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float.jl
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float.jl
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## conversions to floating-point ##
convert(::Type{Float32}, x::Int128) = float32(uint128(abs(x)))*(1-2(x<0))
convert(::Type{Float32}, x::Uint128) = float32(uint64(x)) + ldexp(float32(uint64(x>>>64)),64)
promote_rule(::Type{Float32}, ::Type{Int128} ) = Float32
promote_rule(::Type{Float32}, ::Type{Uint128}) = Float32
convert(::Type{Float64}, x::Int128) = float64(uint128(abs(x)))*(1-2(x<0))
convert(::Type{Float64}, x::Uint128) = float64(uint64(x)) + ldexp(float64(uint64(x>>>64)),64)
promote_rule(::Type{Float64}, ::Type{Int128} ) = Float64
promote_rule(::Type{Float64}, ::Type{Uint128}) = Float64
convert(::Type{Float16}, x::Union(Signed,Unsigned)) = convert(Float16, convert(Float32,x))
for t in (Bool,Char,Int8,Int16,Int32,Int64,Uint8,Uint16,Uint32,Uint64)
@eval promote_rule(::Type{Float16}, ::Type{$t}) = Float32
end
for t1 in (Float32,Float64)
for st in (Int8,Int16,Int32,Int64)
@eval begin
convert(::Type{$t1},x::($st)) = box($t1,sitofp($t1,unbox($st,x)))
promote_rule(::Type{$t1}, ::Type{$st} ) = $t1
end
end
for ut in (Bool,Char,Uint8,Uint16,Uint32,Uint64)
@eval begin
convert(::Type{$t1},x::($ut)) = box($t1,uitofp($t1,unbox($ut,x)))
promote_rule(::Type{$t1}, ::Type{$ut} ) = $t1
end
end
end
#convert(::Type{Float16}, x::Float32) = box(Float16,fptrunc(Float16,x))
convert(::Type{Float16}, x::Float64) = convert(Float16, convert(Float32,x))
convert(::Type{Float32}, x::Float64) = box(Float32,fptrunc(Float32,x))
#convert(::Type{Float32}, x::Float16) = box(Float32,fpext(Float32,x))
convert(::Type{Float64}, x::Float16) = convert(Float64, convert(Float32,x))
convert(::Type{Float64}, x::Float32) = box(Float64,fpext(Float64,x))
convert(::Type{FloatingPoint}, x::Bool) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Char) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Int8) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Int16) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Int32) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Int64) = convert(Float64, x) # LOSSY
convert(::Type{FloatingPoint}, x::Int128) = convert(Float64, x) # LOSSY
convert(::Type{FloatingPoint}, x::Uint8) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Uint16) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Uint32) = convert(Float64, x)
convert(::Type{FloatingPoint}, x::Uint64) = convert(Float64, x) # LOSSY
convert(::Type{FloatingPoint}, x::Uint128) = convert(Float64, x) # LOSSY
float16(x) = convert(Float16, x)
float32(x) = convert(Float32, x)
float64(x) = convert(Float64, x)
float(x) = convert(FloatingPoint, x)
## conversions from floating-point ##
# fallbacks using only convert, trunc, ceil, floor, round
itrunc(x::FloatingPoint) = convert(Integer,trunc(x))
iceil (x::FloatingPoint) = convert(Integer,ceil(x)) # TODO: fast primitive for iceil
ifloor(x::FloatingPoint) = convert(Integer,floor(x)) # TOOD: fast primitive for ifloor
iround(x::FloatingPoint) = convert(Integer,round(x))
itrunc{T<:Integer}(::Type{T}, x::FloatingPoint) = convert(T,trunc(x))
iceil {T<:Integer}(::Type{T}, x::FloatingPoint) = convert(T,ceil(x))
ifloor{T<:Integer}(::Type{T}, x::FloatingPoint) = convert(T,floor(x))
iround{T<:Integer}(::Type{T}, x::FloatingPoint) = convert(T,round(x))
## fast specific type conversions ##
iround(x::Float32) = iround(Int, x)
iround(x::Float64) = iround(Int, x)
itrunc(x::Float32) = itrunc(Int, x)
itrunc(x::Float64) = itrunc(Int, x)
for to in (Int8, Int16, Int32, Int64)
@eval begin
iround(::Type{$to}, x::Float32) = box($to,fpsiround($to,unbox(Float32,x)))
iround(::Type{$to}, x::Float64) = box($to,fpsiround($to,unbox(Float64,x)))
itrunc(::Type{$to}, x::Float32) = box($to,fptosi($to,unbox(Float32,x)))
itrunc(::Type{$to}, x::Float64) = box($to,fptosi($to,unbox(Float64,x)))
end
end
for to in (Uint8, Uint16, Uint32, Uint64)
@eval begin
iround(::Type{$to}, x::Float32) = box($to,fpuiround($to,unbox(Float32,x)))
iround(::Type{$to}, x::Float64) = box($to,fpuiround($to,unbox(Float64,x)))
itrunc(::Type{$to}, x::Float32) = box($to,fptoui($to,unbox(Float32,x)))
itrunc(::Type{$to}, x::Float64) = box($to,fptoui($to,unbox(Float64,x)))
end
end
iround(::Type{Int128}, x::Float32) = convert(Int128,round(x))
iround(::Type{Int128}, x::Float64) = convert(Int128,round(x))
iround(::Type{Uint128}, x::Float32) = convert(Uint128,round(x))
iround(::Type{Uint128}, x::Float64) = convert(Uint128,round(x))
# this is needed very early because it is used by Range and colon
round(x::Float64) = ccall((:round, Base.libm_name), Float64, (Float64,), x)
floor(x::Float64) = ccall((:floor, Base.libm_name), Float64, (Float64,), x)
## floating point promotions ##
promote_rule(::Type{Float32}, ::Type{Float16}) = Float32
promote_rule(::Type{Float64}, ::Type{Float16}) = Float64
promote_rule(::Type{Float64}, ::Type{Float32}) = Float64
widen(::Type{Float16}) = Float32
widen(::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)))
mod{T<:FloatingPoint}(x::T, y::T) = rem(y+rem(x,y),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) = fpiseq(unbox(Float32,x),unbox(Float32,y))
isequal(x::Float64, y::Float64) = fpiseq(unbox(Float64,x),unbox(Float64,y))
isless (x::Float32, y::Float32) = fpislt(unbox(Float32,x),unbox(Float32,y))
isless (x::Float64, y::Float64) = fpislt(unbox(Float64,x),unbox(Float64,y))
function cmp(x::FloatingPoint, y::FloatingPoint)
(isnan(x) || isnan(y)) && throw(DomainError())
ifelse(x<y, -1, ifelse(x>y, 1, 0))
end
function cmp(x::Real, y::FloatingPoint)
isnan(y) && throw(DomainError())
ifelse(x<y, -1, ifelse(x>y, 1, 0))
end
function cmp(x::FloatingPoint, y::Real)
isnan(x) && throw(DomainError())
ifelse(x<y, -1, ifelse(x>y, 1, 0))
end
==(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(Float32,x),unbox(Int64,y))
==(x::Float32, y::Uint64 ) = eqfui64(unbox(Float32,x),unbox(Uint64,y))
==(x::Int64 , y::Float32) = eqfsi64(unbox(Float32,y),unbox(Int64,x))
==(x::Uint64 , y::Float32) = eqfui64(unbox(Float32,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)))
==(x::Float32, y::Union(Int32,Uint32)) = float64(x)==float64(y)
==(x::Union(Int32,Uint32), y::Float32) = float64(x)==float64(y)
<(x::Float32, y::Union(Int32,Uint32)) = float64(x)<float64(y)
<(x::Union(Int32,Uint32), y::Float32) = float64(x)<float64(y)
<=(x::Float32, y::Union(Int32,Uint32)) = float64(x)<=float64(y)
<=(x::Union(Int32,Uint32), y::Float32) = float64(x)<=float64(y)
abs(x::Float64) = box(Float64,abs_float(unbox(Float64,x)))
abs(x::Float32) = box(Float32,abs_float(unbox(Float32,x)))
isnan(x::FloatingPoint) = x != x
isnan(x::Real) = false
isfinite(x::FloatingPoint) = x - x == 0
isfinite(x::Real) = decompose(x)[3] != 0
isfinite(x::Integer) = true
isinf(x::Real) = !isnan(x) & !isfinite(x)
## floating point traits ##
const Inf16 = box(Float16,unbox(Uint16,0x7c00))
const NaN16 = box(Float16,unbox(Uint16,0x7e00))
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))
## precision, as defined by the effective number of bits in the mantissa ##
precision(::Float16) = 11
precision(::Float32) = 24
precision(::Float64) = 53
function float_lex_order(f::Integer, delta::Integer)
# convert from signed magnitude to 2's complement and back
neg = f < 0
if neg
f = oftype(f, -(f & typemax(f)))
end
f = oftype(f, f + delta)
neg && f == 0 && return typemin(f) # nextfloat(-5e-324) === -0.0
f < 0 ? oftype(f, -(f & typemax(f))) : f
end
nextfloat(x::Float16, i::Integer) =
(isinf(x)&&sign(x)==sign(i)) ? x : reinterpret(Float16,float_lex_order(reinterpret(Int16,x), i))
nextfloat(x::Float32, i::Integer) =
(isinf(x)&&sign(x)==sign(i)) ? x : reinterpret(Float32,float_lex_order(reinterpret(Int32,x), i))
nextfloat(x::Float64, i::Integer) =
(isinf(x)&&sign(x)==sign(i)) ? x : reinterpret(Float64,float_lex_order(reinterpret(Int64,x), i))
nextfloat(x::FloatingPoint) = nextfloat(x,1)
prevfloat(x::FloatingPoint) = nextfloat(x,-1)
@eval begin
inf(::Type{Float16}) = $Inf16
nan(::Type{Float16}) = $NaN16
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)
issubnormal(x::Float32) = (abs(x) < $(box(Float32,unbox(Uint32,0x00800000)))) & (x!=0)
issubnormal(x::Float64) = (abs(x) < $(box(Float64,unbox(Uint64,0x0010000000000000)))) & (x!=0)
typemin(::Type{Float16}) = $(box(Float16,unbox(Uint16,0xfc00)))
typemax(::Type{Float16}) = $(Inf16)
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{Float16}) = $(box(Float16,unbox(Uint16,0x0400)))
realmin(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x00800000)))
realmin(::Type{Float64}) = $(box(Float64,unbox(Uint64,0x0010000000000000)))
realmax(::Type{Float16}) = $(box(Float16,unbox(Uint16,0x7bff)))
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)
eps(x::FloatingPoint) = isfinite(x) ? abs(x) >= realmin(x) ? ldexp(eps(typeof(x)),exponent(x)) : nextfloat(zero(x)) : nan(x)
eps(::Type{Float16}) = $(box(Float16,unbox(Uint16,0x1400)))
eps(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x34000000)))
eps(::Type{Float64}) = $(box(Float64,unbox(Uint64,0x3cb0000000000000)))
eps() = eps(Float64)
end
sizeof(::Type{Float16}) = 2
sizeof(::Type{Float32}) = 4
sizeof(::Type{Float64}) = 8
## 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)))