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#include <boost/math/special_functions/cbrt.hpp>
namespace boost{ namespace math{

template <class T>
calculated-result-type cbrt(T x);

template <class T, class Policy>
calculated-result-type cbrt(T x, const Policy&);

}} // namespaces

Returns the cubed root of x: x1/3.

The return type of this function is computed using the result type calculation rules: the return is double when x is an integer type and T otherwise.

The final Policy argument is optional and can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the policy documentation for more details.

Implemented using Halley iteration.

The following graph illustrates the behaviour of cbrt:


For built in floating-point types cbrt should have approximately 2 epsilon accuracy.

Table 6.80. Error rates for cbrt

Microsoft Visual C++ version 12.0

GNU C++ version 5.1.0

GNU C++ version 5.1.0
long double

Sun compiler version 0x5130
Sun Solaris
long double

cbrt Function

Max = 1.7ε (Mean = 0.565ε)

(<math.h>: Max = 1.7ε (Mean = 0.565ε))

Max = 0ε (Mean = 0ε)

(Cephes: Max = 0ε (Mean = 0ε))

Max = 1.34ε (Mean = 0.471ε)

(<tr1/cmath>: Max = 1.34ε (Mean = 0.471ε))
(<math.h>: Max = 1.34ε (Mean = 0.471ε))

Max = 1.11ε (Mean = 0.424ε)

(<math.h>: Max = 1.11ε (Mean = 0.424ε))


A mixture of spot test sanity checks, and random high precision test values calculated using NTL::RR at 1000-bit precision.