48 lines
1.8 KiB
Rust
48 lines
1.8 KiB
Rust
//find roots of polynomials
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use arrayvec::ArrayVec;
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use std::cmp::Ordering;
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use deferred_division::ratio::Ratio;
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use fixed_wide::typenum::Unsigned;
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use fixed_wide::fixed::Fixed;
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use fixed_wide::wide::WideMul;
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#[inline]
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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>
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where
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Fixed<N,F>:WideMul,
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<Fixed<N,F> as WideMul>::Output:std::ops::Mul<i64>,
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<Fixed<N,F> as WideMul>::Output:std::ops::Sub<<<Fixed<N,F> as WideMul>::Output as std::ops::Mul<i64>>::Output>
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{
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let a2pos=match a2.cmp(&Fixed::<N,F>::ZERO){
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Ordering::Greater=>true,
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Ordering::Equal=>return zeroes1(a0,a1),
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Ordering::Less=>true,
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};
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let radicand=a1.wide_mul(a1)-a2.wide_mul(a0)*4;
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match radicand.cmp(&Fixed::<N,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,Fixed::<N,F>::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<const N:usize,F:Unsigned>(a0:Fixed<N,F>,a1:Fixed<N,F>)->ArrayVec<Ratio<Fixed<N,F>,Fixed<N,F>>,2>{
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if a1==Fixed::<N,F>::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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