// 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)
}
}
}