From de521312d549f5876afdd30d59cf25e818d99cc3 Mon Sep 17 00:00:00 2001
From: Neven Sajko <s@purelymail.com>
Date: Wed, 12 Oct 2022 21:36:05 +0200
Subject: [PATCH] prevent run-time dispatch in roots(::AbstractVector)
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findlast does not necessarily return an Integer, it may also return
Nothing, depending on the value of its arguments.

The latter case needs to be handled to prevent run-time dispatch for
the slicing operation.

Additionally, the truncated coefficients slice is now a view
instead of a copy. This should make things slightly more performant,
apart from making the code simpler.

JET warnings before this commit:

```
julia> @report_opt PolynomialRoots.roots(rand(5))
═════ 1 possible error found ═════
┌ @ /home/nsajko/.julia/packages/PolynomialRoots/1iZQh/src/PolynomialRoots.jl:610 PolynomialRoots.:(var"#roots#2")(PolynomialRoots.NaN, false, #self#, poly)
│┌ @ /home/nsajko/.julia/packages/PolynomialRoots/1iZQh/src/PolynomialRoots.jl:617 1 PolynomialRoots.:(:) %28
││ runtime dispatch detected: (1 PolynomialRoots.:(:) %28::Union{Nothing, Int64})::UnitRange{Int64}
│└─────────────────────────────────────────────────────────────────────────────────
```

After this commit:
```
julia> using JET, PolynomialRoots

julia> PolynomialRoots.roots(rand(5))
4-element Vector{ComplexF64}:
   -31.46526111710419 - 1.6981590262940853e-16im
 -0.13020601478750077 - 0.8162149121849699im
 -0.13020601478750077 + 0.81621491218497im
 -0.48806837350069937 + 2.350988701644575e-38im

julia> @report_opt PolynomialRoots.roots(rand(5))
No errors detected
```
---
 src/PolynomialRoots.jl | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/src/PolynomialRoots.jl b/src/PolynomialRoots.jl
index 1722992..a1e4d87 100644
--- a/src/PolynomialRoots.jl
+++ b/src/PolynomialRoots.jl
@@ -607,15 +607,20 @@ function roots(poly::AbstractVector{<:Number}, roots::AbstractVector{<:Number};
            epsilon, degree, polish)
 end
 
+# Returns a view into the polynomial that excludes any trailing zero
+# coefficients.
+#
+# Errors if the coefficients are all zero.
+function normalized_poly_coefs(poly::AbstractVector{<:Number})
+    l = findlast(!iszero, poly)
+    isnothing(l) && error("zero polynomial")
+    @view poly[begin:l]
+end
+
 function roots(poly::AbstractVector{N}; epsilon::AbstractFloat=NaN,
                polish::Bool=false) where {N<:Number}
     # Before starting, truncate the polynomial if it has zeros in the trailing elements
-    last_nz = findlast(!iszero, poly)
-    if lastindex(poly) == last_nz
-        _poly = poly
-    else
-        _poly = poly[1:last_nz]
-    end
+    _poly = normalized_poly_coefs(poly)
     degree = length(_poly) - 1
     roots!(zeros(Complex{real(float(N))}, degree), float.(complex(_poly)),
            epsilon, degree, polish)