Bring your calculations to Scala!

@MSkarsaune#DV14 #ScalaCalculations

Bring Your Calculations to:[email protected]

Kantega – Norwegian software craftsmanship since 2003

高馬丁

@MSkarsaune#DV14 #ScalaCalculations

1.The Situation

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• Exact representation of values within range

• Interoperable through widening conversion

Integer

float double byte short int long

Java Number Types - Integer

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• Approximate representation of numeric values

• NEVER use for monetary amounts

• Interoperable with integer types through widening

conversion

Floating point Integer

float double byte short int long

Java Number Types – Floating point

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• Immutable

• Calculation possible via primitives

• Interoperability through widening conversion

Floating point Integer Number

Float Double Byte Short Integer Long BigInteger BigDecimal

float double byte short int long

boxingunboxin

g

Java Number Types - Boxed

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• To represent large numbers

• Calculations with methods

• Cumbersome conversions

“Infinite”Floating point Integer Number

Float Double Byte Short Integer Long BigInteger BigDecimal

float double byte short int long

Java Object Number - Extended

Poor

interoperabilit

y

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2. Inspiration

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Smalltalk calculations

Numbers are objects

Binary message selectors (+, -, *, / , ….)

Built in decimals

Overflows handled

Precise division

Interoperable and extendable number types

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The Hope

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Main Scala language number types

AnyVal

Double Int Long

ScalaNumber

BigDecimal BigInt

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1. Decimal Numbers

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Decimal representation

• Integer value and scale

• 123456789

• Scale is important! Know your scale!

Scale = 3

1234567891000

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Decimal notation

• Smalltalk: 2.5s2

• Java: new BigDecimal("2.50")

new BigDecimal(2.5).setScale(2)

• Scala: val dec : BigDecimal = 2.50

How is this possible?

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Scala Implicit Type Conversion

• Implicit type conversion

• Compiler looks for implicit function to convert source type

to target type

• Object scala.math.BigDecimal:

/** Implicit conversion from `Double` to `BigDecimal`. */

implicit def double2bigDecimal(

d: Double): BigDecimal = decimal(d)

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Decimal computation

• Task multiply decimal dec by 100:

• Smalltalk: dec * 100

• Java: dec.multiply(new BigDecimal(100));

• Scala: dec * 100

What does this mean?

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Infix, symbols + implicit conversion

• Special characters as method identifiers (+ , - , ∙, √, ⊂, π

…)

• Infix notation: num.*(100) <==> num * 100

• Class scala.math.BigDecimal:

• Also works: 100 * num

/** Multiplication of BigDecimals */

def * (that: BigDecimal): BigDecimal

= new BigDecimal(

this.bigDecimal.multiply(that.bigDecimal, mc), mc)

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Decimal calculation summary

• Natural syntax

• Operators and literals

• Interoperable with other number types

• Withouth having to change existing number types

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Spire math

• Scala calculation library:

https://github.com/non/spire

• Generic algorithms

• Extended number types, such as

• Rational

• Real

• Complex

• Macros provide additional number literal syntax

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4. Overflow1_000_000 * 1_000_000 = ?

1_000_000_000_000 ?

-727_379_968

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Overflow management

• Smalltalk:

Automatically converts SmallInteger <=> LargeInteger

• Java:

Libraries such as guava or Apache commons-math can

detect

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(Some) Spire number types

• SafeLong detects overflows and ensures optimal

representation

ScalaNumber

SafeLong Real Rational Complex

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SafeLong example

val trillion : SafeLong = 1000000000000l //SafeLongLong

val product = trillion * trillion //SafeLongBigInt

val other = product / trillion //SafeLongLong

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3. Division2 / 3 = ?

0 ?

0.6666666666666666 ?

0.6666666666666667 ?

2

3?

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Precise division

• Smalltalk: 3 / 3 = 1

2 / 3 =2

3* 3 = 2

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(Some) Spire number types

• Real ensures exact division and always chooses the

most precise representation

ScalaNumber

SafeLong Real Rational Complex

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Real example

val numerator: Real = 2 //Real$Exact(2)

val fraction = numerator / 3 //Real$Exact(2/3)

fraction * 3 //Real$Exact(2)

fraction * Real.pi

//Real$Inexact(2.0943951023931954923084289221863352561314)

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Some conversion code of our own

….final class DoubleSyntax(val value : Double) {

def scaled(scale : Int) = BigDecimal(value).setScale(scale)

def i = Complex(0.0, value)

}

object DoubleSyntax {

implicit def doubleToDoubleConverter(value : Double) =

new DoubleSyntax(value)

}

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… that allows us to write

val dec : BigDecimal = 2.50

val dec = 2.5 scaled 2 // BigDecimal(2.50) “2.5s2”

val complex = -1.0 + 1.0.i // Complex(-1.0, 1.0)

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Conclusion

• Scala brings

• Natural syntax: special characters + infix notation

• Extendability and interoperability: implicit type conversions

• Possible improvements (as demonstrated by spire math)

• New number types

• New calculations

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References

http://www.scala-lang.org/

Spire:

https://github.com/non/spire

Sample code:

https://github.com/skarsaune/devoxx.scala.calculations

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Thank you for your time