Add checked arithmetic for / (#222)

This also changes the implementation of `/` for `Fixed`.
`/` (`checked_fdiv`) throws `DivideError` for division by zero and `OverflowError` for overflow.

src/FixedPointNumbers.jl

@@ -38,7 +38,10 @@ export
 # Functions
     scaledual,
     wrapping_neg, wrapping_abs, wrapping_add, wrapping_sub, wrapping_mul,
-    saturating_neg, saturating_abs, saturating_add, saturating_sub, saturating_mul
+    wrapping_fdiv,
+    saturating_neg, saturating_abs, saturating_add, saturating_sub, saturating_mul,
+    saturating_fdiv,
+    checked_fdiv
 
 include("utilities.jl")
 
@@ -207,6 +210,10 @@ wrapping_abs(x::X) where {X <: FixedPoint} = X(abs(x.i), 0)
 wrapping_add(x::X, y::X) where {X <: FixedPoint} = X(x.i + y.i, 0)
 wrapping_sub(x::X, y::X) where {X <: FixedPoint} = X(x.i - y.i, 0)
 wrapping_mul(x::X, y::X) where {X <: FixedPoint} = (float(x) * float(y)) % X
+function wrapping_fdiv(x::X, y::X) where {X <: FixedPoint}
+    z = floattype(X)(x.i) / floattype(X)(y.i)
+    isfinite(z) ? z % X : zero(X)
+end
 
 # saturating arithmetic
 saturating_neg(x::X) where {X <: FixedPoint} = X(~min(x.i - true, x.i), 0)
@@ -225,6 +232,9 @@ saturating_sub(x::X, y::X) where {X <: FixedPoint{<:Unsigned}} = X(x.i - min(x.i
 
 saturating_mul(x::X, y::X) where {X <: FixedPoint} = clamp(float(x) * float(y), X)
 
+saturating_fdiv(x::X, y::X) where {X <: FixedPoint} =
+    clamp(floattype(X)(x.i) / floattype(X)(y.i), X)
+
 # checked arithmetic
 checked_neg(x::X) where {X <: FixedPoint} = checked_sub(zero(X), x)
 function checked_abs(x::X) where {X <: FixedPoint}
@@ -248,6 +258,16 @@ function checked_mul(x::X, y::X) where {X <: FixedPoint}
     typemin(X) - eps(X)/2 <= z < typemax(X) + eps(X)/2 || throw_overflowerror(:*, x, y)
     z % X
 end
+function checked_fdiv(x::X, y::X) where {T, X <: FixedPoint{T}}
+    y === zero(X) && throw(DivideError())
+    z = floattype(X)(x.i) / floattype(X)(y.i)
+    if T <: Unsigned
+        z < typemax(X) + eps(X)/2 || throw_overflowerror(:/, x, y)
+    else
+        typemin(X) - eps(X)/2 <= z < typemax(X) + eps(X)/2 || throw_overflowerror(:/, x, y)
+    end
+    z % X
+end
 
 # default arithmetic
 const DEFAULT_ARITHMETIC = :wrapping
@@ -264,6 +284,7 @@ for (op, name) in ((:+, :add), (:-, :sub), (:*, :mul))
         $op(x::X, y::X) where {X <: FixedPoint} = $f(x, y)
     end
 end
+/(x::X, y::X) where {X <: FixedPoint} = checked_fdiv(x, y) # force checked arithmetic
 
 
 function minmax(x::X, y::X) where {X <: FixedPoint}

src/fixed.jl

@@ -179,7 +179,6 @@ function mul_with_rounding(x::F, y::F, ::RoundingMode{:Down}) where
     F((widemul(x.i, y.i) >> f) % T, 0)
 end
 
-/(x::Fixed{T,f}, y::Fixed{T,f}) where {T,f} = Fixed{T,f}(div(convert(widen(T), x.i) << f, y.i), 0)
 
 function trunc(x::Fixed{T,f}) where {T, f}
     f == 0 && return x

src/normed.jl

@@ -291,7 +291,6 @@ end
 # Override the default arithmetic with `checked` for backward compatibility
 *(x::N, y::N) where {N <: Normed} = checked_mul(x, y)
 
-/(x::T, y::T) where {T <: Normed} = convert(T,convert(floattype(T), x)/convert(floattype(T), y))
 
 # Functions
 trunc(x::N) where {N <: Normed} = floor(x)

test/common.jl

@@ -222,6 +222,18 @@ function test_mul(TX::Type)
     end
 end
 
+function test_fdiv(TX::Type)
+    for X in target(TX, :i8; ex = :thin)
+        xys = xypairs(X)
+        fdiv(x, y) = oftype(float(x), big(x) / big(y))
+        fdivz(x, y) = y === zero(y) ? float(y) : fdiv(x, y)
+        @test all(((x, y),) -> wrapping_fdiv(x, y) === fdivz(x, y) % X, xys)
+        @test all(((x, y),) -> saturating_fdiv(x, y) === clamp(fdiv(x, y), X), xys)
+        @test all(((x, y),) -> !(typemin(X) <= fdiv(x, y) <= typemax(X)) ||
+                               wrapping_fdiv(x, y) === checked_fdiv(x, y), xys)
+    end
+end
+
 function test_isapprox(TX::Type)
     @testset "approx $X" for X in target(TX, :i8, :i16; ex = :light)
         xs = typemin(X):eps(X):typemax(X)-eps(X)

test/fixed.jl

@@ -377,6 +377,31 @@ end
     FixedPointNumbers.mul_with_rounding(1.5Q6f1, -0.5Q6f1, RoundDown) === -1.0Q6f1
 end
 
+@testset "fdiv" begin
+    for F in target(Fixed; ex = :thin)
+        @test   wrapping_fdiv(typemax(F), -typemax(F)) === F(-1)
+        @test saturating_fdiv(typemax(F), -typemax(F)) === F(-1)
+        @test    checked_fdiv(typemax(F), -typemax(F)) === F(-1)
+
+        @test   wrapping_fdiv(zero(F), typemin(F)) === zero(F)
+        @test saturating_fdiv(zero(F), typemin(F)) === zero(F)
+        @test    checked_fdiv(zero(F), typemin(F)) === zero(F)
+
+        @test   wrapping_fdiv(typemin(F), F(-1)) === wrapping_neg(typemin(F))
+        @test saturating_fdiv(typemin(F), F(-1)) === typemax(F)
+        @test_throws OverflowError checked_fdiv(typemin(F), F(-1))
+
+        @test   wrapping_fdiv(zero(F), zero(F)) === zero(F)
+        @test saturating_fdiv(zero(F), zero(F)) === zero(F)
+        @test_throws DivideError checked_fdiv(zero(F), zero(F))
+
+        @test   wrapping_fdiv(-eps(F), zero(F)) === zero(F)
+        @test saturating_fdiv(-eps(F), zero(F)) === typemin(F)
+        @test_throws DivideError checked_fdiv(-eps(F), zero(F))
+    end
+    test_fdiv(Fixed)
+end
+
 @testset "rounding" begin
     for sym in (:i8, :i16, :i32, :i64)
         T = symbol_to_inttype(Fixed, sym)

test/normed.jl

@@ -380,6 +380,31 @@ end
     test_mul(Normed)
 end
 
+@testset "fdiv" begin
+    for N in target(Normed; ex = :thin)
+        @test   wrapping_fdiv(typemax(N), typemax(N)) === one(N)
+        @test saturating_fdiv(typemax(N), typemax(N)) === one(N)
+        @test    checked_fdiv(typemax(N), typemax(N)) === one(N)
+
+        @test   wrapping_fdiv(zero(N), eps(N)) === zero(N)
+        @test saturating_fdiv(zero(N), eps(N)) === zero(N)
+        @test    checked_fdiv(zero(N), eps(N)) === zero(N)
+
+        @test   wrapping_fdiv(typemax(N), eps(N)) === (floattype(N))(typemax(rawtype(N))) % N
+        @test saturating_fdiv(typemax(N), eps(N)) === typemax(N)
+        @test_throws OverflowError checked_fdiv(typemax(N), eps(N))
+
+        @test   wrapping_fdiv(zero(N), zero(N)) === zero(N)
+        @test saturating_fdiv(zero(N), zero(N)) === zero(N)
+        @test_throws DivideError checked_fdiv(zero(N), zero(N))
+
+        @test   wrapping_fdiv(eps(N), zero(N)) === zero(N)
+        @test saturating_fdiv(eps(N), zero(N)) === typemax(N)
+        @test_throws DivideError checked_fdiv(eps(N), zero(N))
+    end
+    test_fdiv(Normed)
+end
+
 @testset "div/fld1" begin
     @test div(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == fld(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == 8
     @test div(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == fld(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == 7