dec

Dec object represents a 64-bit decimal floating-point number.

• Unlike Double, Dec has no binary rounding artifacts.

• Unlike BigDecimal, Dec has a fixed decimal64 precision.

These two qualities make Dec more predictable in arithmetic.

Dec is a thin Kotlin wrapper for Java BigDecimal.

Install

// build.gradle.kts

dependencies {
    implementation("io.github.rtmigo:dec:X.X.X")
    // replace X.X.X with actual version
}

Find the latest version and instructions for other build systems at Maven Central.

Basic use

import io.github.rtmigo.dec.Dec

fun main() {
    val pi = Dec("3.14159265359")
    val r = Dec(5)

    println(pi * (r * r))
}

Dec vs Double

Double introduces rounding artifacts where you wouldn't expect them.

0.1 + 0.2  // = 0.30000000000000004

Because of this rounding the same trivial operations with the same numbers, but in a different order, give different results.

(0.1 + 0.2) - (0.1 + 0.2)  // = 0.0
0.1 + 0.2 - 0.1 - 0.2   // = 2.7755575615628914e-17

Dec behaves more predictably.

Dec(0.1) + Dec(0.2)  // = 0.3

Dec(0.1) + Dec(0.2) - Dec(0.1) - Dec(0.2)  // = 0.0

In fact, Dec also has a rounding problem. But this happens when you literally operate on 16-digit numbers like 2.718281828459045 and some inaccuracy in the lower digits is expected.

More horrors of double arithmetic

Let's sum 0.1 multiple times and compare to the ideal result.

fun difference(summands: Int): Double {
    val ideal = summands * 0.1
    val sum = (1..summands).sumOf { 0.1 }
    return sum - ideal
}

Summands	Difference (plain)	Difference (scientific)
10	-0.000000000000000111	-1.1102230246251565E-16
100	-0.00000000000001954	-1.9539925233402755E-14
1,000	-0.000000000001406875	-1.4068746168049984E-12
10,000	0.000000000158820512	1.588205122970976E-10
100,000	0.0000000188483682	1.8848368199542165E-8
1,000,000	0.000001332882675342	1.3328826753422618E-6
10,000,000	-0.00016102462541312	-1.610246254131198E-4
100,000,000	-0.018870549276471138	-0.018870549276471138
1,000,000,000	-1.2545821815729141	-1.2545821815729141

Dec vs BigDecimal

BigDecimal fixes oddities in Double rounding.

But the syntax for using BigDecimal in Java is far from intuitive. For example, here is how we compute 125 / 100:

BigDecimal("125").divide(BigDecimal("100"), MathContext.DECIMAL64)

Kotlin standard library adds arithmetic operators to the BigDecimal, but the result of the calculations can be surprising.

BigDecimal("125") / BigDecimal("100")      // = 1
BigDecimal("125.0") / BigDecimal("100.0")  // = 1.2
BigDecimal("125.00") / BigDecimal("100")   // = 1.25

Calculations with Dec are both intuitive and predictable.

Dec("125") / Dec("100")      // = 1.25
Dec("125.0") / Dec("100.0")  // = 1.25
Dec("125.00") / Dec("100")   // = 1.25 

Implicit conversions

When the left side of an expression is a Dec instance, the right side can have basic numeric types.

Dec("125") + 8  // = 133.0

BigDecimal("125") + 8  // does not compile in Kotlin 

Speed considerations

Dec is faster than rounding Double

Double with its rounding artifacts is much faster than Dec. It's tempting to use Double and round it up after every calculation. However, properly done rounding can be much slower than just using Dec.

import org.apache.commons.math3.util.Precision
import io.github.rtmigo.dec.*

fun slowest(n: Int): Double {
    var x: Double = 0.0
    for (i in 1..n) {
        x += 0.01
        x = Precision.round(x, 2)  // slow!
    }
    return x
}

fun average(n: Int): Double {
    var x = Dec("0.0")
    for (i in 1..n) {
        x += Dec("0.01")  // faster than Precision.round 
    }
    return x.toDouble()
}

fun fastest(n: Int): Double {
    var x: Double = 0.0
    for (i in 1..n) {
        x += 0.01
        // we can reuse x if we are satisfied with  
        // inaccurate decimal value on each step 
    }
    // we also must be sure that the accumulated error 
    // is less than the rounding
    return Precision.round(x, 2)
}

fun hyperspeed(n: Int) = Precision.round(n * 0.01, 2)  // ;)

Reusing is faster than creation

val CONST_17 = Dec(17)

fun faster(x: Dec) = x * CONST_17

fun slower(x: Dec) = x + Dec(17)
fun also_slower(x: Dec) = x + 17  // this creates Dec(17) anyway

Multiplication is faster than division

Dec(23) / Dec(100)   // slower
Dec(23) * Dec(0.01)  // faster

Dec(string) is faster than Dec(double)

Dec("1.23")  // this is faster
Dec(1.23)  // will create intermediate string "1.23" anyway

Double.toDecBin() does not use intermediate string conversion, but be prepared that:

100.0.toDecBin() - 0.1.toDecBin()  // = 99.90000000000001

License

Copyright © 2022 Artsiom iG. Released under the ISC License.