Inserting let to bind a local variable - ocaml

Question

I'm working through Oleg Kiselyov's tutorial Reconciling Abstraction with High Performance: A MetaOCaml approach. One exercise (exercise 23) asks for a let-insertion to bind an array index access to a local variable.
The function of question is vmult_ca, which generates code for multiplying arrays of complex numbers:
let vmult_ca :
(float_complex array -> float_complex array -> float_complex array -> unit)
code =
.<fun vout v1 v2 ->
let n = Array.length vout in
(* vector representations *)
.~(let vout = OVec (.<n>., fun i v ->
.<vout.(.~i) <- .~(of_code_complex v)>.) in
let v1 = Vec (.<n>., fun i ->
of_complex_code .<v1.(.~i)>.) in
let v2 = Vec (.<n>., fun i ->
of_complex_code .<v2.(.~i)>.) in
let module V = VMULT(FloatCodeComplex)(VecDyn) in
V.vmult vout v1 v2)
>.
;;
Where vout is the output vector that store the result.
Vec (n, fun i -> v) is an abstract vector where n is the length and fun i -> v maps each index to a value.
OVec (n, fun i v -> body) is an abstract "output vector" where n is the length and fun i v -> body runs on each index i and the associated output element v at i.
of_complex_code converts a complex code value to a code complex value, e.g. .<{real=1.0, imag=0.0}>. to {real=.<1.0>., imag=.<0.0>.}.
The module VMULT defines (point-wise) vector multiplication (see the code here for details).
When run, vmult_ca generates the following code:
val vmult_ca :
(float_complex array -> float_complex array -> float_complex array -> unit)
code = .<
fun vout_4 ->
fun v1_5 ->
fun v2_6 ->
let n_7 = Array.length vout_4 in
for i_8 = 0 to n_7 - 1 do
vout_4.(i_8) <-
{
Cmplx.im =
(((v1_5.(i_8)).Cmplx.re *. (v2_6.(i_8)).Cmplx.im) +.
((v1_5.(i_8)).Cmplx.im *. (v2_6.(i_8)).Cmplx.re));
Cmplx.re =
(((v1_5.(i_8)).Cmplx.re *. (v2_6.(i_8)).Cmplx.re) -.
((v1_5.(i_8)).Cmplx.im *. (v2_6.(i_8)).Cmplx.im))
}
done>.
Note v1_5.(i_8) is repeated 4 times. The challenge is to insert a let somewhere in vmult_ca to bind v1_5.(i_8) to a local variable to avoid the repetition. I was able to "cheat" by simply calling genlet on .<v1.(~i)>., but I have no clue where to insert the let without genlet; any hint would be appreciated.

Answer 1

Let-insertion is a primitive operation in BER, that automatically binds the passed code to a freshly generated variable.
Here is a working example, suppose you have the code that returns a square of an array element,
let power_elt xs i = xs.(i) * xs.(i)
and we want to generate an optimized code that has only one array access
let power_elt xs i = let x = xs.(i) in x*x
In the MetaOCaml style we can use genlet for that
let power_elt xs i =
let x = genlet .<xs.(i)>. in
.<.~x * .~x>.
The generated code for
let t = power_elt [|1;2;3|] 1;;
will be
val t : int code = .<let lv_8 = Stdlib.Array.get (* CSP xs *) 1 in lv_8 * lv_8>.