Fix bug when rounding large numbers to floating point types

base/essentials.jl

@@ -399,8 +399,9 @@ Stacktrace:
 [...]
 ```
 
-If `T` is a [`AbstractFloat`](@ref) type,
-then it will return the closest value to `x` representable by `T`.
+If `T` is a [`AbstractFloat`](@ref) type, then it will return the
+closest value to `x` representable by `T`. Inf is treated as one
+ulp greater than `floatmax(T)` for purposes of determining nearest.
 
 ```jldoctest
 julia> x = 1/3

base/float.jl

@@ -464,6 +464,20 @@ round(x::IEEEFloat, ::RoundingMode{:Down})    = floor_llvm(x)
 round(x::IEEEFloat, ::RoundingMode{:Up})      = ceil_llvm(x)
 round(x::IEEEFloat, ::RoundingMode{:Nearest}) = rint_llvm(x)
 
+rounds_up(x, ::RoundingMode{:Down}) = false
+rounds_up(x, ::RoundingMode{:Up}) = true
+rounds_up(x, ::RoundingMode{:ToZero}) = x < 0
+rounds_up(x, ::RoundingMode{:FromZero}) = x > 0
+function round(::Type{T}, x, r::Union{RoundingMode{:ToZero}, RoundingMode{:FromZero}, RoundingMode{:Up}, RoundingMode{:Down}}) where {T<:AbstractFloat}
+    x_int = round(x, r)
+    x_t = convert(T, x_int)
+    if rounds_up(x, r)
+        x_t < x ? nextfloat(x_t) : x_t
+    else
+        x_t > x ? prevfloat(x_t) : x_t
+    end
+end
+
 ## floating point promotions ##
 promote_rule(::Type{Float32}, ::Type{Float16}) = Float32
 promote_rule(::Type{Float64}, ::Type{Float16}) = Float64

base/rounding.jl

@@ -338,6 +338,10 @@ The [`RoundingMode`](@ref) `r` controls the direction of the rounding; the defau
 of 0.5) being rounded to the nearest even integer. Note that `round` may give incorrect
 results if the global rounding mode is changed (see [`rounding`](@ref)).
 
+When rounding to a floating point type, will round to integers representable by that type
+(and Inf) rather than true integers. Inf is treated as one ulp greater than the
+`floatmax(T)` for purposes of determining "nearest", similar to [`convert`](@ref).
+
 # Examples
 ```jldoctest
 julia> round(1.7)
@@ -363,6 +367,12 @@ julia> round(123.456; sigdigits=2)
 
 julia> round(357.913; sigdigits=4, base=2)
 352.0
+
+julia> round(Float16, typemax(UInt128))
+Inf16
+
+julia> floor(Float16, typemax(UInt128))
+Float16(6.55e4)
 ```
 
 !!! note

test/rounding.jl

@@ -458,3 +458,15 @@ end
     @test_throws InexactError round(Int128, -Inf16)
     # More comprehensive testing is present in test/floatfuncs.jl
 end
+
+@test "floor(<:AbstractFloat, large_number) (#52355)" begin
+    @test floor(Float32, 0xffff_ffff) == prevfloat(floatmax(Float32)) <= 0xffff_ffff
+    @test trunc(Float16, typemax(UInt128)) == floatmax(Float16)
+    @test round(Float16, typemax(UInt128)) == Inf16
+    for i in [-BigInt(floatmax(Float64)), -BigInt(floatmax(Float64))*100, BigInt(floatmax(Float64)), BigInt(floatmax(Float64))*100]
+        f = ceil(Float64, i)
+        @test f >= i
+        @test isinteger(f) || isinf(f)
+        @test prevfloat(f) < i
+    end
+end