Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values

Finding the Next Representable Value in a Specific Direction (nextafter)
Finding the Next Greater Representable Value (float_next)
Finding the Next Smaller Representable Value (float_prior)
Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance
Advancing a floating-point Value by a Specific Representation Distance (ULP) float_advance
Obtaining the Size of a Unit In the Last Place - ULP

Unit of Least Precision or Unit in the Last Place is the gap between two different, but as close as possible, floating-point numbers.

Most decimal values, for example 0.1, cannot be exactly represented as floating-point values, but will be stored as the closest representable floating-point.

Functions are provided for finding adjacent greater and lesser floating-point values, and estimating the number of gaps between any two floating-point values.

The floating-point type (FPT) must have has a fixed number of bits in the representation. The number of bits may set at runtime, but must be the same for all numbers. For example, NTL::quad_float type (fixed 128-bit representation), NTL::RR type (arbitrary but fixed decimal digits, default 150) or Boost.Multiprecision cpp_dec_float andcpp_bin_float are fixed at runtime, but not a type that extends the representation to provide an exact representation for any number, for example XRC eXact Real in C.