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From "Luc Maisonobe (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-904) FastMath.pow deviates from Math.pow for negative, finite base values with an exponent 2^52 < y < 2^53
Date Wed, 21 Nov 2012 21:48:58 GMT

    [ https://issues.apache.org/jira/browse/MATH-904?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13502339#comment-13502339
] 

Luc Maisonobe commented on MATH-904:
------------------------------------

bq. Does anyone know the reason why numbers > 2^53 are assumed to be even?

Because the mantissa of a double number encoding using IEEE-754 cannot handle a sufficient
number of digits. If the Most Significant Bit is large enough, the Least Significant Bit becomes
equal to 2.0 (and later when you still increase the MSB, then the LSB will become 4.0, and
after that 8.0...

This is the essence of "floating" in floating point numbers. The decimal separator "floats",
up to the end of the number than it slips out of the number.
                
> FastMath.pow deviates from Math.pow for negative, finite base values with an exponent
2^52 < y < 2^53 
> ------------------------------------------------------------------------------------------------------
>
>                 Key: MATH-904
>                 URL: https://issues.apache.org/jira/browse/MATH-904
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>            Reporter: Thomas Neidhart
>             Fix For: 3.1
>
>
> As reported by Jeff Hain:
> pow(double,double):
> Math.pow(-1.0,5.000000000000001E15) = -1.0
> FastMath.pow(-1.0,5.000000000000001E15) = 1.0
> ===> This is due to considering that power is an even
> integer if it is >= 2^52, while you need to test
> that it is >= 2^53 for it.
> ===> replace
> "if (y >= TWO_POWER_52 || y <= -TWO_POWER_52)"
> with
> "if (y >= 2*TWO_POWER_52 || y <= -2*TWO_POWER_52)"
> and that solves it.

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