BigInt.equals(Number) and BigDecimal.equals(Number) should implement equality in mathematical sense

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The BigInt.equals(that: Any) and BigDecimal.equals(that: Any) should implement
equality in mathematical sense (at least when "that" is primitive.
I mean that BigInt.equals(that: Any) iff "this" and "that" represent the same rational number.

However, this is not always so.
The value 2^64 can be represented exactly both by BigInt, Float and Double, but the assertions below fails.

def testBigIntEquals {
 val bi = BigInt(1) << 64
 assert(bi == bi.toFloat)
 assert(bi == bi.toDouble)
}

The value 2^53 + 1 doesn't equal to 2^53 but the assertions below fails too

def testBigIntEquals2 {
 val l = 1L << 53
 val f = l.toFloat
 val d = l.toDouble
 val bi = BigInt(l + 1)
 assert(bi != f)
 assert(bi != d)
}

I would like the same for equality between primitives too, but I understand
the burden of compatibility with fuzzy Java definition of operators
float == int
double == long

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Imported From: https://issues.scala-lang.org/browse/SI-5627?orig=1
Reporter: @nadezhin
Assignee: @nadezhin
Affected Versions: 2.9.1, 2.10.0
Other Milestones: 2.10.0

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@nadezhin said:
Sorry, I found now that this bug is duplicate of #4540 and it has been fixed already by overriding isValidChar/isValidByte/isValidShort in BigInt/BigDecimal .

Nevertheless, there is still an issue with comparison of BigInt/BigDecimal with Float/Double .

def testBigIntEquals {
val bi = BigInt(1) << 64;
assert(bi == bi.toFloat);
assert(bi == bi.toDouble)
}

This test fails, though 2^64 is represented exactly in both Float and Double.
If you agree that this is a bug, then I can try to prepare a pull request that fixes comparison of BigInt/BigDecimal with Float/Double .

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@nadezhin said:
Fix is in the commit 883ca63361a039f27e412eb0cb1bee7e9742a0bb
that was merged to master on Apr 01, 2012 .

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@paulp said:
Thanks.