use crate::fixed::Fixed;
use crate::ratio::Ratio;

use typenum::{Sum,Unsigned};
use arrayvec::ArrayVec;
use std::cmp::Ordering;
macro_rules! impl_zeroes{
	($n:expr)=>{
		impl<F> Fixed<$n,F>
			where
				F:Unsigned+std::ops::Add,
				<F as std::ops::Add>::Output:Unsigned,
		{
			paste::item!{
			#[inline]
			pub fn zeroes2(a0:Self,a1:Self,a2:Self)->ArrayVec<Ratio<Self,Self>,2>{
				let a2pos=match a2.cmp(&Self::ZERO){
					Ordering::Greater=>true,
					Ordering::Equal=>return ArrayVec::from_iter($crate::zeroes::zeroes1(a0,a1).into_iter()),
					Ordering::Less=>true,
				};
				let radicand=a1.[<wide_mul_ $n _ $n>](a1)-a2.[<wide_mul_ $n _ $n>](a0)*4;
				match radicand.cmp(&Fixed::<{$n*2},Sum<F,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,Self::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(a0:Self,a1:Self)->ArrayVec<Ratio<Self,Self>,1>{
				if a1==Self::ZERO{
					ArrayVec::new_const()
				}else{
					ArrayVec::from_iter([Ratio::new(-a0,a1)])
				}
			}
		}
	};
}
impl_zeroes!(1);
impl_zeroes!(2);
impl_zeroes!(3);
impl_zeroes!(4);
impl_zeroes!(5);
impl_zeroes!(6);
impl_zeroes!(7);
impl_zeroes!(8);