Luc Maisonobe created MATH-1223:
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Summary: Wrong splitting of huge double numbers
Key: MATH-1223
URL: https://issues.apache.org/jira/browse/MATH-1223
Project: Commons Math
Issue Type: Bug
Affects Versions: 3.5
Reporter: Luc Maisonobe
Priority: Minor
Fix For: 4.0
In both MathArrays and FastMath, some computations on double are performed by
firt splitting double numbers in two numbers with about 26 bits.
This splitting fails when the numbers are huge, even if they are still
representable and not infinite (the limit is about 1.0e300, eight orders of
magnitude below infinity).
This can be seen by computing for example
{code}
FastMath.pow(FastMath.scalb(1.0, 500), 4);
{code}
The result is NaN whereas it should be +infinity.
or by modifying test MathArraysTest.testLinearCombination1 and scaling down
first array elements by FastMath.scalb(a[i], -971) and scaling up the second
array elements by FastMath.scalb(b[i], +971), which should not change the
results. Here the result is a loss of precision because a safety check in
MathArrays.linearCombination falls back to naive implementation if the high
accuracy algorithm fails.
The reason for the wrong splitting is an overflow when computing
{code}
final int splitFactor = 0x8000001;
final double cd = splitFactor * d; // <--- overflow
{code}
{code}
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