Float Accuracy in Go

huangapple
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英文:

Float Accuracy in Go

问题

这个问题是我之前提出的问题的后续问题。我收到的答案建议我使用Go的math.Big库。在这个问题中，我使用了这个库，但是效果不佳。

我试图使用Binet公式计算fib(100)。我使用了Go的Big.Float，但是没有成功。我只能得到大约10位小数的精度。请给予建议。

我试图避免使用循环/递归，因为我认为这些方法不会很好地扩展。因此，我尝试利用Binet公式。

  1. // 当输入增加时，目前会产生不准确的结果。
  3. package main
  5. import (
  6. 	"fmt"
  7. 	"math/big"
  8. 	"math"
  9. 	"strconv"
  10. )
  12. func fib(n int) float64  {
  13. 	var sroot5 = new(big.Float).SetPrec(200).SetFloat64(2.236067977499789696409173668731276235440618359611525724270897)
  14.     var phi = new(big.Float).SetPrec(200).SetFloat64(1.61803398874989484820458683436563811772030917980576286213544862)
  15.     var minusPhi = new(big.Float).SetPrec(200).SetFloat64(-0.61803398874989484820458683436563811772030917980576)
  17.     var fltP float64;
  18.     fltP, _ = phi.Float64()
  20.     var fltN float64;
  21.     fltN, _ = minusPhi.Float64()
  22.       
  23.     var denom float64
  24.     denom, _ = sroot5.Float64()
  26. 	// Magic fib formula (Binet) is:
  27. 	// (Phi ^ n - (-phi ^ n)) / sqrt(5)
  29.     z := (math.Pow(fltP, float64(n)) - math.Pow(fltN, float64(n))) / denom 
  31. 	return math.Ceil(z) 
  33. }
  35. func main() {
  36.        
  37.     fib(100)
  39. 	fmt.Println(strconv.FormatFloat(fib(100), 'f', 0, 64))
  40. 	fmt.Println("true answer of fib(100) should be -> 354224848179261915075")
  42. }
英文:

This question is a follow on from a previous question I asked. The answers I received suggested that I make use of the Go math.Big library. In this question I use the library but unfortunately to little effect.

I am trying to using the Binet formula to calculate fib(100). I am using
Go's Big.Float but without success. I get accuracy to about 10 decimal
places. Please advise.

I am trying to avoid loops/recursion as I think these approaches will
not scale well. Hence my attempt to leverage Binet's formula

// currently produces inaccurate results as the input increases.

  1. package main
  3. import (
  4. 	"fmt"
  5. 	"math/big"
  6. 	"math"
  7. 	"strconv"
  8. )
  10. func fib(n int) float64  {
  11. 	var sroot5 = new(big.Float).SetPrec(200).SetFloat64(2.236067977499789696409173668731276235440618359611525724270897)
  12.     var phi = new(big.Float).SetPrec(200).SetFloat64(1.61803398874989484820458683436563811772030917980576286213544862)
  13.     var minusPhi = new(big.Float).SetPrec(200).SetFloat64(-0.61803398874989484820458683436563811772030917980576)
  15.     var fltP float64;
  16.     fltP, _ = phi.Float64()
  18.     var fltN float64;
  19.     fltN, _ = minusPhi.Float64()
  20.       
  21.     var denom float64
  22.     denom, _ = sroot5.Float64()
  24. 	// Magic fib formula (Binet) is:
  25. 	// (Phi ^ n - (-phi ^ n)) / sqrt(5)
  27.     z := (math.Pow(fltP, float64(n)) - math.Pow(fltN, float64(n))) / denom 
  29. 	return math.Ceil(z) 
  31. }
  33. func main() {
  34.        
  35.     fib(100)
  37. 	fmt.Println(strconv.FormatFloat(fib(100), 'f', 0, 64))
  38. 	fmt.Println("true answer of fib(100) should be -> 354224848179261915075")
  40. }

答案1

得分: 6

你正在使用IEEE 754 64位浮点数。

在Go语言中，要准确计算fib(100)，你可以简单地使用以下代码：

  1. package main
  3. import (
  4. 	"fmt"
  5. 	"math/big"
  6. )
  8. func fib(n int) *big.Int {
  9. 	f := big.NewInt(0)
  10. 	a, b := big.NewInt(0), big.NewInt(1)
  11. 	for i := 0; i <= n; i++ {
  12. 		f.Set(a)
  13. 		a.Set(b)
  14. 		b.Add(f, b)
  15. 	}
  16. 	return f
  17. }
  19. func main() {
  20. 	fmt.Println(fib(100))
  21. }

输出结果为：

  1. 354224848179261915075
英文:

You are using IEEE 754 64-bit floating point.

In Go, to calculate fib(100) accurately you could simply say:

  1. package main
  3. import (
  4. 	&quot;fmt&quot;
  5. 	&quot;math/big&quot;
  6. )
  8. func fib(n int) *big.Int {
  9. 	f := big.NewInt(0)
  10. 	a, b := big.NewInt(0), big.NewInt(1)
  11. 	for i := 0; i &lt;= n; i++ {
  12. 		f.Set(a)
  13. 		a.Set(b)
  14. 		b.Add(f, b)
  15. 	}
  16. 	return f
  17. }
  19. func main() {
  20. 	fmt.Println(fib(100))
  21. }

Output:

  1. 354224848179261915075

huangapple
  • 本文由 发表于 2015年8月22日 23:34:09
  • 转载请务必保留本文链接：https://go.coder-hub.com/32157833.html
  • floating-accuracy
  • go
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