Newbie Scala question about simple math array operations

Question

Newbie Scala Question:

Say I want to do this [Java code] in Scala:

public static double[] abs(double[] r, double[] im) {
  double t[] = new double[r.length];
  for (int i = 0; i < t.length; ++i) {
    t[i] = Math.sqrt(r[i] * r[i] + im[i] * im[i]);
  }
  return t;
}  

and also make it generic (since Scala efficiently do generic primitives I have read). Relying only on the core language (no library objects/classes, methods, etc), how would one do this? Truthfully I don't see how to do it at all, so I guess that's just a pure bonus point question.

I ran into sooo many problems trying to do this simple thing that I have given up on Scala for the moment. Hopefully once I see the Scala way I will have an 'aha' moment.

UPDATE: Discussing this with others, this is the best answer I have found so far.

def abs[T](r: Iterable[T], im: Iterable[T])(implicit n: Numeric[T]) = {
   import n.mkNumericOps                                                   
   r zip(im) map(t => math.sqrt((t._1 * t._1 + t._2 * t._2).toDouble))          
}

Answer 1

Doing generic/performant primitives in scala actually involves two related mechanisms which scala uses to avoid boxing/unboxing (e.g. wrapping an int in a java.lang.Integer and vice versa):

• @specialize type annotations
• Using Manifest with arrays

specialize is an annotation that tells the Java compiler to create "primitive" versions of code (akin to C++ templates, so I am told). Check out the type declaration of Tuple2 (which is specialized) compared with List (which isn't). It was added in 2.8 and means that, for example code like CC[Int].map(f : Int => Int) is executed without ever boxing any ints (assuming CC is specialized, of course!).

Manifests are a way of doing reified types in scala (which is limited by the JVM's type erasure). This is particularly useful when you want to have a method genericized on some type T and then create an array of T (i.e. T[]) within the method. In Java this is not possible because new T[] is illegal. In scala this is possible using Manifests. In particular, and in this case it allows us to construct a primitive T-array, like double[] or int[]. (This is awesome, in case you were wondering)

Boxing is so important from a performance perspective because it creates garbage, unless all of your ints are < 127. It also, obviously, adds a level of indirection in terms of extra process steps/method calls etc. But consider that you probably don't give a hoot unless you are absolutely positively sure that you definitely do (i.e. most code does not need such micro-optimization)

---

So, back to the question: in order to do this with no boxing/unboxing, you must use Array (List is not specialized yet, and would be more object-hungry anyway, even if it were!). The zipped function on a pair of collections will return a collection of Tuple2s (which will not require boxing, as this is specialized).

In order to do this generically (i.e. across various numeric types) you must require a context bound on your generic parameter that it is Numeric and that a Manifest can be found (required for array creation). So I started along the lines of...

def abs[T : Numeric : Manifest](rs : Array[T], ims : Array[T]) : Array[T] = {
    import math._
    val num = implicitly[Numeric[T]]
    (rs, ims).zipped.map { (r, i) => sqrt(num.plus(num.times(r,r), num.times(i,i))) }
    //                               ^^^^ no SQRT function for Numeric
}

...but it doesn't quite work. The reason is that a "generic" Numeric value does not have an operation like sqrt -> so you could only do this at the point of knowing you had a Double. For example:

scala> def almostAbs[T : Manifest : Numeric](rs : Array[T], ims : Array[T]) : Array[T] = {
 | import math._
 | val num = implicitly[Numeric[T]]
 | (rs, ims).zipped.map { (r, i) => num.plus(num.times(r,r), num.times(i,i)) }
 | }
almostAbs: [T](rs: Array[T],ims: Array[T])(implicit evidence$1: Manifest[T],implicit     evidence$2: Numeric[T])Array[T]

Excellent - now see this purely generic method do some stuff!

scala> val rs = Array(1.2, 3.4, 5.6); val is = Array(6.5, 4.3, 2.1)
rs: Array[Double] = Array(1.2, 3.4, 5.6)
is: Array[Double] = Array(6.5, 4.3, 2.1)

scala> almostAbs(rs, is)
res0: Array[Double] = Array(43.69, 30.049999999999997, 35.769999999999996)

Now we can sqrt the result, because we have a Array[Double]

scala> res0.map(math.sqrt(_))
res1: Array[Double] = Array(6.609841147864296, 5.481788029466298, 5.980802621722272)

And to prove that this would work even with another Numeric type:

scala> import math._
import math._
scala> val rs = Array(BigDecimal(1.2), BigDecimal(3.4), BigDecimal(5.6)); val is =     Array(BigDecimal(6.5), BigDecimal(4.3), BigDecimal(2.1))
rs: Array[scala.math.BigDecimal] = Array(1.2, 3.4, 5.6)
is: Array[scala.math.BigDecimal] = Array(6.5, 4.3, 2.1)

scala> almostAbs(rs, is)
res6: Array[scala.math.BigDecimal] = Array(43.69, 30.05, 35.77)

scala> res6.map(d => math.sqrt(d.toDouble))
res7: Array[Double] = Array(6.609841147864296, 5.481788029466299, 5.9808026217222725)