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Improve performance for FD multiplication: allow LLVM to optimize away the division by a constant. #43

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Dec 10, 2018
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Improve performance for FD multiplication: allow LLVM to optimize away the division by a constant. #43

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12 changes: 9 additions & 3 deletions src/FixedPointDecimals.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -154,12 +154,18 @@ function _round_to_even(quotient::T, remainder::T, divisor::T) where {T <: Integ
end
_round_to_even(q, r, d) = _round_to_even(promote(q, r, d)...)

# In many of our calls to fldmod, `y` is a constant (the coefficient, 10^f). However, since
# `fldmod` is sometimes not being inlined, that constant information is not available to the
# optimizer. We need an inlined version of fldmod so that the compiler can replace expensive
# divide-by-power-of-ten instructions with the cheaper multiply-by-inverse-coefficient.
@inline fldmodinline(x,y) = (fld(x,y), mod(x,y))

# multiplication rounds to nearest even representation
# TODO: can we use floating point to speed this up? after we build a
# correctness test suite.
function *(x::FD{T, f}, y::FD{T, f}) where {T, f}
powt = coefficient(FD{T, f})
quotient, remainder = fldmod(widemul(x.i, y.i), powt)
quotient, remainder = fldmodinline(widemul(x.i, y.i), powt)
reinterpret(FD{T, f}, _round_to_even(quotient, remainder, powt))
end

Expand Down Expand Up @@ -195,12 +201,12 @@ floor(x::FD{T, f}) where {T, f} = FD{T, f}(fld(x.i, coefficient(FD{T, f})))
# TODO: round with number of digits; should be easy
function round(x::FD{T, f}, ::RoundingMode{:Nearest}=RoundNearest) where {T, f}
powt = coefficient(FD{T, f})
quotient, remainder = fldmod(x.i, powt)
quotient, remainder = fldmodinline(x.i, powt)
FD{T, f}(_round_to_even(quotient, remainder, powt))
end
function ceil(x::FD{T, f}) where {T, f}
powt = coefficient(FD{T, f})
quotient, remainder = fldmod(x.i, powt)
quotient, remainder = fldmodinline(x.i, powt)
if remainder > 0
FD{T, f}(quotient + one(quotient))
else
Expand Down