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Merge pull request #36 from milankl/fastfloat16
fastfloat16sr first implementation
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| name: CI | ||
| on: | ||
| pull_request: | ||
| branches: | ||
| - main | ||
| push: | ||
| branches: | ||
| - main | ||
| jobs: | ||
| test: | ||
| runs-on: ${{ matrix.os }} | ||
| strategy: | ||
| matrix: | ||
| julia-version: ["1.0", "1.5", nightly] | ||
| julia-arch: [x64] | ||
| os: [ubuntu-latest, windows-latest, macOS-latest] | ||
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| steps: | ||
| - uses: actions/checkout@v2 | ||
| - name: "Set up Julia" | ||
| uses: julia-actions/setup-julia@latest | ||
| with: | ||
| version: ${{ matrix.julia-version }} | ||
| arch: ${{ matrix.julia-arch }} | ||
| - uses: julia-actions/julia-runtest@latest | ||
| - uses: julia-actions/julia-uploadcodecov@latest | ||
| env: | ||
| CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }} |
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| import FastFloat16s.FastFloat16 | ||
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| """The Float32 + stochastic rounding type.""" | ||
| primitive type FastFloat16sr <: AbstractFloat 32 end | ||
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| # basic properties | ||
| sign_mask(::Type{FastFloat16sr}) = 0x8000_0000 | ||
| exponent_mask(::Type{FastFloat16sr}) = 0x7f80_0000 | ||
| significand_mask(::Type{FastFloat16sr}) = 0x007f_ffff | ||
| precision(::Type{FastFloat16sr}) = 11 | ||
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| one(::Type{FastFloat16sr}) = reinterpret(FastFloat16sr,one(Float32)) | ||
| zero(::Type{FastFloat16sr}) = reinterpret(FastFloat16sr,0x0000_0000) | ||
| one(::FastFloat16sr) = one(FastFloat16sr) | ||
| zero(::FastFloat16sr) = zero(FlastFloat16r) | ||
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| typemin(::Type{FastFloat16sr}) = Float32sr(typemin(Float16)) | ||
| typemax(::Type{FastFloat16sr}) = Float32sr(typemax(Float16)) | ||
| floatmin(::Type{FastFloat16sr}) = Float32sr(floatmin(Float16)) | ||
| floatmax(::Type{FastFloat16sr}) = Float32sr(floatmax(FastFlaot16)) | ||
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| typemin(::FastFloat16sr) = typemin(FastFloat16sr) | ||
| typemax(::FastFloat16sr) = typemax(FastFloat16sr) | ||
| floatmin(::FastFloat16sr) = floatmin(FastFloat16sr) | ||
| floatmax(::FastFloat16sr) = floatmax(FastFloat16sr) | ||
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| eps(::Type{FastFloat16sr}) = FastFloat16sr(eps(Float16)) | ||
| eps(x::FastFloat16sr) = FastFloat16sr(eps(Float16(x))) | ||
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| const InfF16sr = reinterpret(FastFloat16sr, Inf32) | ||
| const NaNF16sr = reinterpret(FastFloat16sr, NaN32) | ||
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| # basic operations | ||
| abs(x::FastFloat16sr) = reinterpret(FastFloat16sr, abs(Float32(x))) | ||
| isnan(x::FastFloat16sr) = isnan(Float32(x)) | ||
| isfinite(x::FastFloat16sr) = isfinite(Float32(x)) | ||
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| nextfloat(x::FastFloat16sr) = FastFloat16sr(nextfloat(Float16(x))) | ||
| prevfloat(x::FastFloat16sr) = FastFloat16sr(prevfloat(Float16(x))) | ||
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| -(x::FastFloat16sr) = reinterpret(FastFloat16sr, reinterpret(UInt32, x) ⊻ sign_mask(FastFloat16sr)) | ||
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| # conversions | ||
| Float32(x::FastFloat16sr) = reinterpret(Float32,x) | ||
| FastFloat16sr(x::FastFloat16) = reinterpret(FastFloat16sr,x) | ||
| FastFloat16(x::FastFloat16sr) = reinterpret(FastFloat16,x) | ||
| FastFloat16sr(x::Float32) = FastFloat16sr(FastFloat16(x)) | ||
| FastFloat16sr(x::Float16) = FastFloat16sr(Float32(x)) | ||
| FastFloat16sr(x::Float64) = FastFloat16sr(Float32(x)) | ||
| Float16(x::FastFloat16sr) = Float16(Float32(x)) | ||
| Float64(x::FastFloat16sr) = Float64(Float32(x)) | ||
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| FastFloat16sr(x::Integer) = FastFloat16sr(Float32(x)) | ||
| (::Type{T})(x::FastFloat16sr) where {T<:Integer} = T(Float32(x)) | ||
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| """Convert to FastFloat16sr from Float32 with stochastic rounding. | ||
| Binary arithmetic version.""" | ||
| function FastFloat16_stochastic_round(x::Float32) | ||
| ix = reinterpret(Int32,x) | ||
| # if deterministically round to 0 return 0 | ||
| # to avoid a stochastic rounding to NaN | ||
| # push to the left to get rid of sign | ||
| # push to the right to get rid of the insignificant bits | ||
| ((ix << 1) >> 13) == zero(Int32) && return zero(FastFloat16sr) | ||
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| # r are random bits for the last 31 | ||
| # >> either introduces 0s for the first 33 bits | ||
| # or 1s. Interpreted as Int64 this corresponds to [-ulp/2,ulp/2) | ||
| # which is added with binary arithmetic subsequently | ||
| # this is the stochastic perturbation. | ||
| # Then deterministic round to nearest to either round up or round down. | ||
| r = rand(Xor128[],Int32) >> 19 # = preserve 1 sign, 8 ebits, 10sbits | ||
| xr = reinterpret(Float32,ix + r) | ||
| return FastFloat16sr(xr) # round to nearest | ||
| end | ||
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| # # Promotion | ||
| # promote_rule(::Type{Float16}, ::Type{FastFloat32sr}) = Float32 | ||
| # promote_rule(::Type{Float64}, ::Type{Float32sr}) = Float64 | ||
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| for t in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128) | ||
| @eval promote_rule(::Type{FastFloat16sr}, ::Type{$t}) = FastFloat16sr | ||
| end | ||
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| # Rounding | ||
| round(x::FastFloat16sr, r::RoundingMode{:ToZero}) = FastFloat16sr(round(Float32(x), r)) | ||
| round(x::FastFloat16sr, r::RoundingMode{:Down}) = FastFloat16sr(round(Float32(x), r)) | ||
| round(x::FastFloat16sr, r::RoundingMode{:Up}) = FastFloat16sr(round(Float32(x), r)) | ||
| round(x::FastFloat16sr, r::RoundingMode{:Nearest}) = FastFloat16sr(round(Float32(x), r)) | ||
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| # Comparison | ||
| function ==(x::FastFloat16sr, y::FastFloat16sr) | ||
| return Float32(x) == Float32(y) | ||
| end | ||
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| for op in (:<, :<=, :isless) | ||
| @eval ($op)(a::FastFloat16sr, b::FastFloat16sr) = ($op)(Float32(a), Float32(b)) | ||
| end | ||
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| # Arithmetic | ||
| for f in (:+, :-, :*, :/, :^) | ||
| @eval ($f)(x::FastFloat16sr, y::FastFloat16sr) = FastFloat16_stochastic_round($(f)(Float32(x), Float32(y))) | ||
| end | ||
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| for func in (:sin,:cos,:tan,:asin,:acos,:atan,:sinh,:cosh,:tanh,:asinh,:acosh, | ||
| :atanh,:exp,:exp2,:exp10,:expm1,:log,:log2,:log10,:sqrt,:cbrt,:log1p) | ||
| @eval begin | ||
| Base.$func(a::FastFloat16sr) = FastFloat16_stochastic_round($func(Float32(a))) | ||
| end | ||
| end | ||
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| for func in (:atan,:hypot) | ||
| @eval begin | ||
| $func(a::FastFloat16sr,b::FastFloat16sr) = FastFloat16_stochastic_round($func(Float32(a),Float32(b))) | ||
| end | ||
| end | ||
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| # Showing | ||
| function show(io::IO, x::FastFloat16sr) | ||
| if isinf(x) | ||
| print(io, x < 0 ? "-InfF16sr" : "InfF16sr") | ||
| elseif isnan(x) | ||
| print(io, "NaNF16sr") | ||
| else | ||
| io2 = IOBuffer() | ||
| print(io2,Float32(x)) | ||
| f = String(take!(io2)) | ||
| print(io,"FastFloat16sr("*f*")") | ||
| end | ||
| end | ||
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| bitstring(x::FastFloat16sr) = bitstring(reinterpret(UInt32,x)) | ||
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| function bitstring(x::FastFloat16sr,mode::Symbol) | ||
| if mode == :split # split into sign, exponent, signficand | ||
| s = bitstring(x) | ||
| return "$(s[1]) $(s[2:9]) $(s[10:end])" | ||
| else | ||
| return bitstring(x) | ||
| end | ||
| end |
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