var tests = [...]struct {
	name string
	in   float64 // used for error messages, not an input
	got  float64
	want float64
}{
	{"sqrt0", 0, math.Sqrt(0), 0},
	{"sqrt1", 1, math.Sqrt(1), 1},
	{"sqrt2", 2, math.Sqrt(2), math.Sqrt2},
	{"sqrt4", 4, math.Sqrt(4), 2},
	{"sqrt100", 100, math.Sqrt(100), 10},
	{"sqrt101", 101, math.Sqrt(101), 10.04987562112089},
}

var nanTests = [...]struct {
	name string

	Pi  = 3.14159265358979323846264338327950288419716939937510582097494459 // https://oeis.org/A000796
	Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // https://oeis.org/A001622

	Sqrt2   = 1.41421356237309504880168872420969807856967187537694807317667974 // https://oeis.org/A002193
	SqrtE   = 1.64872127070012814684865078781416357165377610071014801157507931 // https://oeis.org/A019774

	switch {
	case math.IsNaN(x) || math.IsInf(x, 1):
		return x
	case x < 0:
		return math.NaN()
	case x == 0:
		return math.Inf(-1)
	}

	// reduce
	f1, ki := math.Frexp(x)
	if f1 < math.Sqrt2/2 {
		f1 *= 2
		ki--
	}
	f := f1 - 1
	k := float64(ki)

	// compute
	s := float64(f / (2 + f))
	s2 := float64(s * s)
	s4 := float64(s2 * s2)

	)

	// special cases
	switch {
	case IsNaN(x) || IsInf(x, 1):
		return x
	case x < 0:
		return NaN()
	case x == 0:
		return Inf(-1)
	}

	// reduce
	f1, ki := Frexp(x)
	if f1 < Sqrt2/2 {
		f1 *= 2
		ki--
	}
	f := f1 - 1
	k := float64(ki)

	// compute
	s := f / (2 + f)
	s2 := s * s
	s4 := s2 * s2
	t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))

	ORPD    X0, X2 // X2= f1
	SHRQ    $52, BX
	ANDL    $0x7FF, BX
	SUBL    $0x3FE, BX
	XORPS   X1, X1 // break dependency for CVTSL2SD
	CVTSL2SD BX, X1 // x1= k, x2= f1
	// if f1 < math.Sqrt2/2 { k -= 1; f1 *= 2 }
	MOVSD   $HSqrt2, X0 // x0= 0.7071, x1= k, x2= f1
	CMPSD   X2, X0, 5 // cmpnlt; x0= 0 or ^0, x1= k, x2 = f1
	MOVSD   $1.0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 1

			return true
		}
	}
	return false
}

// alpha returns 1 if i is 0 and returns √2 otherwise.
func alpha(i int) float64 {
	if i == 0 {
		return 1
	}
	return math.Sqrt2
}

var cosines [32]float64 // cosines[k] = cos(π/2 * k/8)

func init() {
	for k := range cosines {
		cosines[k] = math.Cos(math.Pi * float64(k) / 16)
	}
}

		{"Signbit", Func, 0},
		{"Sin", Func, 0},
		{"Sincos", Func, 0},
		{"Sinh", Func, 0},
		{"SmallestNonzeroFloat32", Const, 0},
		{"SmallestNonzeroFloat64", Const, 0},
		{"Sqrt", Func, 0},
		{"Sqrt2", Const, 0},
		{"SqrtE", Const, 0},
		{"SqrtPhi", Const, 0},
		{"SqrtPi", Const, 0},
		{"Tan", Func, 0},
		{"Tanh", Func, 0},
		{"Trunc", Func, 0},
		{"Y0", Func, 0},
		{"Y1", Func, 0},

pkg math, const MinInt8 ideal-int
pkg math, const Phi ideal-float
pkg math, const Pi ideal-float
pkg math, const SmallestNonzeroFloat32 ideal-float
pkg math, const SmallestNonzeroFloat64 ideal-float
pkg math, const Sqrt2 ideal-float
pkg math, const SqrtE ideal-float
pkg math, const SqrtPhi ideal-float
pkg math, const SqrtPi ideal-float
pkg math, func Abs(float64) float64
pkg math, func Acos(float64) float64

dragend"),i=null,o=r(g,Xo.mouse,"mousemove","mouseup"),a=r(t,e,"touchmove","touchend");return n.origin=function(t){return arguments.length?(i=t,n):i},Xo.rebind(n,u,"on")};var Sa=Math.PI,ka=2*Sa,Ea=Sa/2,Aa=1e-6,Ca=Aa*Aa,Na=Sa/180,La=180/Sa,Ta=Math.SQRT2,qa=2,za=4;Xo.interpolateZoom=function(n,t){function e(n){var t=n*y;if(m){var e=B(v),o=i/(qa*h)*(e*W(Ta*t+v)-$(v));return[r+o*s,u+o*l,i*e/B(Ta*t+v)]}return[r+n*s,u+n*l,i*Math.exp(Ta*t)]}var r=n[0],u=n[1],i=n[2],o=t[0],a=t[1],c=t[2],s=o-r,l=a-u,f=s*...

pkg math, const Sqrt2 = 1.41421  // 70710678118654752440084436210484903928483593768847403658833987/50000000000000000000000000000000000000000000000000000000000000