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From "Joerg Huber (JIRA)" <j...@apache.org>
Subject [jira] Updated: (MATH-306) Method 'divide' in class 'Complex' uses a false formula for a special case resulting in erroneous division by zero.
Date Sat, 24 Oct 2009 14:31:59 GMT
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[ https://issues.apache.org/jira/browse/MATH-306?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Joerg Huber updated MATH-306:
-----------------------------

Description:
The formula that 'divide' wants to implement is

( a + bi )  /  ( c + di )  =  ( ac + bd + ( bc - ad ) i )  /  ( c^2 + d^2 )

as correctly written in the description.

When c == 0.0 this leads to the special case

( a + bi )  /  di  = ( b / d ) - ( a / d ) i

But the corresponding code is:

if (c == 0.0) {
return createComplex(imaginary/d, -real/c);
}

The bug is the last division -real/c, which should obviously be -real/d.

was:
The formula that 'divide' wants to implement is

a + bi          ac + bd + (bc - ad)i
----------- = -------------------------
c + di               c<sup>2</sup> + d<sup>2</sup>

as correctly written in the description.

When c == 0.0 this leads to the special case

a + bi          b - a i
----------- = ------------
di                  d

But the corresponding code is:

if (c == 0.0) {
return createComplex(imaginary/d, -real/c);
}

The bug is the last division -real/c, which should obviously be -real/d.

Other layout and an additional formula conversion for better readability

> Method 'divide' in class 'Complex' uses a false formula for a special case resulting
in erroneous division by zero.
> -------------------------------------------------------------------------------------------------------------------
>
>                 Key: MATH-306
>                 URL: https://issues.apache.org/jira/browse/MATH-306
>             Project: Commons Math
>          Issue Type: Bug
>         Environment: all
>            Reporter: Joerg Huber
>
> The formula that 'divide' wants to implement is
> ( a + bi )  /  ( c + di )  =  ( ac + bd + ( bc - ad ) i )  /  ( c^2 + d^2 )
> as correctly written in the description.
> When c == 0.0 this leads to the special case
> ( a + bi )  /  di  = ( b / d ) - ( a / d ) i
> But the corresponding code is:
> if (c == 0.0) {
>     return createComplex(imaginary/d, -real/c);
> }
> The bug is the last division -real/c, which should obviously be -real/d.

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