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(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the Q Public License version 1.0. *)
(* *)
(***********************************************************************)
(* $Id: fft.ml 7017 2005-08-12 09:22:04Z xleroy $ *)
let pi = 3.14159265358979323846
let tpi = 2.0 *. pi
let fft px py np =
let i = ref 2 in
let m = ref 1 in
while !i < np do
i := !i + !i;
m := !m + 1
done;
let n = !i in
if n <> np
then
for i = np + 1 to n do
px.(i) <- 0.0;
py.(i) <- 0.0
(*
print_string "Use "; print_int n;
print_string " point fft"; print_newline()
*)
done;
let n2 = ref (n + n) in
for _ = 1 to !m - 1 do
n2 := !n2 / 2;
let n4 = !n2 / 4 in
let e = tpi /. float !n2 in
for j = 1 to n4 do
let a = e *. float (j - 1) in
let a3 = 3.0 *. a in
let cc1 = cos a in
let ss1 = sin a in
let cc3 = cos a3 in
let ss3 = sin a3 in
let is = ref j in
let id = ref (2 * !n2) in
while !is < n do
let i0r = ref !is in
while !i0r < n do
let i0 = !i0r in
let i1 = i0 + n4 in
let i2 = i1 + n4 in
let i3 = i2 + n4 in
let r1 = px.(i0) -. px.(i2) in
px.(i0) <- px.(i0) +. px.(i2);
let r2 = px.(i1) -. px.(i3) in
px.(i1) <- px.(i1) +. px.(i3);
let s1 = py.(i0) -. py.(i2) in
py.(i0) <- py.(i0) +. py.(i2);
let s2 = py.(i1) -. py.(i3) in
py.(i1) <- py.(i1) +. py.(i3);
let s3 = r1 -. s2 in
let r1 = r1 +. s2 in
let s2 = r2 -. s1 in
let r2 = r2 +. s1 in
px.(i2) <- (r1 *. cc1) -. (s2 *. ss1);
py.(i2) <- (-.s2 *. cc1) -. (r1 *. ss1);
px.(i3) <- (s3 *. cc3) +. (r2 *. ss3);
py.(i3) <- (r2 *. cc3) -. (s3 *. ss3);
i0r := i0 + !id
done;
is := (2 * !id) - !n2 + j;
id := 4 * !id
done
done
done;
(************************************)
(* Last stage, length=2 butterfly *)
(************************************)
let is = ref 1 in
let id = ref 4 in
while !is < n do
let i0r = ref !is in
while !i0r <= n do
let i0 = !i0r in
let i1 = i0 + 1 in
let r1 = px.(i0) in
px.(i0) <- r1 +. px.(i1);
px.(i1) <- r1 -. px.(i1);
let r1 = py.(i0) in
py.(i0) <- r1 +. py.(i1);
py.(i1) <- r1 -. py.(i1);
i0r := i0 + !id
done;
is := (2 * !id) - 1;
id := 4 * !id
done;
(*************************)
(* Bit reverse counter *)
(*************************)
let j = ref 1 in
for i = 1 to n - 1 do
if i < !j
then (
let xt = px.(!j) in
px.(!j) <- px.(i);
px.(i) <- xt;
let xt = py.(!j) in
py.(!j) <- py.(i);
py.(i) <- xt);
let k = ref (n / 2) in
while !k < !j do
j := !j - !k;
k := !k / 2
done;
j := !j + !k
done;
n
let test np =
(* print_int np; print_string "... "; flush stdout;*)
let enp = float np in
let npm = (np / 2) - 1 in
let pxr = Array.make (np + 2) 0.0 and pxi = Array.make (np + 2) 0.0 in
let t = pi /. enp in
pxr.(1) <- (enp -. 1.0) *. 0.5;
pxi.(1) <- 0.0;
let n2 = np / 2 in
pxr.(n2 + 1) <- -0.5;
pxi.(n2 + 1) <- 0.0;
for i = 1 to npm do
let j = np - i in
pxr.(i + 1) <- -0.5;
pxr.(j + 1) <- -0.5;
let z = t *. float i in
let y = -0.5 *. (cos z /. sin z) in
pxi.(i + 1) <- y;
pxi.(j + 1) <- -.y
done;
(*
print_newline();
for i=0 to 15 do Printf.printf "%d %f %f\n" i pxr.(i+1) pxi.(i+1) done;
*)
let _ = fft pxr pxi np in
(*
for i=0 to 15 do Printf.printf "%d %f %f\n" i pxr.(i+1) pxi.(i+1) done;
*)
let zr = ref 0.0 in
let zi = ref 0.0 in
let kr = ref 0 in
let ki = ref 0 in
for i = 0 to np - 1 do
let a = abs_float (pxr.(i + 1) -. float i) in
if !zr < a
then (
zr := a;
kr := i);
let a = abs_float pxi.(i + 1) in
if !zi < a
then (
zi := a;
ki := i)
done;
(*print !zr; print !zi;*)
if abs_float !zr <= 1e-8 && abs_float !zi <= 1e-8
then ( (*print_string "ok"*) )
else assert false (*print_string "ERROR"*);
( (* print_newline()*) )
let _ =
let np = ref 16 in
for _ = 1 to 16 do
test !np;
np := !np * 2
done
|
