Hello all,

I've been trying to optimize a quick nbody gravitational calculation in 
ocaml (it's for the shootout benchmark at 
http://shootout.alioth.debian.org/ ), and I've been getting some weird 
results out of gprof.  I have a function which is used twice to compute 
the total energy of the system --- once at the beginning of the 
integration, and once at the end.  The output of ocamlprof on a 
bytecode executable reflects the number of times this function is 
called correctly:

let energy bl =
   (* 2 *) let t_accumulator acc b =
     (* 10 *) acc +. (t b) in
   let v_accumulator acc a b =
     (* 20 *) acc +. (v a b) in
   let acc1 = List.fold_left t_accumulator 0.0 bl in
     fold_left_n2 v_accumulator acc1 bl;;

However, no matter how many integration steps I take (1000, 1000000, 
10000000), this function appears to take up the same fraction of the 
runtime according to gprof (after compiling with ocamlopt -p):

  %   cumulative   self              self     total
  time   seconds   seconds    calls  ms/call  ms/call  name
  28.4      28.52    28.52                             
_camlNbody__v_accumulator_198 [1]
  22.8      51.47    22.95                             ___sqrt [2]
  16.8      68.38    16.91                             
_camlNbody__force_on_135 [3]
   6.5      74.95     6.57                             
_camlNbody__norm_93 [4]
   5.0      80.00     5.05                             
_camlList__iter_98 [5]
   4.4      84.41     4.41                             
_camlNbody__update_pos_170 [6]
   4.2      88.60     4.19                             
_camlNbody__norm2_91 [7]
   3.2      91.77     3.17                             
_camlNbody__update_forces_145 [8]
   2.4      94.14     2.37                             
_camlNbody__up_177 [9]
   1.7      95.82     1.68                             
_camlNbody__loop_152 [10]
   1.2      97.04     1.22                             _caml_curry2 [11]
   0.8      97.88     0.84                             
_camlNbody__zero_body_force_133 [12]
   0.6      98.52     0.64                             _caml_curry2_1 
[13]
   0.4      98.95     0.43                             
_camlNbody__iter_n2_149 [14]
   0.4      99.35     0.40                             
_camlNbody__step_174 [15]
   0.3      99.68     0.33                             _camlList__tl_66 
[16]
   0.2      99.90     0.22                             _camlList__hd_63 
[17]
   0.2     100.09     0.19                             
_camlNbody__main_223 [18]
   0.1     100.18     0.09                             
_caml_oldify_local_roots [19]
   0.1     100.24     0.06                             
_caml_major_collection_slice [20]
   0.0     100.29     0.05                             _caml_darken [21]
   0.0     100.33     0.04                             _caml_call_gc [22]
   0.0     100.36     0.03                             
_caml_empty_minor_heap [23]
   0.0     100.39     0.03                             _caml_fl_allocate 
[24]
   0.0     100.42     0.03                             
_caml_minor_collection [25]
   0.0     100.44     0.02                             _caml_gc_message 
[26]
   0.0     100.46     0.02                             _caml_oldify_one 
[27]
   0.0     100.48     0.02                             _szone_malloc [28]
   0.0     100.49     0.01                             _alloc_to_do [29]
   0.0     100.50     0.01                             
_caml_compact_heap_maybe [30]
   0.0     100.51     0.01                             _caml_do_roots 
[31]
   0.0     100.52     0.01                             
_caml_final_do_strong_roots [32]
   0.0     100.53     0.01                             
_caml_final_empty_young [33]
   0.0     100.54     0.01                             
_caml_final_update [34]
   0.0     100.55     0.01                             
_caml_fl_merge_block [35]
   0.0     100.56     0.01                             
_caml_oldify_mopup [36]
   0.0     100.57     0.01                             _mark_slice [37]
   0.0     100.58     0.01                             _sweep_slice [38]

This is on a run with 1 000 000 integration steps.  Is ocamlprof -p 
broken on Mac os X?  There are several candidate functions which could 
be taking that much time and don't appear in the list, so it looks like 
it's just confused the names of various functions; is there a way I can 
fix this?

Thanks for the help!

Will Farr

BTW, on my system, this calculation takes ~2 times as long as a java 
program to do the same thing; if anyone wants to defend the honor of 
ocaml better, I would be happy to pass along source code, and we can 
see whether there's something faster to be done.