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