Calculating the Representation Distance Between Two floating-point Values (ULP) float

Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance

Function float_distance finds the number of gaps/bits/ULP between any two floating-point values. If the significands of floating-point numbers are viewed as integers, then their difference is the number of ULP/gaps/bits different.

Synopsis

#include <boost/math/special_functions/next.hpp>

namespace boost{ namespace math{

template <class FPT>
FPT float_distance(FPT a, FPT b);

}} // namespaces

Description - float_distance

Returns the distance between a and b: the result is always a signed integer value (stored in floating-point type FPT) representing the number of distinct representations between a and b.

Note that

float_distance(a, a) always returns 0.
float_distance(float_next(a), a) always returns -1.
float_distance(float_prior(a), a) always returns 1.

The function float_distance is equivalent to calculating the number of ULP (Units in the Last Place) between a and b except that it returns a signed value indicating whether a > b or not.

If the distance is too great then it may not be able to be represented as an exact integer by type FPT, but in practice this is unlikely to be a issue.