test/fibo: a stand-alone bignum/allocation benchmark and test

Usage:
fibo <n>        compute fibonacci(n), n must be >= 0
fibo -bench     benchmark fibonacci computation (takes about 1 min)

Additional flags:
-half           add values using two half-digit additions
-opt            optimize memory allocation through reuse
-short          only print the first 10 digits of very large fibonacci numbers

This change was reviewed in detail as https://codereview.appspot.com/168480043 .

Change-Id: I7c86d49c5508532ea6206d00f424cf2117d2fe41
Reviewed-on: https://go-review.googlesource.com/1211
Reviewed-by: Russ Cox <rsc@golang.org>

1 files changed, 310 insertions, 0 deletions

diff --git a/test/fibo.go b/test/fibo.go
new file mode 100644
index 0000000000..21cb8e925e
--- /dev/null
+++ b/test/fibo.go
@@ -0,0 +1,310 @@
+// skip
+
+// Copyright 2014 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.
+
+// Usage:
+// fibo <n>	compute fibonacci(n), n must be >= 0
+// fibo -bench	benchmark fibonacci computation (takes about 1 min)
+//
+// Additional flags:
+// -half        add values using two half-digit additions
+// -opt		optimize memory allocation through reuse
+// -short	only print the first 10 digits of very large fibonacci numbers
+
+// Command fibo is a stand-alone test and benchmark to
+// evaluate the performance of bignum arithmetic written
+// entirely in Go.
+package main
+
+import (
+	"flag"
+	"fmt"
+	"math/big" // only used for printing
+	"os"
+	"strconv"
+	"testing"
+	"text/tabwriter"
+	"time"
+)
+
+var (
+	bench = flag.Bool("bench", false, "run benchmarks")
+	half  = flag.Bool("half", false, "use half-digit addition")
+	opt   = flag.Bool("opt", false, "optimize memory usage")
+	short = flag.Bool("short", false, "only print first 10 digits of result")
+)
+
+// A large natural number is represented by a nat, each "digit" is
+// a big.Word; the value zero corresponds to the empty nat slice.
+type nat []big.Word
+
+const W = 1 << (5 + ^big.Word(0)>>63) // big.Word size in bits
+
+// The following methods are extracted from math/big to make this a
+// stand-alone program that can easily be run without dependencies
+// and compiled with different compilers.
+
+func (z nat) make(n int) nat {
+	if n <= cap(z) {
+		return z[:n] // reuse z
+	}
+	// Choosing a good value for e has significant performance impact
+	// because it increases the chance that a value can be reused.
+	const e = 4 // extra capacity
+	return make(nat, n, n+e)
+}
+
+// z = x
+func (z nat) set(x nat) nat {
+	z = z.make(len(x))
+	copy(z, x)
+	return z
+}
+
+// z = x + y
+// (like add, but operating on half-digits at a time)
+func (z nat) halfAdd(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+
+	switch {
+	case m < n:
+		return z.add(y, x)
+	case m == 0:
+		// n == 0 because m >= n; result is 0
+		return z.make(0)
+	case n == 0:
+		// result is x
+		return z.set(x)
+	}
+	// m >= n > 0
+
+	const W2 = W / 2         // half-digit size in bits
+	const M2 = (1 << W2) - 1 // lower half-digit mask
+
+	z = z.make(m + 1)
+	var c big.Word
+	for i := 0; i < n; i++ {
+		// lower half-digit
+		c += x[i]&M2 + y[i]&M2
+		d := c & M2
+		c >>= W2
+		// upper half-digit
+		c += x[i]>>W2 + y[i]>>W2
+		z[i] = c<<W2 | d
+		c >>= W2
+	}
+	for i := n; i < m; i++ {
+		// lower half-digit
+		c += x[i] & M2
+		d := c & M2
+		c >>= W2
+		// upper half-digit
+		c += x[i] >> W2
+		z[i] = c<<W2 | d
+		c >>= W2
+	}
+	if c != 0 {
+		z[m] = c
+		m++
+	}
+	return z[:m]
+}
+
+// z = x + y
+func (z nat) add(x, y nat) nat {
+	m := len(x)
+	n := len(y)
+
+	switch {
+	case m < n:
+		return z.add(y, x)
+	case m == 0:
+		// n == 0 because m >= n; result is 0
+		return z.make(0)
+	case n == 0:
+		// result is x
+		return z.set(x)
+	}
+	// m >= n > 0
+
+	z = z.make(m + 1)
+	var c big.Word
+
+	for i, xi := range x[:n] {
+		yi := y[i]
+		zi := xi + yi + c
+		z[i] = zi
+		// see "Hacker's Delight", section 2-12 (overflow detection)
+		c = ((xi & yi) | ((xi | yi) &^ zi)) >> (W - 1)
+	}
+	for i, xi := range x[n:] {
+		zi := xi + c
+		z[n+i] = zi
+		c = (xi &^ zi) >> (W - 1)
+		if c == 0 {
+			copy(z[n+i+1:], x[i+1:])
+			break
+		}
+	}
+	if c != 0 {
+		z[m] = c
+		m++
+	}
+	return z[:m]
+}
+
+func bitlen(x big.Word) int {
+	n := 0
+	for x > 0 {
+		x >>= 1
+		n++
+	}
+	return n
+}
+
+func (x nat) bitlen() int {
+	if i := len(x); i > 0 {
+		return (i-1)*W + bitlen(x[i-1])
+	}
+	return 0
+}
+
+func (x nat) String() string {
+	const shortLen = 10
+	s := new(big.Int).SetBits(x).String()
+	if *short && len(s) > shortLen {
+		s = s[:shortLen] + "..."
+	}
+	return s
+}
+
+func fibo(n int, half, opt bool) nat {
+	switch n {
+	case 0:
+		return nil
+	case 1:
+		return nat{1}
+	}
+	f0 := nat(nil)
+	f1 := nat{1}
+	if half {
+		if opt {
+			var f2 nat // reuse f2
+			for i := 1; i < n; i++ {
+				f2 = f2.halfAdd(f1, f0)
+				f0, f1, f2 = f1, f2, f0
+			}
+		} else {
+			for i := 1; i < n; i++ {
+				f2 := nat(nil).halfAdd(f1, f0) // allocate a new f2 each time
+				f0, f1 = f1, f2
+			}
+		}
+	} else {
+		if opt {
+			var f2 nat // reuse f2
+			for i := 1; i < n; i++ {
+				f2 = f2.add(f1, f0)
+				f0, f1, f2 = f1, f2, f0
+			}
+		} else {
+			for i := 1; i < n; i++ {
+				f2 := nat(nil).add(f1, f0) // allocate a new f2 each time
+				f0, f1 = f1, f2
+			}
+		}
+	}
+	return f1 // was f2 before shuffle
+}
+
+var tests = []struct {
+	n    int
+	want string
+}{
+	{0, "0"},
+	{1, "1"},
+	{2, "1"},
+	{3, "2"},
+	{4, "3"},
+	{5, "5"},
+	{6, "8"},
+	{7, "13"},
+	{8, "21"},
+	{9, "34"},
+	{10, "55"},
+	{100, "354224848179261915075"},
+	{1000, "43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"},
+}
+
+func test(half, opt bool) {
+	for _, test := range tests {
+		got := fibo(test.n, half, opt).String()
+		if got != test.want {
+			fmt.Printf("error: got std fibo(%d) = %s; want %s\n", test.n, got, test.want)
+			os.Exit(1)
+		}
+	}
+}
+
+func selfTest() {
+	if W != 32 && W != 64 {
+		fmt.Printf("error: unexpected wordsize %d", W)
+		os.Exit(1)
+	}
+	for i := 0; i < 4; i++ {
+		test(i&2 == 0, i&1 != 0)
+	}
+}
+
+func doFibo(n int) {
+	start := time.Now()
+	f := fibo(n, *half, *opt)
+	t := time.Since(start)
+	fmt.Printf("fibo(%d) = %s (%d bits, %s)\n", n, f, f.bitlen(), t)
+}
+
+func benchFibo(b *testing.B, n int, half, opt bool) {
+	for i := 0; i < b.N; i++ {
+		fibo(n, half, opt)
+	}
+}
+
+func doBench(half, opt bool) {
+	w := tabwriter.NewWriter(os.Stdout, 0, 8, 2, ' ', tabwriter.AlignRight)
+	fmt.Fprintf(w, "wordsize = %d, half = %v, opt = %v\n", W, half, opt)
+	fmt.Fprintf(w, "n\talloc count\talloc bytes\tns/op\ttime/op\t\n")
+	for n := 1; n <= 1e6; n *= 10 {
+		res := testing.Benchmark(func(b *testing.B) { benchFibo(b, n, half, opt) })
+		fmt.Fprintf(w, "%d\t%d\t%d\t%d\t%s\t\n", n, res.AllocsPerOp(), res.AllocedBytesPerOp(), res.NsPerOp(), time.Duration(res.NsPerOp()))
+	}
+	fmt.Fprintln(w)
+	w.Flush()
+}
+
+func main() {
+	selfTest()
+	flag.Parse()
+
+	if args := flag.Args(); len(args) > 0 {
+		// command-line use
+		fmt.Printf("half = %v, opt = %v, wordsize = %d bits\n", *half, *opt, W)
+		for _, arg := range args {
+			n, err := strconv.Atoi(arg)
+			if err != nil || n < 0 {
+				fmt.Println("invalid argument", arg)
+				continue
+			}
+			doFibo(n)
+		}
+		return
+	}
+
+	if *bench {
+		for i := 0; i < 4; i++ {
+			doBench(i&2 == 0, i&1 != 0)
+		}
+	}
+}