...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
#include <boost/math/special_functions/sqrt1pm1.hpp>
namespace boost{ namespace math{ template <class T> calculatedresulttype sqrt1pm1(T x); template <class T, class Policy> calculatedresulttype 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 floatingpoint types sqrt1pm1
should have approximately 3 epsilon accuracy.
Table 6.81. Error rates for sqrt1pm1
Microsoft Visual C++ version 12.0 
GNU C++ version 5.1.0 
GNU C++ version 5.1.0 
Sun compiler version 0x5130 


sqrt1pm1 
Max = 1.36ε (Mean = 0.44ε) 
Max = 1.3ε (Mean = 0.404ε) 
Max = 1.33ε (Mean = 0.409ε) 
Max = 1.54ε (Mean = 0.568ε) 
A selection of random high precision test values calculated using NTL::RR at 1000bit precision.