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Annotation of gforth/fft.fs, revision 1.2

1.2     ! anton       1: \ fast fourier transform
        !             2: 
        !             3: \ Copyright (C) 2005 Free Software Foundation, Inc.
        !             4: 
        !             5: \ This file is part of Gforth.
        !             6: 
        !             7: \ Gforth is free software; you can redistribute it and/or
        !             8: \ modify it under the terms of the GNU General Public License
        !             9: \ as published by the Free Software Foundation; either version 2
        !            10: \ of the License, or (at your option) any later version.
        !            11: 
        !            12: \ This program is distributed in the hope that it will be useful,
        !            13: \ but WITHOUT ANY WARRANTY; without even the implied warranty of
        !            14: \ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
        !            15: \ GNU General Public License for more details.
        !            16: 
        !            17: \ You should have received a copy of the GNU General Public License
        !            18: \ along with this program; if not, write to the Free Software
        !            19: \ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA.
        !            20: 
1.1       pazsan     21: \           *** Fast Fourier Transformation ***        15may93py
                     22: 
                     23: require complex.fs
                     24: 
                     25: : Carray ( -- )  Create 0 ,  DOES> @ swap complex' + ;
                     26: Carray values
                     27: Carray expix
                     28: 
                     29: : r+ BEGIN 2dup xor -rot and dup WHILE 1 rshift REPEAT  drop ;
                     30: : reverse  ( n -- )  2/ dup dup 2* 1
                     31:   DO  dup I < IF  dup values I values 2dup z@ z@ z! z! THEN
                     32:       over r+  LOOP  2drop ;
                     33: 
                     34: \ reverse carry add                                    23sep05py
                     35: 8 Value #points
                     36: : realloc ( n addr -- )
                     37:     dup @  IF  dup @ free throw  THEN  swap allocate throw swap ! ;
                     38: : points  ( n --- )  dup to #points dup complex' dup
                     39:   ['] values >body realloc  2/
                     40:   ['] expix  >body realloc
                     41:   dup 0 DO  0e 0e I values z!  LOOP
                     42:   1e 0e 0 expix z! 2/ dup 2/ dup 2/ dup 1+ 1
                     43:   ?DO  pi I I' 1- 2* 2* fm*/ fsincos fswap   I expix z!  LOOP
                     44:   ?DO  I' I - 1- expix z@ fswap    I 1+ expix z!  LOOP  dup 2/
                     45:   ?DO  I' I -    expix z@ fswap fnegate fswap
                     46:                                     I    expix z!  LOOP ;
                     47: : .values  ( -- )  precision  4 set-precision
                     48:   #points 0 DO  I values z@ z. cr  LOOP  set-precision ;
                     49: : .expix  ( -- )   precision  4 set-precision
                     50:   #points 2/ 0 DO  I expix z@ z. cr  LOOP  set-precision ;
                     51: ' .values ALIAS .rvalues
                     52: 
                     53: \ FFT                                                  23sep05py
                     54: 
                     55: : z2dup+ zover zover z+ ;
                     56: 
                     57: : butterfly ( cexpix addr1 addr2 -- cexpix )
                     58:   zdup over z@ z* dup z@ z2dup+ z! zr- z! ;
                     59: : butterflies ( cexpix step off end start -- )
                     60:   ?DO  dup I + values I values butterfly
                     61:   over +LOOP  zdrop drop ;
                     62: : fft-step ( n flag step steps -- n flag step )
                     63:   0 DO  I 2 pick I' */ 2/ expix z@
                     64:         2 pick IF  fnegate  THEN  I' 2 pick I butterflies
                     65:   LOOP ;
                     66: 
                     67: \ FFT                                                  23sep05py
                     68: 
                     69: : (fft ( n flag -- )  swap dup reverse 1
                     70:   BEGIN  2dup >  WHILE  dup 2* swap fft-step
                     71:   REPEAT  2drop drop ;
                     72: 
                     73: : normalize ( -- )  #points dup s>f 1/f
                     74:   0 DO  I values dup z@ 2 fpick zscale z!  LOOP  fdrop ;
                     75: 
                     76: : fft  ( -- )  #points  true (fft ;
                     77: : rfft ( -- )  #points false (fft ;
                     78: