[jira] [Moved] (NUMBERS-193) Add support for extended precision floating-point numbers

["Alex Herbert (Jira)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/NUMBERS-193?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Alex Herbert moved STATISTICS-68 to NUMBERS-193:
------------------------------------------------

         Key: NUMBERS-193  (was: STATISTICS-68)
    Workflow: jira  (was: Default workflow, editable Closed status)
     Project: Commons Numbers  (was: Commons Statistics)

> Add support for extended precision floating-point numbers
> ---------------------------------------------------------
>
>                 Key: NUMBERS-193
>                 URL: https://issues.apache.org/jira/browse/NUMBERS-193
>             Project: Commons Numbers
>          Issue Type: New Feature
>            Reporter: Alex Herbert
>            Priority: Major
>              Labels: full-time, gsoc2023, part-time
>
> 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:
> {noformat}
> double-double (a, b):
> |a| > |b|
> a == a + b{noformat}
> Common representations are double-double and quad-double (see for example David Bailey's paper on a quad-double library: [QD|https://www.davidhbailey.com/dhbpapers/qd.pdf]).
> 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:
> {code:java}
> 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());
> {code}
> Outputs:
> {noformat}
> -1.0
> 9.223372036854776E18
> 0.0
> -0.5{noformat}



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