--- /dev/null
+// 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)
+ }
+ }
+}