Merge pull request #258 from JuliaIntervals/type_stability

Type stability for some functions

src/intervals/arithmetic.jl

@@ -162,8 +162,8 @@ function inv(a::Interval{T}) where T<:Real
     isempty(a) && return emptyinterval(a)
 
     if zero(T) ∈ a
-        a.lo < zero(T) == a.hi && return @round(-Inf, inv(a.lo))
-        a.lo == zero(T) < a.hi && return @round(inv(a.hi), Inf)
+        a.lo < zero(T) == a.hi && return @round(T(-Inf), inv(a.lo))
+        a.lo == zero(T) < a.hi && return @round(inv(a.hi), T(Inf))
         a.lo < zero(T) < a.hi && return entireinterval(T)
         a == zero(a) && return emptyinterval(T)
     end
@@ -195,14 +195,14 @@ function /(a::Interval{T}, b::Interval{T}) where T<:Real
 
         if iszero(b.lo)
 
-            a.lo >= zero(T) && return @round(a.lo/b.hi, Inf)
-            a.hi <= zero(T) && return @round(-Inf, a.hi/b.hi)
+            a.lo >= zero(T) && return @round(a.lo/b.hi, T(Inf))
+            a.hi <= zero(T) && return @round(T(-Inf), a.hi/b.hi)
             return entireinterval(S)
 
         elseif iszero(b.hi)
 
-            a.lo >= zero(T) && return @round(-Inf, a.lo/b.lo)
-            a.hi <= zero(T) && return @round(a.hi/b.lo, Inf)
+            a.lo >= zero(T) && return @round(T(-Inf), a.lo/b.lo)
+            a.hi <= zero(T) && return @round(a.hi/b.lo, T(Inf))
             return entireinterval(S)
 
         else
@@ -218,10 +218,10 @@ function extended_div(a::Interval{T}, b::Interval{T}) where T<:Real
     S = typeof(a.lo / b.lo)
     if 0 < b.hi && 0 > b.lo && 0 ∉ a
         if a.hi < 0
-            return (Interval(-Inf, a.hi / b.hi), Interval(a.hi / b.lo, Inf))
+            return (Interval(T(-Inf), a.hi / b.hi), Interval(a.hi / b.lo, T(Inf)))
 
         elseif a.lo > 0
-            return (Interval(-Inf, a.lo / b.lo), Interval(a.lo / b.hi, Inf))
+            return (Interval(T(-Inf), a.lo / b.lo), Interval(a.lo / b.hi, T(Inf)))
 
         end
     elseif 0 ∈ a && 0 ∈ b
@@ -394,7 +394,7 @@ The default is the true midpoint at `α = 0.5`.
 
 Assumes 0 ≤ α ≤ 1.
 
-Warning: if the parameter `α = 0.5` is explicitely set, the behavior differs
+Warning: if the parameter `α = 0.5` is explicitly set, the behavior differs
 from the default case if the provided `Interval` is not finite, since when
 `α` is provided `mid` simply replaces `+∞` (respectively `-∞`) by `prevfloat(+∞)`
 (respecively `nextfloat(-∞)`) for the computation of the intermediate point.
@@ -403,16 +403,18 @@ function mid(a::Interval{T}, α) where T
 
     isempty(a) && return convert(T, NaN)
 
-    lo = (a.lo == -∞ ? nextfloat(-∞) : a.lo)
-    hi = (a.hi == +∞ ? prevfloat(+∞) : a.hi)
+    lo = (a.lo == -∞ ? nextfloat(T(-∞)) : a.lo)
+    hi = (a.hi == +∞ ? prevfloat(T(+∞)) : a.hi)
 
-    midpoint = α * (hi - lo) + lo
+    β = convert(T, α)
+
+    midpoint = β * (hi - lo) + lo
     isfinite(midpoint) && return midpoint
     #= Fallback in case of overflow: hi - lo == +∞.
        This case can not be the default one as it does not pass several
        IEEE1788-2015 tests for small floats.
     =#
-    return (1-α) * lo + α * hi
+    return (1 - β) * lo + β * hi
 end
 
 """
@@ -432,13 +434,13 @@ function mid(a::Interval{T}) where T
     a.lo == -∞ && return nextfloat(a.lo)
     a.hi == +∞ && return prevfloat(a.hi)
 
-    midpoint = 0.5 * (a.lo + a.hi)
+    midpoint = (a.lo + a.hi) / 2
     isfinite(midpoint) && return midpoint
     #= Fallback in case of overflow: a.hi + a.lo == +∞ or a.hi + a.lo == -∞.
        This case can not be the default one as it does not pass several
        IEEE1788-2015 tests for small floats.
     =#
-    return 0.5 * a.lo + 0.5 * a.hi
+    return a.lo / 2 + a.hi / 2
 end
 
 mid(a::Interval{Rational{T}}) where T = (1//2) * (a.lo + a.hi)

src/intervals/rounding_macros.jl

@@ -22,7 +22,7 @@ function round_expr(ex::Expr, rounding_mode::RoundingMode)
             return :( $(esc(op))( $(esc(ex.args[2])), $(esc(ex.args[3])), $rounding_mode) )
 
         else  # unary operator
-            return :( $op($(esc(ex.args[2])), $rounding_mode ) )
+            return :( $(esc(op))($(esc(ex.args[2])), $rounding_mode ) )
         end
     else
         return ex

test/interval_tests/consistency.jl

@@ -388,4 +388,26 @@ setprecision(Interval, Float64)
 
     end
 
+    @testset "Type stability" begin
+        for T in (Float32, Float64, BigFloat)
+
+            xs = [3..4, 0..4, 0..0, -4..0, -4..4, -Inf..4, 4..Inf, -Inf..Inf]
+
+            for x in xs
+                for y in xs
+                    xx = Interval{T}(x)
+                    yy = Interval{T}(y)
+
+                    for op in (+, -, *, /, atan)
+                        @inferred op(x, y)
+                    end
+                end
+
+                for op in (sin, cos, exp, log, tan, abs, mid, diam)
+                    @inferred op(x)
+                end
+            end
+        end
+    end
+
 end