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https://issues.apache.org/jira/browse/MATH-475?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12982004#action_12982004
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Gilles commented on MATH-475:
-----------------------------
{quote}
assertTrue(MathUtils.equals(top, pen, 1.0)); // OK - implies the difference is
<= 1.0
{quote}
The comment seems reasonable but I'm not sure that it must be correct when
dealing with floating point numbers.
If we change the definition of {{equals(a, b, eps)}} to
{noformat}
min(a, b) + abs(eps) >= max(a, b)
{noformat}
then
{noformat}
equals(top, pen, 1.0)
{noformat}
will return {{true}}, because
{noformat}
pen + 1.0 = top
{noformat}
although
{noformat}
pen - top == 2.0
{noformat}
However,
{noformat}
equals(top, pen, 0.98)
{noformat}
will return {{false}} because
{noformat}
pen + 0.98 == pen
{noformat}
IIUC, the issue is: What is the meaning of {{equals(a, b, eps)}} when {{eps <
ulp(max(a, b))}} ?
Because in that case, I think that the call is equivalent to the strict
equality test: {{a == b}}, I'd say that the call to "equals" is also
meaningless.
The current implementation short-circuits the problem by assuming that two
floating point numbers {{a}} and {{b}} separated by 1 ulp are equally likely
representations of any real number within the interval {{[a, b]}}.
> MathUtils.equals(double, double, double) does not agree with Javadoc
> --------------------------------------------------------------------
>
> Key: MATH-475
> URL: https://issues.apache.org/jira/browse/MATH-475
> Project: Commons Math
> Issue Type: Bug
> Reporter: Sebb
>
> MathUtils.equals(double, double, double) does not agree with its Javadoc.
> The Javadoc says:
> "Returns true if both arguments are equal or within the range of allowed
> error (inclusive)."
> However the following test fails:
> {code}
> double top=1.7976931348623184E16;
> double pen=1.7976931348623182E16;
> double diff=Math.abs(top-pen);
> assertTrue(MathUtils.equals(top, pen, 1.0)); // OK - implies the difference
> is <= 1.0
> assertTrue("expected < 1.0, but was: "+diff,diff <= 1.0); // reports:
> expected < 1.0, but was: 2.0
> {code}
> This discrepancy is because the equals(double, double, double) method also
> checks to see if the numbers are within one ULP of each other.
> Either the Javadoc needs to be corrected, or the code needs to be corrected
> to drop the ULP comparison.
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