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\ complex numbers
\ Copyright (C) 2005 Free Software Foundation, Inc.
\ This file is part of Gforth.
\ Gforth 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., 59 Temple Place, Suite 330, Boston, MA 02111, USA.
\ *** Complex arithmetic *** 23sep91py
: complex' 2* floats ;
: complex+ float+ float+ ;
\ simple operations 02mar05py
: fl> f@local0 lp+ ;
: zdup fover fover ;
: zdrop fdrop fdrop ;
: zover 3 fpick 3 fpick ;
: z>r f>l f>l ;
: zr> fl> fl> ;
: zswap frot f>l frot fl> ;
: zpick 2* 1+ >r r@ fpick r> fpick ;
\ : zpin 2* 1+ >r r@ fpin r> fpin ;
: zdepth fdepth 2/ ;
: zrot z>r zswap zr> zswap ;
: z-rot zswap z>r zswap zr> ;
: z@ dup >r f@ r> float+ f@ ;
: z! dup >r float+ f! r> f! ;
\ simple operations 02mar05py
: z+ frot f+ f>l f+ fl> ;
: z- fnegate frot f+ f>l f- fl> ;
: zr- frot f- f>l fswap f- fl> ;
: x+ frot f+ fswap ;
: x- fnegate x+ ;
: z* fdup 4 fpick f* f>l fover 3 fpick f* f>l
f>l fswap fl> f* f>l f* fl> f- fl> fl> f+ ;
: zscale ftuck f* f>l f* fl> ;
\ simple operations 02mar05py
: znegate fnegate fswap fnegate fswap ;
: zconj fnegate ;
: z*i fnegate fswap ;
: z/i fswap fnegate ;
: zsqabs fdup f* fswap fdup f* f+ ;
: 1/z zconj zdup zsqabs 1/f zscale ;
: z/ 1/z z* ;
: |z| zsqabs fsqrt ;
: zabs |z| 0e ;
: z2/ f2/ f>l f2/ fl> ;
: z2* f2* f>l f2* fl> ;
: >polar ( z -- r theta ) zdup |z| fswap frot fatan2 ;
: polar> ( r theta -- z ) fsincos frot zscale fswap ;
\ zexp zln 02mar05py
: zexp fsincos fswap frot fexp zscale ;
: pln zdup fswap fatan2 frot frot |z| fln fswap ;
: zln >polar fswap fln fswap ;
: z0= f0= >r f0= r> and ;
: zsqrt zdup z0= 0= IF
fdup f0= IF fdrop fsqrt 0e EXIT THEN
zln z2/ zexp THEN ;
: z** zswap zln z* zexp ;
\ Test: Fibonacci-Zahlen
1e 5e fsqrt f+ f2/ fconstant g 1e g f- fconstant -h
: zfib zdup z>r g 0e zswap z**
zr> zswap z>r -h 0e zswap z** znegate zr> z+
[ g -h f- 1/f ] FLiteral zscale ;
\ complexe Operationen 02mar05py
: zsinh zexp zdup 1/z z- z2/ ;
: zcosh zexp zdup 1/z z+ z2/ ;
: ztanh z2* zexp zdup 1e 0e z- zswap 1e 0e z+ z/ ;
: zsin z*i zsinh z/i ;
: zcos z*i zcosh ;
: ztan z*i ztanh z/i ;
: Real fdrop ;
: Imag fnip ;
: Re Real 0e ;
: Im Imag 0e ;
\ complexe Operationen 02mar05py
: zasinh zdup 1e f+ zover 1e f- z* zsqrt z+ pln ;
: zacosh zdup 1e x- z2/ zsqrt zswap 1e x+ z2/ zsqrt z+
pln z2* ;
: zatanh zdup 1e x+ zln zswap 1e x- znegate pln z- z2/ ;
: zacoth znegate zdup 1e x- pln zswap 1e x+ pln z- z2/ ;
pi f2/ FConstant pi/2
: zasin ( f: z -- -iln[iz+sqrt[1-z^~2]] ) z*i zasinh z/i ;
: zacos ( f: z -- pi/2-asin[z] ) pi/2 0e zswap zasin z- ;
: zatan ( f: z -- [ln[1+iz]-ln[1-iz]]/2i ) z*i zatanh z/i ;
: zacot ( f: z -- [ln[[z+i]/[z-i]]/2i ) z*i zacoth z/i ;
\ Ausgabe 24sep05py
Defer fc. ' f. IS fc.
: z. zdup z0= IF zdrop ." 0 " exit THEN
fdup f0= IF fdrop fc. exit THEN fswap
fdup f0= IF fdrop
ELSE fc.
fdup f0> IF ." +" THEN THEN
fc. ." i " ;
: z.s zdepth 0 ?DO i zpick zswap z>r z. zr> LOOP ;
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