I am playing around with code generation for the evaluation of multivariate polynomials and hit a problem which I do not completely understand. The problem is already ocurring for the following function
function strange_allocations!(u, coefficients, x)
x1 = x[1]
x1_1 = x1
x1_2 = x1_1 * x1
x2 = x[2]
x2_1 = x2
x2_2 = x2_1 * x2
x3 = x[3]
x3_1 = x3
x3_2 = x3_1 * x3
x4 = x[4]
x4_1 = x4
x4_2 = x4_1 * x4
x5 = x[5]
x5_1 = x5
x5_2 = x5_1 * x5
x6 = x[6]
x6_1 = x6
x6_2 = x6_1 * x6
x7 = x[7]
x7_1 = x7
x7_2 = x7_1 * x7
x8 = x[8]
x8_1 = x8
x8_2 = x8_1 * x8
x9 = x[9]
x9_1 = x9
x9_2 = x9_1 * x9
x10 = x[10]
x10_1 = x10
x10_2 = x10_1 * x10
x11 = x[11]
x11_1 = x11
x11_2 = x11_1 * x11
x12 = x[12]
x12_1 = x12
x12_2 = x12_1 * x12
x13 = x[13]
x13_1 = x13
x13_2 = x13_1 * x13
x14 = x[14]
x14_1 = x14
x14_2 = x14_1 * x14
x15 = x[15]
x15_1 = x15
x15_2 = x15_1 * x15
u .= zero(Float64)
c = coefficients[1] * x1_1 * x5_1 * x6_1 * x7_1 * x10_1 * x11_1 * x12_1 * x15_2
_x1 = x1
_x2 = _x1 * x2
_x3 = _x2 * x3
_x4 = _x3 * x4
_x5 = _x4 * x5
_x6 = _x5 * x6
_x7 = _x6 * x7
_x8 = _x7 * x8
_x9 = _x8 * x9
_x10 = _x9 * x10
_x11 = _x10 * x11
_x12 = _x11 * x12
_x13 = _x12 * x13
_x14 = _x13 * x14
_y15 = x15
_y14 = _y15 * x14
_y13 = _y14 * x13
_y12 = _y13 * x12
_y11 = _y12 * x11
_y10 = _y11 * x10
_y9 = _y10 * x9
_y8 = _y9 * x8
_y7 = _y8 * x7
_y6 = _y7 * x6
_y5 = _y6 * x5
_y4 = _y5 * x4
_y3 = _y4 * x3
_y2 = _y3 * x2
u[1] = muladd(c * 2, _y2, u[1])
u[2] = muladd(c * _x1, _y3, u[2])
u[3] = muladd(c * _x2, _y4, u[3])
u[4] = muladd(c * _x3, _y5, u[4])
u[5] = muladd(c * 2 * _x4, _y6, u[5])
u[6] = muladd(c * 2 * _x5, _y7, u[6])
u[7] = muladd(c * 2 * _x6, _y8, u[7])
u[8] = muladd(c * _x7, _y9, u[8])
u[9] = muladd(c * _x8, _y10, u[9])
u[10] = muladd(c * 2 * _x9, _y11, u[10])
u[11] = muladd(c * 2 * _x10, _y12, u[11])
u[12] = muladd(c * 2 * _x11, _y13, u[12])
u[13] = muladd(c * _x12, _y14, u[13])
u[14] = muladd(c * _x13, _y15, u[14])
u[15] = muladd(c * 3, _x14, u[15])
u
end
If you call the function with
coefficients = rand(1)
x = rand(15)
u = zeros(15)
@btime strange_allocations!($u, $coefficients, $x)
Then @btime reports 40.967 ns (7 allocations: 112 bytes). Why are allocations happening? Is the function exceeding the stack limit and then moving things to the heap instead? Is the limit somewhere documented?
Update: This behaviour seems only to happen for Julia v0.6.1, on master (8 days old) everything works as expected! Does anybody know wether this change will be backported?