reduce: simplify the calcualtion

Hacker news didn't understand why we needed to "prime the pump".
Because we don't.

https://www.reddit.com/r/golang/comments/peh2m6/a_question_on_rob_pikes_reduce_function/

Author: robpike

go.mod

@@ -0,0 +1,3 @@
+module robpike.io/filter
+
+go 1.17

reduce.go

@@ -24,25 +24,19 @@ func Reduce(slice, pairFunction, zero interface{}) interface{} {
 		panic("reduce: not slice")
 	}
 	n := in.Len()
-	switch n {
-	case 0:
+	if n == 0 {
 		return zero
-	case 1:
-		return in.Index(0)
 	}
 	elemType := in.Type().Elem()
 	fn := reflect.ValueOf(pairFunction)
 	if !goodFunc(fn, elemType, elemType, elemType) {
 		str := elemType.String()
 		panic("apply: function must be of type func(" + str + ", " + str + ") " + str)
 	}
-	// Do the first two by hand to prime the pump.
 	var ins [2]reflect.Value
-	ins[0] = in.Index(0)
-	ins[1] = in.Index(1)
-	out := fn.Call(ins[:])[0]
-	// Run from index 2 to the end.
-	for i := 2; i < n; i++ {
+	out := in.Index(0) // By convention, fn(zero, in[0]) = in[0].
+	// Run from index 1 to the end.
+	for i := 1; i < n; i++ {
 		ins[0] = out
 		ins[1] = in.Index(i)
 		out = fn.Call(ins[:])[0]

reduce_test.go

@@ -12,18 +12,24 @@ func mul(a, b int) int {
 	return a * b
 }
 
+func fac(n int) int {
+	if n <= 1 {
+		return 1
+	}
+	return n * fac(n-1)
+}
+
 func TestReduce(t *testing.T) {
-	a := make([]int, 10)
+	const size = 10
+	a := make([]int, size)
 	for i := range a {
 		a[i] = i + 1
 	}
-	// Compute 10!
-	out := Reduce(a, mul, 1).(int)
-	expect := 1
-	for i := range a {
-		expect *= a[i]
-	}
-	if expect != out {
-		t.Fatalf("expected %d got %d", expect, out)
+	for i := 1; i < 10; i++ {
+		out := Reduce(a[:i], mul, 1).(int)
+		expect := fac(i)
+		if expect != out {
+			t.Fatalf("expected %d got %d", expect, out)
+		}
 	}
 }