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
5package big_test
6
7import (
8	"fmt"
9	"math/big"
10)
11
12// Use the classic continued fraction for e
13//
14//	e = [1; 0, 1, 1, 2, 1, 1, ... 2n, 1, 1, ...]
15//
16// i.e., for the nth term, use
17//
18//	   1          if   n mod 3 != 1
19//	(n-1)/3 * 2   if   n mod 3 == 1
20func recur(n, lim int64) *big.Rat {
21	term := new(big.Rat)
22	if n%3 != 1 {
23		term.SetInt64(1)
24	} else {
25		term.SetInt64((n - 1) / 3 * 2)
26	}
27
28	if n > lim {
29		return term
30	}
31
32	// Directly initialize frac as the fractional
33	// inverse of the result of recur.
34	frac := new(big.Rat).Inv(recur(n+1, lim))
35
36	return term.Add(term, frac)
37}
38
39// This example demonstrates how to use big.Rat to compute the
40// first 15 terms in the sequence of rational convergents for
41// the constant e (base of natural logarithm).
42func Example_eConvergents() {
43	for i := 1; i <= 15; i++ {
44		r := recur(0, int64(i))
45
46		// Print r both as a fraction and as a floating-point number.
47		// Since big.Rat implements fmt.Formatter, we can use %-13s to
48		// get a left-aligned string representation of the fraction.
49		fmt.Printf("%-13s = %s\n", r, r.FloatString(8))
50	}
51
52	// Output:
53	// 2/1           = 2.00000000
54	// 3/1           = 3.00000000
55	// 8/3           = 2.66666667
56	// 11/4          = 2.75000000
57	// 19/7          = 2.71428571
58	// 87/32         = 2.71875000
59	// 106/39        = 2.71794872
60	// 193/71        = 2.71830986
61	// 1264/465      = 2.71827957
62	// 1457/536      = 2.71828358
63	// 2721/1001     = 2.71828172
64	// 23225/8544    = 2.71828184
65	// 25946/9545    = 2.71828182
66	// 49171/18089   = 2.71828183
67	// 517656/190435 = 2.71828183
68}
69