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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 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 } 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 } 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) } } }