Numeric Programming with Spire

Abstract

Numeric programming is a notoriously difficult topic. For number crunching, e.g. solving systems of linear equations, we need raw performance. However, using floating-point numbers may lead to inaccurate results. On top of that, as functional programmers, we’d really like to abstract over concrete number types, which is where abstract algebra comes into play. This interplay between abstract and concrete, and the fact that everything needs to run on finite hardware, is what makes good library support necessary for writing fast & correct programs. Spire is such a library in the Typelevel Scala ecosystem. This talk is an introduction to Spire, showcasing the ‘number tower’, real-ish numbers and how to obey the law.

Slides

Recording

Events

Interview at J On The Beach

Testimonials

Trains are monoids and now I finally understand better my commuting issues: that's the “zero train”!
If you liked @larsr_h's talk, put a `SemiRing` on it. Crystal clear intro to numeric programming with Spire/Cats/Algebra. Kudos!

Demo code

All code snippets are tested with version 0.15.0 and assume the following imports:

import spire._
import spire.algebra._
import spire.math._
import spire.implicits._
import spire.laws._
import spire.syntax.literals._
import org.scalacheck._

Maps

val cities1 = Map("Portugal" -> List("Lisbon"), "Spain" -> List("Madrid"))
val cities2 = Map("Portugal" -> List("Coimbra"))

cities1 |+| cities2

Laws

RingLaws[Int].ring.all.check()
RingLaws[Float].ring.all.check()

Monoids

val score = r"5/7"

def twice[A : AdditiveMonoid](a: A) = a + a

twice(score)
twice(3)
twice(Map("Score" -> score))

score.toBigDecimal()

Reals

Real.pi
Real.pi.doubleValue()
Real.pi.toRational(1).toBigDecimal()
Real.pi.toRational(2).toBigDecimal()
Real.pi.toRational(4).toBigDecimal()

Rationals and Intervals

val score = r"5/7"

val confidence = score ± r"1/7"

confidence.intersects(r"3/4" ± r"1/8")
confidence.intersect(r"3/4" ± r"1/8")