Add floating-point reduction ordering demo

timings/src/main/java/com/ankurm/vectorapi/ReductionOrder.java

@@ -0,0 +1,35 @@
+package com.ankurm.vectorapi;
+
+import jdk.incubator.vector.*;
+
+/** Why a vector reduction and a scalar loop disagree in the last bits. */
+public final class ReductionOrder {
+
+    static final VectorSpecies<Float> SP = FloatVector.SPECIES_PREFERRED;
+
+    static float scalarSum(float[] a) {
+        float sum = 0;
+        for (float v : a) sum += v;      // strictly left to right
+        return sum;
+    }
+
+    static float vectorSum(float[] a) {
+        FloatVector acc = FloatVector.zero(SP);
+        int i = 0, bound = SP.loopBound(a.length);
+        for (; i < bound; i += SP.length()) acc = acc.add(FloatVector.fromArray(SP, a, i));
+        float sum = acc.reduceLanes(VectorOperators.ADD);   // lanes combined at the end
+        for (; i < a.length; i++) sum += a[i];
+        return sum;
+    }
+
+    static void run() {
+        float[] a = Data.randomFloats(8192, 5);
+        System.out.println("--- floating-point reduction ordering ---");
+        System.out.printf("scalar (left to right) : %.6f%n", scalarSum(a));
+        System.out.printf("vector (lanes, then reduce): %.6f%n", vectorSum(a));
+        System.out.println("Same mathematical sum; different addition order, so different rounding.");
+        System.out.println();
+    }
+
+    private ReductionOrder() {}
+}