// license that can be found in the LICENSE file.

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 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
	}
	s, c := math.Sincos(real(x))
	sh, ch := sinhcosh(imag(x))

package runtime

import "unsafe"

var inf = float64frombits(0x7FF0000000000000)

// isNaN reports whether f is an IEEE 754 “not-a-number” value.
func isNaN(f float64) (is bool) {
	// IEEE 754 says that only NaNs satisfy f != f.
	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 {

type orderedSlice[Elem Ordered] []Elem

func (s orderedSlice[Elem]) Len() int { return len(s) }
func (s orderedSlice[Elem]) Less(i, j int) bool {
	if s[i] < s[j] {
		return true
	}
	isNaN := func(f Elem) bool { return f != f }
	if isNaN(s[i]) && !isNaN(s[j]) {
		return true
	}
	return false
}
func (s orderedSlice[Elem]) Swap(i, j int) { s[i], s[j] = s[j], s[i] }

func _OrderedSlice[Elem Ordered](s []Elem) {

func Less[T Ordered](x, y T) bool {
	return (isNaN(x) && !isNaN(y)) || x < y
}

// Compare returns
//
//	-1 if x is less than y,
//	 0 if x equals y,
//	+1 if x is greater than y.
//
// For floating-point types, a NaN is considered less than any non-NaN,
// a NaN is considered equal to a NaN, and -0.0 is equal to 0.0.
func Compare[T Ordered](x, y T) int {
	xNaN := isNaN(x)
	yNaN := isNaN(y)
	if xNaN {
		if yNaN {
			return 0

//
// Special cases are:
//
//	Nextafter32(x, x)   = x
//	Nextafter32(NaN, y) = NaN
//	Nextafter32(x, NaN) = NaN
func Nextafter32(x, y float32) (r float32) {
	switch {
	case IsNaN(float64(x)) || IsNaN(float64(y)): // special case
		r = float32(NaN())
	case x == y:
		r = x
	case x == 0:
		r = float32(Copysign(float64(Float32frombits(1)), float64(y)))
	case (y > x) == (x > 0):

	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
}

// Min returns the smaller of x or y.
//

		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)

	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
//	Ilogb(0) = MinInt32
//	Ilogb(NaN) = MaxInt32
func Ilogb(x float64) int {
	// special cases
	switch {
	case x == 0:
		return MinInt32
	case IsNaN(x):
		return MaxInt32
	case IsInf(x, 0):

	return remainder(x, y)
}

func remainder(x, y float64) float64 {
	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 {