Round from zero support for non-BigFloats (#41246)

Co-authored-by: Steven G. Johnson <stevenj@alum.mit.edu>

Co-authored-by: Steven G. Johnson <stevenj@mit.edu>

Co-authored-by: Mosè Giordano <giordano@users.noreply.github.com>

Co-authored-by: Dilum Aluthge <dilum@aluthge.com>

NEWS.md

@@ -44,6 +44,7 @@ Library changes
   now be called on a dictionary or set shared by arbitrary tasks provided that there are no
   tasks mutating the dictionary or set ([#44534]).
 * Predicate function negation `!f` now returns a composed function `(!) ∘ f` instead of an anonymous function ([#44752]).
+* `RoundFromZero` now works for non-`BigFloat` types ([#41246]).
 
 
 Standard library changes

base/div.jl

@@ -17,6 +17,9 @@ without any intermediate rounding.
 
 See also [`fld`](@ref) and [`cld`](@ref), which are special cases of this function.
 
+!!! compat "Julia 1.9"
+    `RoundFromZero` requires at least Julia 1.9.
+
 # Examples:
 ```jldoctest
 julia> div(4, 3, RoundDown) # Matches fld(4, 3)
@@ -33,6 +36,10 @@ julia> div(-5, 2, RoundNearestTiesAway)
 -3
 julia> div(-5, 2, RoundNearestTiesUp)
 -2
+julia> div(4, 3, RoundFromZero)
+2
+julia> div(-4, 3, RoundFromZero)
+-2
 ```
 """
 div(x, y, r::RoundingMode)
@@ -63,6 +70,13 @@ without any intermediate rounding.
   `[0,-y)` otherwise. The result may not be exact if `x` and `y` have the same sign, and
   `abs(x) < abs(y)`. See also [`RoundUp`](@ref).
 
+- if `r == RoundFromZero`, then the result is in the interval `(-y, 0]` if `y` is positive, or
+  `[0, -y)` otherwise. The result may not be exact if `x` and `y` have the same sign, and
+  `abs(x) < abs(y)`. See also [`RoundFromZero`](@ref).
+
+!!! compat "Julia 1.9"
+    `RoundFromZero` requires at least Julia 1.9.
+
 # Examples:
 ```jldoctest
 julia> x = 9; y = 4;
@@ -86,6 +100,10 @@ rem(x, y, ::RoundingMode{:Up}) = mod(x, -y)
 rem(x, y, r::RoundingMode{:Nearest}) = x - y*div(x, y, r)
 rem(x::Integer, y::Integer, r::RoundingMode{:Nearest}) = divrem(x, y, r)[2]
 
+function rem(x, y, ::typeof(RoundFromZero))
+    signbit(x) == signbit(y) ? rem(x, y, RoundUp) : rem(x, y, RoundDown)
+end
+
 """
     fld(x, y)
 
@@ -240,6 +258,10 @@ function divrem(x::Integer, y::Integer, rnd::typeof(RoundNearestTiesUp))
     end
 end
 
+function divrem(x, y, ::typeof(RoundFromZero))
+    signbit(x) == signbit(y) ? divrem(x, y, RoundUp) : divrem(x, y, RoundDown)
+end
+
 """
     fldmod(x, y)
 
@@ -276,12 +298,16 @@ function div(x::Integer, y::Integer, rnd::Union{typeof(RoundNearest),
     divrem(x, y, rnd)[1]
 end
 
+function div(x::Integer, y::Integer, ::typeof(RoundFromZero))
+    signbit(x) == signbit(y) ? div(x, y, RoundUp) : div(x, y, RoundDown)
+end
+
 # For bootstrapping purposes, we define div for integers directly. Provide the
 # generic signature also
 div(a::T, b::T, ::typeof(RoundToZero)) where {T<:Union{BitSigned, BitUnsigned64}} = div(a, b)
 div(a::Bool, b::Bool, r::RoundingMode) = div(a, b)
 # Prevent ambiguities
-for rm in (RoundUp, RoundDown, RoundToZero)
+for rm in (RoundUp, RoundDown, RoundToZero, RoundFromZero)
     @eval div(a::Bool, b::Bool, r::$(typeof(rm))) = div(a, b)
 end
 function div(x::Bool, y::Bool, rnd::Union{typeof(RoundNearest),

base/floatfuncs.jl

@@ -236,6 +236,10 @@ function round(x::T, ::RoundingMode{:NearestTiesUp}) where {T <: AbstractFloat}
     copysign(floor((x + (T(0.25) - eps(T(0.5)))) + (T(0.25) + eps(T(0.5)))), x)
 end
 
+function Base.round(x::AbstractFloat, ::typeof(RoundFromZero))
+    signbit(x) ? round(x, RoundDown) : round(x, RoundUp)
+end
+
 # isapprox: approximate equality of numbers
 """
     isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])

base/rounding.jl

@@ -37,9 +37,13 @@ Currently supported rounding modes are:
 - [`RoundNearestTiesAway`](@ref)
 - [`RoundNearestTiesUp`](@ref)
 - [`RoundToZero`](@ref)
-- [`RoundFromZero`](@ref) ([`BigFloat`](@ref) only)
+- [`RoundFromZero`](@ref)
 - [`RoundUp`](@ref)
 - [`RoundDown`](@ref)
+
+!!! compat "Julia 1.9"
+    `RoundFromZero` requires at least Julia 1.9. Prior versions support
+    `RoundFromZero` for `BigFloat`s only.
 """
 struct RoundingMode{T} end
 
@@ -76,15 +80,18 @@ const RoundDown = RoundingMode{:Down}()
     RoundFromZero
 
 Rounds away from zero.
-This rounding mode may only be used with `T == BigFloat` inputs to [`round`](@ref).
+
+!!! compat "Julia 1.9"
+    `RoundFromZero` requires at least Julia 1.9. Prior versions support
+    `RoundFromZero` for `BigFloat`s only.
 
 # Examples
 ```jldoctest
 julia> BigFloat("1.0000000000000001", 5, RoundFromZero)
 1.06
 ```
 """
-const RoundFromZero = RoundingMode{:FromZero}() # mpfr only
+const RoundFromZero = RoundingMode{:FromZero}()
 
 """
     RoundNearestTiesAway

test/int.jl

@@ -352,25 +352,28 @@ end
 @testset "rounding division" begin
     for x = -100:100
         for y = 1:100
-            for rnd in (RoundNearest, RoundNearestTiesAway, RoundNearestTiesUp)
+            for rnd in (RoundNearest, RoundNearestTiesAway, RoundNearestTiesUp, RoundFromZero)
                 @test div(x,y,rnd) == round(x/y,rnd)
                 @test div(x,-y,rnd) == round(x/-y,rnd)
             end
+            @test divrem(x,y,RoundFromZero) == (div(x,y,RoundFromZero), rem(x,y,RoundFromZero))
+            @test divrem(x,-y,RoundFromZero) == (div(x,-y,RoundFromZero), rem(x,-y,RoundFromZero))
         end
     end
-    for (a, b, nearest, away, up) in (
-            (3, 2, 2, 2, 2),
-            (5, 3, 2, 2, 2),
-            (-3, 2, -2, -2, -1),
-            (5, 2, 2, 3, 3),
-            (-5, 2, -2, -3, -2),
-            (-5, 3, -2, -2, -2),
-            (5, -3, -2, -2, -2))
+    for (a, b, nearest, away, up, from_zero) in (
+            (3, 2, 2, 2, 2, 2),
+            (5, 3, 2, 2, 2, 2),
+            (-3, 2, -2, -2, -1, -2),
+            (5, 2, 2, 3, 3, 3),
+            (-5, 2, -2, -3, -2, -3),
+            (-5, 3, -2, -2, -2, -2),
+            (5, -3, -2, -2, -2, -2))
         for sign in (+1, -1)
             (a, b) = (a*sign, b*sign)
             @test div(a, b, RoundNearest) === nearest
             @test div(a, b, RoundNearestTiesAway) === away
             @test div(a, b, RoundNearestTiesUp) === up
+            @test div(a, b, RoundFromZero) === from_zero
         end
     end
 
@@ -381,7 +384,7 @@ end
     @test div(typemax(Int)-2, typemax(Int), RoundNearest) === 1
 
     # Exhaustively test (U)Int8 to catch any overflow-style issues
-    for r in (RoundNearest, RoundNearestTiesAway, RoundNearestTiesUp)
+    for r in (RoundNearest, RoundNearestTiesAway, RoundNearestTiesUp, RoundFromZero)
         for T in (UInt8, Int8)
             for x in typemin(T):typemax(T)
                 for y in typemin(T):typemax(T)

test/numbers.jl

@@ -2519,29 +2519,34 @@ end
     @test rem(T(1), T(2), RoundNearest) == 1
     @test rem(T(1), T(2), RoundDown)    == 1
     @test rem(T(1), T(2), RoundUp)      == -1
+    @test rem(T(1), T(2), RoundFromZero) == -1
     @test rem(T(1.5), T(2), RoundToZero)  == 1.5
     @test rem(T(1.5), T(2), RoundNearest) == -0.5
     @test rem(T(1.5), T(2), RoundDown)    == 1.5
     @test rem(T(1.5), T(2), RoundUp)      == -0.5
+    @test rem(T(1.5), T(2), RoundFromZero) == -0.5
     @test rem(T(-1), T(2), RoundToZero)  == -1
     @test rem(T(-1), T(2), RoundNearest) == -1
     @test rem(T(-1), T(2), RoundDown)    == 1
     @test rem(T(-1), T(2), RoundUp)      == -1
+    @test rem(T(-1), T(2), RoundFromZero) == 1
     @test rem(T(-1.5), T(2), RoundToZero)  == -1.5
     @test rem(T(-1.5), T(2), RoundNearest) == 0.5
     @test rem(T(-1.5), T(2), RoundDown)    == 0.5
     @test rem(T(-1.5), T(2), RoundUp)      == -1.5
-    for mode in [RoundToZero, RoundNearest, RoundDown, RoundUp]
+    @test rem(T(-1.5), T(2), RoundFromZero) == 0.5
+    for mode in [RoundToZero, RoundNearest, RoundDown, RoundUp, RoundFromZero]
         @test isnan(rem(T(1), T(0), mode))
         @test isnan(rem(T(Inf), T(2), mode))
         @test isnan(rem(T(1), T(NaN), mode))
         # FIXME: The broken case erroneously returns -Inf
-        @test rem(T(4), floatmin(T) * 2, mode) == 0 broken=(T == BigFloat && mode == RoundUp)
+        @test rem(T(4), floatmin(T) * 2, mode) == 0 broken=(T == BigFloat && mode in (RoundUp,RoundFromZero))
     end
     @test isequal(rem(nextfloat(typemin(T)), T(2), RoundToZero),  -0.0)
     @test isequal(rem(nextfloat(typemin(T)), T(2), RoundNearest), -0.0)
-    @test isequal(rem(nextfloat(typemin(T)), T(2), RoundDown),    0.0)
-    @test isequal(rem(nextfloat(typemin(T)), T(2), RoundUp),      0.0)
+    @test isequal(rem(nextfloat(typemin(T)), T(2), RoundDown),     0.0)
+    @test isequal(rem(nextfloat(typemin(T)), T(2), RoundUp),       0.0)
+    @test isequal(rem(nextfloat(typemin(T)), T(2), RoundFromZero), 0.0)
 end
 
 @testset "rem for $T RoundNearest" for T in (Int8, Int16, Int32, Int64, Int128)

test/rounding.jl

@@ -128,6 +128,16 @@ end
             else
                 @test u === r
             end
+
+            r = round(u, RoundFromZero)
+            if isfinite(u)
+                @test isfinite(r)
+                @test isinteger(r)
+                @test signbit(u) ? (r == floor(u)) : (r == ceil(u))
+                @test signbit(u) == signbit(r)
+            else
+                @test u === r
+            end
         end
     end
 end
@@ -171,6 +181,7 @@ end
                 @test round.(y) ≈ t[(i+1+isodd(i>>2))>>2 for i in r]
                 @test broadcast(x -> round(x, RoundNearestTiesAway), y) ≈ t[(i+1+(i>=0))>>2 for i in r]
                 @test broadcast(x -> round(x, RoundNearestTiesUp), y) ≈ t[(i+2)>>2 for i in r]
+                @test broadcast(x -> round(x, RoundFromZero), y) ≈ t[(i+3*(i>=0))>>2 for i in r]
             end
         end
     end
@@ -190,6 +201,10 @@ end
     @test round(Int,-2.5,RoundNearestTiesUp) == -2
     @test round(Int,-1.5,RoundNearestTiesUp) == -1
     @test round(Int,-1.9) == -2
+    @test round(Int,nextfloat(1.0),RoundFromZero) == 2
+    @test round(Int,-nextfloat(1.0),RoundFromZero) == -2
+    @test round(Int,prevfloat(1.0),RoundFromZero) == 1
+    @test round(Int,-prevfloat(1.0),RoundFromZero) == -1
     @test_throws InexactError round(Int64, 9.223372036854776e18)
     @test       round(Int64, 9.223372036854775e18) == 9223372036854774784
     @test_throws InexactError round(Int64, -9.223372036854778e18)