Fix ITP for problems with flipped sign

src/itp.jl

@@ -113,10 +113,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
 
         ## Update ##
         yp = f(xp)
-        if yp > 0
+        yps = yp * sign(fr)
+        if yps > 0
             right = xp
             fr = yp
-        elseif yp < 0
+        elseif yps < 0
             left = xp
             fl = yp
         else

test/basictests.jl

@@ -539,3 +539,19 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
     sol = solve(probN, alg)
     @test abs.(sol.u) ≈ sqrt.(p)
 end
+
+# Flipped signs test
+f1(u, p) = u * u - p 
+f2(u, p) = p - u * u
+
+for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
+    alg = Alg()
+    for p ∈ 1:4
+        inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+        inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+        sol = solve(inp1, alg)
+        @test abs.(sol.u) ≈ sqrt.(p)
+        sol = solve(inp2, alg)
+        @test abs.(sol.u) ≈ sqrt.(p)
+    end
+end