Refactor rounding (including bugfixes) and document API

base/Base.jl

@@ -222,7 +222,6 @@ include(strcat((length(Core.ARGS)>=2 ? Core.ARGS[2] : ""), "version_git.jl")) #
 # numeric operations
 include("hashing.jl")
 include("rounding.jl")
-using .Rounding
 include("div.jl")
 include("rawbigints.jl")
 include("float.jl")

base/boot.jl

@@ -328,9 +328,8 @@ TypeError(where, @nospecialize(expected::Type), @nospecialize(got)) =
     TypeError(Symbol(where), "", expected, got)
 struct InexactError <: Exception
     func::Symbol
-    T  # Type
-    val
-    InexactError(f::Symbol, @nospecialize(T), @nospecialize(val)) = (@noinline; new(f, T, val))
+    args
+    InexactError(f::Symbol, @nospecialize(args...)) = (@noinline; new(f, args))
 end
 struct OverflowError <: Exception
     msg::AbstractString
@@ -630,8 +629,6 @@ eval(Core, :(NamedTuple{names,T}(args::T) where {names, T <: Tuple} =
 
 import .Intrinsics: eq_int, trunc_int, lshr_int, sub_int, shl_int, bitcast, sext_int, zext_int, and_int
 
-throw_inexacterror(f::Symbol, ::Type{T}, val) where {T} = (@noinline; throw(InexactError(f, T, val)))
-
 function is_top_bit_set(x)
     @inline
     eq_int(trunc_int(UInt8, lshr_int(x, sub_int(shl_int(sizeof(x), 3), 1))), trunc_int(UInt8, 1))
@@ -642,6 +639,9 @@ function is_top_bit_set(x::Union{Int8,UInt8})
     eq_int(lshr_int(x, 7), trunc_int(typeof(x), 1))
 end
 
+#TODO delete this function (but see #48097):
+throw_inexacterror(args...) = throw(InexactError(args...))
+
 function check_top_bit(::Type{To}, x) where {To}
     @inline
     is_top_bit_set(x) && throw_inexacterror(:check_top_bit, To, x)

base/errorshow.jl

@@ -173,8 +173,10 @@ end
 
 function showerror(io::IO, ex::InexactError)
     print(io, "InexactError: ", ex.func, '(')
-    nameof(ex.T) === ex.func || print(io, ex.T, ", ")
-    print(io, ex.val, ')')
+    T = first(ex.args)
+    nameof(T) === ex.func || print(io, T, ", ")
+    join(io, ex.args[2:end], ", ")
+    print(io, ")")
     Experimental.show_error_hints(io, ex)
 end
 

base/float.jl

@@ -436,21 +436,15 @@ unsafe_trunc(::Type{UInt128}, x::Float16) = unsafe_trunc(UInt128, Float32(x))
 unsafe_trunc(::Type{Int128}, x::Float16) = unsafe_trunc(Int128, Float32(x))
 
 # matches convert methods
-# also determines floor, ceil, round
-trunc(::Type{Signed}, x::IEEEFloat) = trunc(Int,x)
-trunc(::Type{Unsigned}, x::IEEEFloat) = trunc(UInt,x)
-trunc(::Type{Integer}, x::IEEEFloat) = trunc(Int,x)
-
-# Bool
-trunc(::Type{Bool}, x::AbstractFloat) = (-1 < x < 2) ? 1 <= x : throw(InexactError(:trunc, Bool, x))
-floor(::Type{Bool}, x::AbstractFloat) = (0 <= x < 2) ? 1 <= x : throw(InexactError(:floor, Bool, x))
-ceil(::Type{Bool}, x::AbstractFloat)  = (-1 < x <= 1) ? 0 < x : throw(InexactError(:ceil, Bool, x))
-round(::Type{Bool}, x::AbstractFloat) = (-0.5 <= x < 1.5) ? 0.5 < x : throw(InexactError(:round, Bool, x))
-
-round(x::IEEEFloat, r::RoundingMode{:ToZero})  = trunc_llvm(x)
-round(x::IEEEFloat, r::RoundingMode{:Down})    = floor_llvm(x)
-round(x::IEEEFloat, r::RoundingMode{:Up})      = ceil_llvm(x)
-round(x::IEEEFloat, r::RoundingMode{:Nearest}) = rint_llvm(x)
+# also determines trunc, floor, ceil
+round(::Type{Signed},   x::IEEEFloat, r::RoundingMode) = round(Int, x, r)
+round(::Type{Unsigned}, x::IEEEFloat, r::RoundingMode) = round(UInt, x, r)
+round(::Type{Integer},  x::IEEEFloat, r::RoundingMode) = round(Int, x, r)
+
+round(x::IEEEFloat, ::RoundingMode{:ToZero})  = trunc_llvm(x)
+round(x::IEEEFloat, ::RoundingMode{:Down})    = floor_llvm(x)
+round(x::IEEEFloat, ::RoundingMode{:Up})      = ceil_llvm(x)
+round(x::IEEEFloat, ::RoundingMode{:Nearest}) = rint_llvm(x)
 
 ## floating point promotions ##
 promote_rule(::Type{Float32}, ::Type{Float16}) = Float32
@@ -931,11 +925,11 @@ for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UIn
             # directly. `Tf(typemax(Ti))+1` is either always exactly representable, or
             # rounded to `Inf` (e.g. when `Ti==UInt128 && Tf==Float32`).
             @eval begin
-                function trunc(::Type{$Ti},x::$Tf)
+                function round(::Type{$Ti},x::$Tf,::RoundingMode{:ToZero})
                     if $(Tf(typemin(Ti))-one(Tf)) < x < $(Tf(typemax(Ti))+one(Tf))
                         return unsafe_trunc($Ti,x)
                     else
-                        throw(InexactError(:trunc, $Ti, x))
+                        throw(InexactError(:round, $Ti, x, RoundToZero))
                     end
                 end
                 function (::Type{$Ti})(x::$Tf)
@@ -955,11 +949,11 @@ for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UIn
             # be rounded up. This assumes that `Tf(typemin(Ti)) > -Inf`, which is true for
             # these types, but not for `Float16` or larger integer types.
             @eval begin
-                function trunc(::Type{$Ti},x::$Tf)
+                function round(::Type{$Ti},x::$Tf,::RoundingMode{:ToZero})
                     if $(Tf(typemin(Ti))) <= x < $(Tf(typemax(Ti)))
                         return unsafe_trunc($Ti,x)
                     else
-                        throw(InexactError(:trunc, $Ti, x))
+                        throw(InexactError(:round, $Ti, x, RoundToZero))
                     end
                 end
                 function (::Type{$Ti})(x::$Tf)

base/floatfuncs.jl

@@ -46,11 +46,6 @@ isinteger(x::AbstractFloat) = (x - trunc(x) == 0)
 
 # See rounding.jl for docstring.
 
-function round(::Type{T}, x::AbstractFloat, r::RoundingMode) where {T<:Integer}
-    r != RoundToZero && (x = round(x,r))
-    trunc(T, x)
-end
-
 # NOTE: this relies on the current keyword dispatch behaviour (#9498).
 function round(x::Real, r::RoundingMode=RoundNearest;
                digits::Union{Nothing,Integer}=nothing, sigdigits::Union{Nothing,Integer}=nothing, base::Union{Nothing,Integer}=nothing)
@@ -77,20 +72,6 @@ function round(x::Real, r::RoundingMode=RoundNearest;
     end
 end
 
-trunc(x::Real; kwargs...) = round(x, RoundToZero; kwargs...)
-floor(x::Real; kwargs...) = round(x, RoundDown; kwargs...)
-ceil(x::Real; kwargs...)  = round(x, RoundUp; kwargs...)
-
-# fallbacks
-trunc(::Type{T}, x::Real; kwargs...) where {T} = round(T, x, RoundToZero; kwargs...)
-floor(::Type{T}, x::Real; kwargs...) where {T} = round(T, x, RoundDown; kwargs...)
-ceil(::Type{T}, x::Real; kwargs...) where {T} = round(T, x, RoundUp; kwargs...)
-round(::Type{T}, x::Real; kwargs...) where {T} = round(T, x, RoundNearest; kwargs...)
-
-round(::Type{T}, x::Real, r::RoundingMode) where {T} = convert(T, round(x, r))
-
-round(x::Integer, r::RoundingMode) = x
-
 # round x to multiples of 1/invstep
 function _round_invstep(x, invstep, r::RoundingMode)
     y = round(x * invstep, r) / invstep

base/gmp.jl

@@ -320,7 +320,7 @@ function BigInt(x::Float64)
     unsafe_trunc(BigInt,x)
 end
 
-function trunc(::Type{BigInt}, x::Union{Float16,Float32,Float64})
+function round(::Type{BigInt}, x::Union{Float16,Float32,Float64}, r::RoundingMode{:ToZero})
     isfinite(x) || throw(InexactError(:trunc, BigInt, x))
     unsafe_trunc(BigInt,x)
 end

base/int.jl

@@ -629,70 +629,6 @@ mod(x::Integer, ::Type{T}) where {T<:Integer} = rem(x, T)
 
 unsafe_trunc(::Type{T}, x::Integer) where {T<:Integer} = rem(x, T)
 
-"""
-    trunc([T,] x)
-    trunc(x; digits::Integer= [, base = 10])
-    trunc(x; sigdigits::Integer= [, base = 10])
-
-`trunc(x)` returns the nearest integral value of the same type as `x` whose absolute value
-is less than or equal to the absolute value of `x`.
-
-`trunc(T, x)` converts the result to type `T`, throwing an `InexactError` if the truncated
-value is not representable a `T`.
-
-Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
-
-See also: [`%`](@ref rem), [`floor`](@ref), [`unsigned`](@ref), [`unsafe_trunc`](@ref).
-
-# Examples
-```jldoctest
-julia> trunc(2.22)
-2.0
-
-julia> trunc(-2.22, digits=1)
--2.2
-
-julia> trunc(Int, -2.22)
--2
-```
-"""
-function trunc end
-
-"""
-    floor([T,] x)
-    floor(x; digits::Integer= [, base = 10])
-    floor(x; sigdigits::Integer= [, base = 10])
-
-`floor(x)` returns the nearest integral value of the same type as `x` that is less than or
-equal to `x`.
-
-`floor(T, x)` converts the result to type `T`, throwing an `InexactError` if the floored
-value is not representable a `T`.
-
-Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
-"""
-function floor end
-
-"""
-    ceil([T,] x)
-    ceil(x; digits::Integer= [, base = 10])
-    ceil(x; sigdigits::Integer= [, base = 10])
-
-`ceil(x)` returns the nearest integral value of the same type as `x` that is greater than or
-equal to `x`.
-
-`ceil(T, x)` converts the result to type `T`, throwing an `InexactError` if the ceiled
-value is not representable as a `T`.
-
-Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
-"""
-function ceil end
-
-round(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
-trunc(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
-floor(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
- ceil(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
-
 ## integer construction ##
 
 """

base/missing.jl

@@ -150,19 +150,6 @@ round(::Type{T}, x::Real, r::RoundingMode=RoundNearest) where {T>:Missing} = rou
 round(::Type{T}, x::Rational{Tr}, r::RoundingMode=RoundNearest) where {T>:Missing,Tr} = round(nonmissingtype_checked(T), x, r)
 round(::Type{T}, x::Rational{Bool}, r::RoundingMode=RoundNearest) where {T>:Missing} = round(nonmissingtype_checked(T), x, r)
 
-# Handle ceil, floor, and trunc separately as they have no RoundingMode argument
-for f in (:(ceil), :(floor), :(trunc))
-    @eval begin
-        ($f)(::Missing; sigdigits::Integer=0, digits::Integer=0, base::Integer=0) = missing
-        ($f)(::Type{>:Missing}, ::Missing) = missing
-        ($f)(::Type{T}, ::Missing) where {T} = throw(MissingException(missing_conversion_msg(T)))
-        ($f)(::Type{T}, x::Any) where {T>:Missing} = $f(nonmissingtype_checked(T), x)
-        # to fix ambiguities
-        ($f)(::Type{T}, x::Rational) where {T>:Missing} = $f(nonmissingtype_checked(T), x)
-        ($f)(::Type{T}, x::Real) where {T>:Missing} = $f(nonmissingtype_checked(T), x)
-    end
-end
-
 # to avoid ambiguity warnings
 (^)(::Missing, ::Integer) = missing
 

base/mpfr.jl

@@ -380,18 +380,15 @@ round(::Type{T}, x::BigFloat, r::RoundingMode) where T<:Union{Signed, Unsigned}
     invoke(round, Tuple{Type{<:Union{Signed, Unsigned}}, BigFloat, Union{RoundingMode, MPFRRoundingMode}}, T, x, r)
 round(::Type{BigInt}, x::BigFloat, r::RoundingMode) =
     invoke(round, Tuple{Type{BigInt}, BigFloat, Union{RoundingMode, MPFRRoundingMode}}, BigInt, x, r)
-round(::Type{<:Integer}, x::BigFloat, r::RoundingMode) = throw(MethodError(round, (Integer, x, r)))
 
 
 unsafe_trunc(::Type{T}, x::BigFloat) where {T<:Integer} = unsafe_trunc(T, _unchecked_cast(T, x, RoundToZero))
 unsafe_trunc(::Type{BigInt}, x::BigFloat) = _unchecked_cast(BigInt, x, RoundToZero)
 
-# TODO: Ideally the base fallbacks for these would already exist
-for (f, rnd) in zip((:trunc, :floor, :ceil, :round),
-                 (RoundToZero, RoundDown, RoundUp, :(ROUNDING_MODE[])))
-    @eval $f(::Type{T}, x::BigFloat) where T<:Union{Unsigned, Signed, BigInt} = round(T, x, $rnd)
-    @eval $f(::Type{Integer}, x::BigFloat) = $f(BigInt, x)
-end
+round(::Type{T}, x::BigFloat) where T<:Integer = round(T, x, ROUNDING_MODE[])
+# these two methods are split to increase their precedence in disambiguation:
+round(::Type{Integer}, x::BigFloat, r::RoundingMode) = round(BigInt, x, r)
+round(::Type{Integer}, x::BigFloat, r::MPFRRoundingMode) = round(BigInt, x, r)
 
 function Bool(x::BigFloat)
     iszero(x) && return false

base/rounding.jl

@@ -283,6 +283,8 @@ function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:ToZero}) where T
     end
 end
 
+# Default definitions
+
 """
     set_zero_subnormals(yes::Bool) -> Bool
 
@@ -313,8 +315,8 @@ for IEEE arithmetic, and `true` if they might be converted to zeros.
 get_zero_subnormals() = ccall(:jl_get_zero_subnormals,Int32,())!=0
 
 end #module
+using .Rounding
 
-# Docstring listed here so it appears above the complex docstring.
 """
     round([T,] x, [r::RoundingMode])
     round(x, [r::RoundingMode]; digits::Integer=0, base = 10)
@@ -388,4 +390,83 @@ julia> round(357.913; sigdigits=4, base=2)
 
 To extend `round` to new numeric types, it is typically sufficient to define `Base.round(x::NewType, r::RoundingMode)`.
 """
-round(T::Type, x)
+function round end
+
+"""
+    trunc([T,] x)
+    trunc(x; digits::Integer= [, base = 10])
+    trunc(x; sigdigits::Integer= [, base = 10])
+
+`trunc(x)` returns the nearest integral value of the same type as `x` whose absolute value
+is less than or equal to the absolute value of `x`.
+
+`trunc(T, x)` converts the result to type `T`, throwing an `InexactError` if the truncated
+value is not representable a `T`.
+
+Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
+
+To support `trunc` for a new type, define `Base.round(x::NewType, ::RoundingMode{:ToZero})`.
+
+See also: [`%`](@ref rem), [`floor`](@ref), [`unsigned`](@ref), [`unsafe_trunc`](@ref).
+
+# Examples
+```jldoctest
+julia> trunc(2.22)
+2.0
+
+julia> trunc(-2.22, digits=1)
+-2.2
+
+julia> trunc(Int, -2.22)
+-2
+```
+"""
+function trunc end
+
+"""
+    floor([T,] x)
+    floor(x; digits::Integer= [, base = 10])
+    floor(x; sigdigits::Integer= [, base = 10])
+
+`floor(x)` returns the nearest integral value of the same type as `x` that is less than or
+equal to `x`.
+
+`floor(T, x)` converts the result to type `T`, throwing an `InexactError` if the floored
+value is not representable a `T`.
+
+Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
+
+To support `floor` for a new type, define `Base.round(x::NewType, ::RoundingMode{:Down})`.
+"""
+function floor end
+
+"""
+    ceil([T,] x)
+    ceil(x; digits::Integer= [, base = 10])
+    ceil(x; sigdigits::Integer= [, base = 10])
+
+`ceil(x)` returns the nearest integral value of the same type as `x` that is greater than or
+equal to `x`.
+
+`ceil(T, x)` converts the result to type `T`, throwing an `InexactError` if the ceiled
+value is not representable as a `T`.
+
+Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
+
+To support `ceil` for a new type, define `Base.round(x::NewType, ::RoundingMode{:Up})`.
+"""
+function ceil end
+
+trunc(x; kws...) = round(x, RoundToZero; kws...)
+floor(x; kws...) = round(x, RoundDown; kws...)
+ ceil(x; kws...) = round(x, RoundUp; kws...)
+round(x; kws...) = round(x, RoundNearest; kws...)
+
+trunc(::Type{T}, x) where T = round(T, x, RoundToZero)
+floor(::Type{T}, x) where T = round(T, x, RoundDown)
+ ceil(::Type{T}, x) where T = round(T, x, RoundUp)
+round(::Type{T}, x) where T = round(T, x, RoundNearest)
+
+round(::Type{T}, x, r::RoundingMode) where T = convert(T, round(x, r))
+
+round(x::Integer, r::RoundingMode) = x

doc/src/base/math.md

@@ -118,7 +118,7 @@ Base.exp10
 Base.Math.ldexp
 Base.Math.modf
 Base.expm1
-Base.round(::Type, ::Any)
+Base.round
 Base.Rounding.RoundingMode
 Base.Rounding.RoundNearest
 Base.Rounding.RoundNearestTiesAway