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📄 accuracy_string.go(414 B)
📄 alias_test.go(8.81 KB)
📄 arith.go(8.28 KB)
📄 arith_386.s(4.07 KB)
📄 arith_amd64.go(306 B)
📄 arith_amd64.s(9.09 KB)
📄 arith_arm.s(4.03 KB)
📄 arith_arm64.s(11.88 KB)
📄 arith_decl.go(594 B)
📄 arith_decl_pure.go(1.04 KB)
📄 arith_decl_s390x.go(531 B)
📄 arith_loong64.s(745 B)
📄 arith_mips64x.s(817 B)
📄 arith_mipsx.s(809 B)
📄 arith_ppc64x.s(16.36 KB)
📄 arith_riscv64.s(786 B)
📄 arith_s390x.s(20.32 KB)
📄 arith_s390x_test.go(812 B)
📄 arith_test.go(19.88 KB)
📄 arith_wasm.s(641 B)
📄 bits_test.go(5.07 KB)
📄 calibrate_test.go(4.63 KB)
📄 decimal.go(6.63 KB)
📄 decimal_test.go(3.33 KB)
📄 doc.go(3.79 KB)
📄 example_rat_test.go(1.68 KB)
📄 example_test.go(4.05 KB)
📄 float.go(44.28 KB)
📄 float_test.go(51.94 KB)
📄 floatconv.go(8.34 KB)
📄 floatconv_test.go(24.27 KB)
📄 floatexample_test.go(3.63 KB)
📄 floatmarsh.go(3.53 KB)
📄 floatmarsh_test.go(3.92 KB)
📄 ftoa.go(13.55 KB)
📄 gcd_test.go(2.16 KB)
📄 hilbert_test.go(2.88 KB)
📄 int.go(30.26 KB)
📄 int_test.go(53.14 KB)
📄 intconv.go(6.69 KB)
📄 intconv_test.go(10.01 KB)
📄 intmarsh.go(2.14 KB)
📄 intmarsh_test.go(3.07 KB)
📄 link_test.go(1.4 KB)
📄 nat.go(26.73 KB)
📄 nat_test.go(23.56 KB)
📄 natconv.go(14.55 KB)
📄 natconv_test.go(16.85 KB)
📄 natdiv.go(34.15 KB)
📄 prime.go(10.34 KB)
📄 prime_test.go(7.1 KB)
📄 rat.go(13.47 KB)
📄 rat_test.go(18.89 KB)
📄 ratconv.go(9.78 KB)
📄 ratconv_test.go(15.75 KB)
📄 ratmarsh.go(2.1 KB)
📄 ratmarsh_test.go(3.3 KB)
📄 roundingmode_string.go(501 B)
📄 sqrt.go(2.79 KB)
📄 sqrt_test.go(4.81 KB)

Editing: calibrate_test.go

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Calibration used to determine thresholds for using
// different algorithms.  Ideally, this would be converted
// to go generate to create thresholds.go

// This file prints execution times for the Mul benchmark
// given different Karatsuba thresholds. The result may be
// used to manually fine-tune the threshold constant. The
// results are somewhat fragile; use repeated runs to get
// a clear picture.

// Calculates lower and upper thresholds for when basicSqr
// is faster than standard multiplication.

// Usage: go test -run=TestCalibrate -v -calibrate

package big

import (
	"flag"
	"fmt"
	"testing"
	"time"
)

var calibrate = flag.Bool("calibrate", false, "run calibration test")

const (
	sqrModeMul       = "mul(x, x)"
	sqrModeBasic     = "basicSqr(x)"
	sqrModeKaratsuba = "karatsubaSqr(x)"
)

func TestCalibrate(t *testing.T) {
	if !*calibrate {
		return
	}

computeKaratsubaThresholds()

// compute basicSqrThreshold where overhead becomes negligible
	minSqr := computeSqrThreshold(10, 30, 1, 3, sqrModeMul, sqrModeBasic)
	// compute karatsubaSqrThreshold where karatsuba is faster
	maxSqr := computeSqrThreshold(200, 500, 10, 3, sqrModeBasic, sqrModeKaratsuba)
	if minSqr != 0 {
		fmt.Printf("found basicSqrThreshold = %d\n", minSqr)
	} else {
		fmt.Println("no basicSqrThreshold found")
	}
	if maxSqr != 0 {
		fmt.Printf("found karatsubaSqrThreshold = %d\n", maxSqr)
	} else {
		fmt.Println("no karatsubaSqrThreshold found")
	}
}

func karatsubaLoad(b *testing.B) {
	BenchmarkMul(b)
}

// measureKaratsuba returns the time to run a Karatsuba-relevant benchmark
// given Karatsuba threshold th.
func measureKaratsuba(th int) time.Duration {
	th, karatsubaThreshold = karatsubaThreshold, th
	res := testing.Benchmark(karatsubaLoad)
	karatsubaThreshold = th
	return time.Duration(res.NsPerOp())
}

func computeKaratsubaThresholds() {
	fmt.Printf("Multiplication times for varying Karatsuba thresholds\n")
	fmt.Printf("(run repeatedly for good results)\n")

// determine Tk, the work load execution time using basic multiplication
	Tb := measureKaratsuba(1e9) // th == 1e9 => Karatsuba multiplication disabled
	fmt.Printf("Tb = %10s\n", Tb)

// thresholds
	th := 4
	th1 := -1
	th2 := -1

var deltaOld time.Duration
	for count := -1; count != 0 && th < 128; count-- {
		// determine Tk, the work load execution time using Karatsuba multiplication
		Tk := measureKaratsuba(th)

// improvement over Tb
		delta := (Tb - Tk) * 100 / Tb

fmt.Printf("th = %3d  Tk = %10s  %4d%%", th, Tk, delta)

// determine break-even point
		if Tk < Tb && th1 < 0 {
			th1 = th
			fmt.Print("  break-even point")
		}

// determine diminishing return
		if 0 < delta && delta < deltaOld && th2 < 0 {
			th2 = th
			fmt.Print("  diminishing return")
		}
		deltaOld = delta

fmt.Println()

// trigger counter
		if th1 >= 0 && th2 >= 0 && count < 0 {
			count = 10 // this many extra measurements after we got both thresholds
		}

th++
	}
}

func measureSqr(words, nruns int, mode string) time.Duration {
	// more runs for better statistics
	initBasicSqr, initKaratsubaSqr := basicSqrThreshold, karatsubaSqrThreshold

switch mode {
	case sqrModeMul:
		basicSqrThreshold = words + 1
	case sqrModeBasic:
		basicSqrThreshold, karatsubaSqrThreshold = words-1, words+1
	case sqrModeKaratsuba:
		karatsubaSqrThreshold = words - 1
	}

var testval int64
	for i := 0; i < nruns; i++ {
		res := testing.Benchmark(func(b *testing.B) { benchmarkNatSqr(b, words) })
		testval += res.NsPerOp()
	}
	testval /= int64(nruns)

basicSqrThreshold, karatsubaSqrThreshold = initBasicSqr, initKaratsubaSqr

return time.Duration(testval)
}

func computeSqrThreshold(from, to, step, nruns int, lower, upper string) int {
	fmt.Printf("Calibrating threshold between %s and %s\n", lower, upper)
	fmt.Printf("Looking for a timing difference for x between %d - %d words by %d step\n", from, to, step)
	var initPos bool
	var threshold int
	for i := from; i <= to; i += step {
		baseline := measureSqr(i, nruns, lower)
		testval := measureSqr(i, nruns, upper)
		pos := baseline > testval
		delta := baseline - testval
		percent := delta * 100 / baseline
		fmt.Printf("words = %3d deltaT = %10s (%4d%%) is %s better: %v", i, delta, percent, upper, pos)
		if i == from {
			initPos = pos
		}
		if threshold == 0 && pos != initPos {
			threshold = i
			fmt.Printf("  threshold  found")
		}
		fmt.Println()

}
	if threshold != 0 {
		fmt.Printf("Found threshold = %d between %d - %d\n", threshold, from, to)
	} else {
		fmt.Printf("Found NO threshold between %d - %d\n", from, to)
	}
	return threshold
}

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Editing: calibrate_test.go

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