From 86406479a8ae8b0eb704395ad07d910678580016 Mon Sep 17 00:00:00 2001
From: James Chen <100195398+jamiecjx@users.noreply.github.com>
Date: Sat, 9 Sep 2023 14:55:03 +0100
Subject: [PATCH] tweak mu to fix #30 (#31)

* tweak mu to fix #30

* unit test for memory
---
 src/recurrence.jl       | 2 +-
 test/test_recurrence.jl | 6 ++++++
 2 files changed, 7 insertions(+), 1 deletion(-)

diff --git a/src/recurrence.jl b/src/recurrence.jl
index 474f8e7..7085a6d 100644
--- a/src/recurrence.jl
+++ b/src/recurrence.jl
@@ -118,7 +118,7 @@ function backwardrecurrence!(K, A, B, C, z, nN::AbstractUnitRange, j...)
             μ = min(abs(data[k,j...]/data[k-1,j...]), abs(data[k-1,j...]/data[k-2,j...]))
             # data[k] * μ^M ≤ ε
             #  M ≥ log(ε/data[k])/log(μ)
-            N = ceil(Int, max(2N, min(maxiterations, log(eps(real(T))/100)/log(μ))))
+            N = ceil(Int, max(2N, min(maxiterations, log(eps(real(T))/100)/log(μ+eps(real(T))))))
             _growdata!(K, N, j...)
             resize!(u, N)
             data = K.data
diff --git a/test/test_recurrence.jl b/test/test_recurrence.jl
index 1fdc521..d9fe361 100644
--- a/test/test_recurrence.jl
+++ b/test/test_recurrence.jl
@@ -22,6 +22,12 @@ using ClassicalOrthogonalPolynomials: recurrencecoefficients
             @test r[1:1000] ≈ ξ.^(1:1000)
             @test r[10_000] ≈ ξ.^(10_000) atol=3E-10
         end
+
+        for z in (0.2567881003580743 - 0.33437737333561895im)
+            ξ = π * (z - √(z-1) * √(z+1))
+            r = RecurrenceArray(z, recurrencecoefficients(U), [ξ,2z*ξ-π])
+            @test sizeof(r.data) < 1000_000
+        end
     end
 
     @testset "RecurrenceMatrix" begin