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Source file src/math/big/example_test.go

Documentation: math/big

  // 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 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
  }
  

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