dec: optimize expNN performance for large x with y = 1 and 1 < m < x

dec.go

@@ -35,6 +35,7 @@ type dec []Word
 
 var (
 	decOne = dec{1}
+	decTwo = dec{2}
 	decTen = dec{10}
 )
 
@@ -699,7 +700,6 @@ func (z dec) expNN(x, y, m dec) dec {
 		// We likely end up being as long as the modulus.
 		z = z.make(len(m))
 	}
-	z = z.set(x)
 
 	// If the base is non-trivial and the exponent is large, we use
 	// 4-bit, windowed exponentiation. This involves precomputing 14 values
@@ -715,13 +715,22 @@ func (z dec) expNN(x, y, m dec) dec {
 	// }
 
 	// convert y from dec to base2 nat
-	// TODO(db47h): better way to do this?
-	yy := y.toNat(nil)
+	yy := y.toNat(make([]Word, 1))
 
 	v := yy[len(yy)-1] // v > 0 because yy is normalized and y > 0
 	shift := nlz(v) + 1
 	v <<= shift
-	var q dec
+
+	// zz and r are used to avoid allocating in mul and div as
+	// otherwise the arguments would alias.
+	var zz, r dec
+
+	// set x = x % m, this speeds up cases with large x even if len(y) == 1
+	if len(m) != 0 {
+		zz, r = zz.div(r, x, m)
+		x = dec(nil).set(r)
+	}
+	z = z.set(x)
 
 	const mask = 1 << (_W - 1)
 
@@ -730,9 +739,7 @@ func (z dec) expNN(x, y, m dec) dec {
 	// we also multiply by x, thus adding one to the power.
 
 	w := _W - int(shift)
-	// zz and r are used to avoid allocating in mul and div as
-	// otherwise the arguments would alias.
-	var zz, r dec
+
 	for j := 0; j < w; j++ {
 		zz = zz.sqr(z)
 		zz, z = z, zz
@@ -744,7 +751,7 @@ func (z dec) expNN(x, y, m dec) dec {
 
 		if len(m) != 0 {
 			zz, r = zz.div(r, z, m)
-			zz, r, q, z = q, z, zz, r
+			z, r = r, z
 		}
 
 		v <<= 1
@@ -764,7 +771,7 @@ func (z dec) expNN(x, y, m dec) dec {
 
 			if len(m) != 0 {
 				zz, r = zz.div(r, z, m)
-				zz, r, q, z = q, z, zz, r
+				z, r = r, z
 			}
 
 			v <<= 1

dec_test.go

@@ -543,6 +543,29 @@ func TestDecExpNN(t *testing.T) {
 	}
 }
 
+func BenchmarkDecExpNN(b *testing.B) {
+	for i, test := range decExpNNTests {
+		x := decFromString(test.x)
+		y := decFromString(test.y)
+		out := decFromString(test.out)
+
+		var m dec
+		if len(test.m) > 0 {
+			m = decFromString(test.m)
+		}
+
+		b.Run(fmt.Sprintf("#%d", i), func(b *testing.B) {
+			var z dec
+			for it := 0; it < b.N; it++ {
+				z = z.expNN(x, y, m)
+				if z.cmp(out) != 0 {
+					b.Fatalf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
+				}
+			}
+		})
+	}
+}
+
 func BenchmarkDecExp3Power(b *testing.B) {
 	const x = 3
 	for _, y := range []Word{
@@ -786,3 +809,33 @@ func TestDecDiv(t *testing.T) {
 		}
 	}
 }
+
+// TODO(bd47h): move this to decimal_test
+func benchmarkDiv(b *testing.B, aSize, bSize int) {
+	aa := rndDec1(aSize)
+	// bb := rndDec1(bSize)
+	bb := dec(nil).setWord(Word(rnd.Intn(_W-1)) + 1)
+	if aa.cmp(bb) < 0 {
+		aa, bb = bb, aa
+	}
+	x := dec(nil)
+	y := dec(nil)
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		x.div(y, aa, bb)
+	}
+}
+
+func BenchmarkDiv(b *testing.B) {
+	sizes := []int{
+		10, 20, 50, 100, 200, 500, 1000,
+		// 1e4, 1e5, 1e6, 1e7,
+	}
+	for _, i := range sizes {
+		j := 2 * i
+		b.Run(fmt.Sprintf("%d/%d", j, i), func(b *testing.B) {
+			benchmarkDiv(b, j, i)
+		})
+	}
+}