Calculate relative error of two numbers:

\[ \frac{|a - b|}{\max(|a|,|b|)} \]

It lies in [0,1) interval for numbers with same sign and (1,2] for numbers with different sign. If both arguments are zero or negative zero function returns 0. If at least one argument is transfinite it returns NaN

Check that relative error between two numbers a and b . If relativeError returns NaN it returns False .

Add N ULPs (units of least precision) to Double number.

Measure distance between two Double s in ULPs (units of least precision). Note that it's different from abs (ulpDelta a b) since it returns correct result even when ulpDelta overflows.

Measure signed distance between two Double s in ULPs (units of least precision). Note that unlike ulpDistance it can overflow.

>>> ulpDelta 1 (1 + m_epsilon)
1

Compare two Double values for approximate equality, using Dawson's method.

The required accuracy is specified in ULPs (units of least precision). If the two numbers differ by the given number of ULPs or less, this function returns True .