//find roots of polynomials
use arrayvec::ArrayVec;
use std::cmp::Ordering;
use deferred_division::ratio::Ratio;
use fixed_wide::typenum::Unsigned;
use fixed_wide::fixed::Fixed;
use fixed_wide::wide::WideMul;

#[inline]
pub fn zeroes2<const N:usize,F:Unsigned>(a0:Fixed<N,F>,a1:Fixed<N,F>,a2:Fixed<N,F>)->ArrayVec<Ratio<Fixed<N,F>,Fixed<N,F>>,2>
	where
		Fixed<N,F>:WideMul,
		<Fixed<N,F> as WideMul>::Output:std::ops::Mul<i64>,
		<Fixed<N,F> as WideMul>::Output:std::ops::Sub<<<Fixed<N,F> as WideMul>::Output as std::ops::Mul<i64>>::Output>
{
	let a2pos=match a2.cmp(&Fixed::<N,F>::ZERO){
		Ordering::Greater=>true,
		Ordering::Equal=>return zeroes1(a0,a1),
		Ordering::Less=>true,
	};
	let radicand=a1.wide_mul(a1)-a2.wide_mul(a0)*4;
	match radicand.cmp(&Fixed::<N,F>::ZERO){
		Ordering::Greater=>{
			//start with f64 sqrt
			//failure case: 2^63 < sqrt(2^127)
			let planar_radicand=radicand.sqrt();
			//TODO: one or two newtons
			//sort roots ascending and avoid taking the difference of large numbers
			match (a2pos,Fixed::<N,F>::ZERO<a1){
				(true, true )=>[Ratio::new(-a1-planar_radicand,a2*2),Ratio::new(a0*2,-a1-planar_radicand)].into(),
				(true, false)=>[Ratio::new(a0*2,-a1+planar_radicand),Ratio::new(-a1+planar_radicand,a2*2)].into(),
				(false,true )=>[Ratio::new(a0*2,-a1-planar_radicand),Ratio::new(-a1-planar_radicand,a2*2)].into(),
				(false,false)=>[Ratio::new(-a1+planar_radicand,a2*2),Ratio::new(a0*2,-a1+planar_radicand)].into(),
			}
		},
		Ordering::Equal=>ArrayVec::from_iter([Ratio::new(a1,a2*-2)]),
		Ordering::Less=>ArrayVec::new_const(),
	}
}
#[inline]
pub fn zeroes1<const N:usize,F:Unsigned>(a0:Fixed<N,F>,a1:Fixed<N,F>)->ArrayVec<Ratio<Fixed<N,F>,Fixed<N,F>>,2>{
	if a1==Fixed::<N,F>::ZERO{
		ArrayVec::new_const()
	}else{
		ArrayVec::from_iter([Ratio::new(-a0,a1)])
	}
}