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https://issues.apache.org/jira/browse/NUMBERS-193?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17751734#comment-17751734
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Alex Herbert commented on NUMBERS-193:
--------------------------------------
I have updated the previous post by adding:
* An abs() method to the API
* Data for the sqrt accuracy
I added an accurate sqrt that uses a Newton iteration to improve the estimate:
{noformat}
c = sqrt(x)
c = 0.5 * (c + x/c){noformat}
This is limited by the accuracy of division (x/c) and multiple iterations do
not help. It improves the accuracy to within 1 epsilon which is the limit of
division.
I will update with performance data when I can run the method on the original
machine.
> 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
> Components: ext
> Reporter: Alex Herbert
> Assignee: 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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