rounding.jl

# This file is a part of Julia. License is MIT: https://julialang.org/license

module Rounding

let fenv_consts = Vector{Cint}(undef, 9)
    ccall(:jl_get_fenv_consts, Cvoid, (Ptr{Cint},), fenv_consts)
    global const JL_FE_INEXACT = fenv_consts[1]
    global const JL_FE_UNDERFLOW = fenv_consts[2]
    global const JL_FE_OVERFLOW = fenv_consts[3]
    global const JL_FE_DIVBYZERO = fenv_consts[4]
    global const JL_FE_INVALID = fenv_consts[5]

    global const JL_FE_TONEAREST = fenv_consts[6]
    global const JL_FE_UPWARD = fenv_consts[7]
    global const JL_FE_DOWNWARD = fenv_consts[8]
    global const JL_FE_TOWARDZERO = fenv_consts[9]
end

export
    RoundingMode, RoundNearest, RoundToZero, RoundUp, RoundDown, RoundFromZero,
    RoundNearestTiesAway, RoundNearestTiesUp,
    rounding, setrounding,
    get_zero_subnormals, set_zero_subnormals

## rounding modes ##
"""
    RoundingMode

A type used for controlling the rounding mode of floating point operations (via
[`rounding`](@ref)/[`setrounding`](@ref) functions), or as
optional arguments for rounding to the nearest integer (via the [`round`](@ref)
function).

Currently supported rounding modes are:

- [`RoundNearest`](@ref) (default)
- [`RoundNearestTiesAway`](@ref)
- [`RoundNearestTiesUp`](@ref)
- [`RoundToZero`](@ref)
- [`RoundFromZero`](@ref) ([`BigFloat`](@ref) only)
- [`RoundUp`](@ref)
- [`RoundDown`](@ref)
"""
struct RoundingMode{T} end

"""
    RoundNearest

The default rounding mode. Rounds to the nearest integer, with ties (fractional values of
0.5) being rounded to the nearest even integer.
"""
const RoundNearest = RoundingMode{:Nearest}()

"""
    RoundToZero

[`round`](@ref) using this rounding mode is an alias for [`trunc`](@ref).
"""
const RoundToZero = RoundingMode{:ToZero}()

"""
    RoundUp

[`round`](@ref) using this rounding mode is an alias for [`ceil`](@ref).
"""
const RoundUp = RoundingMode{:Up}()

"""
    RoundDown

[`round`](@ref) using this rounding mode is an alias for [`floor`](@ref).
"""
const RoundDown = RoundingMode{:Down}()

"""
    RoundFromZero

Rounds away from zero.
This rounding mode may only be used with `T == BigFloat` inputs to [`round`](@ref).

# Examples
```jldoctest
julia> BigFloat("1.0000000000000001", 5, RoundFromZero)
1.06
```
"""
const RoundFromZero = RoundingMode{:FromZero}() # mpfr only

"""
    RoundNearestTiesAway

Rounds to nearest integer, with ties rounded away from zero (C/C++
[`round`](@ref) behaviour).
"""
const RoundNearestTiesAway = RoundingMode{:NearestTiesAway}()

"""
    RoundNearestTiesUp

Rounds to nearest integer, with ties rounded toward positive infinity (Java/JavaScript
[`round`](@ref) behaviour).
"""
const RoundNearestTiesUp = RoundingMode{:NearestTiesUp}()

to_fenv(::RoundingMode{:Nearest}) = JL_FE_TONEAREST
to_fenv(::RoundingMode{:ToZero}) = JL_FE_TOWARDZERO
to_fenv(::RoundingMode{:Up}) = JL_FE_UPWARD
to_fenv(::RoundingMode{:Down}) = JL_FE_DOWNWARD

function from_fenv(r::Integer)
    if r == JL_FE_TONEAREST
        return RoundNearest
    elseif r == JL_FE_DOWNWARD
        return RoundDown
    elseif r == JL_FE_UPWARD
        return RoundUp
    elseif r == JL_FE_TOWARDZERO
        return RoundToZero
    else
        throw(ArgumentError("invalid rounding mode code: $r"))
    end
end

"""
    setrounding(T, mode)

Set the rounding mode of floating point type `T`, controlling the rounding of basic
arithmetic functions ([`+`](@ref), [`-`](@ref), [`*`](@ref),
[`/`](@ref) and [`sqrt`](@ref)) and type conversion. Other numerical
functions may give incorrect or invalid values when using rounding modes other than the
default [`RoundNearest`](@ref).

Note that this is currently only supported for `T == BigFloat`.

!!! warning

    This function is not thread-safe. It will affect code running on all threads, but
    its behavior is undefined if called concurrently with computations that use the
    setting.
"""
setrounding(T::Type, mode)

"""
    rounding(T)

Get the current floating point rounding mode for type `T`, controlling the rounding of basic
arithmetic functions ([`+`](@ref), [`-`](@ref), [`*`](@ref), [`/`](@ref)
and [`sqrt`](@ref)) and type conversion.

See [`RoundingMode`](@ref) for available modes.
"""
:rounding

setrounding_raw(::Type{<:Union{Float32,Float64}}, i::Integer) = ccall(:fesetround, Int32, (Int32,), i)
rounding_raw(::Type{<:Union{Float32,Float64}}) = ccall(:fegetround, Int32, ())

rounding(::Type{T}) where {T<:Union{Float32,Float64}} = from_fenv(rounding_raw(T))

"""
    setrounding(f::Function, T, mode)

Change the rounding mode of floating point type `T` for the duration of `f`. It is logically
equivalent to:

    old = rounding(T)
    setrounding(T, mode)
    f()
    setrounding(T, old)

See [`RoundingMode`](@ref) for available rounding modes.
"""
function setrounding(f::Function, ::Type{T}, rounding::RoundingMode) where T
    old_rounding_raw = rounding_raw(T)
    setrounding(T,rounding)
    try
        return f()
    finally
        setrounding_raw(T,old_rounding_raw)
    end
end
function setrounding_raw(f::Function, ::Type{T}, rounding) where T
    old_rounding_raw = rounding_raw(T)
    setrounding_raw(T,rounding)
    try
        return f()
    finally
        setrounding_raw(T,old_rounding_raw)
    end
end


# Should be equivalent to:
#   setrounding(Float64,r) do
#       convert(T,x)
#   end
# but explicit checks are currently quicker (~20x).
# Assumes conversion is performed by rounding to nearest value.

# To avoid ambiguous dispatch with methods in mpfr.jl:
(::Type{T})(x::Real, r::RoundingMode) where {T<:AbstractFloat} = _convert_rounding(T,x,r)

_convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Nearest}) where {T<:AbstractFloat} = convert(T,x)
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Down}) where T<:AbstractFloat
    y = convert(T,x)
    y > x ? prevfloat(y) : y
end
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Up}) where T<:AbstractFloat
    y = convert(T,x)
    y < x ? nextfloat(y) : y
end
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:ToZero}) where T<:AbstractFloat
    y = convert(T,x)
    if x > 0.0
        y > x ? prevfloat(y) : y
    else
        y < x ? nextfloat(y) : y
    end
end

"""
    set_zero_subnormals(yes::Bool) -> Bool

If `yes` is `false`, subsequent floating-point operations follow rules for IEEE arithmetic
on subnormal values ("denormals"). Otherwise, floating-point operations are permitted (but
not required) to convert subnormal inputs or outputs to zero. Returns `true` unless
`yes==true` but the hardware does not support zeroing of subnormal numbers.

`set_zero_subnormals(true)` can speed up some computations on some hardware. However, it can
break identities such as `(x-y==0) == (x==y)`.

!!! warning

    This function only affects the current thread.
"""
set_zero_subnormals(yes::Bool) = ccall(:jl_set_zero_subnormals,Int32,(Int8,),yes)==0

"""
    get_zero_subnormals() -> Bool

Return `false` if operations on subnormal floating-point values ("denormals") obey rules
for IEEE arithmetic, and `true` if they might be converted to zeros.

!!! warning

    This function only affects the current thread.
"""
get_zero_subnormals() = ccall(:jl_get_zero_subnormals,Int32,())!=0

end #module