allow starting forwardrecurrence! from a shifted start for adaptive (#216)

* allow starting forwardrecurrence! from a shifted start for adaptive

* Update clenshaw.jl

Author: dlfivefifty

Project.toml

@@ -1,6 +1,6 @@
 name = "FastTransforms"
 uuid = "057dd010-8810-581a-b7be-e3fc3b93f78c"
-version = "0.15.2"
+version = "0.15.3"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/clenshaw.jl

@@ -29,7 +29,14 @@ function _forwardrecurrence!(v::AbstractVector, A::AbstractVector, B::AbstractVe
     v[1] = p0
     N == 1 && return v
     v[2] = p1
-    @inbounds for n = 2:N-1
+    _forwardrecurrence!(v, A, B, C, x, 2:N)
+end
+
+function _forwardrecurrence!(v::AbstractVector, A::AbstractVector, B::AbstractVector, C::AbstractVector, x, kr::AbstractUnitRange)
+    n₀, N = first(kr), last(kr)
+    @boundscheck N > length(v) && throw(BoundsError(v, N))
+    p0, p1 = v[n₀-1], v[n₀]
+    @inbounds for n = n₀:N-1
         p1,p0 = _forwardrecurrence_next(n, A, B, C, x, p0, p1),p1
         v[n+1] = p1
     end
@@ -38,6 +45,7 @@ end
 
 
 
+
 forwardrecurrence(N::Integer, A::AbstractVector, B::AbstractVector, C::AbstractVector, x) =
     forwardrecurrence!(Vector{promote_type(eltype(A),eltype(B),eltype(C),typeof(x))}(undef, N), A, B, C, x)