Go中的浮点精度

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.

package main

import (
    "fmt"
    "math/big"
    "math"
    "strconv"
)

func fib(n int) float64  {
    var sroot5 = new(big.Float).SetPrec(200).SetFloat64(2.236067977499789696409173668731276235440618359611525724270897)
    var phi = new(big.Float).SetPrec(200).SetFloat64(1.61803398874989484820458683436563811772030917980576286213544862)
    var minusPhi = new(big.Float).SetPrec(200).SetFloat64(-0.61803398874989484820458683436563811772030917980576)

    var fltP float64;
    fltP, _ = phi.Float64()

    var fltN float64;
    fltN, _ = minusPhi.Float64()

    var denom float64
    denom, _ = sroot5.Float64()

    // Magic fib formula (Binet) is:
    // (Phi ^ n - (-phi ^ n)) / sqrt(5)

    z := (math.Pow(fltP, float64(n)) - math.Pow(fltN, float64(n))) / denom 

    return math.Ceil(z) 

}

func main() {

    fib(100)

    fmt.Println(strconv.FormatFloat(fib(100), 'f', 0, 64))
    fmt.Println("true answer of fib(100) should be -> 354224848179261915075")

}

You are using IEEE 754 64-bit floating point.

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

package main

import (
    "fmt"
    "math/big"
)

func fib(n int) *big.Int {
    f := big.NewInt(0)
    a, b := big.NewInt(0), big.NewInt(1)
    for i := 0; i <= n; i++ {
        f.Set(a)
        a.Set(b)
        b.Add(f, b)
    }
    return f
}

func main() {
    fmt.Println(fib(100))
}

Output:

354224848179261915075