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779682107f
Change-Id: I73ecfe8f1e46e4821dafc6ed5788f48a1f0deeea Reviewed-on: https://go-review.googlesource.com/1213 Reviewed-by: Alan Donovan <adonovan@google.com>
310 lines
6.3 KiB
Go
310 lines
6.3 KiB
Go
// skip
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// Copyright 2014 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Usage:
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// fibo <n> compute fibonacci(n), n must be >= 0
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// fibo -bench benchmark fibonacci computation (takes about 1 min)
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//
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// Additional flags:
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// -half add values using two half-digit additions
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// -opt optimize memory allocation through reuse
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// -short only print the first 10 digits of very large fibonacci numbers
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// Command fibo is a stand-alone test and benchmark to
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// evaluate the performance of bignum arithmetic written
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// entirely in Go.
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package main
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import (
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"flag"
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"fmt"
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"math/big" // only used for printing
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"os"
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"strconv"
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"testing"
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"text/tabwriter"
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"time"
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)
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var (
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bench = flag.Bool("bench", false, "run benchmarks")
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half = flag.Bool("half", false, "use half-digit addition")
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opt = flag.Bool("opt", false, "optimize memory usage")
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short = flag.Bool("short", false, "only print first 10 digits of result")
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)
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// A large natural number is represented by a nat, each "digit" is
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// a big.Word; the value zero corresponds to the empty nat slice.
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type nat []big.Word
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const W = 1 << (5 + ^big.Word(0)>>63) // big.Word size in bits
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// The following methods are extracted from math/big to make this a
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// stand-alone program that can easily be run without dependencies
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// and compiled with different compilers.
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func (z nat) make(n int) nat {
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if n <= cap(z) {
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return z[:n] // reuse z
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}
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// Choosing a good value for e has significant performance impact
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// because it increases the chance that a value can be reused.
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const e = 4 // extra capacity
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return make(nat, n, n+e)
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}
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// z = x
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func (z nat) set(x nat) nat {
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z = z.make(len(x))
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copy(z, x)
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return z
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}
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// z = x + y
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// (like add, but operating on half-digits at a time)
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func (z nat) halfAdd(x, y nat) nat {
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m := len(x)
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n := len(y)
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switch {
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case m < n:
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return z.add(y, x)
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case m == 0:
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// n == 0 because m >= n; result is 0
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return z.make(0)
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case n == 0:
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// result is x
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return z.set(x)
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}
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// m >= n > 0
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const W2 = W / 2 // half-digit size in bits
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const M2 = (1 << W2) - 1 // lower half-digit mask
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z = z.make(m + 1)
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var c big.Word
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for i := 0; i < n; i++ {
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// lower half-digit
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c += x[i]&M2 + y[i]&M2
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d := c & M2
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c >>= W2
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// upper half-digit
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c += x[i]>>W2 + y[i]>>W2
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z[i] = c<<W2 | d
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c >>= W2
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}
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for i := n; i < m; i++ {
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// lower half-digit
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c += x[i] & M2
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d := c & M2
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c >>= W2
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// upper half-digit
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c += x[i] >> W2
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z[i] = c<<W2 | d
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c >>= W2
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}
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if c != 0 {
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z[m] = c
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m++
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}
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return z[:m]
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}
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// z = x + y
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func (z nat) add(x, y nat) nat {
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m := len(x)
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n := len(y)
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switch {
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case m < n:
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return z.add(y, x)
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case m == 0:
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// n == 0 because m >= n; result is 0
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return z.make(0)
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case n == 0:
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// result is x
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return z.set(x)
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}
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// m >= n > 0
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z = z.make(m + 1)
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var c big.Word
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for i, xi := range x[:n] {
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yi := y[i]
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zi := xi + yi + c
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z[i] = zi
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// see "Hacker's Delight", section 2-12 (overflow detection)
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c = ((xi & yi) | ((xi | yi) &^ zi)) >> (W - 1)
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}
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for i, xi := range x[n:] {
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zi := xi + c
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z[n+i] = zi
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c = (xi &^ zi) >> (W - 1)
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if c == 0 {
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copy(z[n+i+1:], x[i+1:])
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break
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}
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}
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if c != 0 {
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z[m] = c
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m++
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}
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return z[:m]
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}
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func bitlen(x big.Word) int {
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n := 0
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for x > 0 {
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x >>= 1
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n++
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}
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return n
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}
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func (x nat) bitlen() int {
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if i := len(x); i > 0 {
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return (i-1)*W + bitlen(x[i-1])
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}
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return 0
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}
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func (x nat) String() string {
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const shortLen = 10
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s := new(big.Int).SetBits(x).String()
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if *short && len(s) > shortLen {
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s = s[:shortLen] + "..."
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}
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return s
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}
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func fibo(n int, half, opt bool) nat {
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switch n {
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case 0:
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return nil
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case 1:
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return nat{1}
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}
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f0 := nat(nil)
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f1 := nat{1}
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if half {
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if opt {
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var f2 nat // reuse f2
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for i := 1; i < n; i++ {
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f2 = f2.halfAdd(f1, f0)
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f0, f1, f2 = f1, f2, f0
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}
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} else {
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for i := 1; i < n; i++ {
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f2 := nat(nil).halfAdd(f1, f0) // allocate a new f2 each time
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f0, f1 = f1, f2
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}
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}
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} else {
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if opt {
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var f2 nat // reuse f2
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for i := 1; i < n; i++ {
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f2 = f2.add(f1, f0)
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f0, f1, f2 = f1, f2, f0
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}
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} else {
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for i := 1; i < n; i++ {
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f2 := nat(nil).add(f1, f0) // allocate a new f2 each time
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f0, f1 = f1, f2
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}
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}
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}
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return f1 // was f2 before shuffle
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}
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var tests = []struct {
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n int
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want string
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}{
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{0, "0"},
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{1, "1"},
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{2, "1"},
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{3, "2"},
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{4, "3"},
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{5, "5"},
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{6, "8"},
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{7, "13"},
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{8, "21"},
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{9, "34"},
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{10, "55"},
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{100, "354224848179261915075"},
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{1000, "43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"},
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}
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func test(half, opt bool) {
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for _, test := range tests {
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got := fibo(test.n, half, opt).String()
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if got != test.want {
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fmt.Printf("error: got std fibo(%d) = %s; want %s\n", test.n, got, test.want)
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os.Exit(1)
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}
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}
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}
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func selfTest() {
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if W != 32 && W != 64 {
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fmt.Printf("error: unexpected wordsize %d", W)
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os.Exit(1)
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}
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for i := 0; i < 4; i++ {
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test(i&2 == 0, i&1 != 0)
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}
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}
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func doFibo(n int) {
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start := time.Now()
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f := fibo(n, *half, *opt)
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t := time.Since(start)
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fmt.Printf("fibo(%d) = %s (%d bits, %s)\n", n, f, f.bitlen(), t)
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}
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func benchFibo(b *testing.B, n int, half, opt bool) {
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for i := 0; i < b.N; i++ {
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fibo(n, half, opt)
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}
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}
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func doBench(half, opt bool) {
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w := tabwriter.NewWriter(os.Stdout, 0, 8, 2, ' ', tabwriter.AlignRight)
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fmt.Fprintf(w, "wordsize = %d, half = %v, opt = %v\n", W, half, opt)
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fmt.Fprintf(w, "n\talloc count\talloc bytes\tns/op\ttime/op\t\n")
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for n := 1; n <= 1e6; n *= 10 {
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res := testing.Benchmark(func(b *testing.B) { benchFibo(b, n, half, opt) })
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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()))
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}
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fmt.Fprintln(w)
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w.Flush()
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}
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func main() {
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selfTest()
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flag.Parse()
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if args := flag.Args(); len(args) > 0 {
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// command-line use
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fmt.Printf("half = %v, opt = %v, wordsize = %d bits\n", *half, *opt, W)
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for _, arg := range args {
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n, err := strconv.Atoi(arg)
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if err != nil || n < 0 {
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fmt.Println("invalid argument", arg)
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continue
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}
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doFibo(n)
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}
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return
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}
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if *bench {
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for i := 0; i < 4; i++ {
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doBench(i&2 == 0, i&1 != 0)
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}
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}
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}
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