// Sin returns the sine of x.
func Sin(x complex128) complex128 {
	switch re, im := real(x), imag(x); {
	case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
		return complex(math.NaN(), im)
	case math.IsInf(im, 0):
		switch {
		case re == 0:
			return x
		case math.IsInf(re, 0) || math.IsNaN(re):
			return complex(math.NaN(), im)
		}
	case re == 0 && math.IsNaN(im):
		return x
	}

		}
		return Copysign(Pi, y)
	case x == 0:
		return Copysign(Pi/2, y)
	case IsInf(x, 0):
		if IsInf(x, 1) {
			switch {
			case IsInf(y, 0):
				return Copysign(Pi/4, y)
			default:
				return Copysign(0, y)
			}
		}
		switch {
		case IsInf(y, 0):
			return Copysign(3*Pi/4, y)
		default:
			return Copysign(Pi, y)
		}
	case IsInf(y, 0):
		return Copysign(Pi/2, y)
	}

	//	return uint32(x>>shift)&mask == mask && x != uvinf && x != uvneginf
	return f != f
}

// IsInf reports whether f is an infinity, according to sign.
// If sign > 0, IsInf reports whether f is positive infinity.
// If sign < 0, IsInf reports whether f is negative infinity.
// If sign == 0, IsInf reports whether f is either infinity.
func IsInf(f float64, sign int) bool {
	// Test for infinity by comparing against maximum float.

//
// Special cases are:
//
//	Logb(±Inf) = +Inf
//	Logb(0) = -Inf
//	Logb(NaN) = NaN
func Logb(x float64) float64 {
	// special cases
	switch {
	case x == 0:
		return Inf(-1)
	case IsInf(x, 0):
		return Inf(1)
	case IsNaN(x):
		return x
	}
	return float64(ilogb(x))
}

// Ilogb returns the binary exponent of x as an integer.
//
// Special cases are:
//
//	Ilogb(±Inf) = MaxInt32

// with NaN and +Inf.
func Max(x, y float64) float64 {
	if haveArchMax {
		return archMax(x, y)
	}
	return max(x, y)
}

func max(x, y float64) float64 {
	// special cases
	switch {
	case IsInf(x, 1) || IsInf(y, 1):
		return Inf(1)
	case IsNaN(x) || IsNaN(y):
		return NaN()
	case x == 0 && x == y:
		if Signbit(x) {
			return y
		}
		return x
	}
	if x > y {
		return x
	}
	return y
}

package cmplx

import "math"

// IsNaN reports whether either real(x) or imag(x) is NaN
// and neither is an infinity.
func IsNaN(x complex128) bool {
	switch {
	case math.IsInf(real(x), 0) || math.IsInf(imag(x), 0):
		return false
	case math.IsNaN(real(x)) || math.IsNaN(imag(x)):
		return true
	}
	return false
}

// NaN returns a complex “not-a-number” value.
func NaN() complex128 {

func Hypot(p, q float64) float64 {
	if haveArchHypot {
		return archHypot(p, q)
	}
	return hypot(p, q)
}

func hypot(p, q float64) float64 {
	p, q = Abs(p), Abs(q)
	// special cases
	switch {
	case IsInf(p, 1) || IsInf(q, 1):
		return Inf(1)
	case IsNaN(p) || IsNaN(q):
		return NaN()
	}
	if p < q {
		p, q = q, p
	}
	if p == 0 {
		return 0
	}
	q = q / p
	return p * Sqrt(1+q*q)

			}
			return Inf(1)
		case y > 0:
			if Signbit(x) && isOddInt(y) {
				return x
			}
			return 0
		}
	case IsInf(y, 0):
		switch {
		case x == -1:
			return 1
		case (Abs(x) < 1) == IsInf(y, 1):
			return 0
		default:
			return Inf(1)
		}
	case IsInf(x, 0):
		if IsInf(x, -1) {
			return Pow(1/x, -y) // Pow(-0, -y)
		}
		switch {
		case y < 0:
			return 0
		case y > 0:
			return Inf(1)

	return f != f
}

// isFinite reports whether f is neither NaN nor an infinity.
func isFinite(f float64) bool {
	return !isNaN(f - f)
}

// isInf reports whether f is an infinity.
func isInf(f float64) bool {
	return !isNaN(f) && !isFinite(f)
}

// abs returns the absolute value of x.
//
// Special cases are:
//
//	abs(±Inf) = +Inf
//	abs(NaN) = NaN

	const (
		Tiny    = 4.45014771701440276618e-308 // 0x0020000000000000
		HalfMax = MaxFloat64 / 2
	)
	// special cases
	switch {
	case IsNaN(x) || IsNaN(y) || IsInf(x, 0) || y == 0:
		return NaN()
	case IsInf(y, 0):
		return x
	}
	sign := false
	if x < 0 {
		x = -x
		sign = true
	}
	if y < 0 {
		y = -y
	}
	if x == y {
		if sign {
			zero := 0.0
			return -zero
		}