Create Double64.jl

Author: JeffreySarnoff

src/Double64.jl

@@ -0,0 +1,78 @@
+#=
+struct MultiFloat{T,N} <: AbstractFloat
+    _limbs::NTuple{N,T}
+end
+=#
+
+# This function is needed to work around the following SIMD bug:
+# https://github.com/eschnett/SIMD.jl/issues/115
+@inline _ntuple_equal(x::NTuple{2,Float64}, y::NTuple{2,Float64}) = (x[1] === y[1]) && (x[2] === y[2])
+@inline _ntuple_equal(x::NTuple{N,Vec{M,T}}, y::NTuple{N,Vec{M,T}}) where {N,M,T} = all(all.(x .== y))
+
+const Tuple2 = NTuple{2, Float64]
+
+struct Double64 <: AbstractFloat
+    hilo::NTuple{2,Float64}
+end
+
+Double64() = Double64((0.0, 0.0))
+Double64(hi::Float64) = Double64((hi, 0.0))
+
+Base.zero(::Type{Double64}) = Double64((0.0, 0.0))
+Base.one(::Type{Double64}) = Double64((1.0, 0.0))
+
+Base.length(::Type{Double64}) = 2
+Base.getindex(x::Double64, idx::Integer) = getindex(x, x.hilo[idx])
+
+#
+
+@inline function fast_twosum(a::T, b::T) where {T}
+    sum = a + b
+    b_prime = sum - a
+    b_err = b - b_prime
+    return (sum, b_err)
+end
+
+@inline function fast_twodiff(a::T, b::T) where {T}
+    diff = a - b
+    b_prime = a - diff
+    b_err = b_prime - b
+    return (diff, b_err)
+end
+
+@inline function twosum(a::T, b::T) where {T}
+    sum = a + b
+    a_prime = sum - b
+    b_prime = sum - a_prime
+    a_err = a - a_prime
+    b_err = b - b_prime
+    err = a_err + b_err
+    return (sum, err)
+end
+
+@inline function twodiff(a::T, b::T) where {T}
+    diff = a - b
+    a_prime = diff + b
+    b_prime = a_prime - diff
+    a_err = a - a_prime
+    b_err = b - b_prime
+    err = a_err - b_err
+    return (diff, err)
+end
+
+@inline function twoprod(a::T, b::T) where {T}
+    prod = a * b
+    err = fma(a, b, -prod)
+    return (prod, err)
+end
+
+@inline function renormalize(x::Float64, y::Float64)
+    return( twosum(x, y) )
+end
+@inline function renormalize(a::Tuple2)
+    return( twosum(a[1], a[2]) )
+end
+@inline function renormalize(a::Double64)
+    Double64(renormalize(a.hilo))
+end
+