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 ExampleFloat_SetString() { 29 f := new(big.Float) 30 f.SetString("3.14159") 31 fmt.Println(f) 32 // Output: 3.14159 33 } 34 35 func ExampleRat_Scan() { 36 // The Scan function is rarely used directly; 37 // the fmt package recognizes it as an implementation of fmt.Scanner. 38 r := new(big.Rat) 39 _, err := fmt.Sscan("1.5000", r) 40 if err != nil { 41 log.Println("error scanning value:", err) 42 } else { 43 fmt.Println(r) 44 } 45 // Output: 3/2 46 } 47 48 func ExampleInt_Scan() { 49 // The Scan function is rarely used directly; 50 // the fmt package recognizes it as an implementation of fmt.Scanner. 51 i := new(big.Int) 52 _, err := fmt.Sscan("18446744073709551617", i) 53 if err != nil { 54 log.Println("error scanning value:", err) 55 } else { 56 fmt.Println(i) 57 } 58 // Output: 18446744073709551617 59 } 60 61 func ExampleFloat_Scan() { 62 // The Scan function is rarely used directly; 63 // the fmt package recognizes it as an implementation of fmt.Scanner. 64 f := new(big.Float) 65 _, err := fmt.Sscan("1.19282e99", f) 66 if err != nil { 67 log.Println("error scanning value:", err) 68 } else { 69 fmt.Println(f) 70 } 71 // Output: 1.19282e+99 72 } 73 74 // This example demonstrates how to use big.Int to compute the smallest 75 // Fibonacci number with 100 decimal digits and to test whether it is prime. 76 func Example_fibonacci() { 77 // Initialize two big ints with the first two numbers in the sequence. 78 a := big.NewInt(0) 79 b := big.NewInt(1) 80 81 // Initialize limit as 10^99, the smallest integer with 100 digits. 82 var limit big.Int 83 limit.Exp(big.NewInt(10), big.NewInt(99), nil) 84 85 // Loop while a is smaller than 1e100. 86 for a.Cmp(&limit) < 0 { 87 // Compute the next Fibonacci number, storing it in a. 88 a.Add(a, b) 89 // Swap a and b so that b is the next number in the sequence. 90 a, b = b, a 91 } 92 fmt.Println(a) // 100-digit Fibonacci number 93 94 // Test a for primality. 95 // (ProbablyPrimes' argument sets the number of Miller-Rabin 96 // rounds to be performed. 20 is a good value.) 97 fmt.Println(a.ProbablyPrime(20)) 98 99 // Output: 100 // 1344719667586153181419716641724567886890850696275767987106294472017884974410332069524504824747437757 101 // false 102 } 103 104 // This example shows how to use big.Float to compute the square root of 2 with 105 // a precision of 200 bits, and how to print the result as a decimal number. 106 func Example_sqrt2() { 107 // We'll do computations with 200 bits of precision in the mantissa. 108 const prec = 200 109 110 // Compute the square root of 2 using Newton's Method. We start with 111 // an initial estimate for sqrt(2), and then iterate: 112 // x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) ) 113 114 // Since Newton's Method doubles the number of correct digits at each 115 // iteration, we need at least log_2(prec) steps. 116 steps := int(math.Log2(prec)) 117 118 // Initialize values we need for the computation. 119 two := new(big.Float).SetPrec(prec).SetInt64(2) 120 half := new(big.Float).SetPrec(prec).SetFloat64(0.5) 121 122 // Use 1 as the initial estimate. 123 x := new(big.Float).SetPrec(prec).SetInt64(1) 124 125 // We use t as a temporary variable. There's no need to set its precision 126 // since big.Float values with unset (== 0) precision automatically assume 127 // the largest precision of the arguments when used as the result (receiver) 128 // of a big.Float operation. 129 t := new(big.Float) 130 131 // Iterate. 132 for i := 0; i <= steps; i++ { 133 t.Quo(two, x) // t = 2.0 / x_n 134 t.Add(x, t) // t = x_n + (2.0 / x_n) 135 x.Mul(half, t) // x_{n+1} = 0.5 * t 136 } 137 138 // We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter 139 fmt.Printf("sqrt(2) = %.50f\n", x) 140 141 // Print the error between 2 and x*x. 142 t.Mul(x, x) // t = x*x 143 fmt.Printf("error = %e\n", t.Sub(two, t)) 144 145 // Output: 146 // sqrt(2) = 1.41421356237309504880168872420969807856967187537695 147 // error = 0.000000e+00 148 } 149