Performance testing of ForwardDiff and the role of parentheses

perf_parens.jl

using ForwardDiff

Base.real(x::ForwardDiff.GradientNumber) = real(x.value)

SimpleRatio(i,j) = i/j

function mygetindex_slow(itp::Matrix, x_1::Number, x_2::Number)
    begin
        begin  # line 34:
            ix_1 = clamp(round(Int,real(x_1)),1,size(itp,1)) # line 35:
            fx_1 = x_1 - ix_1 # line 36:
            ix_1 += 0 # line 37:
            ixp_1 = min(size(itp,1),ix_1 + 1) # line 38:
            ixm_1 = max(1,ix_1 - 1)
        end
        begin  # line 34:
            ix_2 = clamp(round(Int,real(x_2)),1,size(itp,2)) # line 35:
            fx_2 = x_2 - ix_2 # line 36:
            ix_2 += 0 # line 37:
            ixp_2 = min(size(itp,2),ix_2 + 1) # line 38:
            ixm_2 = max(1,ix_2 - 1)
        end
    end # line 18:
    begin
        begin  # line 46:
            cm_1 = sqr(fx_1 - SimpleRatio(1,2)) / 2 # line 47:
            c_1 = SimpleRatio(3,4) - sqr(fx_1) # line 48:
            cp_1 = sqr(fx_1 + SimpleRatio(1,2)) / 2
        end
        begin  # line 46:
            cm_2 = sqr(fx_2 - SimpleRatio(1,2)) / 2 # line 47:
            c_2 = SimpleRatio(3,4) - sqr(fx_2) # line 48:
            cp_2 = sqr(fx_2 + SimpleRatio(1,2)) / 2
        end
    end # line 21:
    begin
        @inbounds begin
            itp1 = (cm_2 * itp[ixm_1,ixm_2]) + (c_2 * itp[ixm_1,ix_2]) + (cp_2 * itp[ixm_1,ixp_2])
            itp2 = (cm_2 * itp[ix_1,ixm_2]) + (c_2 * itp[ix_1,ix_2]) + (cp_2 * itp[ix_1,ixp_2])
            itp3 = (cm_2 * itp[ixp_1,ixm_2]) + (c_2 * itp[ixp_1,ix_2]) + (cp_2 * itp[ixp_1,ixp_2])
            ret  = (cm_1 * itp1) + (c_1 * itp2) + (cp_1 * itp3)
        end
    end # line 22:
    ret
end

function mygetindex_fast(itp::Matrix, x_1::Number, x_2::Number)
    begin
        begin  # line 34:
            ix_1 = clamp(round(Int,real(x_1)),1,size(itp,1)) # line 35:
            fx_1 = x_1 - ix_1 # line 36:
            ix_1 += 0 # line 37:
            ixp_1 = min(size(itp,1),ix_1 + 1) # line 38:
            ixm_1 = max(1,ix_1 - 1)
        end
        begin  # line 34:
            ix_2 = clamp(round(Int,real(x_2)),1,size(itp,2)) # line 35:
            fx_2 = x_2 - ix_2 # line 36:
            ix_2 += 0 # line 37:
            ixp_2 = min(size(itp,2),ix_2 + 1) # line 38:
            ixm_2 = max(1,ix_2 - 1)
        end
    end # line 18:
    begin
        begin  # line 46:
            cm_1 = sqr(fx_1 - SimpleRatio(1,2)) / 2 # line 47:
            c_1 = SimpleRatio(3,4) - sqr(fx_1) # line 48:
            cp_1 = sqr(fx_1 + SimpleRatio(1,2)) / 2
        end
        begin  # line 46:
            cm_2 = sqr(fx_2 - SimpleRatio(1,2)) / 2 # line 47:
            c_2 = SimpleRatio(3,4) - sqr(fx_2) # line 48:
            cp_2 = sqr(fx_2 + SimpleRatio(1,2)) / 2
        end
    end # line 21:
    begin
        @inbounds begin
            itp1 = ((cm_2 * itp[ixm_1,ixm_2]) + (c_2 * itp[ixm_1,ix_2])) + (cp_2 * itp[ixm_1,ixp_2])
            itp2 = ((cm_2 * itp[ix_1,ixm_2]) + (c_2 * itp[ix_1,ix_2])) + (cp_2 * itp[ix_1,ixp_2])
            itp3 = ((cm_2 * itp[ixp_1,ixm_2]) + (c_2 * itp[ixp_1,ix_2])) + (cp_2 * itp[ixp_1,ixp_2])
            ret = ((cm_1 * itp1) + (c_1 * itp2)) + (cp_1 * itp3)
        end
    end # line 22:
    ret
end

sqr(x) = x*x

function sumA_slow(itp, dz, irng, jrng)
    s = zero(eltype(dz))
    dx, dy = dz[1], dz[2]
    for j in jrng
        for i in irng
            s += mygetindex_slow(itp, i+dx, j+dy)
        end
    end
    s
end

function sumA_fast(itp, dz, irng, jrng)
    s = zero(eltype(dz))
    dx, dy = dz[1], dz[2]
    for j in jrng
        for i in irng
            s += mygetindex_fast(itp, i+dx, j+dy)
        end
    end
    s
end

A = rand(3,3)
irng = linspace(1.5,2.4999,1000)
jrng = linspace(1.5,2.4999,1000)

println("Warmup @time")
@time 1

g = ForwardDiff.gradient(dz->sumA_slow(A, dz, irng, jrng))
dz = rand(2)
g(dz)
println("Without parentheses:")
@time g(dz)

g = ForwardDiff.gradient(dz->sumA_fast(A, dz, irng, jrng))
dz = rand(2)
g(dz)
println("With parentheses:")
@time g(dz)