Merge pull request #209 from jbgi/log-nmultiply

mperry · mperry · commit 553d833170dd · 2015-12-29T00:23:39.000+10:00
Merged #209: O(log n) multiply for Semigroup/Monoid
diff --git a/core/src/main/java/fj/Monoid.java b/core/src/main/java/fj/Monoid.java
@@ -8,6 +8,8 @@
 import fj.data.Option;
 import fj.data.Set;
 import fj.data.Stream;
+
+import static fj.Semigroup.multiply1p;
 import static fj.data.Stream.iterableStream;
 
 import java.math.BigInteger;
@@ -90,15 +92,20 @@ public A zero() {
   }
 
   /**
-   * Returns a value summed <code>n</code> times (<code>a + a + ... + a</code>)
+   * Returns a value summed <code>n</code> times (<code>a + a + ... + a</code>).
+   * The default definition uses peasant multiplication, exploiting
+   * associativity to only require `O(log n)` uses of
+   * {@link #sum(Object, Object)}.
+   *
    * @param n multiplier
-   * @param a the value to multiply
-   * @return <code>a</code> summed <code>n</code> times. If <code>n <= 0</code>, returns <code>zero()</code>
+   * @param a the value to be reapeatly summed
+   * @return {@code a} summed {@code n} times. If {@code n <= 0}, returns
+   * {@code zero()}
    */
   public A multiply(final int n, final A a) {
-    A m = zero();
-    for (int i = 0; i < n; i++) { m = sum(m, a); }
-    return m;
+    return (n <= 0)
+        ? zero
+        : multiply1p(sum, n - 1, a);
   }
 
   /**
diff --git a/core/src/main/java/fj/Semigroup.java b/core/src/main/java/fj/Semigroup.java
@@ -1,7 +1,5 @@
 package fj;
 
-import static fj.Function.curry;
-
 import fj.data.Array;
 import fj.data.List;
 import fj.data.Natural;
@@ -10,8 +8,10 @@
 import fj.data.Set;
 import fj.data.Stream;
 
-import java.math.BigInteger;
 import java.math.BigDecimal;
+import java.math.BigInteger;
+
+import static fj.Function.curry;
 
 /**
  * Implementations must satisfy the law of associativity:
@@ -58,6 +58,42 @@ public F<A, F<A, A>> sum() {
     return sum;
   }
 
+  /**
+   * Returns a value summed <code>n + 1</code> times (
+   * <code>a + a + ... + a</code>) The default definition uses peasant
+   * multiplication, exploiting associativity to only require `O(log n)` uses of
+   * {@link #sum(Object, Object)}.
+   *
+   * @param n multiplier
+   * @param a the value to be reapeatly summed n + 1 times
+   * @return {@code a} summed {@code n} times. If {@code n <= 0}, returns
+   * {@code zero()}
+   */
+  public A multiply1p(int n, A a) {
+    return multiply1p(sum, n, a);
+  }
+
+  // shared implementation between Semigroup and Monoid
+  static <A> A multiply1p(F<A, F<A, A>> sum, int n, A a) {
+    if (n <= 0) {
+      return a;
+    }
+
+    A xTmp = a;
+    int yTmp = n;
+    A zTmp = a;
+    while (true) {
+      if ((yTmp & 1) == 1) {
+        zTmp = sum.f(xTmp).f(zTmp);
+        if (yTmp == 1) {
+          return zTmp;
+        }
+      }
+      xTmp = sum.f(xTmp).f(xTmp);
+      yTmp = (yTmp) >>> 1;
+    }
+  }
+
   /**
    * Constructs a semigroup from the given function.
    *
@@ -316,7 +352,7 @@ public static <A> Semigroup<P1<A>> p1Semigroup(final Semigroup<A> sa) {
    * @return A semigroup for binary products.
    */
   public static <A, B> Semigroup<P2<A, B>> p2Semigroup(final Semigroup<A> sa, final Semigroup<B> sb) {
-      return semigroup((a1, a2) -> P.lazy(() -> sa.sum(a1._1(), a2._1()), () -> sb.sum(a1._2(), a2._2())));
+    return semigroup((a1, a2) -> P.lazy(() -> sa.sum(a1._1(), a2._1()), () -> sb.sum(a1._2(), a2._2())));
   }
 
   /**
