...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/expm1.hpp>
namespace boost{ namespace math{ template <class T> calculatedresulttype expm1(T x); template <class T, class Policy> calculatedresulttype expm1(T x, const Policy&); }} // namespaces
Returns e^{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.
For small x, then e^{x}
is very close to 1, as a result calculating e^{x}  1
results in
catastrophic cancellation errors when x is small. expm1
calculates e^{x}  1
using rational approximations (for up to 128bit long doubles),
otherwise via a series expansion when x is small (giving an accuracy of less
than 2ɛ).
Finally when BOOST_HAS_EXPM1 is defined then the float/double/long double
specializations of this template simply forward to the platform's native
(POSIX) implementation of this function.
The following graph illustrates the behaviour of expm1:
For built in floating point types expm1
should have approximately 1 epsilon accuracy.
Table 6.79. Error rates for expm1
GNU C++ version 7.1.0 
GNU C++ version 7.1.0 
Sun compiler version 0x5150 
Microsoft Visual C++ version 14.1 


Random test data 
Max = 0.992ε (Mean = 0.402ε) 
Max = 0.793ε (Mean = 0.126ε) 
Max = 1.31ε (Mean = 0.428ε) 
Max = 1.31ε (Mean = 0.496ε) 
A mixture of spot test sanity checks, and random high precision test values calculated using NTL::RR at 1000bit precision.