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  //
    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
    20  func 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).
    42  func 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
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