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Sorted-batch evaluators for LinearInterpolation and CubicSpline (~9x speedup) #527

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Sorted-batch evaluators for LinearInterpolation and CubicSpline (~9x speedup) #527

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245 changes: 245 additions & 0 deletions src/interpolation_methods.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -130,6 +130,108 @@ function _interpolate(A::LinearInterpolation{<:AbstractArray}, t::Number, iguess
return A.u[ax..., idx] + slope * Δt
end

# Sorted-batch fast path for LinearInterpolation.
function (A::LinearInterpolation{<:AbstractVector{<:Number}})(
out::AbstractVector, tt::AbstractVector
)
if length(out) != length(tt)
throw(
DimensionMismatch(
"number of evaluation points and length of the result vector must be equal"
)
)
end
if _linear_eval_fast_applicable(A) && !any(isnan, A.u) && issorted(tt)
_linear_eval_sorted!(out, A, tt)
else
map!(A, out, tt)
end
return out
end

@inline function _linear_eval_fast_applicable(A::LinearInterpolation)
el = A.extrapolation_left
er = A.extrapolation_right
el_ok = el == ExtrapolationType.None ||
el == ExtrapolationType.Constant ||
el == ExtrapolationType.Linear ||
el == ExtrapolationType.Extension
er_ok = er == ExtrapolationType.None ||
er == ExtrapolationType.Constant ||
er == ExtrapolationType.Linear ||
er == ExtrapolationType.Extension
return el_ok && er_ok
end

function _linear_eval_sorted!(
out::AbstractVector, A::LinearInterpolation{<:AbstractVector{<:Number}}, tt::AbstractVector
)
u = A.u
t = A.t
el = A.extrapolation_left
er = A.extrapolation_right
n = length(t)
m = length(tt)
t1 = @inbounds t[1]
tn = @inbounds t[n]

i = 1

# Left extrapolation
if el == ExtrapolationType.None
@inbounds if i <= m && tt[i] < t1
throw(LeftExtrapolationError())
end
elseif el == ExtrapolationType.Constant
u1 = @inbounds u[1]
@inbounds while i <= m && tt[i] < t1
out[i] = u1
i += 1
end
else # Linear or Extension — both reduce to the first-segment line
u1 = @inbounds u[1]
slope1 = get_parameters(A, 1)
@inbounds while i <= m && tt[i] < t1
out[i] = u1 + slope1 * (tt[i] - t1)
i += 1
end
end

# Interior: per-segment outer loop, hoist coefficients
@inbounds for idx in 1:(n - 1)
ti = t[idx]
tip1 = t[idx + 1]
ui = u[idx]
slope = get_parameters(A, idx)
while i <= m && tt[i] <= tip1
out[i] = ui + slope * (tt[i] - ti)
i += 1
end
end

# Right extrapolation
if er == ExtrapolationType.None
@inbounds if i <= m
throw(RightExtrapolationError())
end
elseif er == ExtrapolationType.Constant
un = @inbounds u[n]
@inbounds while i <= m
out[i] = un
i += 1
end
else # Linear or Extension — both reduce to the last-segment line
un = @inbounds u[n]
slope_n = get_parameters(A, n - 1)
@inbounds while i <= m
out[i] = un + slope_n * (tt[i] - tn)
i += 1
end
end

return nothing
end

# Quadratic Interpolation
function _interpolate(A::QuadraticInterpolation, t::Number, iguess)
idx = get_idx(A, t, iguess)
Expand Down Expand Up @@ -405,6 +507,149 @@ function _interpolate(A::CubicSpline{<:AbstractArray}, t::Number, iguess)
return I + C + D
end

# Sorted-batch fast path for CubicSpline.
function (A::CubicSpline{<:AbstractVector{<:Number}})(
out::AbstractVector, tt::AbstractVector
)
if length(out) != length(tt)
throw(
DimensionMismatch(
"number of evaluation points and length of the result vector must be equal"
)
)
end
if _cubicspline_eval_fast_applicable(A) && issorted(tt)
_cubicspline_eval_sorted!(out, A, tt)
else
map!(A, out, tt)
end
return out
end

@inline function _cubicspline_eval_fast_applicable(A::CubicSpline)
el = A.extrapolation_left
er = A.extrapolation_right
el_ok = el == ExtrapolationType.None ||
el == ExtrapolationType.Constant ||
el == ExtrapolationType.Linear ||
el == ExtrapolationType.Extension
er_ok = er == ExtrapolationType.None ||
er == ExtrapolationType.Constant ||
er == ExtrapolationType.Linear ||
er == ExtrapolationType.Extension
return el_ok && er_ok
end

@inline function _cubicspline_segment_eval(
ttt, ti, tip1, zi, zip1, hinv6, c1, c2
)
dt1 = ttt - ti
dt2 = tip1 - ttt
return (zi * dt2 * dt2 * dt2 + zip1 * dt1 * dt1 * dt1) * hinv6 +
c1 * dt1 + c2 * dt2
end

function _cubicspline_eval_sorted!(
out::AbstractVector, A::CubicSpline{<:AbstractVector{<:Number}}, tt::AbstractVector
)
u = A.u
t = A.t
z = A.z
h = A.h
el = A.extrapolation_left
er = A.extrapolation_right
n = length(t)
m = length(tt)
t1 = @inbounds t[1]
tn = @inbounds t[n]

i = 1

# Left extrapolation
if el == ExtrapolationType.None
@inbounds if i <= m && tt[i] < t1
throw(LeftExtrapolationError())
end
elseif el == ExtrapolationType.Constant
u1 = @inbounds u[1]
@inbounds while i <= m && tt[i] < t1
out[i] = u1
i += 1
end
elseif el == ExtrapolationType.Linear
u1 = @inbounds u[1]
slope1 = _derivative(A, t1, 1)
@inbounds while i <= m && tt[i] < t1
out[i] = u1 + slope1 * (tt[i] - t1)
i += 1
end
else # Extension — continue the first-segment cubic
ti = t1
tip1 = @inbounds t[2]
zi = @inbounds z[1]
zip1 = @inbounds z[2]
hinv6 = inv(6 * @inbounds(h[2]))
c1, c2 = get_parameters(A, 1)
@inbounds while i <= m && tt[i] < t1
out[i] = _cubicspline_segment_eval(
tt[i], ti, tip1, zi, zip1, hinv6, c1, c2
)
i += 1
end
end

# Interior: per-segment outer loop with hoisted coefficients
@inbounds for idx in 1:(n - 1)
ti = t[idx]
tip1 = t[idx + 1]
zi = z[idx]
zip1 = z[idx + 1]
hinv6 = inv(6 * h[idx + 1])
c1, c2 = get_parameters(A, idx)
while i <= m && tt[i] <= tip1
out[i] = _cubicspline_segment_eval(
tt[i], ti, tip1, zi, zip1, hinv6, c1, c2
)
i += 1
end
end

# Right extrapolation
if er == ExtrapolationType.None
@inbounds if i <= m
throw(RightExtrapolationError())
end
elseif er == ExtrapolationType.Constant
un = @inbounds u[n]
@inbounds while i <= m
out[i] = un
i += 1
end
elseif er == ExtrapolationType.Linear
un = @inbounds u[n]
slope_n = _derivative(A, tn, n)
@inbounds while i <= m
out[i] = un + slope_n * (tt[i] - tn)
i += 1
end
else # Extension — continue the last-segment cubic
ti = @inbounds t[n - 1]
tip1 = tn
zi = @inbounds z[n - 1]
zip1 = @inbounds z[n]
hinv6 = inv(6 * @inbounds(h[n]))
c1, c2 = get_parameters(A, n - 1)
@inbounds while i <= m
out[i] = _cubicspline_segment_eval(
tt[i], ti, tip1, zi, zip1, hinv6, c1, c2
)
i += 1
end
end

return nothing
end

# BSpline Curve Interpolation
function _interpolate(
A::BSplineInterpolation{<:AbstractVector{<:Number}},
Expand Down
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