Backport ITP bugfixes from DiffEqBase in high precision contexts

src/itp.jl

@@ -78,9 +78,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     k1 = alg.k1
     k2 = alg.k2
     n0 = alg.n0
-    n_h = ceil(log2((right - left) / (2 * ϵ)))
+    n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
     mid = (left + right) / 2
-    x_f = (fr * left - fl * right) / (fr - fl)
+    x_f = left + (right - left) * (fl/(fl - fr))
     xt = left
     xp = left
     r = zero(left) #minmax radius
@@ -89,12 +89,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     ϵ_s = ϵ * 2^(n_h + n0)
     i = 0 #iteration
     while i <= maxiters
-        #mid = (left + right) / 2
-        r = ϵ_s - ((right - left) / 2)
-        δ = k1 * ((right - left)^k2)
+        span = abs(right - left)
+        r = ϵ_s - (span / 2)
+        δ = k1 * (span^k2)
 
         ## Interpolation step ##
-        x_f = (fr * left - fl * right) / (fr - fl)
+        x_f = left + (right - left) * (fl/(fl - fr))
 
         ## Truncation step ##
         σ = sign(mid - x_f)
@@ -112,6 +112,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
         end
 
         ## Update ##
+        tmin, tmax = minmax(left, right)
+        xp >= tmax && (xp = prevfloat(tmax))
+        xp <= tmin && (xp = nextfloat(tmin))
         yp = f(xp)
         yps = yp * sign(fr)
         if yps > 0
@@ -121,16 +124,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             left = xp
             fl = yp
         else
-            left = xp
-            right = xp
+            return SciMLBase.build_solution(prob, alg, xp, yps;
+                                            retcode = ReturnCode.Success, left = xp,
+                                            right = xp)
         end
         i += 1
         mid = (left + right) / 2
         ϵ_s /= 2
 
-        if (right - left < 2 * ϵ)
-            return SciMLBase.build_solution(prob, alg, mid, f(mid);
-                retcode = ReturnCode.Success, left = left,
+        if nextfloat_tdir(left, prob.tspan...) == right
+            return SciMLBase.build_solution(prob, alg, left, fl;
+                retcode = ReturnCode.FloatingPointLimit, left = left,
                 right = right)
         end
     end

test/basictests.jl

@@ -540,18 +540,19 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
     @test abs.(sol.u) ≈ sqrt.(p)
 end
 
-# Flipped signs test
+# Flipped signs & reversed tspan test for bracketing algorithms
 f1(u, p) = u * u - p
 f2(u, p) = p - u * u
 
-for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
-    alg = Alg()
+for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
     for p in 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)
+        inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+        inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+        @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
     end
 end