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  }
    66
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