Add mul_with_rounding for Fixed

This provides the multiplication compatible with v0.8 and earlier as `mul_with_rounding(x, y, RoundNearestTiesUp)`.
This also provides the rounding-down version `mul_with_rounding(x, y, RoundDown)`.
The function is informative and not exported.

Author: kimikage

src/fixed.jl

@@ -152,10 +152,18 @@ function checked_mul(x::F, y::F) where {T <: Union{Int8,Int16,Int32,Int64}, f, F
     F(div_2f(z, Val(Int(f))) % T, 0)
 end
 
-# with truncation:
-#*(x::Fixed{T,f}, y::Fixed{T,f}) = Fixed{T,f}(Base.widemul(x.i,y.i)>>f,0)
-# with rounding up:
-#*(x::Fixed{T,f}, y::Fixed{T,f}) where {T,f} = Fixed{T,f}((Base.widemul(x.i,y.i) + (one(widen(T)) << (f-1)))>>f,0)
+function mul_with_rounding(x::F, y::F, ::RoundingMode{:Nearest}) where {F <: Fixed}
+    wrapping_mul(x, y)
+end
+function mul_with_rounding(x::F, y::F, ::RoundingMode{:NearestTiesUp}) where
+                          {T <: Union{Int8,Int16,Int32,Int64}, f, F <: Fixed{T, f}}
+    z = widemul(x.i, y.i)
+    F(((z + (oftype(z, 1) << f >>> 1)) >> f) % T, 0)
+end
+function mul_with_rounding(x::F, y::F, ::RoundingMode{:Down}) where
+                          {T <: Union{Int8,Int16,Int32,Int64}, f, F <: Fixed{T, f}}
+    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)
 

test/fixed.jl

@@ -389,6 +389,13 @@ end
         @test all(((x, y),) -> !(typemin(F) <= fmul(x, y) <= typemax(F)) ||
                                wrapping_mul(x, y) === checked_mul(x, y), xys)
     end
+
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1,  0.5Q6f1, RoundNearest) ===  1.0Q6f1
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1, -0.5Q6f1, RoundNearest) === -1.0Q6f1
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1,  0.5Q6f1, RoundNearestTiesUp) ===  1.0Q6f1
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1, -0.5Q6f1, RoundNearestTiesUp) === -0.5Q6f1
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1,  0.5Q6f1, RoundDown) ===  0.5Q6f1
+    FixedPointNumbers.mul_with_rounding(1.5Q6f1, -0.5Q6f1, RoundDown) === -1.0Q6f1
 end
 
 @testset "rounding" begin