math/big: Add small complete example of big.Rat usage

Updates #11241

Change-Id: If71f651f3b8aca432c91314358b93f195217d9ec
Reviewed-on: https://go-review.googlesource.com/14317
Reviewed-by: Robert Griesemer <gri@golang.org>

diff --git a/src/math/big/example_rat_test.go b/src/math/big/example_rat_test.go
new file mode 100644 (file)
index 0000000..a971170
--- /dev/null
+++ b/src/math/big/example_rat_test.go
@@ -0,0 +1,65 @@
+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package big_test
+
+import (
+       "fmt"
+       "math/big"
+)
+
+// Use the classic continued fraction for e
+//     e = [1; 0, 1, 1, 2, 1, 1, ... 2n, 1, 1, ...]
+// i.e., for the nth term, use
+//     1          if   n mod 3 != 1
+//  (n-1)/3 * 2   if   n mod 3 == 1
+func recur(n, lim int64) *big.Rat {
+       term := new(big.Rat)
+       if n%3 != 1 {
+               term.SetInt64(1)
+       } else {
+               term.SetInt64((n - 1) / 3 * 2)
+       }
+
+       if n > lim {
+               return term
+       }
+
+       // Directly initialize frac as the fractional
+       // inverse of the result of recur.
+       frac := new(big.Rat).Inv(recur(n+1, lim))
+
+       return term.Add(term, frac)
+}
+
+// This example demonstrates how to use big.Rat to compute the
+// first 15 terms in the sequence of rational convergents for
+// the constant e (base of natural logarithm).
+func Example_eConvergents() {
+       for i := 1; i <= 15; i++ {
+               r := recur(0, int64(i))
+
+               // Print r both as a fraction and as a floating-point number.
+               // Since big.Rat implements fmt.Formatter, we can use %-13s to
+               // get a left-aligned string representation of the fraction.
+               fmt.Printf("%-13s = %s\n", r, r.FloatString(8))
+       }
+
+       // Output:
+       // 2/1           = 2.00000000
+       // 3/1           = 3.00000000
+       // 8/3           = 2.66666667
+       // 11/4          = 2.75000000
+       // 19/7          = 2.71428571
+       // 87/32         = 2.71875000
+       // 106/39        = 2.71794872
+       // 193/71        = 2.71830986
+       // 1264/465      = 2.71827957
+       // 1457/536      = 2.71828358
+       // 2721/1001     = 2.71828172
+       // 23225/8544    = 2.71828184
+       // 25946/9545    = 2.71828182
+       // 49171/18089   = 2.71828183
+       // 517656/190435 = 2.71828183
+}