Replace std::numeric_limits<T>::epsilon calls with boost::math::tools::epsilon<T>

[harris-m]

In lexical_cast_float_types_test, std::numeric_limits::epsilon() is used as a tolerance value when comparing long double values to check the accuracy of lexical_cast.

On PowerPC, this epsilon value is extremely small for the long double type. While the value is technically correct, since adding 1.0L to it does in fact result in a distinct value, it is not suitable for use as a tolerance value in this type of comparison. Instead, we need a value such that:

x + x * eps != x for all x

This value can be found by calculating 2^(1-D), where D is the number of bits of precision in the type.

We found this same issue in many parts of the Boost math library, and resolved it by adding a special case of boost::math::tools::epsilon for platforms that use the strange "double-double" implementation of long double, such as PowerPC. This change is now in the master branch and can be seen here:

https://github.com/boostorg/math/blob/7cb3316d0616db01f6c4a56126d4bf8c73e7b50d/include/boost/math/tools/precision.hpp#L160-178

This pull request replaces all instances of std::numeric_limits::epsilon() with boost::math::tools::epsilon in lexical_cast_float_types_test. This change fixes 5222 of the 5255 failures that currently occur within the test on a PowerPC machine with long double support enabled.

[harris-m]

This issue can also be found on trac:

https://svn.boost.org/trac/boost/ticket/10173

[apolukhin]

Patch is good, great thanks for the work!

But please, make the pull request to the develop branch, not the master.

[harris-m]

You got it, see #5.