Xsum in Swift

This package implments xsum algorithm by Radford M. Neal (https://arxiv.org/abs/1505.05571).

xsum is able to calculate fast exact summation.

Note

Currently, xsum supports Double calculation only.

Xsum Types

• XsumSmall: Optimized for arrays with up to 1,000 elements.
• XsumLarge: Optimized for arrays with more than 1,000 elements.
• XsumAuto: Automatically selects the appropriate variant when the array size is unknown.
• XsumVariant: Provides a convenient interface for managing multiple Xsum structs.

Tip

XsumAuto internally uses XsumSmall and XsumLarge. XsumAuto has runtime overhead to determine when to switch from XsumSmall to XsumLarge. If you already know the input size in advance, consider using XsumVariant instead to avoid this overhead.

Usage

addList() to take array

Calculates the sum of a small-sized array.

import Xsum

var xsmall = XsumSmall()
xsmall.addList([1.0, 2.0, 3.0])
assert(xsmall.sum() == 6.0)

Calculates the sum of a large-sized array (more than 1,000 elements).

import Xsum

var xlarge = XsumLarge()
xlarge.addList(Array(repeating: 1.0, count: 1_500))
assert(xlarge.sum() == 1_500.0)

Calculates the sum of a unknown-sized array.

import Xsum

var xauto = XsumAuto()
xauto.addList(Array(repeating: 1.0, count: 1_500))
assert(xauto.sum() == 1_500.0)

add() to take a floating point number

import Xsum

var xsmall = XsumSmall()
let arr = [1.0, 2.0, 3.0]
for v in arr {
    xsmall.add(v)
}
assert(xsmall.sum() == 6.0)

Chaining Method

import Xsum

let arr = [1.0, 2.0, 3.0]
assert(arr.xsum() == 6.0)

Variant

If you already know the input size in advance, you can directly select the most suitable xsum variant, avoiding unnecessary overhead.

import Xsum

let arr = Array(repeating: 1.0, count: 2_000)
var xVariant: XsumVariant =
    if arr.count < XSUM_THRESHOLD {
        .small(XsumSmall())
    } else {
        .large(XsumLarge())
    }
xVariant.addList(arr)
assert(xVariant.sum() == 2_000.0)

Comformance

xsum comforms to Javascript's Math.sumPrecise behavior.