libgo/go/math/big/example_rat_test.go

   1 // Copyright 2015 The Go Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style
   3 // license that can be found in the LICENSE file.
   4
   5 package big_test
   6
   7 import (
   8         "fmt"
   9         "math/big"
  10 )
  11
  12 // Use the classic continued fraction for e
  13 //     e = [1; 0, 1, 1, 2, 1, 1, ... 2n, 1, 1, ...]
  14 // i.e., for the nth term, use
  15 //     1          if   n mod 3 != 1
  16 //  (n-1)/3 * 2   if   n mod 3 == 1
  17 func recur(n, lim int64) *big.Rat {
  18         term := new(big.Rat)
  19         if n%3 != 1 {
  20                 term.SetInt64(1)
  21         } else {
  22                 term.SetInt64((n - 1) / 3 * 2)
  23         }
  24
  25         if n > lim {
  26                 return term
  27         }
  28
  29         // Directly initialize frac as the fractional
  30         // inverse of the result of recur.
  31         frac := new(big.Rat).Inv(recur(n+1, lim))
  32
  33         return term.Add(term, frac)
  34 }
  35
  36 // This example demonstrates how to use big.Rat to compute the
  37 // first 15 terms in the sequence of rational convergents for
  38 // the constant e (base of natural logarithm).
  39 func Example_eConvergents() {
  40         for i := 1; i <= 15; i++ {
  41                 r := recur(0, int64(i))
  42
  43                 // Print r both as a fraction and as a floating-point number.
  44                 // Since big.Rat implements fmt.Formatter, we can use %-13s to
  45                 // get a left-aligned string representation of the fraction.
  46                 fmt.Printf("%-13s = %s\n", r, r.FloatString(8))
  47         }
  48
  49         // Output:
  50         // 2/1           = 2.00000000
  51         // 3/1           = 3.00000000
  52         // 8/3           = 2.66666667
  53         // 11/4          = 2.75000000
  54         // 19/7          = 2.71428571
  55         // 87/32         = 2.71875000
  56         // 106/39        = 2.71794872
  57         // 193/71        = 2.71830986
  58         // 1264/465      = 2.71827957
  59         // 1457/536      = 2.71828358
  60         // 2721/1001     = 2.71828172
  61         // 23225/8544    = 2.71828184
  62         // 25946/9545    = 2.71828182
  63         // 49171/18089   = 2.71828183
  64         // 517656/190435 = 2.71828183
  65 }