 # Add support for extended precision floating-point numbers

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#### Details

• New Feature
• Status: Open
• Major
• Resolution: Unresolved
• None
• None
• None
• Easy

#### 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)
.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)
.divide(BigDecimal.valueOf(values2.length)).doubleValue());
```

Outputs:

```-1.0
9.223372036854776E18
0.0
-0.5```

#### People Unassigned Alex Herbert