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

use arrayvec::ArrayVec;
use std::cmp::Ordering;
macro_rules! impl_zeroes{
	($n:expr)=>{
		impl Fixed<$n,{$n*32}>{
			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(Self::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},{$n*2*32}>::ZERO){
					Ordering::Greater=>{
						//start with f64 sqrt
						//failure case: 2^63 < sqrt(2^127)
						let planar_radicand_wide=radicand.sqrt();
						//lazy hack
						let planar_radicand=Self::from_bits(bnum::cast::As::as_(planar_radicand_wide.bits.shr($n*32)));
						//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);
//sqrt doubles twice!
//impl_zeroes!(5);
//impl_zeroes!(6);
//impl_zeroes!(7);
//impl_zeroes!(8);