Chris@42: (*
Chris@42:  * Copyright (c) 1997-1999 Massachusetts Institute of Technology
Chris@42:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@42:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@42:  *
Chris@42:  * This program is free software; you can redistribute it and/or modify
Chris@42:  * it under the terms of the GNU General Public License as published by
Chris@42:  * the Free Software Foundation; either version 2 of the License, or
Chris@42:  * (at your option) any later version.
Chris@42:  *
Chris@42:  * This program is distributed in the hope that it will be useful,
Chris@42:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@42:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@42:  * GNU General Public License for more details.
Chris@42:  *
Chris@42:  * You should have received a copy of the GNU General Public License
Chris@42:  * along with this program; if not, write to the Free Software
Chris@42:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@42:  *
Chris@42:  *)
Chris@42: 
Chris@42: (* abstraction layer for complex operations *)
Chris@42: open Littlesimp
Chris@42: open Expr
Chris@42: 
Chris@42: (* type of complex expressions *)
Chris@42: type expr = CE of Expr.expr * Expr.expr
Chris@42: 
Chris@42: let two = CE (makeNum Number.two, makeNum Number.zero)
Chris@42: let one = CE (makeNum Number.one, makeNum Number.zero)
Chris@42: let i = CE (makeNum Number.zero, makeNum Number.one)
Chris@42: let zero = CE (makeNum Number.zero, makeNum Number.zero)
Chris@42: let make (r, i) = CE (r, i)
Chris@42: 
Chris@42: let uminus (CE (a, b)) =  CE (makeUminus a, makeUminus b)
Chris@42: 
Chris@42: let inverse_int n = CE (makeNum (Number.div Number.one (Number.of_int n)),
Chris@42: 			makeNum Number.zero)
Chris@42: 
Chris@42: let inverse_int_sqrt n = 
Chris@42:   CE (makeNum (Number.div Number.one (Number.sqrt (Number.of_int n))),
Chris@42:       makeNum Number.zero)
Chris@42: let int_sqrt n = 
Chris@42:   CE (makeNum (Number.sqrt (Number.of_int n)),
Chris@42:       makeNum Number.zero)
Chris@42: 
Chris@42: let nan x = CE (NaN x, makeNum Number.zero)
Chris@42: 
Chris@42: let half = inverse_int 2
Chris@42: 
Chris@42: let times3x3 (CE (a, b)) (CE (c, d)) = 
Chris@42:   CE (makePlus [makeTimes (c, makePlus [a; makeUminus (b)]);
Chris@42: 	        makeTimes (b, makePlus [c; makeUminus (d)])],
Chris@42:       makePlus [makeTimes (a, makePlus [c; d]);
Chris@42: 	        makeUminus(makeTimes (c, makePlus [a; makeUminus (b)]))])
Chris@42: 
Chris@42: let times (CE (a, b)) (CE (c, d)) = 
Chris@42:   if not !Magic.threemult then
Chris@42:     CE (makePlus [makeTimes (a, c); makeUminus (makeTimes (b, d))],
Chris@42:         makePlus [makeTimes (a, d); makeTimes (b, c)])
Chris@42:   else if is_constant c && is_constant d then
Chris@42:     times3x3 (CE (a, b)) (CE (c, d))
Chris@42:   else (* hope a and b are constant expressions *)
Chris@42:     times3x3 (CE (c, d)) (CE (a, b))
Chris@42: 
Chris@42: let ctimes (CE (a, _)) (CE (c, _)) = 
Chris@42:   CE (CTimes (a, c), makeNum Number.zero)
Chris@42: 
Chris@42: let ctimesj (CE (a, _)) (CE (c, _)) = 
Chris@42:   CE (CTimesJ (a, c), makeNum Number.zero)
Chris@42:       
Chris@42: (* complex exponential (of root of unity); returns exp(2*pi*i/n * m) *)
Chris@42: let exp n i =
Chris@42:   let (c, s) = Number.cexp n i
Chris@42:   in CE (makeNum c, makeNum s)
Chris@42: 
Chris@42: (* various trig functions evaluated at (2*pi*i/n * m) *)
Chris@42: let sec n m =
Chris@42:   let (c, s) = Number.cexp n m
Chris@42:   in CE (makeNum (Number.div Number.one c), makeNum Number.zero)
Chris@42: let csc n m =
Chris@42:   let (c, s) = Number.cexp n m
Chris@42:   in CE (makeNum (Number.div Number.one s), makeNum Number.zero)
Chris@42: let tan n m =
Chris@42:   let (c, s) = Number.cexp n m
Chris@42:   in CE (makeNum (Number.div s c), makeNum Number.zero)
Chris@42: let cot n m =
Chris@42:   let (c, s) = Number.cexp n m
Chris@42:   in CE (makeNum (Number.div c s), makeNum Number.zero)
Chris@42:     
Chris@42: (* complex sum *)
Chris@42: let plus a =
Chris@42:   let rec unzip_complex = function
Chris@42:       [] -> ([], [])
Chris@42:     | ((CE (a, b)) :: s) ->
Chris@42:         let (r,i) = unzip_complex s
Chris@42: 	in
Chris@42: 	(a::r), (b::i) in
Chris@42:   let (c, d) = unzip_complex a in
Chris@42:   CE (makePlus c, makePlus d)
Chris@42: 
Chris@42: (* extract real/imaginary *)
Chris@42: let real (CE (a, b)) = CE (a, makeNum Number.zero)
Chris@42: let imag (CE (a, b)) = CE (b, makeNum Number.zero)
Chris@42: let iimag (CE (a, b)) = CE (makeNum Number.zero, b)
Chris@42: let conj (CE (a, b)) = CE (a, makeUminus b)
Chris@42: 
Chris@42:     
Chris@42: (* abstraction of sum_{i=0}^{n-1} *)
Chris@42: let sigma a b f = plus (List.map f (Util.interval a b))
Chris@42: 
Chris@42: (* store and assignment operations *)
Chris@42: let store_real v (CE (a, b)) = Expr.Store (v, a)
Chris@42: let store_imag v (CE (a, b)) = Expr.Store (v, b)
Chris@42: let store (vr, vi) x = (store_real vr x, store_imag vi x)
Chris@42: 
Chris@42: let assign_real v (CE (a, b)) = Expr.Assign (v, a)
Chris@42: let assign_imag v (CE (a, b)) = Expr.Assign (v, b)
Chris@42: let assign (vr, vi) x = (assign_real vr x, assign_imag vi x)
Chris@42: 
Chris@42: 
Chris@42: (************************
Chris@42:    shortcuts 
Chris@42:  ************************)
Chris@42: let (@*) = times
Chris@42: let (@+) a b = plus [a; b]
Chris@42: let (@-) a b = plus [a; uminus b]
Chris@42: 
Chris@42: (* type of complex signals *)
Chris@42: type signal = int -> expr
Chris@42: 
Chris@42: (* make a finite signal infinite *)
Chris@42: let infinite n signal i = if ((0 <= i) && (i < n)) then signal i else zero
Chris@42: 
Chris@42: let hermitian n a =
Chris@42:   Util.array n (fun i ->
Chris@42:     if (i = 0) then real (a 0)
Chris@42:     else if (i < n - i)  then (a i)
Chris@42:     else if (i > n - i)  then conj (a (n - i))
Chris@42:     else real (a i))
Chris@42: 
Chris@42: let antihermitian n a =
Chris@42:   Util.array n (fun i ->
Chris@42:     if (i = 0) then iimag (a 0)
Chris@42:     else if (i < n - i)  then (a i)
Chris@42:     else if (i > n - i)  then uminus (conj (a (n - i)))
Chris@42:     else iimag (a i))