trick/trick_source/trick_utils/compareFloatingPoint/README.md

Compare Floating Point Numbers

The following functions compare floating-point numbers to determine whether they are within a specified tolerance of each other.

These functions are designed to never generate FP_SUBNORMAL numbers, that could result in a floating point underflow exception, even if the OS doesn't handle floating point underflows by setting their values to zero.

Header

#include "trick/compareFloatingPoint.hh"

Trick::dbl_is_near

bool Trick::dbl_is_near( double A, double B, double tolerance);

This function compares the values of double A and double B to determine whether they are within tolerance of each other. If they are, then the function returns true, otherwise it returns false.

The design of Trick::dbl_is_near requires that the minimum tolerance be DBL_MIN/DBL_EPSILON, which is approximately 1.00208e-292. That is, any two arguments whose difference is less than or equal to 1.00208e-292 are considered to be within tolerance, regardless of the specified tolerance.

Before thinking that doubles should be compared to a tolerance smaller than 1.00208e-292, please consider that the ratio of the Planck length to the size of the observable universe is approximately 1.8e-62. Also consider that our minimum tolerance is 5.4e-231 times smaller than that. So, we think that'll probably be good enough in most cases.

Trick::dbl_is_near

bool Trick::flt_is_near( float A, float B, float tolerance);

This function compares the values of float A and float B to determine whether they are within tolerance of each other. If they are, then the function returns true, otherwise it returns false.

The minimum tolerance for Trick::flt_is_near is FLT_MIN/FLT_EPSILON, which is approximately 9.86076e-32.