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// Copyright 2012 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"
"log"
"math"
"math/big"
)
func ExampleRat_SetString() {
r := new(big.Rat)
r.SetString("355/113")
fmt.Println(r.FloatString(3))
// Output: 3.142
}
func ExampleInt_SetString() {
i := new(big.Int)
i.SetString("644", 8) // octal
fmt.Println(i)
// Output: 420
}
func ExampleFloat_SetString() {
f := new(big.Float)
f.SetString("3.14159")
fmt.Println(f)
// Output: 3.14159
}
func ExampleRat_Scan() {
// The Scan function is rarely used directly;
// the fmt package recognizes it as an implementation of fmt.Scanner.
r := new(big.Rat)
_, err := fmt.Sscan("1.5000", r)
if err != nil {
log.Println("error scanning value:", err)
} else {
fmt.Println(r)
}
// Output: 3/2
}
func ExampleInt_Scan() {
// The Scan function is rarely used directly;
// the fmt package recognizes it as an implementation of fmt.Scanner.
i := new(big.Int)
_, err := fmt.Sscan("18446744073709551617", i)
if err != nil {
log.Println("error scanning value:", err)
} else {
fmt.Println(i)
}
// Output: 18446744073709551617
}
func ExampleFloat_Scan() {
// The Scan function is rarely used directly;
// the fmt package recognizes it as an implementation of fmt.Scanner.
f := new(big.Float)
_, err := fmt.Sscan("1.19282e99", f)
if err != nil {
log.Println("error scanning value:", err)
} else {
fmt.Println(f)
}
// Output: 1.19282e+99
}
// This example demonstrates how to use big.Int to compute the smallest
// Fibonacci number with 100 decimal digits and to test whether it is prime.
func Example_fibonacci() {
// Initialize two big ints with the first two numbers in the sequence.
a := big.NewInt(0)
b := big.NewInt(1)
// Initialize limit as 10^99, the smallest integer with 100 digits.
var limit big.Int
limit.Exp(big.NewInt(10), big.NewInt(99), nil)
// Loop while a is smaller than 1e100.
for a.Cmp(&limit) < 0 {
// Compute the next Fibonacci number, storing it in a.
a.Add(a, b)
// Swap a and b so that b is the next number in the sequence.
a, b = b, a
}
fmt.Println(a) // 100-digit Fibonacci number
// Test a for primality.
// (ProbablyPrimes' argument sets the number of Miller-Rabin
// rounds to be performed. 20 is a good value.)
fmt.Println(a.ProbablyPrime(20))
// Output:
// 1344719667586153181419716641724567886890850696275767987106294472017884974410332069524504824747437757
// false
}
// This example shows how to use big.Float to compute the square root of 2 with
// a precision of 200 bits, and how to print the result as a decimal number.
func Example_sqrt2() {
// We'll do computations with 200 bits of precision in the mantissa.
const prec = 200
// Compute the square root of 2 using Newton's Method. We start with
// an initial estimate for sqrt(2), and then iterate:
// x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) )
// Since Newton's Method doubles the number of correct digits at each
// iteration, we need at least log_2(prec) steps.
steps := int(math.Log2(prec))
// Initialize values we need for the computation.
two := new(big.Float).SetPrec(prec).SetInt64(2)
half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
// Use 1 as the initial estimate.
x := new(big.Float).SetPrec(prec).SetInt64(1)
// We use t as a temporary variable. There's no need to set its precision
// since big.Float values with unset (== 0) precision automatically assume
// the largest precision of the arguments when used as the result (receiver)
// of a big.Float operation.
t := new(big.Float)
// Iterate.
for i := 0; i <= steps; i++ {
t.Quo(two, x) // t = 2.0 / x_n
t.Add(x, t) // t = x_n + (2.0 / x_n)
x.Mul(half, t) // x_{n+1} = 0.5 * t
}
// We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter
fmt.Printf("sqrt(2) = %.50f\n", x)
// Print the error between 2 and x*x.
t.Mul(x, x) // t = x*x
fmt.Printf("error = %e\n", t.Sub(two, t))
// Output:
// sqrt(2) = 1.41421356237309504880168872420969807856967187537695
// error = 0.000000e+00
}