Normal use:
cbrt(729)      = 9.000000
cbrt(-0.125)   = -0.500000
Special values:
cbrt(-0)       = -0.000000
cbrt(+inf)     = inf
Accuracy:
cbrt(343)      = 7.00000000000000000
pow(343,1.0/3) = 6.99999999999999911

References

C17 standard (ISO/IEC 9899:2018):

7.12.7.1 The cbrt functions (p: 180-181)
7.25 Type-generic math <tgmath.h> (p: 272-273)
F.10.4.1 The cbrt functions (p: 381-)

C11 standard (ISO/IEC 9899:2011):

7.12.7.1 The cbrt functions (p: 247)
7.25 Type-generic math <tgmath.h> (p: 373-375)
F.10.4.1 The cbrt functions (p: 524)

C99 standard (ISO/IEC 9899:1999):

7.12.7.1 The cbrt functions (p: 228)
7.22 Type-generic math <tgmath.h> (p: 335-337)
F.9.4.1 The cbrt functions (p: 460)

powpowfpowl (C99)(C99)	computes a number raised to the given power (\(\small{x^y}\)x^y) (function)
sqrtsqrtfsqrtl (C99)(C99)	computes square root (\(\small{\sqrt{x} }\)√x) (function)
hypothypotfhypotl (C99)(C99)(C99)	computes square root of the sum of the squares of two given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x²+y²) (function)
C++ documentation for `cbrt`