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