Details
Major Description
Add implementations of extended precision floating point numbers.
An extended precision floating point number is a series of floating-point numbers that are non-overlapping such that:
double-double (a, b): |a| > |b| a == a + b
Common representations are double-double and quad-double (see for example David Bailey's paper on a quad-double library: QD).
Many computations in the Commons Numbers and Statistics libraries use extended precision computations where the accumulated error of a double would lead to complete cancellation of all significant bits; or create intermediate overflow of integer values.
This project would formalise the code underlying these use cases with a generic library applicable for use in the case where the result is expected to be a finite value and using Java's BigDecimal and/or BigInteger negatively impacts performance.
An example would be the average of long values where the intermediate sum overflows or the conversion to a double loses bits:
long[] values = {Long.MAX_VALUE, Long.MAX_VALUE}; System.out.println(Arrays.stream(values).average().getAsDouble()); System.out.println(Arrays.stream(values).mapToObj(BigDecimal::valueOf) .reduce(BigDecimal.ZERO, BigDecimal::add) .divide(BigDecimal.valueOf(values.length)).doubleValue()); long[] values2 = {Long.MAX_VALUE, Long.MIN_VALUE}; System.out.println(Arrays.stream(values2).asDoubleStream().average().getAsDouble()); System.out.println(Arrays.stream(values2).mapToObj(BigDecimal::valueOf) .reduce(BigDecimal.ZERO, BigDecimal::add) .divide(BigDecimal.valueOf(values2.length)).doubleValue());
Outputs:
-1.0 9.223372036854776E18 0.0 -0.5
Attachments
Issue Links
- relates to
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NUMBERS-203 Add a field for the DD number
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- Closed
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NUMBERS-202 Add double-double DD class to the user guide
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- Closed
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- links to