cannam@127: (* cannam@127: * Copyright (c) 1997-1999 Massachusetts Institute of Technology cannam@127: * Copyright (c) 2003, 2007-14 Matteo Frigo cannam@127: * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology cannam@127: * cannam@127: * This program is free software; you can redistribute it and/or modify cannam@127: * it under the terms of the GNU General Public License as published by cannam@127: * the Free Software Foundation; either version 2 of the License, or cannam@127: * (at your option) any later version. cannam@127: * cannam@127: * This program is distributed in the hope that it will be useful, cannam@127: * but WITHOUT ANY WARRANTY; without even the implied warranty of cannam@127: * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the cannam@127: * GNU General Public License for more details. cannam@127: * cannam@127: * You should have received a copy of the GNU General Public License cannam@127: * along with this program; if not, write to the Free Software cannam@127: * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA cannam@127: * cannam@127: *) cannam@127: cannam@127: open Complex cannam@127: open Util cannam@127: cannam@127: let polyphase m a ph i = a (m * i + ph) cannam@127: cannam@127: let rec divmod n i = cannam@127: if (i < 0) then cannam@127: let (a, b) = divmod n (i + n) cannam@127: in (a - 1, b) cannam@127: else (i / n, i mod n) cannam@127: cannam@127: let unpolyphase m a i = let (x, y) = divmod m i in a y x cannam@127: cannam@127: let lift2 f a b i = f (a i) (b i) cannam@127: cannam@127: (* convolution of signals A and B *) cannam@127: let rec conv na a nb b = cannam@127: let rec naive na a nb b i = cannam@127: sigma 0 na (fun j -> (a j) @* (b (i - j))) cannam@127: cannam@127: and recur na a nb b = cannam@127: if (na <= 1 || nb <= 1) then cannam@127: naive na a nb b cannam@127: else cannam@127: let p = polyphase 2 in cannam@127: let ee = conv (na - na / 2) (p a 0) (nb - nb / 2) (p b 0) cannam@127: and eo = conv (na - na / 2) (p a 0) (nb / 2) (p b 1) cannam@127: and oe = conv (na / 2) (p a 1) (nb - nb / 2) (p b 0) cannam@127: and oo = conv (na / 2) (p a 1) (nb / 2) (p b 1) in cannam@127: unpolyphase 2 (function cannam@127: 0 -> fun i -> (ee i) @+ (oo (i - 1)) cannam@127: | 1 -> fun i -> (eo i) @+ (oe i) cannam@127: | _ -> failwith "recur") cannam@127: cannam@127: cannam@127: (* Karatsuba variant 1: (a+bx)(c+dx) = (ac+bdxx)+((a+b)(c+d)-ac-bd)x *) cannam@127: and karatsuba1 na a nb b = cannam@127: let p = polyphase 2 in cannam@127: let ae = p a 0 and nae = na - na / 2 cannam@127: and ao = p a 1 and nao = na / 2 cannam@127: and be = p b 0 and nbe = nb - nb / 2 cannam@127: and bo = p b 1 and nbo = nb / 2 in cannam@127: let ae = infinite nae ae and ao = infinite nao ao cannam@127: and be = infinite nbe be and bo = infinite nbo bo in cannam@127: let aeo = lift2 (@+) ae ao and naeo = nae cannam@127: and beo = lift2 (@+) be bo and nbeo = nbe in cannam@127: let ee = conv nae ae nbe be cannam@127: and oo = conv nao ao nbo bo cannam@127: and eoeo = conv naeo aeo nbeo beo in cannam@127: cannam@127: let q = function cannam@127: 0 -> fun i -> (ee i) @+ (oo (i - 1)) cannam@127: | 1 -> fun i -> (eoeo i) @- ((ee i) @+ (oo i)) cannam@127: | _ -> failwith "karatsuba1" in cannam@127: unpolyphase 2 q cannam@127: cannam@127: (* Karatsuba variant 2: cannam@127: (a+bx)(c+dx) = ((a+b)c-b(c-dxx))+x((a+b)c-a(c-d)) *) cannam@127: and karatsuba2 na a nb b = cannam@127: let p = polyphase 2 in cannam@127: let ae = p a 0 and nae = na - na / 2 cannam@127: and ao = p a 1 and nao = na / 2 cannam@127: and be = p b 0 and nbe = nb - nb / 2 cannam@127: and bo = p b 1 and nbo = nb / 2 in cannam@127: let ae = infinite nae ae and ao = infinite nao ao cannam@127: and be = infinite nbe be and bo = infinite nbo bo in cannam@127: cannam@127: let c1 = conv nae (lift2 (@+) ae ao) nbe be cannam@127: and c2 = conv nao ao (nbo + 1) (fun i -> be i @- bo (i - 1)) cannam@127: and c3 = conv nae ae nbe (lift2 (@-) be bo) in cannam@127: cannam@127: let q = function cannam@127: 0 -> lift2 (@-) c1 c2 cannam@127: | 1 -> lift2 (@-) c1 c3 cannam@127: | _ -> failwith "karatsuba2" in cannam@127: unpolyphase 2 q cannam@127: cannam@127: and karatsuba na a nb b = cannam@127: let m = na + nb - 1 in cannam@127: if (m < !Magic.karatsuba_min) then cannam@127: recur na a nb b cannam@127: else cannam@127: match !Magic.karatsuba_variant with cannam@127: 1 -> karatsuba1 na a nb b cannam@127: | 2 -> karatsuba2 na a nb b cannam@127: | _ -> failwith "unknown karatsuba variant" cannam@127: cannam@127: and via_circular na a nb b = cannam@127: let m = na + nb - 1 in cannam@127: if (m < !Magic.circular_min) then cannam@127: karatsuba na a nb b cannam@127: else cannam@127: let rec find_min n = if n >= m then n else find_min (2 * n) in cannam@127: circular (find_min 1) a b cannam@127: cannam@127: in cannam@127: let a = infinite na a and b = infinite nb b in cannam@127: let res = array (na + nb - 1) (via_circular na a nb b) in cannam@127: infinite (na + nb - 1) res cannam@127: cannam@127: and circular n a b = cannam@127: let via_dft n a b = cannam@127: let fa = Fft.dft (-1) n a cannam@127: and fb = Fft.dft (-1) n b cannam@127: and scale = inverse_int n in cannam@127: let fab i = ((fa i) @* (fb i)) @* scale in cannam@127: Fft.dft 1 n fab cannam@127: cannam@127: in via_dft n a b