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utils.jl
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utils.jl
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const MANTISSA_MASK = Base.significand_mask(Float64)
const EXP_MASK = Base.exponent_mask(Float64) >> Base.significand_bits(Float64)
# Note: these are smaller than the values given in Figure 4 from the paper
# see https://github.com/ulfjack/ryu/issues/119
pow5_bitcount(::Type{Float16}) = 30
pow5_bitcount(::Type{Float32}) = 61
pow5_bitcount(::Type{Float64}) = 121
pow5_inv_bitcount(::Type{Float16}) = 30
pow5_inv_bitcount(::Type{Float32}) = 59
pow5_inv_bitcount(::Type{Float64}) = 122
qinvbound(::Type{Float16}) = 4
qinvbound(::Type{Float32}) = 9
qinvbound(::Type{Float64}) = 21
qbound(::Type{Float16}) = 15
qbound(::Type{Float32}) = 31
qbound(::Type{Float64}) = 63
"""
Ryu.log10pow2(e::Integer)
Computes `floor(log10(2^e))`. This is valid for all `e < 1651`.
"""
log10pow2(e) = (e * 78913) >> 18
"""
Ryu.log10pow5(e::Integer)
Computes `floor(log10(5^e))`. This is valid for all `e < 2621`.
"""
log10pow5(e) = (e * 732923) >> 20
"""
Ryu.pow5bits(e)
Computes `e == 0 ? 1 : ceil(log2(5^e))`. This is valid for `e < 3529` (if performend in `Int32` arithmetic).
"""
pow5bits(e) = ((e * 1217359) >> 19) + 1
""""
Ryu.mulshift(m::U, mula, j) where {U<:Unsigned}
Compute `(m * mul) >> j`, where `j >= 8*sizeof(U)`. The type of the results is the larger of `U` or `UInt32`.
"""
function mulshift(m::U, mul, j) where {U<:Unsigned}
W = widen(U)
nbits = 8*sizeof(U)
return ((((W(m) * (mul % U)) >> nbits) + W(m) * (mul >> nbits)) >> (j - nbits)) % promote_type(U,UInt32)
end
indexforexp(e) = div(e + 15, 16)
pow10bitsforindex(idx) = 16 * idx + 120
lengthforindex(idx) = div(((Int64(16 * idx) * 1292913986) >> 32) + 1 + 16 + 8, 9)
"""
Ryu.pow5(x, p)
Return `true` if `5^p` is a divisor of `x`.
"""
pow5(x, p) = x % (UInt64(5)^p) == 0
"""
Ryu.pow2(x, p)
Return `true` if `2^p` is a divisor of `x`. In other words, if the trailing `p` bits of `x` are zero.
"""
pow2(x, p) = (x & ((Int64(1) << p) - 1)) == 0
"""
Ryu.decimallength(v)
The number of decimal digits of the integer `v`.
"""
function decimallength(v)
v >= 10000000000000000 && return 17
v >= 1000000000000000 && return 16
v >= 100000000000000 && return 15
v >= 10000000000000 && return 14
v >= 1000000000000 && return 13
v >= 100000000000 && return 12
v >= 10000000000 && return 11
v >= 1000000000 && return 10
v >= 100000000 && return 9
v >= 10000000 && return 8
v >= 1000000 && return 7
v >= 100000 && return 6
v >= 10000 && return 5
v >= 1000 && return 4
v >= 100 && return 3
v >= 10 && return 2
return 1
end
function decimallength(v::UInt32)
v >= 100000000 && return 9
v >= 10000000 && return 8
v >= 1000000 && return 7
v >= 100000 && return 6
v >= 10000 && return 5
v >= 1000 && return 4
v >= 100 && return 3
v >= 10 && return 2
return 1
end
function decimallength(v::UInt16)
v >= 10000 && return 5
v >= 1000 && return 4
v >= 100 && return 3
v >= 10 && return 2
return 1
end
function mulshiftinvsplit(::Type{T}, mv, mp, mm, i, j) where {T}
mul = pow5invsplit_lookup(T, i)
vr = mulshift(mv, mul, j)
vp = mulshift(mp, mul, j)
vm = mulshift(mm, mul, j)
return vr, vp, vm
end
function mulshiftsplit(::Type{T}, mv, mp, mm, i, j) where {T}
mul = pow5split_lookup(T, i)
vr = mulshift(mv, mul, j)
vp = mulshift(mp, mul, j)
vm = mulshift(mm, mul, j)
return vr, vp, vm
end
"""
Ryu.umul256(a::UInt128, bHi::UInt64, bLo::UInt64)::Tuple{UInt128, UInt128}
Compute `p = a*b` where `b = bLo + bHi<<64`, returning the result as `pLo, pHi` where `p = pLo + pHi<<128`.
"""
function umul256(a::UInt128, bHi::UInt64, bLo::UInt64)
aLo = a % UInt64
aHi = (a >> 64) % UInt64
b00 = UInt128(aLo) * bLo
b01 = UInt128(aLo) * bHi
b10 = UInt128(aHi) * bLo
b11 = UInt128(aHi) * bHi
b00Lo = b00 % UInt64
b00Hi = (b00 >> 64) % UInt64
mid1 = b10 + b00Hi
mid1Lo = mid1 % UInt64
mid1Hi = (mid1 >> 64) % UInt64
mid2 = b01 + mid1Lo
mid2Lo = mid2 % UInt64
mid2Hi = (mid2 >> 64) % UInt64
pHi = b11 + mid1Hi + mid2Hi
pLo = (UInt128(mid2Lo) << 64) | b00Lo
return pLo, pHi
end
"""
Ryu.umul256_hi(a::UInt128, bHi::UInt64, bLo::UInt64)::UInt128
Compute `pHi = (a*b)>>128` where `b = bLo + bHi<<64`.
"""
umul256_hi(a::UInt128, bHi::UInt64, bLo::UInt64) = umul256(a, bHi, bLo)[2]
"""
Ryu.mulshiftmod1e9(m, mula, mulb, mulc, j)::UInt32
Compute `(m * mul) >> j % 10^9` where `mul = mula + mulb<<64 + mulc<<128`, and `j >= 128`.
"""
function mulshiftmod1e9(m, mula, mulb, mulc, j)
b0 = UInt128(m) * mula
b1 = UInt128(m) * mulb
b2 = UInt128(m) * mulc
mid = b1 + ((b0 >> 64) % UInt64)
s1 = b2 + ((mid >> 64) % UInt64)
v = s1 >> (j - 128)
multiplied = umul256_hi(v, 0x89705F4136B4A597, 0x31680A88F8953031)
shifted = (multiplied >> 29) % UInt32
return (v % UInt32) - UInt32(1000000000) * shifted
end
function append_sign(x, plus::Bool, space::Bool, buf, pos::Int)
if signbit(x) && !isnan(x) # suppress minus sign for signaling NaNs
buf[pos] = UInt8('-')
pos += 1
elseif plus
buf[pos] = UInt8('+')
pos += 1
elseif space
buf[pos] = UInt8(' ')
pos += 1
end
return pos
end
import Base: append_c_digits_fast as append_c_digits, append_nine_digits
function append_d_digits(olength::Int, digits::Unsigned, buf, pos::Int, decchar)
newpos = append_c_digits(olength, digits, buf, pos + 1)
@inbounds buf[pos] = buf[pos + 1]
@inbounds buf[pos + 1] = decchar
return newpos # == pos + olength + 1
end
const BIG_MASK = (big(1) << 64) - 1
const POW10_SPLIT = collect(Iterators.flatten(map(0:63) do idx
pow10bits = pow10bitsforindex(idx)
map(0:lengthforindex(idx)-1) do i
v = (div(big(1) << pow10bits, big(10)^(9 * i)) + 1) % ((big(10)^9) << 136)
return (UInt64(v & BIG_MASK), UInt64((v >> 64) & BIG_MASK), UInt64((v >> 128) & BIG_MASK))
end
end))
function generateinversetables()
POW10_OFFSET_2 = Vector{UInt16}(undef, 68 + 1)
MIN_BLOCK_2 = fill(0xff, 68 + 1)
POW10_SPLIT_2 = Tuple{UInt64, UInt64, UInt64}[]
lowerCutoff = big(1) << (54 + 8)
for idx = 0:67
POW10_OFFSET_2[idx + 1] = length(POW10_SPLIT_2)
i = 0
while true
v = ((big(10)^(9 * (i + 1)) >> (-(120 - 16 * idx))) % (big(10)^9) << (120 + 16))
if MIN_BLOCK_2[idx + 1] == 0xff && ((v * lowerCutoff) >> 128) == 0
i += 1
continue
end
if MIN_BLOCK_2[idx + 1] == 0xff
MIN_BLOCK_2[idx + 1] = i
end
v == 0 && break
push!(POW10_SPLIT_2, ((v & BIG_MASK) % UInt64, ((v >> 64) & BIG_MASK) % UInt64, ((v >> 128) & BIG_MASK) % UInt64))
i += 1
end
end
POW10_OFFSET_2[end] = length(POW10_SPLIT_2)
MIN_BLOCK_2[end] = 0x00
return POW10_OFFSET_2, MIN_BLOCK_2, POW10_SPLIT_2
end
const POW10_OFFSET_2, MIN_BLOCK_2, POW10_SPLIT_2 = generateinversetables()
"""
Ryu.pow5invsplit(T, i)
Compute `floor(2^k/5^i)+1`, where `k = pow5bits(i) - 1 + pow5_inv_bitcount(T)`. The result
is an unsigned integer twice as wide as `T` (i.e. a `UInt128` if `T == Float64`), with
`pow5_inv_bitcount(T)` significant bits.
"""
function pow5invsplit(::Type{T}, i) where {T<:AbstractFloat}
W = widen(uinttype(T))
pow = big(5)^i
inv = div(big(1) << (ndigits(pow, base=2) - 1 + pow5_inv_bitcount(T)), pow) + 1
return W(inv)
end
"""
Ryu.pow5invsplit_lookup(T, i)
[`pow5invsplit`](@ref) computed via lookup table.
"""
function pow5invsplit_lookup end
for T in (Float64, Float32, Float16)
e2_max = exponent_max(T) - precision(T) - 1
i_max = log10pow2(e2_max)
table_sym = Symbol("pow5invsplit_table_", string(T))
@eval const $table_sym = Tuple(Any[pow5invsplit($T, i) for i = 0:$i_max])
@eval pow5invsplit_lookup(::Type{$T}, i) = @inbounds($table_sym[i+1])
end
"""
Ryu.pow5split(T, i)
Compute `floor(5^i/2^k)`, where `k = pow5bits(i) - pow5_bitcount(T)`. The result is an
unsigned integer twice as wide as `T` (i.e. a `UInt128` if `T == Float64`), with
`pow5_bitcount(T)` significant bits.
"""
function pow5split(::Type{T}, i) where {T<:AbstractFloat}
W = widen(uinttype(T))
pow = big(5)^i
return W(pow >> (ndigits(pow, base=2) - pow5_bitcount(T)))
end
"""
Ryu.pow5split_lookup(T, i)
[`pow5split`](@ref) computed via lookup table.
"""
function pow5split_lookup end
for T in (Float64, Float32, Float16)
e2_min = 1 - exponent_bias(T) - significand_bits(T) - 2
i_max = 1 - e2_min - log10pow5(-e2_min)
table_sym = Symbol("pow5split_table_", string(T))
@eval const $table_sym = Tuple(Any[pow5split($T, i) for i = 0:$i_max])
@eval pow5split_lookup(::Type{$T}, i) = @inbounds($table_sym[i+1])
end
const DIGIT_TABLE16 = Base._dec_d100
const POW10_OFFSET = UInt16[
0, 2, 5, 8, 12, 16, 21, 26, 32, 39,
46, 54, 62, 71, 80, 90, 100, 111, 122, 134,
146, 159, 173, 187, 202, 217, 233, 249, 266, 283,
301, 319, 338, 357, 377, 397, 418, 440, 462, 485,
508, 532, 556, 581, 606, 632, 658, 685, 712, 740,
769, 798, 828, 858, 889, 920, 952, 984, 1017, 1050,
1084, 1118, 1153, 1188
]