Issue #5273 has been updated by naruse (Yui NARUSE).

Status changed from Assigned to Open
Assignee deleted (naruse (Yui NARUSE))

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Bug #5273: Float#round returns the wrong floats for higher precision
https://bugs.ruby-lang.org/issues/5273#change-68110

* Author: marcandre (Marc-Andre Lafortune)
* Status: Open
* Priority: Normal
* Assignee: 
* Target version: next minor
* ruby -v: r33186
* Backport: 2.3: UNKNOWN, 2.4: UNKNOWN
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Float#round returns the wrong floats for higher precision.

Rounding can be off:
    2.5e-22.round(22) # => 2.0e-22

It can also return values that have extra decimals:
    2.5e-31.round(31) # => 3.0000000000000003e-31
    2.5e-36.round(36) # => 2.9999999999999998e-36

Both errors can occur at the same time too:
2.5e-39.round(39) # => 2.0000000000000002e-39

I believe these errors occur only for ndigits >= 22. For ndigits > 22, 10**(-ndigits) is not an exact Float (as 5 ** 23 won't fit in the 53 bits of a double's mantissa). For ndigits < 22, there should be enough bits left to avoid rounding errors.

For ndigits >= 22, the algorithm to use should be similar to the one used to convert doubles to string.

Hopefully, this is the last bug for #round with a given precision.



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