59 lines
1.9 KiB
Rust
59 lines
1.9 KiB
Rust
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use crate::fixed::Fixed;
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use crate::ratio::Ratio;
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use typenum::{Sum,Unsigned};
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use arrayvec::ArrayVec;
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use std::cmp::Ordering;
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macro_rules! impl_zeroes{
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($n:expr)=>{
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impl<F> Fixed<$n,F>
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where
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F:Unsigned+std::ops::Add,
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<F as std::ops::Add>::Output:Unsigned,
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{
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#[inline]
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pub fn zeroes2(a0:Self,a1:Self,a2:Self)->ArrayVec<Ratio<Self,Self>,2>{
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let a2pos=match a2.cmp(&Self::ZERO){
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Ordering::Greater=>true,
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Ordering::Equal=>return ArrayVec::from_iter($crate::zeroes::zeroes1(a0,a1).into_iter()),
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Ordering::Less=>true,
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};
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let radicand=$crate::traits::WideMul::wide_mul(a1,a1)-$crate::traits::WideMul::wide_mul(a2,a0)*4;
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match radicand.cmp(&Fixed::<{$n*2},Sum<F,F>>::ZERO){
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Ordering::Greater=>{
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//start with f64 sqrt
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//failure case: 2^63 < sqrt(2^127)
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let planar_radicand=radicand.sqrt();
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//TODO: one or two newtons
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//sort roots ascending and avoid taking the difference of large numbers
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match (a2pos,Self::ZERO<a1){
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(true, true )=>[Ratio::new(-a1-planar_radicand,a2*2),Ratio::new(a0*2,-a1-planar_radicand)].into(),
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(true, false)=>[Ratio::new(a0*2,-a1+planar_radicand),Ratio::new(-a1+planar_radicand,a2*2)].into(),
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(false,true )=>[Ratio::new(a0*2,-a1-planar_radicand),Ratio::new(-a1-planar_radicand,a2*2)].into(),
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(false,false)=>[Ratio::new(-a1+planar_radicand,a2*2),Ratio::new(a0*2,-a1+planar_radicand)].into(),
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}
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},
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Ordering::Equal=>ArrayVec::from_iter([Ratio::new(a1,a2*-2)]),
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Ordering::Less=>ArrayVec::new_const(),
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}
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}
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#[inline]
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pub fn zeroes1(a0:Self,a1:Self)->ArrayVec<Ratio<Self,Self>,1>{
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if a1==Self::ZERO{
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ArrayVec::new_const()
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}else{
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ArrayVec::from_iter([Ratio::new(-a0,a1)])
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}
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}
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}
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};
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}
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impl_zeroes!(1);
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impl_zeroes!(2);
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impl_zeroes!(3);
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impl_zeroes!(4);
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impl_zeroes!(5);
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impl_zeroes!(6);
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impl_zeroes!(7);
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impl_zeroes!(8);
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