math/big: improved karatsuba calibration code, better mul benchmark

An attempt to profit from CL 6176043 (fix to superpolinomial
runtime of karatsuba multiplication) and determine a better
karatsuba threshold. The result indicates that 32 is still
a reasonable value. Left the threshold as is (== 32), but
made some minor changes to the calibrate code which are
worthwhile saving (use of existing benchmarking code for
better results, better use of package time).

R=golang-dev, rsc
CC=golang-dev
https://golang.org/cl/6260062

src/pkg/math/big/calibrate_test.go

@@ -21,15 +21,17 @@ import (
 
 var calibrate = flag.Bool("calibrate", false, "run calibration test")
 
-// measure returns the time to run f
+func karatsubaLoad(b *testing.B) {
-func measure(f func()) time.Duration {
+	BenchmarkMul(b)
-	const N = 100
+}
-	start := time.Now()
+
-	for i := N; i > 0; i-- {
+// measureKaratsuba returns the time to run a Karatsuba-relevant benchmark
-		f()
+// given Karatsuba threshold th.
-	}
+func measureKaratsuba(th int) time.Duration {
-	stop := time.Now()
+	th, karatsubaThreshold = karatsubaThreshold, th
-	return stop.Sub(start) / N
+	res := testing.Benchmark(karatsubaLoad)
+	karatsubaThreshold = th
+	return time.Duration(res.NsPerOp())
 }
 
 func computeThresholds() {
@@ -37,35 +39,33 @@ func computeThresholds() {
 	fmt.Printf("(run repeatedly for good results)\n")
 
 	// determine Tk, the work load execution time using basic multiplication
-	karatsubaThreshold = 1e9 // disable karatsuba
+	Tb := measureKaratsuba(1e9) // th == 1e9 => Karatsuba multiplication disabled
-	Tb := measure(benchmarkMulLoad)
+	fmt.Printf("Tb = %10s\n", Tb)
-	fmt.Printf("Tb = %dns\n", Tb)
 
 	// thresholds
-	n := 8 // any lower values for the threshold lead to very slow multiplies
+	th := 4
 	th1 := -1
 	th2 := -1
 
 	var deltaOld time.Duration
-	for count := -1; count != 0; count-- {
+	for count := -1; count != 0 && th < 128; count-- {
 		// determine Tk, the work load execution time using Karatsuba multiplication
-		karatsubaThreshold = n // enable karatsuba
+		Tk := measureKaratsuba(th)
-		Tk := measure(benchmarkMulLoad)
 
 		// improvement over Tb
 		delta := (Tb - Tk) * 100 / Tb
 
-		fmt.Printf("n = %3d  Tk = %8dns  %4d%%", n, Tk, delta)
+		fmt.Printf("th = %3d  Tk = %10s  %4d%%", th, Tk, delta)
 
 		// determine break-even point
 		if Tk < Tb && th1 < 0 {
-			th1 = n
+			th1 = th
 			fmt.Print("  break-even point")
 		}
 
 		// determine diminishing return
 		if 0 < delta && delta < deltaOld && th2 < 0 {
-			th2 = n
+			th2 = th
 			fmt.Print("  diminishing return")
 		}
 		deltaOld = delta
@@ -74,10 +74,10 @@ func computeThresholds() {
 
 		// trigger counter
 		if th1 >= 0 && th2 >= 0 && count < 0 {
-			count = 20 // this many extra measurements after we got both thresholds
+			count = 10 // this many extra measurements after we got both thresholds
 		}
 
-		n++
+		th++
 	}
 }
 

src/pkg/math/big/nat_test.go

@@ -6,6 +6,7 @@ package big
 
 import (
 	"io"
+	"math/rand"
 	"strings"
 	"testing"
 )
@@ -135,26 +136,22 @@ func TestMulRangeN(t *testing.T) {
 	}
 }
 
-var mulArg, mulTmp nat
+var rnd = rand.New(rand.NewSource(0x43de683f473542af))
+var mulx = rndNat(1e4)
+var muly = rndNat(1e4)
 
-func init() {
+func rndNat(n int) nat {
-	const n = 1000
+	x := make(nat, n)
-	mulArg = make(nat, n)
 	for i := 0; i < n; i++ {
-		mulArg[i] = _M
+		x[i] = Word(rnd.Int63()<<1 + rnd.Int63n(2))
-	}
-}
-
-func benchmarkMulLoad() {
-	for j := 1; j <= 10; j++ {
-		x := mulArg[0 : j*100]
-		mulTmp.mul(x, x)
 	}
+	return x
 }
 
 func BenchmarkMul(b *testing.B) {
 	for i := 0; i < b.N; i++ {
-		benchmarkMulLoad()
+		var z nat
+		z.mul(mulx, muly)
 	}
 }