```Issue #15811 has been updated by wishdev (John Higgins).

yennguyenh (yen nguyen) wrote:
> wishdev (John Higgins) wrote:
....
> Sorry but I do not really understand what you meant. What I get so far is that you mean the difference of that pair of number (1000020.0E-15 - 1000010.0E-15) results not as expected, 1.0000000000085785e-14 instead of 1.0e-14. I have taken a look on that and realize one mistake on the algorithm. The absolute tolerance is set to check the accuracy to a certain decimal place and so at that place the difference should be less than 1 which is 0. Therefore the equal case should not be considered as the case for equal numbers. It should be fixed like below ( I have also updated the code!)
>

First, my sincere apologies - I missed an email along the way and this just popped up on my radar this evening with the newest message.

However to be clear

Tolerance = 0.01

0.01 - 0.02 = -0.01 (False/True depending on which version of the code)
0.02 - 0.03 = -0.009999999999999998 (True always)
0.03 - 0.04 = -0.010000000000000002 (False always)

Those are not weird e-15 vs e-14 numbers - that's pennies on a dollar transaction.

Sorry

John

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Feature #15811: Propsing new method for comparing equality of 2 (float) numbers relatively
https://bugs.ruby-lang.org/issues/15811#change-80168

* Author: yennguyenh (yen nguyen)
* Status: Open
* Priority: Normal
* Assignee:
* Target version:
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# Background

Equal comparison method between 2 float numbers returns unexpected results sometimes. Therefore, a relative comparison method is needed!

# Proposal

A relative equal comparison method has been written based on a Python project! This method gives the approximation for the equal comparison based on two values: realative tolerance and absolute tolerance. Near zero value will also be considered carefully!

# Implementation

The function for that would be called close?
`close?(a, b, rel_tol, abs_tol)`

`a` and `b`: are the two values to be tested to relative closeness

`rel_tol`: is the relative tolerance -- it is the amount of error allowed, relative to the larger absolute value of a or b. For example, to set a tolerance of 5%, pass tol=0.05. The default tolerance is 1E-9, which assures that the two values are the same within about 9 decimal digits. rel_tol must be greater than 0.0

`abs_tol`: is a minimum absolute tolerance level -- useful for comparisons near zero.

By default, relative tolerance is 1E-9 which is relatively precise enough to compare two float numbers. However it can also be adjusted in case higher accuracy is requested. The absolute tolerance is by default 0.0 and need to be set in case of near-zero numbers.

# Discussion

There are some test cases available for the method which has approved the accuracy of the method. BigNumbers and integers are also tested. However, more test cases are still needed to assure even better the accuracy of the method.

# Gist

Relative equal comparison