# Source file src/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
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
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  }
66
```

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