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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
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@ -21,15 +21,17 @@ import (
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var calibrate = flag.Bool("calibrate", false, "run calibration test")
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var calibrate = flag.Bool("calibrate", false, "run calibration test")
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// measure returns the time to run f
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func karatsubaLoad(b *testing.B) {
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func measure(f func()) time.Duration {
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BenchmarkMul(b)
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const N = 100
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}
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start := time.Now()
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for i := N; i > 0; i-- {
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// measureKaratsuba returns the time to run a Karatsuba-relevant benchmark
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f()
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// given Karatsuba threshold th.
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}
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func measureKaratsuba(th int) time.Duration {
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stop := time.Now()
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th, karatsubaThreshold = karatsubaThreshold, th
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return stop.Sub(start) / N
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res := testing.Benchmark(karatsubaLoad)
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karatsubaThreshold = th
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return time.Duration(res.NsPerOp())
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}
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}
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func computeThresholds() {
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func computeThresholds() {
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@ -37,35 +39,33 @@ func computeThresholds() {
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fmt.Printf("(run repeatedly for good results)\n")
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fmt.Printf("(run repeatedly for good results)\n")
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// determine Tk, the work load execution time using basic multiplication
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// determine Tk, the work load execution time using basic multiplication
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karatsubaThreshold = 1e9 // disable karatsuba
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Tb := measureKaratsuba(1e9) // th == 1e9 => Karatsuba multiplication disabled
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Tb := measure(benchmarkMulLoad)
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fmt.Printf("Tb = %10s\n", Tb)
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fmt.Printf("Tb = %dns\n", Tb)
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// thresholds
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// thresholds
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n := 8 // any lower values for the threshold lead to very slow multiplies
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th := 4
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th1 := -1
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th1 := -1
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th2 := -1
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th2 := -1
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var deltaOld time.Duration
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var deltaOld time.Duration
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for count := -1; count != 0; count-- {
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for count := -1; count != 0 && th < 128; count-- {
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// determine Tk, the work load execution time using Karatsuba multiplication
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// determine Tk, the work load execution time using Karatsuba multiplication
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karatsubaThreshold = n // enable karatsuba
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Tk := measureKaratsuba(th)
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Tk := measure(benchmarkMulLoad)
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// improvement over Tb
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// improvement over Tb
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delta := (Tb - Tk) * 100 / Tb
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delta := (Tb - Tk) * 100 / Tb
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fmt.Printf("n = %3d Tk = %8dns %4d%%", n, Tk, delta)
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fmt.Printf("th = %3d Tk = %10s %4d%%", th, Tk, delta)
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// determine break-even point
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// determine break-even point
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if Tk < Tb && th1 < 0 {
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if Tk < Tb && th1 < 0 {
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th1 = n
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th1 = th
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fmt.Print(" break-even point")
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fmt.Print(" break-even point")
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}
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}
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// determine diminishing return
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// determine diminishing return
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if 0 < delta && delta < deltaOld && th2 < 0 {
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if 0 < delta && delta < deltaOld && th2 < 0 {
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th2 = n
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th2 = th
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fmt.Print(" diminishing return")
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fmt.Print(" diminishing return")
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}
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}
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deltaOld = delta
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deltaOld = delta
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@ -74,10 +74,10 @@ func computeThresholds() {
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// trigger counter
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// trigger counter
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if th1 >= 0 && th2 >= 0 && count < 0 {
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if th1 >= 0 && th2 >= 0 && count < 0 {
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count = 20 // this many extra measurements after we got both thresholds
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count = 10 // this many extra measurements after we got both thresholds
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}
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}
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n++
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th++
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}
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}
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}
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}
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@ -6,6 +6,7 @@ package big
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import (
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import (
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"io"
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"io"
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"math/rand"
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"strings"
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"strings"
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"testing"
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"testing"
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)
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)
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@ -135,26 +136,22 @@ func TestMulRangeN(t *testing.T) {
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}
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}
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}
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}
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var mulArg, mulTmp nat
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var rnd = rand.New(rand.NewSource(0x43de683f473542af))
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var mulx = rndNat(1e4)
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var muly = rndNat(1e4)
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func init() {
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func rndNat(n int) nat {
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const n = 1000
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x := make(nat, n)
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mulArg = make(nat, n)
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for i := 0; i < n; i++ {
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for i := 0; i < n; i++ {
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mulArg[i] = _M
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x[i] = Word(rnd.Int63()<<1 + rnd.Int63n(2))
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}
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}
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func benchmarkMulLoad() {
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for j := 1; j <= 10; j++ {
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x := mulArg[0 : j*100]
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mulTmp.mul(x, x)
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}
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}
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return x
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}
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}
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func BenchmarkMul(b *testing.B) {
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func BenchmarkMul(b *testing.B) {
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for i := 0; i < b.N; i++ {
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for i := 0; i < b.N; i++ {
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benchmarkMulLoad()
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var z nat
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z.mul(mulx, muly)
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}
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}
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}
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}
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