Updates

fftw-3.3.10/genfft/conv.ml

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+(*
+ * Copyright (c) 1997-1999 Massachusetts Institute of Technology
+ * Copyright (c) 2003, 2007-14 Matteo Frigo
+ * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ *
+*)
+
+open Complex
+open Util
+
+let polyphase m a ph i = a (m * i + ph)
+
+let rec divmod n i =
+  if (i < 0) then 
+    let (a, b) = divmod n (i + n)
+    in (a - 1, b)
+  else (i / n, i mod n)
+
+let unpolyphase m a i = let (x, y) = divmod m i in a y x
+
+let lift2 f a b i = f (a i) (b i)
+
+(* convolution of signals A and B *)
+let rec conv na a nb b =
+  let rec naive na a nb b i =
+    sigma 0 na (fun j -> (a j) @* (b (i - j)))
+
+  and recur na a nb b =
+    if (na <= 1 || nb <= 1) then
+      naive na a nb b
+    else
+      let p = polyphase 2 in
+      let ee = conv (na - na / 2) (p a 0) (nb - nb / 2) (p b 0)
+      and eo = conv (na - na / 2) (p a 0) (nb / 2) (p b 1)
+      and oe = conv (na / 2) (p a 1) (nb - nb / 2) (p b 0)
+      and oo = conv (na / 2) (p a 1) (nb / 2) (p b 1) in
+      unpolyphase 2 (function
+	  0 -> fun i -> (ee i) @+ (oo (i - 1))
+	| 1 -> fun i -> (eo i) @+ (oe i) 
+	| _ -> failwith "recur")
+
+
+  (* Karatsuba variant 1: (a+bx)(c+dx) = (ac+bdxx)+((a+b)(c+d)-ac-bd)x *)
+  and karatsuba1 na a nb b =
+      let p = polyphase 2 in
+      let ae = p a 0 and nae = na - na / 2
+      and ao = p a 1 and nao = na / 2
+      and be = p b 0 and nbe = nb - nb / 2
+      and bo = p b 1 and nbo = nb / 2 in
+      let ae = infinite nae ae and ao = infinite nao ao
+      and be = infinite nbe be and bo = infinite nbo bo in
+      let aeo = lift2 (@+) ae ao and naeo = nae
+      and beo = lift2 (@+) be bo and nbeo = nbe in
+      let ee = conv nae ae nbe be 
+      and oo = conv nao ao nbo bo
+      and eoeo = conv naeo aeo nbeo beo in
+
+      let q = function
+	  0 -> fun i -> (ee i)  @+ (oo (i - 1))
+	| 1 -> fun i -> (eoeo i) @- ((ee i) @+ (oo i))
+	| _ -> failwith "karatsuba1" in
+      unpolyphase 2 q
+
+  (* Karatsuba variant 2: 
+     (a+bx)(c+dx) = ((a+b)c-b(c-dxx))+x((a+b)c-a(c-d)) *)
+  and karatsuba2 na a nb b =
+      let p = polyphase 2 in
+      let ae = p a 0 and nae = na - na / 2
+      and ao = p a 1 and nao = na / 2
+      and be = p b 0 and nbe = nb - nb / 2
+      and bo = p b 1 and nbo = nb / 2 in
+      let ae = infinite nae ae and ao = infinite nao ao
+      and be = infinite nbe be and bo = infinite nbo bo in
+
+      let c1 = conv nae (lift2 (@+) ae ao) nbe be
+      and c2 = conv nao ao (nbo + 1) (fun i -> be i @- bo (i - 1))
+      and c3 = conv nae ae nbe (lift2 (@-) be bo) in
+
+      let q = function
+	  0 -> lift2 (@-) c1 c2
+	| 1 -> lift2 (@-) c1 c3
+	| _ -> failwith "karatsuba2" in
+      unpolyphase 2 q
+
+  and karatsuba na a nb b =
+    let m = na + nb - 1 in
+    if (m < !Magic.karatsuba_min) then
+      recur na a nb b
+    else
+      match !Magic.karatsuba_variant with
+	1 -> karatsuba1 na a nb b
+      |	2 -> karatsuba2 na a nb b
+      |	_ -> failwith "unknown karatsuba variant"
+
+  and via_circular na a nb b =
+    let m = na + nb - 1 in
+    if (m < !Magic.circular_min) then
+      karatsuba na a nb b
+    else
+      let rec find_min n = if n >= m then n else find_min (2 * n) in
+      circular (find_min 1) a b
+
+  in
+  let a = infinite na a and b = infinite nb b in
+  let res = array (na + nb - 1) (via_circular na a nb b) in
+  infinite (na + nb - 1) res
+    
+and circular n a b =
+  let via_dft n a b =
+    let fa = Fft.dft (-1) n a 
+    and fb = Fft.dft (-1) n b
+    and scale = inverse_int n in
+    let fab i = ((fa i) @* (fb i)) @* scale in
+    Fft.dft 1 n fab
+
+  in via_dft n a b