1: \ complex numbers
2:
3: \ Copyright (C) 2005,2007 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 3
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, see http://www.gnu.org/licenses/.
19:
20: \ *** Complex arithmetic *** 23sep91py
21:
22: : complex' ( n -- offset ) 2* floats ;
23: : complex+ ( zaddr -- zaddr' ) float+ float+ ;
24:
25: \ simple operations 02mar05py
26:
27: : fl> ( -- r ) f@local0 lp+ ;
28:
29: : zdup ( z -- z z ) fover fover ;
30: : zdrop ( z -- ) fdrop fdrop ;
31: : zover ( z1 z2 -- z1 z2 z1 ) 3 fpick 3 fpick ;
32: : z>r ( z -- r:z) f>l f>l ;
33: : zr> ( r:z -- z ) fl> fl> ;
34: : zswap ( z1 z2 -- z2 z1 ) frot f>l frot fl> ;
35: : zpick ( z1 .. zn n -- z1 .. zn z1 ) 2* 1+ >r r@ fpick r> fpick ;
36: \ : zpin 2* 1+ >r r@ fpin r> fpin ;
37: : zdepth ( -- u ) fdepth 2/ ;
38: : zrot ( z1 z2 z3 -- z2 z3 z1 ) z>r zswap zr> zswap ;
39: : z-rot ( z1 z2 z3 -- z3 z1 z2 ) zswap z>r zswap zr> ;
40: : z@ ( zaddr -- z ) dup >r f@ r> float+ f@ ;
41: : z! ( z zaddr -- ) dup >r float+ f! r> f! ;
42:
43: \ simple operations 02mar05py
44: : z+ ( z1 z2 -- z1+z2 ) frot f+ f>l f+ fl> ;
45: : z- ( z1 z2 -- z1-z2 ) fnegate frot f+ f>l f- fl> ;
46: : zr- ( z1 z2 -- z2-z1 ) frot f- f>l fswap f- fl> ;
47: : x+ ( z r -- z+r ) frot f+ fswap ;
48: : x- ( z r -- z-r ) fnegate x+ ;
49: : z* ( z1 z2 -- z1*z2 )
50: fdup 4 fpick f* f>l fover 3 fpick f* f>l
51: f>l fswap fl> f* f>l f* fl> f- fl> fl> f+ ;
52: : zscale ( z r -- z*r ) ftuck f* f>l f* fl> ;
53:
54: \ simple operations 02mar05py
55:
56: : znegate ( z -- -z ) fnegate fswap fnegate fswap ;
57: : zconj ( rr ri -- rr -ri ) fnegate ;
58: : z*i ( z -- z*i ) fnegate fswap ;
59: : z/i ( z -- z/i ) fswap fnegate ;
60: : zsqabs ( z -- |z|² ) fdup f* fswap fdup f* f+ ;
61: : 1/z ( z -- 1/z ) zconj zdup zsqabs 1/f zscale ;
62: : z/ ( z1 z2 -- z1/z2 ) 1/z z* ;
63: : |z| ( z -- r ) zsqabs fsqrt ;
64: : zabs ( z -- |z| ) |z| 0e ;
65: : z2/ ( z -- z/2 ) f2/ f>l f2/ fl> ;
66: : z2* ( z -- z*2 ) f2* f>l f2* fl> ;
67:
68: : >polar ( z -- r theta ) zdup |z| fswap frot fatan2 ;
69: : polar> ( r theta -- z ) fsincos frot zscale fswap ;
70:
71: \ zexp zln 02mar05py
72:
73: : zexp ( z -- exp[z] ) fsincos fswap frot fexp zscale ;
74: : pln ( z -- pln[z] ) zdup fswap fatan2 frot frot |z| fln fswap ;
75: : zln ( z -- ln[z] ) >polar fswap fln fswap ;
76:
77: : z0= ( z -- flag ) f0= >r f0= r> and ;
78: : zsqrt ( z -- sqrt[z] ) zdup z0= 0= IF
79: fdup f0= IF fdrop fsqrt 0e EXIT THEN
80: zln z2/ zexp THEN ;
81: : z** ( z1 z2 -- z1**z2 ) zswap zln z* zexp ;
82: \ Test: Fibonacci-Zahlen
83: 1e 5e fsqrt f+ f2/ fconstant g 1e g f- fconstant -h
84: : zfib ( z1 -- fib[z1] ) zdup z>r g 0e zswap z**
85: zr> zswap z>r -h 0e zswap z** znegate zr> z+
86: [ g -h f- 1/f ] FLiteral zscale ;
87:
88: \ complexe Operationen 02mar05py
89:
90: : zsinh ( z -- sinh[z] ) zexp zdup 1/z z- z2/ ;
91: : zcosh ( z -- cosh[z] ) zexp zdup 1/z z+ z2/ ;
92: : ztanh ( z -- tanh[z] ) z2* zexp zdup 1e 0e z- zswap 1e 0e z+ z/ ;
93:
94: : zsin ( z -- sin[z] ) z*i zsinh z/i ;
95: : zcos ( z -- cos[z] ) z*i zcosh ;
96: : ztan ( z -- tan[z] ) z*i ztanh z/i ;
97:
98: : Real ( z -- r ) fdrop ;
99: : Imag ( z -- i ) fnip ;
100:
101: : Re ( z -- zr ) Real 0e ;
102: : Im ( z -- zi ) Imag 0e ;
103:
104: \ complexe Operationen 02mar05py
105:
106: : zasinh ( z -- asinh[z] ) zdup 1e f+ zover 1e f- z* zsqrt z+ pln ;
107: : zacosh ( z -- acosh[z] ) zdup 1e x- z2/ zsqrt zswap 1e x+ z2/ zsqrt z+
108: pln z2* ;
109: : zatanh ( z -- atanh[z] ) zdup 1e x+ zln zswap 1e x- znegate pln z- z2/ ;
110: : zacoth ( z -- acoth[z] ) znegate zdup 1e x- pln zswap 1e x+ pln z- z2/ ;
111:
112: pi f2/ FConstant pi/2
113:
114: : zasin ( z -- -iln[iz+sqrt[1-z^~2]] ) z*i zasinh z/i ;
115: : zacos ( z -- pi/2-asin[z] ) pi/2 0e zswap zasin z- ;
116: : zatan ( z -- [ln[1+iz]-ln[1-iz]]/2i ) z*i zatanh z/i ;
117: : zacot ( z -- [ln[[z+i]/[z-i]]/2i ) z*i zacoth z/i ;
118:
119: \ Ausgabe 24sep05py
120:
121: Defer fc. ' f. IS fc.
122: : z. ( z -- )
123: zdup z0= IF zdrop ." 0 " exit THEN
124: fdup f0= IF fdrop fc. exit THEN fswap
125: fdup f0= IF fdrop
126: ELSE fc.
127: fdup f0> IF ." +" THEN THEN
128: fc. ." i " ;
129: : z.s ( z1 .. zn -- z1 .. zn )
130: zdepth 0 ?DO i zpick zswap z>r z. zr> LOOP ;
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