Avoid type promotions due to hard-coded tolerances (#438)

* Avoid type promotions due to hard-coded tolerances

...in the `AlefieldPotraShi` solver.

* Fix a unit handling problem

src/Bracketing/alefeld_potra_shi.jl

@@ -92,8 +92,8 @@ function update_state(
     options,
     l=NullTracks(),
 ) where {T,S}
-    μ, λ = 0.5, 0.7
     atol, rtol = options.xabstol, options.xreltol
+    μ, λ = oftype(rtol, 0.5), oftype(rtol, 0.7)
     tols = (; λ=λ, atol=atol, rtol=rtol)
 
     a::T, b::T, d::T, ee::T = o.xn0, o.xn1, o.d, o.ee
@@ -187,7 +187,7 @@ struct A2425{K} <: AbstractAlefeldPotraShi end
 function calculateΔ(::A2425{K}, F::Callable_Function, c₀::T, ps) where {K,T}
     a, b, d, ee = ps.a, ps.b, ps.d, ps.ee
     fa, fb, fd, fee = ps.fa, ps.fb, ps.fd, ps.fee
-    tols = (λ=0.7, atol=ps.atol, rtol=ps.rtol)
+    tols = (λ=oftype(ps.rtol, 0.7), atol=ps.atol, rtol=ps.rtol)
 
     c = a
     for k in 1:K
@@ -236,7 +236,7 @@ fncalls_per_step(::A57{K}) where {K} = K - 1
 function calculateΔ(::A57{K}, F::Callable_Function, c₀::T, ps) where {K,T}
     a, b, d, ee = ps.a, ps.b, ps.d, ps.ee
     fa, fb, fd, fee = ps.fa, ps.fb, ps.fd, ps.fee
-    tols = (λ=0.7, atol=ps.atol, rtol=ps.rtol)
+    tols = (λ=oftype(ps.rtol, 0.7), atol=ps.atol, rtol=ps.rtol)
     c, fc = a, fa
 
     for k in 1:K

src/convergence.jl

@@ -205,7 +205,7 @@ function is_small_Δx(
     state::AbstractUnivariateZeroState,
     options,
 )
-    δ = abs(state.xn1 - state.xn0)
+    δ = _unitless(abs(state.xn1 - state.xn0))
     δₐ, δᵣ = options.xabstol, options.xreltol
     Δₓ = max(_unitless(δₐ), _unitless(abs(state.xn1)) * δᵣ)
     Δₓ = sqrt(sqrt(sqrt((abs(_unitless(Δₓ)))))) # faster than x^(1/8)

test/test_composable.jl

@@ -24,17 +24,19 @@ using ForwardDiff
     @testset "find zero(s) with Unitful" begin
         s = u"s"
         m = u"m"
-        g = 9.8 * m / s^2
+        g = (9 + 8//10) * m / s^2
         v0 = 10m / s
         y0 = 16m
         y(t) = -g * t^2 + v0 * t + y0
 
         for order in orders
             @test find_zero(y, 1.8s, order) ≈ 1.886053370668014s
+            @test find_zero(y, 1.8f0s, order) isa typeof(1.88f0s)
         end
 
         for M in [Roots.Bisection(), Roots.A42(), Roots.AlefeldPotraShi()]
             @test find_zero(y, (1.8s, 1.9s), M) ≈ 1.886053370668014s
+            @test find_zero(y, (1.8f0s, 1.9f0s), M) isa typeof(1.88f0s)
         end
 
         xrts = find_zeros(y, 0s, 10s)
@@ -44,6 +46,10 @@ using ForwardDiff
         # issue #434
         xzs1 = find_zeros(x -> cos(x / 1u"m"), -1.6u"m", 2u"m")
         @test length(xzs1) == 2 && maximum(xzs1) ≈ 1.5707963267948966 * u"m"
+
+        FX = ZeroProblem(y, (0f0s, 2f0s))
+        prob = Roots.init(FX, Roots.AlefeldPotraShi())
+        @test Roots.is_small_Δx(prob.M, prob.state, prob.options) isa Bool  # does not throw
     end
 
     # Polynomials