Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Faster implementation of Float64(::BigInt), Float32(::BigInt) and Float16(::BigInt) #31502

Merged
merged 6 commits into from
Apr 22, 2019
Merged

Faster implementation of Float64(::BigInt), Float32(::BigInt) and Float16(::BigInt) #31502

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
6 commits
Select commit Hold shift + click to select a range
cff0094
basic implementation of 64 bit version Float64(::BigInt)
narendrakpatel Mar 27, 2019
06eaa2e
basic implementation of 32 bit version Float64(::BigInt)
narendrakpatel Mar 29, 2019
c851665
refactor Float64(::BigInt)
narendrakpatel Mar 31, 2019
e33edbf
implement Float32(::BigInt)
narendrakpatel Apr 1, 2019
2b5377f
implement Float16(::BigInt)
narendrakpatel Apr 1, 2019
d965683
add tests for BigInt to Float conversions
narendrakpatel Apr 1, 2019
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
80 changes: 63 additions & 17 deletions base/gmp.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -374,26 +374,72 @@ function (::Type{T})(n::BigInt, ::RoundingMode{:Up}) where T<:CdoubleMax
x < n ? nextfloat(x) : x
end

function (::Type{T})(n::BigInt, ::RoundingMode{:Nearest}) where T<:CdoubleMax
x = T(n,RoundToZero)
if maxintfloat(T) <= abs(x) < T(Inf)
r = n-BigInt(x)
h = eps(x)/2
if iseven(reinterpret(Unsigned,x)) # check if last bit is odd/even
if r < -h
return prevfloat(x)
elseif r > h
return nextfloat(x)
end
function Float64(x::BigInt, ::RoundingMode{:Nearest})
x == 0 && return 0.0
xsize = abs(x.size)
if xsize*BITS_PER_LIMB > 1024
z = Inf64
elseif xsize == 1
z = Float64(unsafe_load(x.d))
elseif Limb == UInt32 && xsize == 2
z = Float64((unsafe_load(x.d, 2) % UInt64) << BITS_PER_LIMB + unsafe_load(x.d))
else
y1 = unsafe_load(x.d, xsize) % UInt64
n = 64 - leading_zeros(y1)
# load first 54(1 + 52 bits of fraction + 1 for rounding)
y = y1 >> (n - (precision(Float64)+1))
if Limb == UInt64
y += n > precision(Float64) ? 0 : (unsafe_load(x.d, xsize-1) >> (10+n))
else
if r <= -h
return prevfloat(x)
elseif r >= h
return nextfloat(x)
end
y += (unsafe_load(x.d, xsize-1) % UInt64) >> (n-22)
y += n > (precision(Float64) - 32) ? 0 : (unsafe_load(x.d, xsize-2) >> (10+n))
end
y = (y + 1) >> 1 # round, ties up
y &= ~UInt64(trailing_zeros(x) == (n-54 + (xsize-1)*BITS_PER_LIMB)) # fix last bit to round to even
d = ((n+1021) % UInt64) << 52
z = reinterpret(Float64, d+y)
z = ldexp(z, (xsize-1)*BITS_PER_LIMB)
end
return flipsign(z, x.size)
end

function Float32(x::BigInt, ::RoundingMode{:Nearest})
x == 0 && return 0f0
xsize = abs(x.size)
if xsize*BITS_PER_LIMB > 128
z = Inf32
elseif xsize == 1
z = Float32(unsafe_load(x.d))
else
y1 = unsafe_load(x.d, xsize)
n = BITS_PER_LIMB - leading_zeros(y1)
# load first 25(1 + 23 bits of fraction + 1 for rounding)
y = (y1 >> (n - (precision(Float32)+1))) % UInt32
y += (n > precision(Float32) ? 0 : unsafe_load(x.d, xsize-1) >> (BITS_PER_LIMB - (25-n))) % UInt32
y = (y + one(UInt32)) >> 1 # round, ties up
y &= ~UInt32(trailing_zeros(x) == (n-25 + (xsize-1)*BITS_PER_LIMB)) # fix last bit to round to even
d = ((n+125) % UInt32) << 23
z = reinterpret(Float32, d+y)
z = ldexp(z, (xsize-1)*BITS_PER_LIMB)
end
return flipsign(z, x.size)
end

function Float16(x::BigInt, ::RoundingMode{:Nearest})
x == 0 && return Float16(0.0)
y1 = unsafe_load(x.d)
n = BITS_PER_LIMB - leading_zeros(y1)
if n > 16 || abs(x.size) > 1
z = Inf16
else
# load first 12(1 + 10 bits for fraction + 1 for rounding)
y = (y1 >> (n - (precision(Float16)+1))) % UInt16
y = (y + one(UInt16)) >> 1 # round, ties up
y &= ~UInt16(trailing_zeros(x) == (n-12)) # fix last bit to round to even
d = ((n+13) % UInt16) << 10
z = reinterpret(Float16, d+y)
end
x
return flipsign(z, x.size)
end

Float64(n::BigInt) = Float64(n, RoundNearest)
Expand Down
30 changes: 30 additions & 0 deletions test/bigint.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -440,3 +440,33 @@ end
@test big(Int64(-9223372036854775808)) == big"-9223372036854775808"
@test big(Int128(-170141183460469231731687303715884105728)) == big"-170141183460469231731687303715884105728"
end

@testset "conversion to Float" begin
x = big"2"^256 + big"2"^(256-53) + 1
@test Float64(x) == reinterpret(Float64, 0x4ff0000000000001)
@test Float64(-x) == -Float64(x)
x = (x >> 1) + 1
@test Float64(x) == reinterpret(Float64, 0x4fe0000000000001)
@test Float64(-x) == -Float64(x)

x = big"2"^64 + big"2"^(64-24) + 1
@test Float32(x) == reinterpret(Float32, 0x5f800001)
@test Float32(-x) == -Float32(x)
x = (x >> 1) + 1
@test Float32(x) == reinterpret(Float32, 0x5f000001)
@test Float32(-x) == -Float32(x)

x = big"2"^15 + big"2"^(15-11) + 1
@test Float16(x) == reinterpret(Float16, 0x7801)
@test Float16(-x) == -Float16(x)
x = (x >> 1) + 1
@test Float16(x) == reinterpret(Float16, 0x7401)
@test Float16(-x) == -Float16(x)

for T in (Float16, Float32, Float64)
n = exponent(floatmax(T))
@test T(big"2"^(n+1)) === T(Inf)
@test T(big"2"^(n+1) - big"2"^(n-precision(T))) === T(Inf)
@test T(big"2"^(n+1) - big"2"^(n-precision(T)) - 1) === floatmax(T)
end
end