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#include <boost/math/special_functions/sqrt1pm1.hpp>
namespace boost{ namespace math{
template <class T> calculated-result-type sqrt1pm1(T x); template <class T, class Policy> calculated-result-type sqrt1pm1(T x, const Policy&); }} // namespaces
Returns sqrt(1+x) - 1
.
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.
This function is useful when you need the difference between sqrt(x)
and 1, when x is itself
close to 1.
Implemented in terms of log1p
and expm1
.
The following graph illustrates the behaviour of sqrt1pm1:
For built in floating-point types sqrt1pm1
should have approximately 3 epsilon accuracy.
Table 8.84. Error rates for sqrt1pm1
GNU C++ version 7.1.0 |
GNU C++ version 7.1.0 |
Sun compiler version 0x5150 |
Microsoft Visual C++ version 14.1 |
|
---|---|---|---|---|
sqrt1pm1 |
Max = 1.3ε (Mean = 0.404ε) |
Max = 1.33ε (Mean = 0.404ε) |
Max = 1.54ε (Mean = 0.563ε) |
Max = 1.35ε (Mean = 0.497ε) |
A selection of random high precision test values calculated using NTL::RR at 1000-bit precision.