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Source file src/math/big/example_test.go

Documentation: math/big

     1  // Copyright 2012 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  	"log"
    10  	"math"
    11  	"math/big"
    12  )
    13  
    14  func ExampleRat_SetString() {
    15  	r := new(big.Rat)
    16  	r.SetString("355/113")
    17  	fmt.Println(r.FloatString(3))
    18  	// Output: 3.142
    19  }
    20  
    21  func ExampleInt_SetString() {
    22  	i := new(big.Int)
    23  	i.SetString("644", 8) // octal
    24  	fmt.Println(i)
    25  	// Output: 420
    26  }
    27  
    28  func ExampleRat_Scan() {
    29  	// The Scan function is rarely used directly;
    30  	// the fmt package recognizes it as an implementation of fmt.Scanner.
    31  	r := new(big.Rat)
    32  	_, err := fmt.Sscan("1.5000", r)
    33  	if err != nil {
    34  		log.Println("error scanning value:", err)
    35  	} else {
    36  		fmt.Println(r)
    37  	}
    38  	// Output: 3/2
    39  }
    40  
    41  func ExampleInt_Scan() {
    42  	// The Scan function is rarely used directly;
    43  	// the fmt package recognizes it as an implementation of fmt.Scanner.
    44  	i := new(big.Int)
    45  	_, err := fmt.Sscan("18446744073709551617", i)
    46  	if err != nil {
    47  		log.Println("error scanning value:", err)
    48  	} else {
    49  		fmt.Println(i)
    50  	}
    51  	// Output: 18446744073709551617
    52  }
    53  
    54  func ExampleFloat_Scan() {
    55  	// The Scan function is rarely used directly;
    56  	// the fmt package recognizes it as an implementation of fmt.Scanner.
    57  	f := new(big.Float)
    58  	_, err := fmt.Sscan("1.19282e99", f)
    59  	if err != nil {
    60  		log.Println("error scanning value:", err)
    61  	} else {
    62  		fmt.Println(f)
    63  	}
    64  	// Output: 1.19282e+99
    65  }
    66  
    67  // This example demonstrates how to use big.Int to compute the smallest
    68  // Fibonacci number with 100 decimal digits and to test whether it is prime.
    69  func Example_fibonacci() {
    70  	// Initialize two big ints with the first two numbers in the sequence.
    71  	a := big.NewInt(0)
    72  	b := big.NewInt(1)
    73  
    74  	// Initialize limit as 10^99, the smallest integer with 100 digits.
    75  	var limit big.Int
    76  	limit.Exp(big.NewInt(10), big.NewInt(99), nil)
    77  
    78  	// Loop while a is smaller than 1e100.
    79  	for a.Cmp(&limit) < 0 {
    80  		// Compute the next Fibonacci number, storing it in a.
    81  		a.Add(a, b)
    82  		// Swap a and b so that b is the next number in the sequence.
    83  		a, b = b, a
    84  	}
    85  	fmt.Println(a) // 100-digit Fibonacci number
    86  
    87  	// Test a for primality.
    88  	// (ProbablyPrimes' argument sets the number of Miller-Rabin
    89  	// rounds to be performed. 20 is a good value.)
    90  	fmt.Println(a.ProbablyPrime(20))
    91  
    92  	// Output:
    93  	// 1344719667586153181419716641724567886890850696275767987106294472017884974410332069524504824747437757
    94  	// false
    95  }
    96  
    97  // This example shows how to use big.Float to compute the square root of 2 with
    98  // a precision of 200 bits, and how to print the result as a decimal number.
    99  func Example_sqrt2() {
   100  	// We'll do computations with 200 bits of precision in the mantissa.
   101  	const prec = 200
   102  
   103  	// Compute the square root of 2 using Newton's Method. We start with
   104  	// an initial estimate for sqrt(2), and then iterate:
   105  	//     x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) )
   106  
   107  	// Since Newton's Method doubles the number of correct digits at each
   108  	// iteration, we need at least log_2(prec) steps.
   109  	steps := int(math.Log2(prec))
   110  
   111  	// Initialize values we need for the computation.
   112  	two := new(big.Float).SetPrec(prec).SetInt64(2)
   113  	half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
   114  
   115  	// Use 1 as the initial estimate.
   116  	x := new(big.Float).SetPrec(prec).SetInt64(1)
   117  
   118  	// We use t as a temporary variable. There's no need to set its precision
   119  	// since big.Float values with unset (== 0) precision automatically assume
   120  	// the largest precision of the arguments when used as the result (receiver)
   121  	// of a big.Float operation.
   122  	t := new(big.Float)
   123  
   124  	// Iterate.
   125  	for i := 0; i <= steps; i++ {
   126  		t.Quo(two, x)  // t = 2.0 / x_n
   127  		t.Add(x, t)    // t = x_n + (2.0 / x_n)
   128  		x.Mul(half, t) // x_{n+1} = 0.5 * t
   129  	}
   130  
   131  	// We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter
   132  	fmt.Printf("sqrt(2) = %.50f\n", x)
   133  
   134  	// Print the error between 2 and x*x.
   135  	t.Mul(x, x) // t = x*x
   136  	fmt.Printf("error = %e\n", t.Sub(two, t))
   137  
   138  	// Output:
   139  	// sqrt(2) = 1.41421356237309504880168872420969807856967187537695
   140  	// error = 0.000000e+00
   141  }
   142  

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