Golang big.Float類代碼示例

func Fconv(fvp *Mpflt, flag int) string {
	if flag&obj.FmtSharp == 0 {
		return fvp.Val.Text('b', 0)
	}

	// use decimal format for error messages

	// determine sign
	f := &fvp.Val
	var sign string
	if f.Sign() < 0 {
		sign = "-"
		f = new(big.Float).Abs(f)
	} else if flag&obj.FmtSign != 0 {
		sign = "+"
	}

	// Don't try to convert infinities (will not terminate).
	if f.IsInf() {
		return sign + "Inf"
	}

	// Use exact fmt formatting if in float64 range (common case):
	// proceed if f doesn't underflow to 0 or overflow to inf.
	if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
		return fmt.Sprintf("%s%.6g", sign, x)
	}

	// Out of float64 range. Do approximate manual to decimal
	// conversion to avoid precise but possibly slow Float
	// formatting.
	// f = mant * 2**exp
	var mant big.Float
	exp := f.MantExp(&mant) // 0.5 <= mant < 1.0

	// approximate float64 mantissa m and decimal exponent d
	// f ~ m * 10**d
	m, _ := mant.Float64()                     // 0.5 <= m < 1.0
	d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)

	// adjust m for truncated (integer) decimal exponent e
	e := int64(d)
	m *= math.Pow(10, d-float64(e))

	// ensure 1 <= m < 10
	switch {
	case m < 1-0.5e-6:
		// The %.6g format below rounds m to 5 digits after the
		// decimal point. Make sure that m*10 < 10 even after
		// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
		m *= 10
		e--
	case m >= 10:
		m /= 10
		e++
	}

	return fmt.Sprintf("%s%.6ge%+d", sign, m, e)
}

func Fconv(fvp *Mpflt, flag int) string {
	if flag&obj.FmtSharp == 0 {
		return fvp.Val.Text('b', 0)
	}

	// use decimal format for error messages

	// determine sign
	f := &fvp.Val
	var sign string
	if f.Sign() < 0 {
		sign = "-"
		f = new(big.Float).Abs(f)
	} else if flag&obj.FmtSign != 0 {
		sign = "+"
	}

	// Don't try to convert infinities (will not terminate).
	if f.IsInf() {
		return sign + "Inf"
	}

	// Use fmt formatting if in float64 range (common case).
	if x, _ := f.Float64(); !math.IsInf(x, 0) {
		return fmt.Sprintf("%s%.6g", sign, x)
	}

	// Out of float64 range. Do approximate manual to decimal
	// conversion to avoid precise but possibly slow Float
	// formatting. The exponent is > 0 since a negative out-
	// of-range exponent would have underflowed and led to 0.
	// f = mant * 2**exp
	var mant big.Float
	exp := float64(f.MantExp(&mant)) // 0.5 <= mant < 1.0, exp > 0

	// approximate float64 mantissa m and decimal exponent d
	// f ~ m * 10**d
	m, _ := mant.Float64()            // 0.5 <= m < 1.0
	d := exp * (math.Ln2 / math.Ln10) // log_10(2)

	// adjust m for truncated (integer) decimal exponent e
	e := int64(d)
	m *= math.Pow(10, d-float64(e))
	for m >= 10 {
		m /= 10
		e++
	}

	return fmt.Sprintf("%s%.5fe+%d", sign, m, e)
}

func (p *exporter) float(x *Mpflt) {
	// extract sign (there is no -0)
	f := &x.Val
	sign := f.Sign()
	if sign == 0 {
		// x == 0
		p.int(0)
		return
	}
	// x != 0

	// extract exponent such that 0.5 <= m < 1.0
	var m big.Float
	exp := f.MantExp(&m)

	// extract mantissa as *big.Int
	// - set exponent large enough so mant satisfies mant.IsInt()
	// - get *big.Int from mant
	m.SetMantExp(&m, int(m.MinPrec()))
	mant, acc := m.Int(nil)
	if acc != big.Exact {
		Fatalf("internal error")
	}

	p.int(sign)
	p.int(exp)
	p.string(string(mant.Bytes()))
}

func mpmovefltfix(a *Mpint, b *Mpflt) int {
	// avoid converting huge floating-point numbers to integers
	// (2*Mpprec is large enough to permit all tests to pass)
	if b.Val.MantExp(nil) > 2*Mpprec {
		return -1
	}

	if _, acc := b.Val.Int(&a.Val); acc == big.Exact {
		return 0
	}

	const delta = 16 // a reasonably small number of bits > 0
	var t big.Float
	t.SetPrec(Mpprec - delta)

	// try rounding down a little
	t.SetMode(big.ToZero)
	t.Set(&b.Val)
	if _, acc := t.Int(&a.Val); acc == big.Exact {
		return 0
	}

	// try rounding up a little
	t.SetMode(big.AwayFromZero)
	t.Set(&b.Val)
	if _, acc := t.Int(&a.Val); acc == big.Exact {
		return 0
	}

	return -1
}

func mpmovefltfix(a *Mpint, b *Mpflt) int {
	if _, acc := b.Val.Int(&a.Val); acc == big.Exact {
		return 0
	}

	const delta = 16 // a reasonably small number of bits > 0
	var t big.Float
	t.SetPrec(Mpprec - delta)

	// try rounding down a little
	t.SetMode(big.ToZero)
	t.Set(&b.Val)
	if _, acc := t.Int(&a.Val); acc == big.Exact {
		return 0
	}

	// try rounding up a little
	t.SetMode(big.AwayFromZero)
	t.Set(&b.Val)
	if _, acc := t.Int(&a.Val); acc == big.Exact {
		return 0
	}

	return -1
}

func ExampleFloat_Add() {
	// Operating on numbers of different precision.
	var x, y, z big.Float
	x.SetInt64(1000)          // x is automatically set to 64bit precision
	y.SetFloat64(2.718281828) // y is automatically set to 53bit precision
	z.SetPrec(32)
	z.Add(&x, &y)
	fmt.Printf("x = %.10g (%s, prec = %d, acc = %s)\n", &x, x.Text('p', 0), x.Prec(), x.Acc())
	fmt.Printf("y = %.10g (%s, prec = %d, acc = %s)\n", &y, y.Text('p', 0), y.Prec(), y.Acc())
	fmt.Printf("z = %.10g (%s, prec = %d, acc = %s)\n", &z, z.Text('p', 0), z.Prec(), z.Acc())
	// Output:
	// x = 1000 (0x.fap+10, prec = 64, acc = Exact)
	// y = 2.718281828 (0x.adf85458248cd8p+2, prec = 53, acc = Exact)
	// z = 1002.718282 (0x.faadf854p+10, prec = 32, acc = Below)
}

// 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
}