/
float.jl
233 lines (190 loc) · 11.9 KB
/
float.jl
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## conversions to floating-point ##
convert(::Type{Float32}, x::Bool) = box(Float32,sitofp32(unbox(Bool,x)))
convert(::Type{Float32}, x::Char) = box(Float32,uitofp32(unbox(Float32,x)))
convert(::Type{Float32}, x::Int8) = box(Float32,sitofp32(unbox(Int8,x)))
convert(::Type{Float32}, x::Int16) = box(Float32,sitofp32(unbox(Int16,x)))
convert(::Type{Float32}, x::Int32) = box(Float32,sitofp32(unbox(Int32,x)))
convert(::Type{Float32}, x::Int64) = box(Float32,sitofp32(unbox(Int64,x)))
convert(::Type{Float32}, x::Uint8) = box(Float32,uitofp32(unbox(Uint8,x)))
convert(::Type{Float32}, x::Uint16) = box(Float32,uitofp32(unbox(Uint16,x)))
convert(::Type{Float32}, x::Uint32) = box(Float32,uitofp32(unbox(Uint32,x)))
convert(::Type{Float32}, x::Uint64) = box(Float32,uitofp32(unbox(Uint64,x)))
convert(::Type{Float32}, x::Float64) = box(Float32,fptrunc32(unbox(Float64,x)))
convert(::Type{Float64}, x::Bool) = box(Float64,sitofp64(unbox(Bool,x)))
convert(::Type{Float64}, x::Char) = box(Float64,uitofp64(unbox(Char,x)))
convert(::Type{Float64}, x::Int8) = box(Float64,sitofp64(unbox(Int8,x)))
convert(::Type{Float64}, x::Int16) = box(Float64,sitofp64(unbox(Int16,x)))
convert(::Type{Float64}, x::Int32) = box(Float64,sitofp64(unbox(Int32,x)))
convert(::Type{Float64}, x::Int64) = box(Float64,sitofp64(unbox(Int64,x)))
convert(::Type{Float64}, x::Uint8) = box(Float64,uitofp64(unbox(Uint8,x)))
convert(::Type{Float64}, x::Uint16) = box(Float64,uitofp64(unbox(Uint16,x)))
convert(::Type{Float64}, x::Uint32) = box(Float64,uitofp64(unbox(Uint32,x)))
convert(::Type{Float64}, x::Uint64) = box(Float64,uitofp64(unbox(Uint64,x)))
convert(::Type{Float64}, x::Float32) = box(Float64,fpext64(unbox(Float32,x)))
convert(::Type{FloatingPoint}, x::Bool) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Char) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Int8) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Int16) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Int32) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Int64) = convert(Float64, x) # LOSSY
convert(::Type{FloatingPoint}, x::Uint8) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Uint16) = convert(Float32, x)
convert(::Type{FloatingPoint}, x::Uint32) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Uint64) = convert(Float64, x) # LOSSY
float32(x) = convert(Float32, x)
float64(x) = convert(Float64, x)
float(x) = convert(FloatingPoint, x)
## conversions from floating-point ##
if WORD_SIZE == 64
iround(x::Float32) = iround(float64(x))
itrunc(x::Float32) = itrunc(float64(x))
else
iround(x::Float32) = box(Int32,fpsiround32(unbox(Float32,x)))
itrunc(x::Float32) = box(Int32,fptosi32(unbox(Float32,x)))
end
iround(x::Float64) = box(Int64,fpsiround64(unbox(Float64,x)))
itrunc(x::Float64) = box(Int64,fptosi64(unbox(Float64,x)))
iround(::Type{Int8}, x::Float32) = box(Int8,trunc8(fpsiround32(unbox(Float32,x))))
iround(::Type{Int8}, x::Float64) = box(Int8,trunc8(fpsiround64(unbox(Float64,x))))
iround(::Type{Uint8}, x::Float32) = box(Uint8,trunc8(fpuiround32(unbox(Float32,x))))
iround(::Type{Uint8}, x::Float64) = box(Uint8,trunc8(fpuiround64(unbox(Float64,x))))
iround(::Type{Int16}, x::Float32) = box(Int16,trunc16(fpsiround32(unbox(Float32,x))))
iround(::Type{Int16}, x::Float64) = box(Int16,trunc16(fpsiround64(unbox(Float64,x))))
iround(::Type{Uint16}, x::Float32) = box(Uint16,trunc16(fpuiround32(unbox(Float32,x))))
iround(::Type{Uint16}, x::Float64) = box(Uint16,trunc16(fpuiround64(unbox(Float64,x))))
iround(::Type{Int32}, x::Float32) = box(Int32,fpsiround32(unbox(Float32,x)))
iround(::Type{Int32}, x::Float64) = box(Int32,trunc32(fpsiround64(unbox(Float64,x))))
iround(::Type{Uint32}, x::Float32) = box(Uint32,fpuiround32(unbox(Float32,x)))
iround(::Type{Uint32}, x::Float64) = box(Uint32,trunc32(fpuiround64(unbox(Float64,x))))
iround(::Type{Int64}, x::Float32) = box(Int64,fpsiround64(fpext64(unbox(Float32,x))))
iround(::Type{Int64}, x::Float64) = box(Int64,fpsiround64(unbox(Float64,x)))
iround(::Type{Uint64}, x::Float32) = box(Uint64,fpuiround64(fpext64(unbox(Float32,x))))
iround(::Type{Uint64}, x::Float64) = box(Uint64,fpuiround64(unbox(Float64,x)))
# TODO: Int128
# this is needed very early because it is used by Range and colon
floor(x::Float64) = ccall(dlsym(_jl_libfdm,:floor), Float64, (Float64,), x)
iceil(x::FloatingPoint) = itrunc(ceil(x)) # TODO: fast primitive for iceil
ifloor(x::FloatingPoint) = itrunc(floor(x)) # TOOD: fast primitive for ifloor
## floating point promotions ##
promote_rule(::Type{Float64}, ::Type{Float32}) = Float64
promote_rule(::Type{Float32}, ::Type{Int8} ) = Float32
promote_rule(::Type{Float32}, ::Type{Int16}) = Float32
promote_rule(::Type{Float32}, ::Type{Int32}) = Float64
promote_rule(::Type{Float32}, ::Type{Int64}) = Float64 # TODO: should be Float80
promote_rule(::Type{Float64}, ::Type{Int8} ) = Float64
promote_rule(::Type{Float64}, ::Type{Int16}) = Float64
promote_rule(::Type{Float64}, ::Type{Int32}) = Float64
promote_rule(::Type{Float64}, ::Type{Int64}) = Float64 # TODO: should be Float80
promote_rule(::Type{Float32}, ::Type{Uint8} ) = Float32
promote_rule(::Type{Float32}, ::Type{Uint16}) = Float32
promote_rule(::Type{Float32}, ::Type{Uint32}) = Float64
promote_rule(::Type{Float32}, ::Type{Uint64}) = Float64 # TODO: should be Float80
promote_rule(::Type{Float64}, ::Type{Uint8} ) = Float64
promote_rule(::Type{Float64}, ::Type{Uint16}) = Float64
promote_rule(::Type{Float64}, ::Type{Uint32}) = Float64
promote_rule(::Type{Float64}, ::Type{Uint64}) = Float64 # TODO: should be Float80
promote_rule(::Type{Float32}, ::Type{Char}) = Float32
promote_rule(::Type{Float64}, ::Type{Char}) = Float64
morebits(::Type{Float32}) = Float64
## floating point arithmetic ##
-(x::Float32) = box(Float32,neg_float(unbox(Float32,x)))
-(x::Float64) = box(Float64,neg_float(unbox(Float64,x)))
+(x::Float32, y::Float32) = box(Float32,add_float(unbox(Float32,x),unbox(Float32,y)))
+(x::Float64, y::Float64) = box(Float64,add_float(unbox(Float64,x),unbox(Float64,y)))
-(x::Float32, y::Float32) = box(Float32,sub_float(unbox(Float32,x),unbox(Float32,y)))
-(x::Float64, y::Float64) = box(Float64,sub_float(unbox(Float64,x),unbox(Float64,y)))
*(x::Float32, y::Float32) = box(Float32,mul_float(unbox(Float32,x),unbox(Float32,y)))
*(x::Float64, y::Float64) = box(Float64,mul_float(unbox(Float64,x),unbox(Float64,y)))
/(x::Float32, y::Float32) = box(Float32,div_float(unbox(Float32,x),unbox(Float32,y)))
/(x::Float64, y::Float64) = box(Float64,div_float(unbox(Float64,x),unbox(Float64,y)))
# TODO: faster floating point div?
# TODO: faster floating point fld?
# TODO: faster floating point mod?
rem(x::Float32, y::Float32) = box(Float32,rem_float(unbox(Float32,x),unbox(Float32,y)))
rem(x::Float64, y::Float64) = box(Float64,rem_float(unbox(Float64,x),unbox(Float64,y)))
## floating point comparisons ##
==(x::Float32, y::Float32) = eq_float(unbox(Float32,x),unbox(Float32,y))
==(x::Float64, y::Float64) = eq_float(unbox(Float64,x),unbox(Float64,y))
!=(x::Float32, y::Float32) = ne_float(unbox(Float32,x),unbox(Float32,y))
!=(x::Float64, y::Float64) = ne_float(unbox(Float64,x),unbox(Float64,y))
< (x::Float32, y::Float32) = lt_float(unbox(Float32,x),unbox(Float32,y))
< (x::Float64, y::Float64) = lt_float(unbox(Float64,x),unbox(Float64,y))
<=(x::Float32, y::Float32) = le_float(unbox(Float32,x),unbox(Float32,y))
<=(x::Float64, y::Float64) = le_float(unbox(Float64,x),unbox(Float64,y))
isequal(x::Float32, y::Float32) = fpiseq32(unbox(Float32,x),unbox(Float32,y))
isequal(x::Float64, y::Float64) = fpiseq64(unbox(Float64,x),unbox(Float64,y))
isless (x::Float32, y::Float32) = fpislt32(unbox(Float32,x),unbox(Float32,y))
isless (x::Float64, y::Float64) = fpislt64(unbox(Float64,x),unbox(Float64,y))
isequal(a::Integer, b::FloatingPoint) = (a==b) & isequal(float(a),b)
isequal(a::FloatingPoint, b::Integer) = isequal(b, a)
isless (a::Integer, b::FloatingPoint) = (a<b) | isless(float(a),b)
isless (a::FloatingPoint, b::Integer) = (a<b) | isless(a,float(b))
==(x::Float64, y::Int64 ) = eqfsi64(unbox(Float64,x),unbox(Int64,y))
==(x::Float64, y::Uint64 ) = eqfui64(unbox(Float64,x),unbox(Uint64,y))
==(x::Int64 , y::Float64) = eqfsi64(unbox(Float64,y),unbox(Int64,x))
==(x::Uint64 , y::Float64) = eqfui64(unbox(Float64,y),unbox(Uint64,x))
==(x::Float32, y::Int64 ) = eqfsi64(unbox(Float64,float64(x)),unbox(Int64,y))
==(x::Float32, y::Uint64 ) = eqfui64(unbox(Float64,float64(x)),unbox(Uint64,y))
==(x::Int64 , y::Float32) = eqfsi64(unbox(Float64,float64(y)),unbox(Int64,x))
==(x::Uint64 , y::Float32) = eqfui64(unbox(Float64,float64(y)),unbox(Uint64,x))
< (x::Float64, y::Int64 ) = ltfsi64(unbox(Float64,x),unbox(Int64,y))
< (x::Float64, y::Uint64 ) = ltfui64(unbox(Float64,x),unbox(Uint64,y))
< (x::Int64 , y::Float64) = ltsif64(unbox(Int64,x),unbox(Float64,y))
< (x::Uint64 , y::Float64) = ltuif64(unbox(Uint64,x),unbox(Float64,y))
< (x::Float32, y::Int64 ) = ltfsi64(unbox(Float64,float64(x)),unbox(Int64,y))
< (x::Float32, y::Uint64 ) = ltfui64(unbox(Float64,float64(x)),unbox(Uint64,y))
< (x::Int64 , y::Float32) = ltsif64(unbox(Int64,x),unbox(Float64,float64(y)))
< (x::Uint64 , y::Float32) = ltuif64(unbox(Uint64,x),unbox(Float64,float64(y)))
<=(x::Float64, y::Int64 ) = lefsi64(unbox(Float64,x),unbox(Int64,y))
<=(x::Float64, y::Uint64 ) = lefui64(unbox(Float64,x),unbox(Uint64,y))
<=(x::Int64 , y::Float64) = lesif64(unbox(Int64,x),unbox(Float64,y))
<=(x::Uint64 , y::Float64) = leuif64(unbox(Uint64,x),unbox(Float64,y))
<=(x::Float32, y::Int64 ) = lefsi64(unbox(Float64,float64(x)),unbox(Int64,y))
<=(x::Float32, y::Uint64 ) = lefui64(unbox(Float64,float64(x)),unbox(Uint64,y))
<=(x::Int64 , y::Float32) = lesif64(unbox(Int64,x),unbox(Float64,float64(y)))
<=(x::Uint64 , y::Float32) = leuif64(unbox(Uint64,x),unbox(Float64,float64(y)))
## floating point traits ##
const Inf32 = box(Float32,unbox(Uint32,0x7f800000))
const NaN32 = box(Float32,unbox(Uint32,0x7fc00000))
const Inf = box(Float64,unbox(Uint64,0x7ff0000000000000))
const NaN = box(Float64,unbox(Uint64,0x7ff8000000000000))
@eval begin
inf(::Type{Float32}) = $Inf32
nan(::Type{Float32}) = $NaN32
inf(::Type{Float64}) = $Inf
nan(::Type{Float64}) = $NaN
inf{T<:FloatingPoint}(x::T) = inf(T)
nan{T<:FloatingPoint}(x::T) = nan(T)
isdenormal(x::Float32) = (abs(x) < $(box(Float32,unbox(Uint32,0x00800000))))
isdenormal(x::Float64) = (abs(x) < $(box(Float64,unbox(Uint64,0x0010000000000000))))
typemin(::Type{Float32}) = $(-Inf32)
typemax(::Type{Float32}) = $(Inf32)
typemin(::Type{Float64}) = $(-Inf)
typemax(::Type{Float64}) = $(Inf)
typemin{T<:Real}(x::T) = typemin(T)
typemax{T<:Real}(x::T) = typemax(T)
realmin(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x00800000)))
realmin(::Type{Float64}) = $(box(Float64,unbox(Uint64,0x0010000000000000)))
realmax(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x7f7fffff)))
realmax(::Type{Float64}) = $(box(Float64,unbox(Uint64,0x7fefffffffffffff)))
realmin{T<:FloatingPoint}(x::T) = realmin(T)
realmax{T<:FloatingPoint}(x::T) = realmax(T)
realmin() = realmin(Float64)
realmax() = realmax(Float64)
nextfloat(x::Float32, i::Integer) = box(Float32,add_int(unbox(Float32,x),unbox(Int32,int32(i))))
nextfloat(x::Float64, i::Integer) = box(Float64,add_int(unbox(Float64,x),unbox(Int64,int64(i))))
nextfloat(x::FloatingPoint) = nextfloat(x,1)
prevfloat(x::FloatingPoint) = nextfloat(x,-1)
eps(x::FloatingPoint) = isfinite(x) ? abs(nextfloat(x)-x) : nan(x)
eps(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x34000000)))
eps(::Type{Float64}) = $(box(Float64,unbox(Uint64,0x3cb0000000000000)))
eps() = eps(Float64)
end
sizeof(::Type{Float32}) = 4
sizeof(::Type{Float64}) = 8
## mathematical constants ##
const e = 2.71828182845904523536
const pi = 3.14159265358979323846
## byte order swaps for arbitrary-endianness serialization/deserialization ##
bswap(x::Float32) = box(Float32,bswap_int(unbox(Float32,x)))
bswap(x::Float64) = box(Float64,bswap_int(unbox(Float64,x)))