python math problem

[Steven D'Aprano]

Dennis Lee Bieber wrote:

> Classical CompSci teachings when working with floating point numbers
> is to NEVER compare for equality. Instead one should compare against
> some epsilon:

"Don't compare floats for equality" is reasonably good advice.

Adding "never" to that advice, especially when shouting as you do, moves it
into the category "superstition".

Consider:

- Python floating point integers are exact for entire range of -2**53 
  to 2**53, or about -9 million million to +9 million million; if you
  are working with floats that have integral values in this range, 
  testing for equality is perfectly fine.

- If you work exclusively with fractional powers of two, such as 1/2, 
  1/4, 1/8, 1/16, etc. floats are typically exact.

- Testing against an epsilon raises as many problems as it solves:

  + What epsilon should I pick? How do I know if my epsilon is too small,
    and therefore I'm rejecting values that I should accept, or too large,
    and so I'm accepting values I should reject?

  + If my epsilon is too small, calculating "abs(x - y) <= epsilon" is 
    exactly equivalent to "x == y", only slower.

  + Should I test for absolute error, or relative error?

  + If relative error, how do I deal with values around zero where 
    division is likely to introduce excessive rounding error?

  + Not to mention the risk of dividing by zero.

- And how do I deal with INFs?

  py> x = float('inf')
  py> x == x
  True
  py> abs(x - x) <= 1e-14
  False



-- 
Steven