[Caml-list] optimizing numerical code

[Joel Reymont <joelr1@gmail.com>]

Consider the following two functions that I'm trying to optimize.

Why is there an allocation for every iteration of the loop in divergence1 but not in divergence2?

What else can I do to make divergence2 faster, apart from using -unsafe?

	Thanks in advance, Joel

---

let js_divergence1 v1 v2 =
  let acc = ref 0. in
  for i = 0 to (Array.length v1) - 1 do
    let x = v1.(i)
    and y = v2.(i) in
    let m = 0.5 *. (x +. y) in
    let d1 = x *. log (x /. m) 
    and d2 = y *. log (y /. m) in
    acc := !acc +. d1 +. d2
  done;
  (!acc)

let js_divergence2 v1 v2 =
  let sum1 = ref 0.
  and sum2 = ref 0. in
  for i = 0 to (Array.length v1) - 1 do
    let x = v1.(i)
    and y = v2.(i) in
    let m = 2. /. (x +. y) in
    let d1 = x *. log (x *. m) 
    and d2 = y *. log (y *. m) in
    sum1 := !sum1 +. d1;
    sum2 := !sum2 +. d2;
  done;
  !sum1 +. !sum2

ocamlopt -dcmm

(function camlFoo__js_divergence1_1030 (v1/1031: addr v2/1032: addr)
 (let acc/1033 "camlFoo__3"
   (let (i/1034 1 bound/1066 (+ (or (>>u (load (+a v1/1031 -8)) 9) 1) -2))
     (catch
       (if (> i/1034 bound/1066) (exit 17)
         (loop
           (let
             (x/1067
                (seq (checkbound (>>u (load (+a v1/1031 -8)) 9) i/1034)
                  (load float64u (+a (+a v1/1031 (<< i/1034 2)) -4)))
              y/1068
                (seq (checkbound (>>u (load (+a v2/1032 -8)) 9) i/1034)
                  (load float64u (+a (+a v2/1032 (<< i/1034 2)) -4)))
              m/1069 (*f 0.5 (+f x/1067 y/1068))
              d1/1070 (*f x/1067 (extcall "log" (/f x/1067 m/1069) float))
              d2/1071 (*f y/1068 (extcall "log" (/f y/1068 m/1069) float)))
             (assign acc/1033
                       (alloc 1277
                         (+f (+f (load float64u acc/1033) d1/1070) d2/1071))))
           (let i/1065 i/1034 (assign i/1034 (+ i/1034 2))
             (if (== i/1065 bound/1066) (exit 17) []))))
     with(17) []))
   acc/1033))

(function camlFoo__js_divergence2_1040 (v1/1041: addr v2/1042: addr)
 (let (sum1/1055 0. sum2/1056 0.)
   (let (i/1045 1 bound/1058 (+ (or (>>u (load (+a v1/1041 -8)) 9) 1) -2))
     (catch
       (if (> i/1045 bound/1058) (exit 16)
         (loop
           (let
             (x/1059
                (seq (checkbound (>>u (load (+a v1/1041 -8)) 9) i/1045)
                  (load float64u (+a (+a v1/1041 (<< i/1045 2)) -4)))
              y/1060
                (seq (checkbound (>>u (load (+a v2/1042 -8)) 9) i/1045)
                  (load float64u (+a (+a v2/1042 (<< i/1045 2)) -4)))
              m/1061 (/f 2. (+f x/1059 y/1060))
              d1/1062 (*f x/1059 (extcall "log" (*f x/1059 m/1061) float))
              d2/1063 (*f y/1060 (extcall "log" (*f y/1060 m/1061) float)))
             (assign sum1/1055 (+f sum1/1055 d1/1062))
             (assign sum2/1056 (+f sum2/1056 d2/1063)))
           (let i/1057 i/1045 (assign i/1045 (+ i/1045 2))
             (if (== i/1057 bound/1058) (exit 16) []))))
     with(16) []))
   (alloc 1277 (+f sum1/1055 sum2/1056))))

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