Golang Float.Set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)
	}
}

func (a *Mpint) SetFloat(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 mandelbrotFloat(a, b *big.Float) color.Color {
	var x, y, nx, ny, x2, y2, f2, f4, r2, tmp big.Float
	f2.SetInt64(2)
	f4.SetInt64(4)
	x.SetInt64(0)
	y.SetInt64(0)

	defer func() { recover() }()

	for n := uint8(0); n < iterations; n++ {
		// Not update x2 and y2
		// because they are already updated in the previous loop
		nx.Sub(&x2, &y2)
		nx.Add(&nx, a)

		tmp.Mul(&x, &y)
		ny.Mul(&f2, &tmp)
		ny.Add(&ny, b)

		x.Set(&nx)
		y.Set(&ny)

		x2.Mul(&x, &x)
		y2.Mul(&y, &y)
		r2.Add(&x2, &y2)

		if r2.Cmp(&f4) > 0 {
			return color.Gray{255 - contrast*n}
		}
	}
	return color.Black
}

// ToInt converts x to an Int value if x is representable as an Int.
// Otherwise it returns an Unknown.
func ToInt(x Value) Value {
	switch x := x.(type) {
	case int64Val, intVal:
		return x

	case ratVal:
		if x.val.IsInt() {
			return makeInt(x.val.Num())
		}

	case floatVal:
		// avoid creation of huge integers
		// (Existing tests require permitting exponents of at least 1024;
		// allow any value that would also be permissible as a fraction.)
		if smallRat(x.val) {
			i := newInt()
			if _, acc := x.val.Int(i); acc == big.Exact {
				return makeInt(i)
			}

			// If we can get an integer by rounding up or down,
			// assume x is not an integer because of rounding
			// errors in prior computations.

			const delta = 4 // a small number of bits > 0
			var t big.Float
			t.SetPrec(prec - delta)

			// try rounding down a little
			t.SetMode(big.ToZero)
			t.Set(x.val)
			if _, acc := t.Int(i); acc == big.Exact {
				return makeInt(i)
			}

			// try rounding up a little
			t.SetMode(big.AwayFromZero)
			t.Set(x.val)
			if _, acc := t.Int(i); acc == big.Exact {
				return makeInt(i)
			}
		}

	case complexVal:
		if re := ToFloat(x); re.Kind() == Float {
			return ToInt(re)
		}
	}

	return unknownVal{}
}

// 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)
	}
}

// Log returns a big.Float representation of the natural logarithm of
// z. Precision is the same as the one of the argument. The function
// panics if z is negative, returns -Inf when z = 0, and +Inf when z =
// +Inf
func Log(z *big.Float) *big.Float {

	// panic on negative z
	if z.Sign() == -1 {
		panic("Log: argument is negative")
	}

	// Log(0) = -Inf
	if z.Sign() == 0 {
		return big.NewFloat(math.Inf(-1)).SetPrec(z.Prec())
	}

	prec := z.Prec() + 64 // guard digits

	one := big.NewFloat(1).SetPrec(prec)
	two := big.NewFloat(2).SetPrec(prec)
	four := big.NewFloat(4).SetPrec(prec)

	// Log(1) = 0
	if z.Cmp(one) == 0 {
		return big.NewFloat(0).SetPrec(z.Prec())
	}

	// Log(+Inf) = +Inf
	if z.IsInf() {
		return big.NewFloat(math.Inf(+1)).SetPrec(z.Prec())
	}

	x := new(big.Float).SetPrec(prec)

	// if 0 < z < 1 we compute log(z) as -log(1/z)
	var neg bool
	if z.Cmp(one) < 0 {
		x.Quo(one, z)
		neg = true
	} else {
		x.Set(z)
	}

	// We scale up x until x >= 2**(prec/2), and then we'll be allowed
	// to use the AGM formula for Log(x).
	//
	// Double x until the condition is met, and keep track of the
	// number of doubling we did (needed to scale back later).

	lim := new(big.Float)
	lim.SetMantExp(two, int(prec/2))

	k := 0
	for x.Cmp(lim) < 0 {
		x.Mul(x, x)
		k++
	}

	// Compute the natural log of x using the fact that
	//     log(x) = π / (2 * AGM(1, 4/x))
	// if
	//     x >= 2**(prec/2),
	// where prec is the desired precision (in bits)
	pi := pi(prec)
	agm := agm(one, x.Quo(four, x)) // agm = AGM(1, 4/x)

	x.Quo(pi, x.Mul(two, agm)) // reuse x, we don't need it

	if neg {
		x.Neg(x)
	}

	// scale the result back multiplying by 2**-k
	// reuse lim to reduce allocations.
	x.Mul(x, lim.SetMantExp(one, -k))

	return x.SetPrec(z.Prec())
}

// Given a vector of real numbers x = [x_0, x_1, ..., x_n], this
// uses the PSLQ algorithm to find a list of integers
// [c_0, c_1, ..., c_n] such that
//
//     |c_1 * x_1 + c_2 * x_2 + ... + c_n * x_n| < tolerance
//
// and such that max |c_k| < maxcoeff. If no such vector exists, Pslq
// returns one of the errors in this package depending on whether it
// has run out of iterations, precision or explored up to the
// maxcoeff. The tolerance defaults to 3/4 of the precision.
//
// This is a fairly direct translation of the pseudocode given by
// David Bailey, "The PSLQ Integer Relation Algorithm":
// http://www.cecm.sfu.ca/organics/papers/bailey/paper/html/node3.html
//
// If a result is returned, the first non-zero element will be positive
func (e *Pslq) Run(x []big.Float) ([]big.Int, error) {
	n := len(x)
	if n <= 1 {
		return nil, ErrorBadArguments
	}

	// At too low precision, the algorithm becomes meaningless
	if e.prec < 64 {
		return nil, ErrorPrecisionTooLow
	}

	if e.verbose && int(e.prec)/max(2, int(n)) < 5 {
		log.Printf("Warning: precision for PSLQ may be too low")
	}

	if e.verbose {
		log.Printf("PSLQ using prec %d and tol %g", e.prec, e.tol)
	}

	if e.tol.Sign() == 0 {
		return nil, ErrorToleranceRoundsToZero
	}

	// Temporary variables
	tmp0 := new(big.Float).SetPrec(e.prec)
	tmp1 := new(big.Float).SetPrec(e.prec)
	bigTmp := new(big.Int)

	// Convert to use 1-based indexing to allow us to be
	// consistent with Bailey's indexing.
	xNew := make([]big.Float, len(x)+1)
	minx := new(big.Float).SetPrec(e.prec)
	minxFirst := true
	for i, xk := range x {
		p := &xNew[i+1]
		p.Set(&xk)
		tmp0.Abs(p)
		if minxFirst || tmp0.Cmp(minx) < 0 {
			minxFirst = false
			minx.Set(tmp0)
		}
	}
	x = xNew
	if debug {
		printVector("x", x)
	}

	// Sanity check on magnitudes
	if minx.Sign() == 0 {
		return nil, ErrorZeroArguments
	}
	tmp1.SetInt64(128)
	tmp0.Quo(&e.tol, tmp1)
	if minx.Cmp(tmp0) < 0 { //  minx < tol/128
		return nil, ErrorArgumentTooSmall
	}

	tmp0.SetInt64(4)
	tmp1.SetInt64(3)
	tmp0.Quo(tmp0, tmp1)
	var γ big.Float
	e.Sqrt(tmp0, &γ) // sqrt(4<<prec)/3)
	if debug {
		fmt.Printf("γ = %f\n", &γ)
	}
	A := newBigIntMatrix(n+1, n+1)
	B := newBigIntMatrix(n+1, n+1)
	H := newMatrix(n+1, n+1)
	// Initialization Step 1
	//
	// Set the n×n matrices A and B to the identity.
	for i := 1; i <= n; i++ {
		for j := 1; j <= n; j++ {
			if i == j {
				A[i][j].SetInt64(1)
				B[i][j].SetInt64(1)
			} else {
				A[i][j].SetInt64(0)
				B[i][j].SetInt64(0)
			}
			H[i][j].SetInt64(0)
		}
	}
	if debug {
//.........这里部分代码省略.........