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Source file src/math/big/example_rat_test.go

Documentation: math/big

  // 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
  }
  

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