How to use Spire's Ops macros in your own project

What are Spire's Ops macros?

Spire's type classes abstract over very basic operators like + and *. These operations are normally very fast. This means that any extra work that happens on a per-operation basis (like boxing or object allocation) will cause generic code to be slower than its direct equivalent.

Efficient, generic numeric programming is Spire's raison d'être. We have developed a set of Ops macros to avoid unnecessary object instantiations at compile-time. This post explains how, and illustrates how you can use these macros in your code!

How implicit operators on type classes usually work

When using type classes in Scala, we rely on implicit conversions to "add" operators to an otherwise generic type.

In this example, A is the generic type, Ordering is the type class, and > is the implicit operator. foo1 is the code that the programmer writes, and foo4 is a translation of that code after implicits are resolved, and syntactic sugar is expanded.

import scala.math.Ordering
import Ordering.Implicits._

def foo1[A: Ordering](x: A, y: A): A =
  x > y

def foo2[A](x: A, y: A)(implicit ev: Ordering[A]): A =
  x > y

def foo3[A](x: A, y: A)(implicit ev: Ordering[A]): A =
  infixOrderingOps[A](x)(ev) > y

def foo4[A](x: A, y: A)(implicit ev: Ordering[A]): A =
  new ev.Ops(x) > y

(This is actually slightly wrong. The expansion to foo4 won't happen until runtime, when infixOrderingOps is called. But it helps illustrate the point.)

Notice that we instantiate an ev.Ops instance for every call to >. This is not a big deal in many cases, but for a call that is normally quite fast it will add up when done many (e.g. millions) of times.

It is possible to work around this:

def bar[A](x: A, y: A)(implicit ev: Ordering[A]): A =, y)

The ev parameter contains the method we actually want (gt), so instead of instantiating ev.Ops this code calls directly. But this approach is ugly. Compare these two methods:

def qux1[A: Field](x: A, y: A): A =
  ((x pow 2) + (y pow 2)).sqrt

def qux2[A](x: A, y: A)(implicit ev: Field[A]): A =
  ev.sqrt(, 2), ev.pow(y, 2)))

If you have trouble reading qux2, you are not alone.

At this point, it looks like we can either write clean, readable code (qux1), or code defensively to avoid object allocations (qux2). Most programmers will just choose one or the other (probably the former) and go on with their lives.

However, since this issue affects Spire deeply, we spent a bit more time looking at this problem to see what could be done.

Having our cake and eating it too

Let's look at another example, to compare how the "nice" and "fast" code snippets look after implicits are resolved:

def niceBefore[A: Ring](x: A, y: A): A =
  (x + y) * z

def niceAfter[A](x: A, y: A)(implicit ev: Ring[A]): A =
  new RingOps(new RingOps(x)(ev).+(y))(ev).*(z)

def fast[A](x: A, y: A)(implicit ev: Ring[A]): A =
  ev.times(, y), z)

As we can see, niceAfter and fast are actually quite similar. If we wanted to transform niceAfter into fast, we'd just have to:

  1. Figure out the appropriate name for symbolic operators. In this example, + becomes plus and * becomes times.

  2. Rewrite the object instantiation and method call, calling the method on ev instead and passing x and y as arguments. In this example, new Ops(x)(ev).foo(y) becomes, y).

In a nutshell, this transformation is what Spire's Ops macros do.

Using the Ops macros

Your project must use Scala 2.10+ to be able to use macros.

To use Spire's Ops macros, you'll need to depend on the spire-macros package. If you use SBT, you can do this by adding the following line to build.sbt:

libraryDependencies += "org.spire-math" %% "spire-macros" % "0.6.1"

You will also need to enable macros at the declaration site of your ops classes:

import scala.language.experimental.macros

Let's see an example

Consider Sized, a type class that abstracts over the notion of having a size. Type class instances for Char, Map, and List are provided in the companion object. Of course, users can also provide their own instances.

Here's the code:

trait Sized[A] {
  def size(a: A): Int
  def isEmpty(a: A): Boolean = size(a) == 0
  def nonEmpty(a: A): Boolean = !isEmpty(a)
  def sizeCompare(x: A, y: A): Int = size(x) compare size(y)

object Sized {
  implicit val charSized = new Sized[Char] {
    def size(a: Char): Int = a.toInt

  implicit def mapSized[K, V] = new Sized[Map[K, V]] {
    def size(a: Map[K, V]): Int = a.size

  implicit def listSized[A] = new Sized[List[A]] {
    def size(a: List[A]): Int = a.length
    override def isEmpty(a: List[A]): Boolean = a.isEmpty
    override def sizeCompare(x: List[A], y: List[A]): Int = (x, y) match {
      case (Nil, Nil) => 0
      case (Nil, _) => -1
      case (_, Nil) => 1
      case (_ :: xt, _ :: yt) => sizeCompare(xt, yt)

(Notice that Sized[List[A]] overrides some of the "default" implementations to be more efficient, since taking the full length of a list is an O(n) operation.)

We'd like to be able to call these methods directly on a generic type A when we have an implicit instance of Sized[A] available. So let's define a SizedOps class, using Spire's Ops macros:

import spire.macrosk.Ops
import scala.language.experimental.macros

object Implicits {
  implicit class SizedOps[A: Sized](lhs: A) {
    def size(): Int = macro Ops.unop[Int]
    def isEmpty(): Boolean = macro Ops.unop[Boolean]
    def nonEmpty(): Boolean = macro Ops.unop[Boolean]
    def sizeCompare(rhs: A): Int = macro Ops.binop[A, Int]

That's it!

Here's what it would look like to use this type class:

import Implicits._

def findSmallest[A: Sized](as: Iterable[A]): A =
  as.reduceLeft { (x, y) =>
    if ((x sizeCompare y) < 0) x else y

def compact[A: Sized](as: Vector[A]): Vector[A] =

def totalSize[A: Sized](as: Seq[A]): Int =
  as.foldLeft(0)(_ + _.size)

Not bad, eh?

The fine print

Of course, there's always some fine-print.

In this case, the implicit class must use the same parameter names as above. The constructor parameter to SizedOps must be called lhs and the method parameter (if any) must be called rhs. Also, unary operators (methods that take no parameters, like size) must have parenthesis.

How the macros handle classes with multiple constructor parameters, or multiple method parameters? They don't. We haven't needed to support these kinds of exotic classes, but it would probably be easy to extend Spire's Ops macros to support other shapes as well.

If you fail to follow these rules, or if your class has the wrong shape, your code will fail to compile. So don't worry. If your code compiles, it means you got it right!

Symbolic names

The previous example illustrates rewriting method calls to avoid allocations, but what about mapping symbolic operators to method names?

Here's an example showing the mapping from * to times:

trait CanMultiply[A] {
  def times(x: A, y: A): A

object Implicits {
  implicit class MultiplyOps[A: CanMultiply](lhs: A) {
    def *(rhs: A): A = macro Ops.binop[A, A]

object Example {
  import Implicits._

  def gak[A: CanMultiply](a: A, as: List[A]): A =
    as.foldLeft(a)(_ * _)

Currently, the Ops macros have a large (but Spire-specific) mapping from symbols to names. However, your project may want to use different names (or different symbols). What then?

For now, you are out of luck. In Spire 0.7.0, we plan to make it possible to use your own mapping. This should make it easier for other libraries that make heavy use of implicit symbolic operators (e.g. Scalaz) to use these macros as well.

Other considerations

You might wonder how the Ops macros interact with specialization. Fortunately, macros are expanded before the specialization phase. This means you don't need to worry about it! If your type class is specialized, and you invoke the implicit from a specialized (or non-generic) context, the result will be a specialized call.

(Of course, using Scala's specialization is tricky, and deserves its own blog post. The good news is that type classes are some of the easiest structures to specialize correctly in Scala.)

Evaluating the macros at compile-time also means that if there are problems with the macro, you'll find out about those at compile-time as well. While we expect that many projects will benefit from the Ops macros, they were designed specifically for Spire so it's possible that your project will discover problems, or need new features.

If you do end up using these macros, let us know how they work for you. If you have problems, please open an issue, and if you have bug fixes (or new features) feel free to open a pull request!


We are used to thinking about abstractions having a cost. So we often end up doing mental accounting: "Is it worth making this generic? Can I afford this syntactic sugar? What will the runtime impact of this code be?" These condition us to expect that code can either be beautiful or fast, but not both.

By removing the cost of implicit object instantiation, Spire's Ops macros raise the abstraction ceiling. They allow us to make free use of type classes without compromising performance. Our goal is to close the gap between direct and generic performance, and to encourage the widest possible use of generic types and type classes in Scala.

Posted on Oct 13, 2013 by Erik Osheim

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