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Use vfma in TwoProduct paths of special/double.jl (fix SLEEFPirates accuracy regression) #129

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Merged
ChrisRackauckas merged 1 commit into from
May 28, 2026
Merged

Use vfma in TwoProduct paths of special/double.jl (fix SLEEFPirates accuracy regression) #129

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30 changes: 20 additions & 10 deletions src/special/double.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -315,9 +315,19 @@ end
end

# two-prod-fma
#
# These `::True` branches implement the TwoProduct error-free transformation
# (e.g. `Double(z, fma(x, y, -z))`), which extracts the rounding error of
# `x*y` as the low part of a double-double. The identity requires a
# **single-rounded** FMA; using the may-fuse `vfmsub`/`vfnmadd` lets LLVM
# constant-fold `(x*y) + (-(x*y))` to `0` even on hardware that has FMA,
# which destroys every double-double error term and propagates as wildly
# wrong results in downstream `asinh`/`sin`/`cos`/etc. (e.g. ~10^5 ULP on
# Float32). Call `vfma` (which lowers to `llvm.fma`) directly with an
# explicit negation so the FMA is preserved.
@inline function dmul(x::vIEEEFloat, y::vIEEEFloat, ::True)
z = (x * y)
Double(z, vfmsub(x, y, z))
Double(z, vfma(x, y, -z))
end
@inline function dmul(x::vIEEEFloat, y::vIEEEFloat, ::False)
hx, lx = splitprec(x)
Expand All @@ -329,7 +339,7 @@ end
end
@inline function dmul(x::Double{<:vIEEEFloat}, y::vIEEEFloat, ::True)
z = (x.hi * y)
Double(z, vfmsub(x.hi, y, z) + x.lo * y)
Double(z, vfma(x.hi, y, -z) + x.lo * y)
end
@inline function dmul(x::Double{<:vIEEEFloat}, y::vIEEEFloat, ::False)
hx, lx = splitprec(x.hi)
Expand All @@ -341,7 +351,7 @@ end
end
@inline function dmul(x::Double{<:vIEEEFloat}, y::Double{<:vIEEEFloat}, ::True)
z = x.hi * y.hi
Double(z, vfmsub(x.hi, y.hi, z) + x.hi * y.lo + x.lo * y.hi)
Double(z, vfma(x.hi, y.hi, -z) + x.hi * y.lo + x.lo * y.hi)
end
@inline function dmul(x::Double{<:vIEEEFloat}, y::Double{<:vIEEEFloat}, ::False)
hx, lx = splitprec(x.hi)
Expand All @@ -361,7 +371,7 @@ end
# x^2
@inline function dsqu(x::T, ::True) where {T<:vIEEEFloat}
z = x * x
Double(z, vfmsub(x, x, z))
Double(z, vfma(x, x, -z))
end
@inline function dsqu(x::T, ::False) where {T<:vIEEEFloat}
hx, lx = splitprec(x)
Expand All @@ -372,7 +382,7 @@ end
end
@inline function dsqu(x::Double{T}, ::True) where {T<:vIEEEFloat}
z = x.hi * x.hi
Double(z, vfmsub(x.hi, x.hi, z) + (x.hi * (x.lo + x.lo)))
Double(z, vfma(x.hi, x.hi, -z) + (x.hi * (x.lo + x.lo)))
end
@inline function dsqu(x::Double{T}, ::False) where {T<:vIEEEFloat}
hx, lx = splitprec(x.hi)
Expand All @@ -386,7 +396,7 @@ end
# sqrt(x)
@inline function dsqrt(x::Double{T}, ::True) where {T<:vIEEEFloat}
zhi = @fastmath sqrt(x.hi)
Double(zhi, (x.lo + vfnmadd(zhi, zhi, x.hi)) / (zhi + zhi))
Double(zhi, (x.lo + vfma(-zhi, zhi, x.hi)) / (zhi + zhi))
end
@inline function dsqrt(x::Double{T}, ::False) where {T<:vIEEEFloat}
c = @fastmath sqrt(x.hi)
Expand All @@ -399,7 +409,7 @@ end
@inline function ddiv(x::Double{<:vIEEEFloat}, y::Double{<:vIEEEFloat}, ::True)
invy = inv(y.hi)
zhi = (x.hi * invy)
Double(zhi, ((vfnmadd(zhi, y.hi, x.hi) + vfnmadd(zhi, y.lo, x.lo)) * invy))
Double(zhi, ((vfma(-zhi, y.hi, x.hi) + vfma(-zhi, y.lo, x.lo)) * invy))
end
@inline function ddiv(x::Double{<:vIEEEFloat}, y::Double{<:vIEEEFloat}, ::False)
@ieee begin
Expand All @@ -412,7 +422,7 @@ end
@inline function ddiv(x::vIEEEFloat, y::vIEEEFloat, ::True)
ry = inv(y)
r = (x * ry)
Double(r, (vfnmadd(r, y, x) * ry))
Double(r, (vfma(-r, y, x) * ry))
end
@inline function ddiv(x::vIEEEFloat, y::vIEEEFloat, ::False)
@ieee begin
Expand All @@ -427,7 +437,7 @@ end
# 1/x
@inline function drec(x::vIEEEFloat, ::True)
zhi = inv(x)
Double(zhi, (vfnmadd(zhi, x, one(eltype(x))) * zhi))
Double(zhi, (vfma(-zhi, x, one(eltype(x))) * zhi))
end
@inline function drec(x::vIEEEFloat, ::False)
@ieee begin
Expand All @@ -439,7 +449,7 @@ end

@inline function drec(x::Double{<:vIEEEFloat}, ::True)
zhi = inv(x.hi)
Double(zhi, ((vfnmadd(zhi, x.hi, one(eltype(x))) - (zhi * x.lo)) * zhi))
Double(zhi, ((vfma(-zhi, x.hi, one(eltype(x))) - (zhi * x.lo)) * zhi))
end
@inline function drec(x::Double{<:vIEEEFloat}, ::False)
@ieee begin
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