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// 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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