Golang Float.Add方法代码示例

// Compute the square root of n using Newton's Method. We start with
// an initial estimate for sqrt(n), and then iterate
//     x_{i+1} = 1/2 * ( x_i + (n / x_i) )
// Result is returned in x
func (e *Pslq) Sqrt(n, x *big.Float) {
	if n == x {
		panic("need distinct input and output")
	}
	if n.Sign() == 0 {
		x.Set(n)
		return
	} else if n.Sign() < 0 {
		panic("Sqrt of negative number")
	}
	prec := n.Prec()

	// Use the floating point square root as initial estimate
	nFloat64, _ := n.Float64()
	x.SetPrec(prec).SetFloat64(math.Sqrt(nFloat64))

	// 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.
	var t big.Float

	// Iterate.
	for {
		t.Quo(n, x)        // t = n / x_i
		t.Add(x, &t)       // t = x_i + (n / x_i)
		t.Mul(&e.half, &t) // x_{i+1} = 0.5 * t
		if x.Cmp(&t) == 0 {
			// Exit loop if no change to result
			break
		}
		x.Set(&t)
	}
}

// Add
func (a Scalar) Add_S(b S) S {
	var x, y big.Float
	x = big.Float(a)
	y = big.Float(b.(Scalar))
	z := x.Add(&x, &y)
	return (Scalar)(*z)
}

// sincos iterates a sin or cos Taylor series.
func sincos(name string, c Context, index int, x *big.Float, z *big.Float, exp uint64, factorial *big.Float) *big.Float {
	term := newFloat(c).Set(floatOne)
	for j := 0; j < index; j++ {
		term.Mul(term, x)
	}
	xN := newFloat(c).Set(term)
	x2 := newFloat(c).Mul(x, x)
	n := newFloat(c)

	for loop := newLoop(c.Config(), name, x, 4); ; {
		// Invariant: factorial holds -1ⁿ*exponent!.
		factorial.Neg(factorial)
		term.Quo(term, factorial)
		z.Add(z, term)

		if loop.done(z) {
			break
		}
		// Advance x**index (multiply by x²).
		term.Mul(xN, x2)
		xN.Set(term)
		// Advance factorial.
		factorial.Mul(factorial, n.SetUint64(exp+1))
		factorial.Mul(factorial, n.SetUint64(exp+2))
		exp += 2
	}
	return z
}

func quo(x, y *complexFloat) *complexFloat {
	z := newComplexFloat()
	denominator := new(big.Float).SetPrec(prec)
	c2 := new(big.Float).SetPrec(prec)
	d2 := new(big.Float).SetPrec(prec)
	c2.Mul(y.r, y.r)
	d2.Mul(y.i, y.i)
	denominator.Add(c2, d2)

	if denominator.Cmp(zero) == 0 || denominator.IsInf() {
		return newComplexFloat()
	}

	ac := new(big.Float).SetPrec(prec)
	bd := new(big.Float).SetPrec(prec)
	ac.Mul(x.r, y.r)
	bd.Mul(x.i, y.i)

	bc := new(big.Float).SetPrec(prec)
	ad := new(big.Float).SetPrec(prec)
	bc.Mul(x.i, y.r)
	ad.Mul(x.r, y.i)

	z.r.Add(ac, bd)
	z.r.Quo(z.r, denominator)

	z.i.Add(bc, ad.Neg(ad))
	z.i.Quo(z.i, denominator)

	return z
}

func renderFloat(img *image.RGBA) {
	var yminF, ymaxMinF, heightF big.Float
	yminF.SetInt64(ymin)
	ymaxMinF.SetInt64(ymax - ymin)
	heightF.SetInt64(height)

	var xminF, xmaxMinF, widthF big.Float
	xminF.SetInt64(xmin)
	xmaxMinF.SetInt64(xmax - xmin)
	widthF.SetInt64(width)

	var y, x big.Float
	for py := int64(0); py < height; py++ {
		// y := float64(py)/height*(ymax-ymin) + ymin
		y.SetInt64(py)
		y.Quo(&y, &heightF)
		y.Mul(&y, &ymaxMinF)
		y.Add(&y, &yminF)

		for px := int64(0); px < width; px++ {
			// x := float64(px)/width*(xmax-xmin) + xmin
			x.SetInt64(px)
			x.Quo(&x, &widthF)
			x.Mul(&x, &xmaxMinF)
			x.Add(&x, &xminF)

			c := mandelbrotFloat(&x, &y)
			if c == nil {
				c = color.Black
			}
			img.Set(int(px), int(py), c)
		}
	}
}

func opsum(a, b *big.Float) *big.Float {
	if a == nil {
		return b
	} else if b == nil {
		return a
	}
	return a.Add(a, b)
}

// NearestInt set res to the nearest integer to x
func (e *Pslq) NearestInt(x *big.Float, res *big.Int) {
	prec := x.Prec()
	var tmp big.Float
	tmp.SetPrec(prec)
	if x.Sign() >= 0 {
		tmp.Add(x, &e.half)
	} else {
		tmp.Sub(x, &e.half)
	}
	tmp.Int(res)
}

func abs(x *complexFloat) *big.Float {
	r := new(big.Float).SetPrec(prec)
	i := new(big.Float).SetPrec(prec)
	r.Copy(x.r)
	i.Copy(x.i)

	r.Mul(r, x.r) // r^2
	i.Mul(i, x.i) // i^2

	r.Add(r, i) // r^2 + i^2

	return sqrtFloat(r) // sqrt(r^2 + i^2)
}

// sqrt for big.Float
func sqrt(given *big.Float) *big.Float {
	const prec = 200
	steps := int(math.Log2(prec))
	given.SetPrec(prec)
	half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
	x := new(big.Float).SetPrec(prec).SetInt64(1)
	t := new(big.Float)
	for i := 0; i <= steps; i++ {
		t.Quo(given, x)
		t.Add(x, t)
		t.Mul(half, t)
	}
	return x
}

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 = %s (%s, prec = %d, acc = %s)\n", &x, x.Format('p', 0), x.Prec(), x.Acc())
	fmt.Printf("y = %s (%s, prec = %d, acc = %s)\n", &y, y.Format('p', 0), y.Prec(), y.Acc())
	fmt.Printf("z = %s (%s, prec = %d, acc = %s)\n", &z, z.Format('p', 0), z.Prec(), z.Acc())
	// Output:
	// x = 1000 (0x.fap10, prec = 64, acc = Exact)
	// y = 2.718281828 (0x.adf85458248cd8p2, prec = 53, acc = Exact)
	// z = 1002.718282 (0x.faadf854p10, prec = 32, acc = Below)
}

// Implements the nth root algorithm from
// https://en.wikipedia.org/wiki/Nth_root_algorithm
// return: nth root of x within some epsilon
func Root(x *big.Float, n int64) *big.Float {
	guess := new(big.Float).Quo(x, big.NewFloat(float64(n)))
	diff := big.NewFloat(1)
	ep := big.NewFloat(0.00000001)
	abs := new(big.Float).Abs(diff)
	for abs.Cmp(ep) >= 0 {
		//fmt.Println(guess, abs)
		prev := Pow(guess, n-1)
		diff = new(big.Float).Quo(x, prev)
		diff = diff.Sub(diff, guess)
		diff = diff.Quo(diff, big.NewFloat(float64(n)))

		guess = guess.Add(guess, diff)
		abs = new(big.Float).Abs(diff)
	}
	return guess
}

func sqrtFloat(x *big.Float) *big.Float {
	t1 := new(big.Float).SetPrec(prec)
	t2 := new(big.Float).SetPrec(prec)
	t1.Copy(x)

	// Iterate.
	// x{n} = (x{n-1}+x{0}/x{n-1}) / 2
	for i := 0; i <= steps; i++ {
		if t1.Cmp(zero) == 0 || t1.IsInf() {
			return t1
		}
		t2.Quo(x, t1)
		t2.Add(t2, t1)
		t1.Mul(half, t2)
	}

	return t1
}

// 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
}

func main() {
	i1, i2, i3 := 12, 45, 68
	intSum := i1 + i2 + i3

	fmt.Println("Integer Sum:", intSum)

	f1, f2, f3 := 23.5, 65.1, 76.3
	floatSum := f1 + f2 + f3
	fmt.Println("Float Sum:", floatSum)

	var b1, b2, b3, bigSum big.Float
	b1.SetFloat64(23.5)
	b2.SetFloat64(65.1)
	b3.SetFloat64(76.3)
	bigSum.Add(&b1, &b2).Add(&bigSum, &b3)
	fmt.Printf("BigSum = %.10g\n", &bigSum)

	circleRadius := 15.5
	circumference := 2 * circleRadius * math.Pi
	fmt.Printf("Circumference: %.2f\n", circumference)
}

// sincos iterates a sin or cos Taylor series.
func sincos(name string, index int, x, z, exponent, factorial *big.Float) *big.Float {
	plus := false
	term := newF().Set(floatOne)
	for j := 0; j < index; j++ {
		term.Mul(term, x)
	}
	xN := newF().Set(term)
	x2 := newF().Mul(x, x)

	loop := newLoop(name, x, 4)
	for {
		// Invariant: factorial holds exponent!.
		term.Quo(term, factorial)
		if plus {
			z.Add(z, term)
		} else {
			z.Sub(z, term)
		}
		plus = !plus

		if loop.terminate(z) {
			break
		}
		// Advance x**index (multiply by x²).
		term.Mul(xN, x2)
		xN.Set(term)
		// Advance exponent and factorial.
		exponent.Add(exponent, floatOne)
		factorial.Mul(factorial, exponent)
		exponent.Add(exponent, floatOne)
		factorial.Mul(factorial, exponent)
	}
	return z
}