Golang Float.Quo方法代码示例

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)
		}
	}
}

// Sqrt returns the square root n.
func Sqrt(n *big.Float) *big.Float {
	prec := n.Prec()

	x := new(big.Float).SetPrec(prec).SetInt64(1)
	z := new(big.Float).SetPrec(prec).SetInt64(1)

	half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
	t := new(big.Float).SetPrec(prec)

	for {
		z.Copy(x)

		t.Mul(x, x)
		t.Sub(t, n)
		t.Quo(t, x)
		t.Mul(t, half)
		x.Sub(x, t)

		if x.Cmp(z) == 0 {
			break
		}
	}

	return x
}

// 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)
	}
}

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

func splitRangeString(start, end string, splits int) []string {
	results := []string{start}
	if start == end {
		return results
	}
	if end < start {
		tmp := start
		start = end
		end = tmp
	}

	// find longest common prefix between strings
	minLen := len(start)
	if len(end) < minLen {
		minLen = len(end)
	}
	prefix := ""
	for i := 0; i < minLen; i++ {
		if start[i] == end[i] {
			prefix = start[0 : i+1]
		} else {
			break
		}
	}

	// remove prefix from strings to split
	start = start[len(prefix):]
	end = end[len(prefix):]

	ordStart := stringToOrd(start)
	ordEnd := stringToOrd(end)

	tmp := new(big.Int)
	tmp.Sub(ordEnd, ordStart)

	stride := new(big.Float)
	stride.SetInt(tmp)
	stride.Quo(stride, big.NewFloat(float64(splits)))

	for i := 1; i <= splits; i++ {
		tmp := new(big.Float)
		tmp.Mul(stride, big.NewFloat(float64(i)))
		tmp.Add(tmp, new(big.Float).SetInt(ordStart))

		result, _ := tmp.Int(new(big.Int))

		value := prefix + ordToString(result, 0)

		if value != results[len(results)-1] {
			results = append(results, value)
		}
	}

	return results
}

// floatLog computes natural log(x) using the Maclaurin series for log(1-x).
func floatLog(c Context, x *big.Float) *big.Float {
	if x.Sign() <= 0 {
		Errorf("log of non-positive value")
	}
	// The series wants x < 1, and log 1/x == -log x, so exploit that.
	invert := false
	if x.Cmp(floatOne) > 0 {
		invert = true
		x.Quo(floatOne, x)
	}

	// x = mantissa * 2**exp, and 0.5 <= mantissa < 1.
	// So log(x) is log(mantissa)+exp*log(2), and 1-x will be
	// between 0 and 0.5, so the series for 1-x will converge well.
	// (The series converges slowly in general.)
	mantissa := newFloat(c)
	exp2 := x.MantExp(mantissa)
	exp := newFloat(c).SetInt64(int64(exp2))
	exp.Mul(exp, floatLog2)
	if invert {
		exp.Neg(exp)
	}

	// y = 1-x (whereupon x = 1-y and we use that in the series).
	y := newFloat(c).SetInt64(1)
	y.Sub(y, mantissa)

	// The Maclaurin series for log(1-y) == log(x) is: -y - y²/2 - y³/3 ...

	yN := newFloat(c).Set(y)
	term := newFloat(c)
	n := newFloat(c).Set(floatOne)
	z := newFloat(c)

	// This is the slowest-converging series, so we add a factor of ten to the cutoff.
	// Only necessary when FloatPrec is at or beyond constPrecisionInBits.

	for loop := newLoop(c.Config(), "log", x, 40); ; {
		term.Quo(yN, n.SetUint64(loop.i+1))
		z.Sub(z, term)
		if loop.done(z) {
			break
		}
		// Advance y**index (multiply by y).
		yN.Mul(yN, y)
	}

	if invert {
		z.Neg(z)
	}
	z.Add(z, exp)

	return z
}

// 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
}

// compute √z using newton to solve
// t² - z = 0 for t
func sqrtDirect(z *big.Float) *big.Float {
	// f(t)/f'(t) = 0.5(t² - z)/t
	half := big.NewFloat(0.5)
	f := func(t *big.Float) *big.Float {
		x := new(big.Float).Mul(t, t) // x = t²
		x.Sub(x, z)                   // x = t² - z
		x.Mul(half, x)                // x = 0.5(t² - z)
		return x.Quo(x, t)            // return x = 0.5(t² - z)/t
	}

	// initial guess
	zf, _ := z.Float64()
	guess := big.NewFloat(math.Sqrt(zf))

	return newton(f, guess, z.Prec())
}

// hypot for big.Float
func hypot(p, q *big.Float) *big.Float {
	// special cases
	switch {
	case p.IsInf() || q.IsInf():
		return big.NewFloat(math.Inf(1))
	}
	p = p.Abs(p)
	q = q.Abs(q)
	if p.Cmp(p) < 0 {
		p, q = q, p
	}
	if p.Cmp(big.NewFloat(0)) == 0 {
		return big.NewFloat(0)
	}
	q = q.Quo(q, p)
	return sqrt(q.Mul(q, q).Add(q, big.NewFloat(1))).Mul(q, p)
}

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
}

// return: x^y
func Pow(x *big.Float, n int64) *big.Float {
	res := new(big.Float).Copy(x)
	if n < 0 {
		res = res.Quo(big.NewFloat(1), res)
		n = -n
	} else if n == 0 {
		return big.NewFloat(1)
	}
	y := big.NewFloat(1)
	for i := n; i > 1; {
		if i%2 == 0 {
			i /= 2
		} else {
			y = y.Mul(res, y)
			i = (i - 1) / 2
		}
		res = res.Mul(res, res)
	}
	return res.Mul(res, y)
}

// Pow returns a big.Float representation of z**w. Precision is the same as the one
// of the first argument. The function panics when z is negative.
func Pow(z *big.Float, w *big.Float) *big.Float {

	if z.Sign() < 0 {
		panic("Pow: negative base")
	}

	// Pow(z, 0) = 1.0
	if w.Sign() == 0 {
		return big.NewFloat(1).SetPrec(z.Prec())
	}

	// Pow(z, 1) = z
	// Pow(+Inf, n) = +Inf
	if w.Cmp(big.NewFloat(1)) == 0 || z.IsInf() {
		return new(big.Float).Copy(z)
	}

	// Pow(z, -w) = 1 / Pow(z, w)
	if w.Sign() < 0 {
		x := new(big.Float)
		zExt := new(big.Float).Copy(z).SetPrec(z.Prec() + 64)
		wNeg := new(big.Float).Neg(w)
		return x.Quo(big.NewFloat(1), Pow(zExt, wNeg)).SetPrec(z.Prec())
	}

	// w integer fast path
	if w.IsInt() {
		wi, _ := w.Int64()
		return powInt(z, int(wi))
	}

	// compute w**z as exp(z log(w))
	x := new(big.Float).SetPrec(z.Prec() + 64)
	logZ := Log(new(big.Float).Copy(z).SetPrec(z.Prec() + 64))
	x.Mul(w, logZ)
	x = Exp(x)
	return x.SetPrec(z.Prec())

}

// Evaluates a BBP term
//
// sum(k=0->inf)(1/base**k * (1/a*k + b))
func bbp(prec uint, base, a, b int64, result *big.Float) {
	var term, power, aFp, bFp, _1, k, _base, oldresult big.Float
	power.SetPrec(prec).SetInt64(1)
	result.SetPrec(prec).SetInt64(0)
	aFp.SetPrec(prec).SetInt64(a)
	bFp.SetPrec(prec).SetInt64(b)
	_1.SetPrec(prec).SetInt64(1)
	k.SetPrec(prec).SetInt64(0)
	_base.SetPrec(prec).SetInt64(base)
	for {
		oldresult.Set(result)
		term.Mul(&aFp, &k)
		term.Add(&term, &bFp)
		term.Quo(&_1, &term)
		term.Mul(&term, &power)
		result.Add(result, &term)
		if oldresult.Cmp(result) == 0 {
			break
		}
		power.Quo(&power, &_base)
		k.Add(&k, &_1)
	}
}

// Returns acot(x) in result
func acot(prec uint, x int64, result *big.Float) {
	var term, power, _x, _kp, x2, oldresult big.Float
	_x.SetPrec(prec).SetInt64(x)
	power.SetPrec(prec).SetInt64(1)
	power.Quo(&power, &_x) // 1/x
	x2.Mul(&_x, &_x)
	result.SetPrec(prec).SetInt64(0)
	positive := true
	for k := int64(1); ; k += 2 {
		oldresult.Set(result)
		kp := k
		if !positive {
			kp = -k
		}
		positive = !positive
		_kp.SetPrec(prec).SetInt64(kp)
		term.Quo(&power, &_kp)
		result.Add(result, &term)
		if oldresult.Cmp(result) == 0 {
			break
		}
		power.Quo(&power, &x2)
	}
}