mirror of
https://github.com/golang/go
synced 2024-11-23 04:30:03 -07:00
779682107f
Change-Id: I73ecfe8f1e46e4821dafc6ed5788f48a1f0deeea Reviewed-on: https://go-review.googlesource.com/1213 Reviewed-by: Alan Donovan <adonovan@google.com>
311 lines
6.3 KiB
Go
311 lines
6.3 KiB
Go
// 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)
|
|
}
|
|
}
|
|
}
|