Home » Archimedes archive » Micro User » MU 1992-05.adf » PD » Fractal/!Fractal/Asm/SampNewton
Fractal/!Fractal/Asm/SampNewton
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Micro User » MU 1992-05.adf » PD |
| Filename: | Fractal/!Fractal/Asm/SampNewton |
| Read OK: | ✔ |
| File size: | 17DF bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
10REM > <Frac$Dir>.Asm.SampNewton
20REM Newton : z*z*z-1=0 plotter
30REM Algorithm from Becker & Dorfler
40LIBRARY "<Frac$Dir>.Asm.Fraclib":PROCfracvars
50LIBRARY "<Frac$Dir>.Asm.FPlib":PROCfpinit
60LIBRARY "<Frac$Dir>.Asm.FPElib"
70REM === Function specific code follows
80newton=0:nvarstart=0:nvarend=0:REM initialise to a dummy value
90REM === End of function specific code
100DIM code% 10000
110FOR asm=4 TO 7 STEP 3
120P%=0:O%=code%
130[OPT asm
140; Following is the list of fractal functions in this module
150FNfrachdr ; Identify ourselves as a fractal module
160;
170; One or more function definition pointers follow
180DCD newton_func
190;
200DCD -1 ; End of functions
210;--------------------------------------------------------------
220; Now we define Newton's characteristics
230;
240.newton_func FNfracfunc("SampNewton",newton,fZoom+fheight+fxy,0,5,nvarend-nvarstart)
250;
260; Newton's Variables after here
270.nvarstart
280FNafg2var(AFG_dbl,0,8):.nx0 FNfp("DFD -2.00")
290FNafg2var(AFG_dbl,0,8):.ny0 FNfp("DFD -1.60")
300FNafg2var(AFG_dbl,0,8):.nw FNfp("DFD 4.0")
310FNafg2var(AFG_dbl,0,8):.nh FNfp("DFD 3.2")
320FNafg2var(AFG_int,0,4):.niter DCD 128
330.nvarend ; End of variables
340;
350; Variable names after here; 1 for each variable above
360FNvarname(" x0")
370FNvarname(" y0")
380FNvarname(" width")
390FNvarname(" height")
400FNvarname(" Max. Iter")
410;-------------------------------------
420; The entry point to Newton
430.newton
440FNfenter ; Initialise
450; R0=Fractal Event, R1=Address of Data
460MOV R9,#0
470STR R9,[R1,#fevent_rc] ; clear return code
480CMP R0,#fplotinit
490BEQ nplotinit
500CMP R0,#fdatainit
510BEQ ndatainit
520CMP R0,#fdatachk
530BEQ ndatachk
540; Unsupported event - just return
550FNfexit
560;
570; Init Newton data
580.ndatainit
590FNfp("LDFD F0,inx")
600FNfp("STFD F0,nx0")
610FNfp("LDFD F0,iny")
620FNfp("STFD F0,ny0")
630FNfp("LDFD F0,inw")
640FNfp("STFD F0,nw ")
650FNfp("LDFD F0,inh")
660FNfp("STFD F0,nh ")
670LDR R0,initer
680STR R0,niter
690FNfexit
700.inx FNfp("DFD -2.00") ; Initial values
710.iny FNfp("DFD -1.60")
720.inw FNfp("DFD 4.0")
730.inh FNfp("DFD 3.2")
740.initer DCD 128
750;
760; Verify data input or zoom range
770.ndatachk
780FNfp("LDFD F0,nx0")
790FNfp("CMFD F0,#4")
800BGT nbaddata ; x0 too large
810FNfp("CNFD F0,#4") ; <-4?
820BLT nbaddata ; x0 too small
830FNfp("LDFD F0,ny0")
840FNfp("CMFD F0,#4")
850BGT nbaddata ; y0 too large
860FNfp("CNFD F0,#4") ; <-4?
870BLT nbaddata ; y0 too small
880;
890; For width & height, check not smaller than integer fp range.
900FNfp("LDFD F1,ninint") ; smallest value for fp integer
910FNfp("LDFD F0,nw ")
920FNfp("CMFD F0,#4")
930BGT nbaddata ; w too large
940FNfp("CMFD F0,F1") ; within accuracy range?
950BLT nbaddata ; w too small
960FNfp("LDFD F0,nh ")
970FNfp("CMFD F0,#4")
980BGT nbaddata ; h too large
990FNfp("CMFD F0,F1") ; within accuracy range?
1000BLT nbaddata ; h too small
1010;
1020; Verify maxiter not too small
1030LDR R0,niter
1040CMP R0,#10 ; too small?
1050MOVLT R0,#10
1060STRLT R0,niter ; yes - set to 10
1070FNfexit
1080;
1090.nbaddata
1100MOV R0,#1
1110STR R0,[R1,#fevent_rc] ; set return code
1120FNfexit
1130
1140.ninint FNfp("DFD 1e-5")
1150;-------------------------------------
1160; Initialise ready for a plot
1170.nplotinit
1180LDR R0,[R1,#plot_flags]
1190ORR R0,R0,#plot_ffp ; fast float maths
1200STR R0,[R1,#plot_flags] ; tell Fractal
1210ADR R0,newtonfp
1220STR R0,newton_func+fdefn_xyrtn ; Our plot routine
1230FNfexit
1240;----------------------------------
1250]
1260REM newton registers
1270REM x & y set on entry
1280x=2:y=3:xy=4:x2=5:y2=6:wrk1=7:wrk2=8:wrk3=9:root=10:e=11:depth=12
1290[OPT asm
1300.newtonfp
1310STMFD R13!,{R14} ; Return address
1320MOV x,R0
1330MOV y,R1
1340FNfp_sqr(y2,y) ; y*y
1350LDR e,newton_e ; epsilon
1360LDR depth,niter
1370MOV root,#0
1380.nloop ; do for each iteration
1390FNfp_mul(xy,x,y) ; x*y
1400ADD xy,xy,#1<<23 ; 2*x*y
1410;
1420FNfp_sqr(x2,x) ; x*x
1430MOV R1,y2
1440BL fp_add ; x*x+y*y
1450MOVS R1,R0
1460BEQ nexit ; too small
1470BL fp_sqr ; d4=(x*x+y*y)*(x*x+y*y)
1480LDR R1,fp_three
1490BL fp_mul ; 3*d4
1500MOVS wrk1,R0
1510BEQ nexit ; underflow
1520; calc new x
1530LDR R1,twothird
1540FNfp_mul(wrk2,x,1) ; x*2/3
1550FNfp_sub(0,x2,y2) ; x*x-y*y
1560FNfp_div(0,0,wrk1) ; (x*x-y*y)/d4
1570FNfp_add(x,0,wrk2) ; x=x*2/3+(x2-y2)/d4
1580; calc new y
1590FNfp_div(wrk2,xy,wrk1) ; (2*x*y)/d4
1600LDR R1,twothird
1610FNfp_mul(0,y,1) ; y*2/3
1620FNfp_sub(y,0,wrk2) ; y=y*2/3-(2*x*y)/d4
1630;
1640FNfp_sqr(y2,y) ; y*y
1650; Check for root=1
1660MOV R1,#127<<23 ; 1.0
1670FNfp_sub(0,x,1) ; x-1
1680FNfp_sqr(0,0) ; (x-1)*(x-1)
1690FNfp_add(0,0,y2) ; (x-1)*(x-1)+y2
1700CMP R0,e ; ((x-1)*(x-1)+y2)<e?
1710MOVLT root,#1
1720BLT nexit ; root=1
1730; Check for root=2
1740MOV R1,#126<<23 ; 0.5
1750FNfp_add(0,x,1) ; x+0.5
1760FNfp_sqr(wrk1,0) ; xr=(x+0.5)*(x+0.5)
1770LDR wrk2,newton_r2
1780FNfp_sub(0,y,wrk2) ; y-0.8660254
1790FNfp_sqr(0,0) ; yr=(y-0.8660254)*(y-0.8660254)
1800FNfp_add(0,wrk1,0) ; xr+yr
1810CMP R0,e ; Root 2?
1820MOVLT root,#2
1830BLT nexit
1840; Check for root=3
1850FNfp_add(0,y,wrk2) ; y+0.8660254
1860FNfp_sqr(0,0) ; yr=(y+0.8660254)*(y+0.8660254)
1870FNfp_add(0,wrk1,0) ; xr+yr
1880CMP R0,e ; Root 3?
1890MOVLT root,#3
1900BLT nexit
1910;
1920SUBS depth,depth,#1
1930BNE nloop
1940LDR depth,niter ; No colour if at max
1950.nexit
1960LDR R0,niter
1970SUB R0,R0,depth ; return colour
1980ADD R0,R0,#16 ; avoid dark colours
1990LDMFD R13!,{PC}^ ; exit
2000;
2010.twothird FNfp("DFS 0.66666666")
2020.newton_e FNfp("DFS 0.0025")
2030.newton_r2 FNfp("DFS 0.8660254")
2040.fp_three FNfp("DFS 3.0")
2050;--------------------------
2060FNfinterface ; Necessary C Interface code
2070FNfpeasm(FALSE) ; FPE routines
2080]:NEXT
2090SYS "OS_File",10,"<Frac$Dir>.SampNewton",&FFA,,code%,O%
2100END
!� > <Frac$Dir>.Asm.SampNewton
� Newton : z*z*z-1=0 plotter
%� Algorithm from Becker & Dorfler
()ț "<Frac$Dir>.Asm.Fraclib":�fracvars
2%ț "<Frac$Dir>.Asm.FPlib":�fpinit
< ț "<Frac$Dir>.Asm.FPElib"
F(� === Function specific code follows
P@newton=0:nvarstart=0:nvarend=0:� initialise to a dummy value
Z'� === End of function specific code
d� code% 10000
n� asm=4 � 7 � 3
xP%=0:O%=code%
� [OPT asm
�?; Following is the list of fractal functions in this module
�5�frachdr ; Identify ourselves as a fractal module
�;
�5; One or more function definition pointers follow
�DCD newton_func
�;
� DCD -1 ; End of functions
�C;--------------------------------------------------------------
�,; Now we define Newton's characteristics
�;
�W.newton_func �fracfunc("SampNewton",newton,fZoom+fheight+fxy,0,5,nvarend-nvarstart)
�;
#; Newton's Variables after here
.nvarstart
/�afg2var(AFG_dbl,0,8):.nx0 �fp("DFD -2.00")
"/�afg2var(AFG_dbl,0,8):.ny0 �fp("DFD -1.60")
,,�afg2var(AFG_dbl,0,8):.nw �fp("DFD 4.0")
6,�afg2var(AFG_dbl,0,8):.nh �fp("DFD 3.2")
@(�afg2var(AFG_int,0,4):.niter DCD 128
J .nvarend ; End of variables
T;
^:; Variable names after here; 1 for each variable above
h�varname(" x0")
r�varname(" y0")
|�varname(" width")
��varname(" height")
��varname(" Max. Iter")
�*;-------------------------------------
� ; The entry point to Newton
� .newton
��fenter ; Initialise
�*; R0=Fractal Event, R1=Address of Data
�
MOV R9,#0
�.STR R9,[R1,#fevent_rc] ; clear return code
�CMP R0,#fplotinit
�BEQ nplotinit
�CMP R0,#fdatainit
�BEQ ndatainit
CMP R0,#fdatachk
BEQ ndatachk
%; Unsupported event - just return
&
�fexit
0;
:; Init Newton data
D.ndatainit
N�fp("LDFD F0,inx")
X�fp("STFD F0,nx0")
b�fp("LDFD F0,iny")
l�fp("STFD F0,ny0")
v�fp("LDFD F0,inw")
��fp("STFD F0,nw ")
��fp("LDFD F0,inh")
��fp("STFD F0,nh ")
�LDR R0,initer
�STR R0,niter
�
�fexit
�*.inx �fp("DFD -2.00") ; Initial values
�.iny �fp("DFD -1.60")
�.inw �fp("DFD 4.0")
�.inh �fp("DFD 3.2")
�.initer DCD 128
�;
�%; Verify data input or zoom range
.ndatachk
�fp("LDFD F0,nx0")
�fp("CMFD F0,#4")
*BGT nbaddata ; x0 too large
*!�fp("CNFD F0,#4") ; <-4?
4*BLT nbaddata ; x0 too small
>�fp("LDFD F0,ny0")
H�fp("CMFD F0,#4")
R*BGT nbaddata ; y0 too large
\!�fp("CNFD F0,#4") ; <-4?
f*BLT nbaddata ; y0 too small
p;
zB; For width & height, check not smaller than integer fp range.
�:�fp("LDFD F1,ninint") ; smallest value for fp integer
��fp("LDFD F0,nw ")
��fp("CMFD F0,#4")
�)BGT nbaddata ; w too large
�2�fp("CMFD F0,F1") ; within accuracy range?
�)BLT nbaddata ; w too small
��fp("LDFD F0,nh ")
��fp("CMFD F0,#4")
�(BGT nbaddata ; h too large
�2�fp("CMFD F0,F1") ; within accuracy range?
�(BLT nbaddata ; h too small
�;
�"; Verify maxiter not too small
LDR R0,niter
'CMP R0,#10 ; too small?
MOVLT R0,#10
$,STRLT R0,niter ; yes - set to 10
.
�fexit
8;
B
.nbaddata
L
MOV R0,#1
V,STR R0,[R1,#fevent_rc] ; set return code
`
�fexit
j
t.ninint �fp("DFD 1e-5")
~*;-------------------------------------
�!; Initialise ready for a plot
�.nplotinit
�LDR R0,[R1,#plot_flags]
�-�R R0,R0,#plot_ffp ; fast float maths
�*STR R0,[R1,#plot_flags] ; tell Fractal
�ADR R0,newtonfp
�6STR R0,newton_func+fdefn_xyrtn ; Our plot routine
�
�fexit
�';----------------------------------
�]
�� newton registers
�� x & y set on entry
Ex=2:y=3:xy=4:x2=5:y2=6:wrk1=7:wrk2=8:wrk3=9:root=10:e=11:depth=12
[OPT asm
.newtonfp
,STMFD R13!,{R14} ; Return address
( MOV x,R0
2 MOV y,R1
< �fp_sqr(y2,y) ; y*y
F%LDR e,newton_e ; epsilon
PLDR depth,niter
ZMOV root,#0
d3.nloop ; do for each iteration
n �fp_mul(xy,x,y) ; x*y
x#ADD xy,xy,#1<<23 ; 2*x*y
�;
� �fp_sqr(x2,x) ; x*x
�
MOV R1,y2
�%BL fp_add ; x*x+y*y
�MOVS R1,R0
�'BEQ nexit ; too small
�4BL fp_sqr ; d4=(x*x+y*y)*(x*x+y*y)
�LDR R1,fp_three
�"BL fp_mul ; 3*d4
�MOVS wrk1,R0
�'BEQ nexit ; underflow
�; calc new x
�LDR R1,twothird
"�fp_mul(wrk2,x,1) ; x*2/3
$�fp_sub(0,x2,y2) ; x*x-y*y
)�fp_div(0,0,wrk1) ; (x*x-y*y)/d4
"/�fp_add(x,0,wrk2) ; x=x*2/3+(x2-y2)/d4
,; calc new y
6'�fp_div(wrk2,xy,wrk1) ; (2*x*y)/d4
@LDR R1,twothird
J"�fp_mul(0,y,1) ; y*2/3
T/�fp_sub(y,0,wrk2) ; y=y*2/3-(2*x*y)/d4
^;
h �fp_sqr(y2,y) ; y*y
r; Check for root=1
|!MOV R1,#127<<23 ; 1.0
� �fp_sub(0,x,1) ; x-1
�(�fp_sqr(0,0) ; (x-1)*(x-1)
�+�fp_add(0,0,y2) ; (x-1)*(x-1)+y2
�1CMP R0,e ; ((x-1)*(x-1)+y2)<e?
�MOVLT root,#1
�$BLT nexit ; root=1
�; Check for root=2
�!MOV R1,#126<<23 ; 0.5
�"�fp_add(0,x,1) ; x+0.5
�/�fp_sqr(wrk1,0) ; xr=(x+0.5)*(x+0.5)
�LDR wrk2,newton_r2
�(�fp_sub(0,y,wrk2) ; y-0.8660254
�;�fp_sqr(0,0) ; yr=(y-0.8660254)*(y-0.8660254)
"�fp_add(0,wrk1,0) ; xr+yr
%CMP R0,e ; Root 2?
MOVLT root,#2
&
BLT nexit
0; Check for root=3
:(�fp_add(0,y,wrk2) ; y+0.8660254
D;�fp_sqr(0,0) ; yr=(y+0.8660254)*(y+0.8660254)
N"�fp_add(0,wrk1,0) ; xr+yr
X%CMP R0,e ; Root 3?
bMOVLT root,#3
l
BLT nexit
v;
�SUBS depth,depth,#1
�
BNE nloop
�1LDR depth,niter ; No colour if at max
�
.nexit
�LDR R0,niter
�+SUB R0,R0,depth ; return colour
�0ADD R0,R0,#16 ; avoid dark colours
�"LDMFD R13!,{PC}^ ; exit
�;
�#.twothird �fp("DFS 0.66666666")
� .newton_e �fp("DFS 0.0025")
�#.newton_r2 �fp("DFS 0.8660254")
� .fp_three �fp("DFS 3.0")
;--------------------------
7�finterface ; Necessary C Interface code
%�fpeasm(�) ; FPE routines
]:�
*:ș "OS_File",10,"<Frac$Dir>.SampNewton",&FFA,,code%,O%
4�
� 00000000 0d 00 0a 21 f4 20 3e 20 3c 46 72 61 63 24 44 69 |...!. > <Frac$Di|
00000010 72 3e 2e 41 73 6d 2e 53 61 6d 70 4e 65 77 74 6f |r>.Asm.SampNewto|
00000020 6e 0d 00 14 20 f4 20 4e 65 77 74 6f 6e 20 3a 20 |n... . Newton : |
00000030 7a 2a 7a 2a 7a 2d 31 3d 30 20 70 6c 6f 74 74 65 |z*z*z-1=0 plotte|
00000040 72 0d 00 1e 25 f4 20 41 6c 67 6f 72 69 74 68 6d |r...%. Algorithm|
00000050 20 66 72 6f 6d 20 42 65 63 6b 65 72 20 26 20 44 | from Becker & D|
00000060 6f 72 66 6c 65 72 0d 00 28 29 c8 9b 20 22 3c 46 |orfler..().. "<F|
00000070 72 61 63 24 44 69 72 3e 2e 41 73 6d 2e 46 72 61 |rac$Dir>.Asm.Fra|
00000080 63 6c 69 62 22 3a f2 66 72 61 63 76 61 72 73 0d |clib":.fracvars.|
00000090 00 32 25 c8 9b 20 22 3c 46 72 61 63 24 44 69 72 |.2%.. "<Frac$Dir|
000000a0 3e 2e 41 73 6d 2e 46 50 6c 69 62 22 3a f2 66 70 |>.Asm.FPlib":.fp|
000000b0 69 6e 69 74 0d 00 3c 1e c8 9b 20 22 3c 46 72 61 |init..<... "<Fra|
000000c0 63 24 44 69 72 3e 2e 41 73 6d 2e 46 50 45 6c 69 |c$Dir>.Asm.FPEli|
000000d0 62 22 0d 00 46 28 f4 20 3d 3d 3d 20 46 75 6e 63 |b"..F(. === Func|
000000e0 74 69 6f 6e 20 73 70 65 63 69 66 69 63 20 63 6f |tion specific co|
000000f0 64 65 20 66 6f 6c 6c 6f 77 73 0d 00 50 40 6e 65 |de follows..P@ne|
00000100 77 74 6f 6e 3d 30 3a 6e 76 61 72 73 74 61 72 74 |wton=0:nvarstart|
00000110 3d 30 3a 6e 76 61 72 65 6e 64 3d 30 3a f4 20 69 |=0:nvarend=0:. i|
00000120 6e 69 74 69 61 6c 69 73 65 20 74 6f 20 61 20 64 |nitialise to a d|
00000130 75 6d 6d 79 20 76 61 6c 75 65 0d 00 5a 27 f4 20 |ummy value..Z'. |
00000140 3d 3d 3d 20 45 6e 64 20 6f 66 20 66 75 6e 63 74 |=== End of funct|
00000150 69 6f 6e 20 73 70 65 63 69 66 69 63 20 63 6f 64 |ion specific cod|
00000160 65 0d 00 64 11 de 20 63 6f 64 65 25 20 31 30 30 |e..d.. code% 100|
00000170 30 30 0d 00 6e 13 e3 20 61 73 6d 3d 34 20 b8 20 |00..n.. asm=4 . |
00000180 37 20 88 20 33 0d 00 78 11 50 25 3d 30 3a 4f 25 |7 . 3..x.P%=0:O%|
00000190 3d 63 6f 64 65 25 0d 00 82 0c 5b 4f 50 54 20 61 |=code%....[OPT a|
000001a0 73 6d 0d 00 8c 3f 3b 20 46 6f 6c 6c 6f 77 69 6e |sm...?; Followin|
000001b0 67 20 69 73 20 74 68 65 20 6c 69 73 74 20 6f 66 |g is the list of|
000001c0 20 66 72 61 63 74 61 6c 20 66 75 6e 63 74 69 6f | fractal functio|
000001d0 6e 73 20 69 6e 20 74 68 69 73 20 6d 6f 64 75 6c |ns in this modul|
000001e0 65 0d 00 96 35 a4 66 72 61 63 68 64 72 20 3b 20 |e...5.frachdr ; |
000001f0 49 64 65 6e 74 69 66 79 20 6f 75 72 73 65 6c 76 |Identify ourselv|
00000200 65 73 20 61 73 20 61 20 66 72 61 63 74 61 6c 20 |es as a fractal |
00000210 6d 6f 64 75 6c 65 0d 00 a0 05 3b 0d 00 aa 35 3b |module....;...5;|
00000220 20 4f 6e 65 20 6f 72 20 6d 6f 72 65 20 66 75 6e | One or more fun|
00000230 63 74 69 6f 6e 20 64 65 66 69 6e 69 74 69 6f 6e |ction definition|
00000240 20 70 6f 69 6e 74 65 72 73 20 66 6f 6c 6c 6f 77 | pointers follow|
00000250 0d 00 b4 13 44 43 44 20 6e 65 77 74 6f 6e 5f 66 |....DCD newton_f|
00000260 75 6e 63 0d 00 be 05 3b 0d 00 c8 1d 44 43 44 20 |unc....;....DCD |
00000270 2d 31 20 3b 20 45 6e 64 20 6f 66 20 66 75 6e 63 |-1 ; End of func|
00000280 74 69 6f 6e 73 0d 00 d2 43 3b 2d 2d 2d 2d 2d 2d |tions...C;------|
00000290 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------|
*
000002c0 2d 2d 2d 2d 2d 2d 2d 2d 0d 00 dc 2c 3b 20 4e 6f |--------...,; No|
000002d0 77 20 77 65 20 64 65 66 69 6e 65 20 4e 65 77 74 |w we define Newt|
000002e0 6f 6e 27 73 20 63 68 61 72 61 63 74 65 72 69 73 |on's characteris|
000002f0 74 69 63 73 0d 00 e6 05 3b 0d 00 f0 57 2e 6e 65 |tics....;...W.ne|
00000300 77 74 6f 6e 5f 66 75 6e 63 20 a4 66 72 61 63 66 |wton_func .fracf|
00000310 75 6e 63 28 22 53 61 6d 70 4e 65 77 74 6f 6e 22 |unc("SampNewton"|
00000320 2c 6e 65 77 74 6f 6e 2c 66 5a 6f 6f 6d 2b 66 68 |,newton,fZoom+fh|
00000330 65 69 67 68 74 2b 66 78 79 2c 30 2c 35 2c 6e 76 |eight+fxy,0,5,nv|
00000340 61 72 65 6e 64 2d 6e 76 61 72 73 74 61 72 74 29 |arend-nvarstart)|
00000350 0d 00 fa 05 3b 0d 01 04 23 3b 20 4e 65 77 74 6f |....;...#; Newto|
00000360 6e 27 73 20 56 61 72 69 61 62 6c 65 73 20 61 66 |n's Variables af|
00000370 74 65 72 20 68 65 72 65 0d 01 0e 0e 2e 6e 76 61 |ter here.....nva|
00000380 72 73 74 61 72 74 0d 01 18 2f a4 61 66 67 32 76 |rstart.../.afg2v|
00000390 61 72 28 41 46 47 5f 64 62 6c 2c 30 2c 38 29 3a |ar(AFG_dbl,0,8):|
000003a0 2e 6e 78 30 20 a4 66 70 28 22 44 46 44 20 2d 32 |.nx0 .fp("DFD -2|
000003b0 2e 30 30 22 29 0d 01 22 2f a4 61 66 67 32 76 61 |.00").."/.afg2va|
000003c0 72 28 41 46 47 5f 64 62 6c 2c 30 2c 38 29 3a 2e |r(AFG_dbl,0,8):.|
000003d0 6e 79 30 20 a4 66 70 28 22 44 46 44 20 2d 31 2e |ny0 .fp("DFD -1.|
000003e0 36 30 22 29 0d 01 2c 2c a4 61 66 67 32 76 61 72 |60")..,,.afg2var|
000003f0 28 41 46 47 5f 64 62 6c 2c 30 2c 38 29 3a 2e 6e |(AFG_dbl,0,8):.n|
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00000420 5f 64 62 6c 2c 30 2c 38 29 3a 2e 6e 68 20 a4 66 |_dbl,0,8):.nh .f|
00000430 70 28 22 44 46 44 20 33 2e 32 22 29 0d 01 40 28 |p("DFD 3.2")..@(|
00000440 a4 61 66 67 32 76 61 72 28 41 46 47 5f 69 6e 74 |.afg2var(AFG_int|
00000450 2c 30 2c 34 29 3a 2e 6e 69 74 65 72 20 44 43 44 |,0,4):.niter DCD|
00000460 20 31 32 38 0d 01 4a 1f 2e 6e 76 61 72 65 6e 64 | 128..J..nvarend|
00000470 20 3b 20 45 6e 64 20 6f 66 20 76 61 72 69 61 62 | ; End of variab|
00000480 6c 65 73 0d 01 54 05 3b 0d 01 5e 3a 3b 20 56 61 |les..T.;..^:; Va|
00000490 72 69 61 62 6c 65 20 6e 61 6d 65 73 20 61 66 74 |riable names aft|
000004a0 65 72 20 68 65 72 65 3b 20 31 20 66 6f 72 20 65 |er here; 1 for e|
000004b0 61 63 68 20 76 61 72 69 61 62 6c 65 20 61 62 6f |ach variable abo|
000004c0 76 65 0d 01 68 1b a4 76 61 72 6e 61 6d 65 28 22 |ve..h..varname("|
000004d0 20 20 20 20 20 20 20 20 20 78 30 22 29 0d 01 72 | x0")..r|
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000004f0 20 20 20 20 79 30 22 29 0d 01 7c 1b a4 76 61 72 | y0")..|..var|
00000500 6e 61 6d 65 28 22 20 20 20 20 20 20 77 69 64 74 |name(" widt|
00000510 68 22 29 0d 01 86 1b a4 76 61 72 6e 61 6d 65 28 |h").....varname(|
00000520 22 20 20 20 20 20 68 65 69 67 68 74 22 29 0d 01 |" height")..|
00000530 90 1b a4 76 61 72 6e 61 6d 65 28 22 20 20 4d 61 |...varname(" Ma|
00000540 78 2e 20 49 74 65 72 22 29 0d 01 9a 2a 3b 2d 2d |x. Iter")...*;--|
00000550 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------|
*
00000570 2d 2d 2d 0d 01 a4 1f 3b 20 54 68 65 20 65 6e 74 |---....; The ent|
00000580 72 79 20 70 6f 69 6e 74 20 74 6f 20 4e 65 77 74 |ry point to Newt|
00000590 6f 6e 0d 01 ae 0b 2e 6e 65 77 74 6f 6e 0d 01 b8 |on.....newton...|
000005a0 18 a4 66 65 6e 74 65 72 20 3b 20 49 6e 69 74 69 |..fenter ; Initi|
000005b0 61 6c 69 73 65 0d 01 c2 2a 3b 20 52 30 3d 46 72 |alise...*; R0=Fr|
000005c0 61 63 74 61 6c 20 45 76 65 6e 74 2c 20 52 31 3d |actal Event, R1=|
000005d0 41 64 64 72 65 73 73 20 6f 66 20 44 61 74 61 0d |Address of Data.|
000005e0 01 cc 0d 4d 4f 56 20 52 39 2c 23 30 0d 01 d6 2e |...MOV R9,#0....|
000005f0 53 54 52 20 52 39 2c 5b 52 31 2c 23 66 65 76 65 |STR R9,[R1,#feve|
00000600 6e 74 5f 72 63 5d 20 3b 20 63 6c 65 61 72 20 72 |nt_rc] ; clear r|
00000610 65 74 75 72 6e 20 63 6f 64 65 0d 01 e0 15 43 4d |eturn code....CM|
00000620 50 20 52 30 2c 23 66 70 6c 6f 74 69 6e 69 74 0d |P R0,#fplotinit.|
00000630 01 ea 11 42 45 51 20 6e 70 6c 6f 74 69 6e 69 74 |...BEQ nplotinit|
00000640 0d 01 f4 15 43 4d 50 20 52 30 2c 23 66 64 61 74 |....CMP R0,#fdat|
00000650 61 69 6e 69 74 0d 01 fe 11 42 45 51 20 6e 64 61 |ainit....BEQ nda|
00000660 74 61 69 6e 69 74 0d 02 08 14 43 4d 50 20 52 30 |tainit....CMP R0|
00000670 2c 23 66 64 61 74 61 63 68 6b 0d 02 12 10 42 45 |,#fdatachk....BE|
00000680 51 20 6e 64 61 74 61 63 68 6b 0d 02 1c 25 3b 20 |Q ndatachk...%; |
00000690 55 6e 73 75 70 70 6f 72 74 65 64 20 65 76 65 6e |Unsupported even|
000006a0 74 20 2d 20 6a 75 73 74 20 72 65 74 75 72 6e 0d |t - just return.|
000006b0 02 26 0a a4 66 65 78 69 74 0d 02 30 05 3b 0d 02 |.&..fexit..0.;..|
000006c0 3a 16 3b 20 49 6e 69 74 20 4e 65 77 74 6f 6e 20 |:.; Init Newton |
000006d0 64 61 74 61 0d 02 44 0e 2e 6e 64 61 74 61 69 6e |data..D..ndatain|
000006e0 69 74 0d 02 4e 16 a4 66 70 28 22 4c 44 46 44 20 |it..N..fp("LDFD |
000006f0 46 30 2c 69 6e 78 22 29 0d 02 58 16 a4 66 70 28 |F0,inx")..X..fp(|
00000700 22 53 54 46 44 20 46 30 2c 6e 78 30 22 29 0d 02 |"STFD F0,nx0")..|
00000710 62 16 a4 66 70 28 22 4c 44 46 44 20 46 30 2c 69 |b..fp("LDFD F0,i|
00000720 6e 79 22 29 0d 02 6c 16 a4 66 70 28 22 53 54 46 |ny")..l..fp("STF|
00000730 44 20 46 30 2c 6e 79 30 22 29 0d 02 76 16 a4 66 |D F0,ny0")..v..f|
00000740 70 28 22 4c 44 46 44 20 46 30 2c 69 6e 77 22 29 |p("LDFD F0,inw")|
00000750 0d 02 80 16 a4 66 70 28 22 53 54 46 44 20 46 30 |.....fp("STFD F0|
00000760 2c 6e 77 20 22 29 0d 02 8a 16 a4 66 70 28 22 4c |,nw ").....fp("L|
00000770 44 46 44 20 46 30 2c 69 6e 68 22 29 0d 02 94 16 |DFD F0,inh")....|
00000780 a4 66 70 28 22 53 54 46 44 20 46 30 2c 6e 68 20 |.fp("STFD F0,nh |
00000790 22 29 0d 02 9e 11 4c 44 52 20 52 30 2c 69 6e 69 |")....LDR R0,ini|
000007a0 74 65 72 0d 02 a8 10 53 54 52 20 52 30 2c 6e 69 |ter....STR R0,ni|
000007b0 74 65 72 0d 02 b2 0a a4 66 65 78 69 74 0d 02 bc |ter.....fexit...|
000007c0 2a 2e 69 6e 78 20 a4 66 70 28 22 44 46 44 20 2d |*.inx .fp("DFD -|
000007d0 32 2e 30 30 22 29 20 3b 20 49 6e 69 74 69 61 6c |2.00") ; Initial|
000007e0 20 76 61 6c 75 65 73 0d 02 c6 19 2e 69 6e 79 20 | values.....iny |
000007f0 a4 66 70 28 22 44 46 44 20 2d 31 2e 36 30 22 29 |.fp("DFD -1.60")|
00000800 0d 02 d0 17 2e 69 6e 77 20 a4 66 70 28 22 44 46 |.....inw .fp("DF|
00000810 44 20 34 2e 30 22 29 0d 02 da 17 2e 69 6e 68 20 |D 4.0").....inh |
00000820 a4 66 70 28 22 44 46 44 20 33 2e 32 22 29 0d 02 |.fp("DFD 3.2")..|
00000830 e4 13 2e 69 6e 69 74 65 72 20 44 43 44 20 31 32 |...initer DCD 12|
00000840 38 0d 02 ee 05 3b 0d 02 f8 25 3b 20 56 65 72 69 |8....;...%; Veri|
00000850 66 79 20 64 61 74 61 20 69 6e 70 75 74 20 6f 72 |fy data input or|
00000860 20 7a 6f 6f 6d 20 72 61 6e 67 65 0d 03 02 0d 2e | zoom range.....|
00000870 6e 64 61 74 61 63 68 6b 0d 03 0c 16 a4 66 70 28 |ndatachk.....fp(|
00000880 22 4c 44 46 44 20 46 30 2c 6e 78 30 22 29 0d 03 |"LDFD F0,nx0")..|
00000890 16 15 a4 66 70 28 22 43 4d 46 44 20 46 30 2c 23 |...fp("CMFD F0,#|
000008a0 34 22 29 0d 03 20 2a 42 47 54 20 6e 62 61 64 64 |4").. *BGT nbadd|
000008b0 61 74 61 20 20 20 20 20 20 20 20 20 20 20 20 3b |ata ;|
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000008f0 34 2a 42 4c 54 20 6e 62 61 64 64 61 74 61 20 20 |4*BLT nbaddata |
00000900 20 20 20 20 20 20 20 20 20 20 3b 20 78 30 20 74 | ; x0 t|
00000910 6f 6f 20 73 6d 61 6c 6c 0d 03 3e 16 a4 66 70 28 |oo small..>..fp(|
00000920 22 4c 44 46 44 20 46 30 2c 6e 79 30 22 29 0d 03 |"LDFD F0,ny0")..|
00000930 48 15 a4 66 70 28 22 43 4d 46 44 20 46 30 2c 23 |H..fp("CMFD F0,#|
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00000950 61 74 61 20 20 20 20 20 20 20 20 20 20 20 20 3b |ata ;|
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00000980 22 29 20 20 20 20 20 20 3b 20 3c 2d 34 3f 0d 03 |") ; <-4?..|
00000990 66 2a 42 4c 54 20 6e 62 61 64 64 61 74 61 20 20 |f*BLT nbaddata |
000009a0 20 20 20 20 20 20 20 20 20 20 3b 20 79 30 20 74 | ; y0 t|
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000009f0 74 65 67 65 72 20 66 70 20 72 61 6e 67 65 2e 0d |teger fp range..|
00000a00 03 84 3a a4 66 70 28 22 4c 44 46 44 20 46 31 2c |..:.fp("LDFD F1,|
00000a10 6e 69 6e 69 6e 74 22 29 20 20 3b 20 73 6d 61 6c |ninint") ; smal|
00000a20 6c 65 73 74 20 76 61 6c 75 65 20 66 6f 72 20 66 |lest value for f|
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00000a60 23 34 22 29 0d 03 a2 29 42 47 54 20 6e 62 61 64 |#4")...)BGT nbad|
00000a70 64 61 74 61 20 20 20 20 20 20 20 20 20 20 20 20 |data |
00000a80 3b 20 77 20 74 6f 6f 20 6c 61 72 67 65 0d 03 ac |; w too large...|
00000a90 32 a4 66 70 28 22 43 4d 46 44 20 46 30 2c 46 31 |2.fp("CMFD F0,F1|
00000aa0 22 29 20 20 20 20 20 3b 20 77 69 74 68 69 6e 20 |") ; within |
00000ab0 61 63 63 75 72 61 63 79 20 72 61 6e 67 65 3f 0d |accuracy range?.|
00000ac0 03 b6 29 42 4c 54 20 6e 62 61 64 64 61 74 61 20 |..)BLT nbaddata |
00000ad0 20 20 20 20 20 20 20 20 20 20 20 3b 20 77 20 74 | ; w t|
00000ae0 6f 6f 20 73 6d 61 6c 6c 0d 03 c0 16 a4 66 70 28 |oo small.....fp(|
00000af0 22 4c 44 46 44 20 46 30 2c 6e 68 20 22 29 0d 03 |"LDFD F0,nh ")..|
00000b00 ca 15 a4 66 70 28 22 43 4d 46 44 20 46 30 2c 23 |...fp("CMFD F0,#|
00000b10 34 22 29 0d 03 d4 28 42 47 54 20 6e 62 61 64 64 |4")...(BGT nbadd|
00000b20 61 74 61 20 20 20 20 20 20 20 20 20 20 20 3b 20 |ata ; |
00000b30 68 20 74 6f 6f 20 6c 61 72 67 65 0d 03 de 32 a4 |h too large...2.|
00000b40 66 70 28 22 43 4d 46 44 20 46 30 2c 46 31 22 29 |fp("CMFD F0,F1")|
00000b50 20 20 20 20 20 3b 20 77 69 74 68 69 6e 20 61 63 | ; within ac|
00000b60 63 75 72 61 63 79 20 72 61 6e 67 65 3f 0d 03 e8 |curacy range?...|
00000b70 28 42 4c 54 20 6e 62 61 64 64 61 74 61 20 20 20 |(BLT nbaddata |
00000b80 20 20 20 20 20 20 20 20 3b 20 68 20 74 6f 6f 20 | ; h too |
00000b90 73 6d 61 6c 6c 0d 03 f2 05 3b 0d 03 fc 22 3b 20 |small....;..."; |
00000ba0 56 65 72 69 66 79 20 6d 61 78 69 74 65 72 20 6e |Verify maxiter n|
00000bb0 6f 74 20 74 6f 6f 20 73 6d 61 6c 6c 0d 04 06 10 |ot too small....|
00000bc0 4c 44 52 20 52 30 2c 6e 69 74 65 72 0d 04 10 27 |LDR R0,niter...'|
00000bd0 43 4d 50 20 52 30 2c 23 31 30 20 20 20 20 20 20 |CMP R0,#10 |
00000be0 20 20 20 20 20 20 20 3b 20 74 6f 6f 20 73 6d 61 | ; too sma|
00000bf0 6c 6c 3f 0d 04 1a 10 4d 4f 56 4c 54 20 52 30 2c |ll?....MOVLT R0,|
00000c00 23 31 30 0d 04 24 2c 53 54 52 4c 54 20 52 30 2c |#10..$,STRLT R0,|
00000c10 6e 69 74 65 72 20 20 20 20 20 20 20 20 20 3b 20 |niter ; |
00000c20 79 65 73 20 2d 20 73 65 74 20 74 6f 20 31 30 0d |yes - set to 10.|
00000c30 04 2e 0a a4 66 65 78 69 74 0d 04 38 05 3b 0d 04 |....fexit..8.;..|
00000c40 42 0d 2e 6e 62 61 64 64 61 74 61 0d 04 4c 0d 4d |B..nbaddata..L.M|
00000c50 4f 56 20 52 30 2c 23 31 0d 04 56 2c 53 54 52 20 |OV R0,#1..V,STR |
00000c60 52 30 2c 5b 52 31 2c 23 66 65 76 65 6e 74 5f 72 |R0,[R1,#fevent_r|
00000c70 63 5d 20 3b 20 73 65 74 20 72 65 74 75 72 6e 20 |c] ; set return |
00000c80 63 6f 64 65 0d 04 60 0a a4 66 65 78 69 74 0d 04 |code..`..fexit..|
00000c90 6a 04 0d 04 74 1b 2e 6e 69 6e 69 6e 74 20 a4 66 |j...t..ninint .f|
00000ca0 70 28 22 44 46 44 20 31 65 2d 35 22 29 0d 04 7e |p("DFD 1e-5")..~|
00000cb0 2a 3b 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |*;--------------|
00000cc0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------|
00000cd0 2d 2d 2d 2d 2d 2d 2d 0d 04 88 21 3b 20 49 6e 69 |-------...!; Ini|
00000ce0 74 69 61 6c 69 73 65 20 72 65 61 64 79 20 66 6f |tialise ready fo|
00000cf0 72 20 61 20 70 6c 6f 74 0d 04 92 0e 2e 6e 70 6c |r a plot.....npl|
00000d00 6f 74 69 6e 69 74 0d 04 9c 1b 4c 44 52 20 52 30 |otinit....LDR R0|
00000d10 2c 5b 52 31 2c 23 70 6c 6f 74 5f 66 6c 61 67 73 |,[R1,#plot_flags|
00000d20 5d 0d 04 a6 2d 84 52 20 52 30 2c 52 30 2c 23 70 |]...-.R R0,R0,#p|
00000d30 6c 6f 74 5f 66 66 70 20 20 20 20 20 3b 20 66 61 |lot_ffp ; fa|
00000d40 73 74 20 66 6c 6f 61 74 20 6d 61 74 68 73 0d 04 |st float maths..|
00000d50 b0 2a 53 54 52 20 52 30 2c 5b 52 31 2c 23 70 6c |.*STR R0,[R1,#pl|
00000d60 6f 74 5f 66 6c 61 67 73 5d 20 3b 20 74 65 6c 6c |ot_flags] ; tell|
00000d70 20 46 72 61 63 74 61 6c 0d 04 ba 13 41 44 52 20 | Fractal....ADR |
00000d80 52 30 2c 6e 65 77 74 6f 6e 66 70 0d 04 c4 36 53 |R0,newtonfp...6S|
00000d90 54 52 20 52 30 2c 6e 65 77 74 6f 6e 5f 66 75 6e |TR R0,newton_fun|
00000da0 63 2b 66 64 65 66 6e 5f 78 79 72 74 6e 20 20 3b |c+fdefn_xyrtn ;|
00000db0 20 4f 75 72 20 70 6c 6f 74 20 72 6f 75 74 69 6e | Our plot routin|
00000dc0 65 0d 04 ce 0a a4 66 65 78 69 74 0d 04 d8 27 3b |e.....fexit...';|
00000dd0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------|
*
00000df0 2d 2d 0d 04 e2 05 5d 0d 04 ec 16 f4 20 6e 65 77 |--....]..... new|
00000e00 74 6f 6e 20 72 65 67 69 73 74 65 72 73 0d 04 f6 |ton registers...|
00000e10 18 f4 20 78 20 26 20 79 20 73 65 74 20 6f 6e 20 |.. x & y set on |
00000e20 65 6e 74 72 79 0d 05 00 45 78 3d 32 3a 79 3d 33 |entry...Ex=2:y=3|
00000e30 3a 78 79 3d 34 3a 78 32 3d 35 3a 79 32 3d 36 3a |:xy=4:x2=5:y2=6:|
00000e40 77 72 6b 31 3d 37 3a 77 72 6b 32 3d 38 3a 77 72 |wrk1=7:wrk2=8:wr|
00000e50 6b 33 3d 39 3a 72 6f 6f 74 3d 31 30 3a 65 3d 31 |k3=9:root=10:e=1|
00000e60 31 3a 64 65 70 74 68 3d 31 32 0d 05 0a 0c 5b 4f |1:depth=12....[O|
00000e70 50 54 20 61 73 6d 0d 05 14 0d 2e 6e 65 77 74 6f |PT asm.....newto|
00000e80 6e 66 70 0d 05 1e 2c 53 54 4d 46 44 20 52 31 33 |nfp...,STMFD R13|
00000e90 21 2c 7b 52 31 34 7d 20 20 20 20 20 20 20 20 3b |!,{R14} ;|
00000ea0 20 52 65 74 75 72 6e 20 61 64 64 72 65 73 73 0d | Return address.|
00000eb0 05 28 0c 4d 4f 56 20 78 2c 52 30 0d 05 32 0c 4d |.(.MOV x,R0..2.M|
00000ec0 4f 56 20 79 2c 52 31 0d 05 3c 20 a4 66 70 5f 73 |OV y,R1..< .fp_s|
00000ed0 71 72 28 79 32 2c 79 29 20 20 20 20 20 20 20 20 |qr(y2,y) |
00000ee0 20 20 3b 20 79 2a 79 0d 05 46 25 4c 44 52 20 65 | ; y*y..F%LDR e|
00000ef0 2c 6e 65 77 74 6f 6e 5f 65 20 20 20 20 20 20 20 |,newton_e |
00000f00 20 20 20 3b 20 65 70 73 69 6c 6f 6e 0d 05 50 13 | ; epsilon..P.|
00000f10 4c 44 52 20 64 65 70 74 68 2c 6e 69 74 65 72 0d |LDR depth,niter.|
00000f20 05 5a 0f 4d 4f 56 20 72 6f 6f 74 2c 23 30 0d 05 |.Z.MOV root,#0..|
00000f30 64 33 2e 6e 6c 6f 6f 70 20 20 20 20 20 20 20 20 |d3.nloop |
00000f40 20 20 20 20 20 20 20 20 20 20 3b 20 64 6f 20 66 | ; do f|
00000f50 6f 72 20 65 61 63 68 20 69 74 65 72 61 74 69 6f |or each iteratio|
00000f60 6e 0d 05 6e 20 a4 66 70 5f 6d 75 6c 28 78 79 2c |n..n .fp_mul(xy,|
00000f70 78 2c 79 29 20 20 20 20 20 20 20 20 3b 20 78 2a |x,y) ; x*|
00000f80 79 0d 05 78 23 41 44 44 20 78 79 2c 78 79 2c 23 |y..x#ADD xy,xy,#|
00000f90 31 3c 3c 32 33 20 20 20 20 20 20 20 20 3b 20 32 |1<<23 ; 2|
00000fa0 2a 78 2a 79 0d 05 82 05 3b 0d 05 8c 20 a4 66 70 |*x*y....;... .fp|
00000fb0 5f 73 71 72 28 78 32 2c 78 29 20 20 20 20 20 20 |_sqr(x2,x) |
00000fc0 20 20 20 20 3b 20 78 2a 78 0d 05 96 0d 4d 4f 56 | ; x*x....MOV|
00000fd0 20 52 31 2c 79 32 0d 05 a0 25 42 4c 20 66 70 5f | R1,y2...%BL fp_|
00000fe0 61 64 64 20 20 20 20 20 20 20 20 20 20 20 20 20 |add |
00000ff0 20 20 3b 20 78 2a 78 2b 79 2a 79 0d 05 aa 0e 4d | ; x*x+y*y....M|
00001000 4f 56 53 20 52 31 2c 52 30 0d 05 b4 27 42 45 51 |OVS R1,R0...'BEQ|
00001010 20 6e 65 78 69 74 20 20 20 20 20 20 20 20 20 20 | nexit |
00001020 20 20 20 20 20 3b 20 74 6f 6f 20 73 6d 61 6c 6c | ; too small|
00001030 0d 05 be 34 42 4c 20 66 70 5f 73 71 72 20 20 20 |...4BL fp_sqr |
00001040 20 20 20 20 20 20 20 20 20 20 20 20 3b 20 64 34 | ; d4|
00001050 3d 28 78 2a 78 2b 79 2a 79 29 2a 28 78 2a 78 2b |=(x*x+y*y)*(x*x+|
00001060 79 2a 79 29 0d 05 c8 13 4c 44 52 20 52 31 2c 66 |y*y)....LDR R1,f|
00001070 70 5f 74 68 72 65 65 0d 05 d2 22 42 4c 20 66 70 |p_three..."BL fp|
00001080 5f 6d 75 6c 20 20 20 20 20 20 20 20 20 20 20 20 |_mul |
00001090 20 20 20 3b 20 33 2a 64 34 0d 05 dc 10 4d 4f 56 | ; 3*d4....MOV|
000010a0 53 20 77 72 6b 31 2c 52 30 0d 05 e6 27 42 45 51 |S wrk1,R0...'BEQ|
000010b0 20 6e 65 78 69 74 20 20 20 20 20 20 20 20 20 20 | nexit |
000010c0 20 20 20 20 20 3b 20 75 6e 64 65 72 66 6c 6f 77 | ; underflow|
000010d0 0d 05 f0 10 3b 20 63 61 6c 63 20 6e 65 77 20 78 |....; calc new x|
000010e0 0d 05 fa 13 4c 44 52 20 52 31 2c 74 77 6f 74 68 |....LDR R1,twoth|
000010f0 69 72 64 0d 06 04 22 a4 66 70 5f 6d 75 6c 28 77 |ird...".fp_mul(w|
00001100 72 6b 32 2c 78 2c 31 29 20 20 20 20 20 20 3b 20 |rk2,x,1) ; |
00001110 78 2a 32 2f 33 0d 06 0e 24 a4 66 70 5f 73 75 62 |x*2/3...$.fp_sub|
00001120 28 30 2c 78 32 2c 79 32 29 20 20 20 20 20 20 20 |(0,x2,y2) |
00001130 3b 20 78 2a 78 2d 79 2a 79 0d 06 18 29 a4 66 70 |; x*x-y*y...).fp|
00001140 5f 64 69 76 28 30 2c 30 2c 77 72 6b 31 29 20 20 |_div(0,0,wrk1) |
00001150 20 20 20 20 3b 20 28 78 2a 78 2d 79 2a 79 29 2f | ; (x*x-y*y)/|
00001160 64 34 0d 06 22 2f a4 66 70 5f 61 64 64 28 78 2c |d4.."/.fp_add(x,|
00001170 30 2c 77 72 6b 32 29 20 20 20 20 20 20 3b 20 78 |0,wrk2) ; x|
00001180 3d 78 2a 32 2f 33 2b 28 78 32 2d 79 32 29 2f 64 |=x*2/3+(x2-y2)/d|
00001190 34 0d 06 2c 10 3b 20 63 61 6c 63 20 6e 65 77 20 |4..,.; calc new |
000011a0 79 0d 06 36 27 a4 66 70 5f 64 69 76 28 77 72 6b |y..6'.fp_div(wrk|
000011b0 32 2c 78 79 2c 77 72 6b 31 29 20 20 3b 20 28 32 |2,xy,wrk1) ; (2|
000011c0 2a 78 2a 79 29 2f 64 34 0d 06 40 13 4c 44 52 20 |*x*y)/d4..@.LDR |
000011d0 52 31 2c 74 77 6f 74 68 69 72 64 0d 06 4a 22 a4 |R1,twothird..J".|
000011e0 66 70 5f 6d 75 6c 28 30 2c 79 2c 31 29 20 20 20 |fp_mul(0,y,1) |
000011f0 20 20 20 20 20 20 3b 20 79 2a 32 2f 33 0d 06 54 | ; y*2/3..T|
00001200 2f a4 66 70 5f 73 75 62 28 79 2c 30 2c 77 72 6b |/.fp_sub(y,0,wrk|
00001210 32 29 20 20 20 20 20 20 3b 20 79 3d 79 2a 32 2f |2) ; y=y*2/|
00001220 33 2d 28 32 2a 78 2a 79 29 2f 64 34 0d 06 5e 05 |3-(2*x*y)/d4..^.|
00001230 3b 0d 06 68 20 a4 66 70 5f 73 71 72 28 79 32 2c |;..h .fp_sqr(y2,|
00001240 79 29 20 20 20 20 20 20 20 20 20 20 3b 20 79 2a |y) ; y*|
00001250 79 0d 06 72 16 3b 20 43 68 65 63 6b 20 66 6f 72 |y..r.; Check for|
00001260 20 72 6f 6f 74 3d 31 0d 06 7c 21 4d 4f 56 20 52 | root=1..|!MOV R|
00001270 31 2c 23 31 32 37 3c 3c 32 33 20 20 20 20 20 20 |1,#127<<23 |
00001280 20 20 20 3b 20 31 2e 30 0d 06 86 20 a4 66 70 5f | ; 1.0... .fp_|
00001290 73 75 62 28 30 2c 78 2c 31 29 20 20 20 20 20 20 |sub(0,x,1) |
000012a0 20 20 20 3b 20 78 2d 31 0d 06 90 28 a4 66 70 5f | ; x-1...(.fp_|
000012b0 73 71 72 28 30 2c 30 29 20 20 20 20 20 20 20 20 |sqr(0,0) |
000012c0 20 20 20 3b 20 28 78 2d 31 29 2a 28 78 2d 31 29 | ; (x-1)*(x-1)|
000012d0 0d 06 9a 2b a4 66 70 5f 61 64 64 28 30 2c 30 2c |...+.fp_add(0,0,|
000012e0 79 32 29 20 20 20 20 20 20 20 20 3b 20 28 78 2d |y2) ; (x-|
000012f0 31 29 2a 28 78 2d 31 29 2b 79 32 0d 06 a4 31 43 |1)*(x-1)+y2...1C|
00001300 4d 50 20 52 30 2c 65 20 20 20 20 20 20 20 20 20 |MP R0,e |
00001310 20 20 20 20 20 20 20 3b 20 28 28 78 2d 31 29 2a | ; ((x-1)*|
00001320 28 78 2d 31 29 2b 79 32 29 3c 65 3f 0d 06 ae 11 |(x-1)+y2)<e?....|
00001330 4d 4f 56 4c 54 20 72 6f 6f 74 2c 23 31 0d 06 b8 |MOVLT root,#1...|
00001340 24 42 4c 54 20 6e 65 78 69 74 20 20 20 20 20 20 |$BLT nexit |
00001350 20 20 20 20 20 20 20 20 20 3b 20 72 6f 6f 74 3d | ; root=|
00001360 31 0d 06 c2 16 3b 20 43 68 65 63 6b 20 66 6f 72 |1....; Check for|
00001370 20 72 6f 6f 74 3d 32 0d 06 cc 21 4d 4f 56 20 52 | root=2...!MOV R|
00001380 31 2c 23 31 32 36 3c 3c 32 33 20 20 20 20 20 20 |1,#126<<23 |
00001390 20 20 20 3b 20 30 2e 35 0d 06 d6 22 a4 66 70 5f | ; 0.5...".fp_|
000013a0 61 64 64 28 30 2c 78 2c 31 29 20 20 20 20 20 20 |add(0,x,1) |
000013b0 20 20 20 3b 20 78 2b 30 2e 35 0d 06 e0 2f a4 66 | ; x+0.5.../.f|
000013c0 70 5f 73 71 72 28 77 72 6b 31 2c 30 29 20 20 20 |p_sqr(wrk1,0) |
000013d0 20 20 20 20 20 3b 20 78 72 3d 28 78 2b 30 2e 35 | ; xr=(x+0.5|
000013e0 29 2a 28 78 2b 30 2e 35 29 0d 06 ea 16 4c 44 52 |)*(x+0.5)....LDR|
000013f0 20 77 72 6b 32 2c 6e 65 77 74 6f 6e 5f 72 32 0d | wrk2,newton_r2.|
00001400 06 f4 28 a4 66 70 5f 73 75 62 28 30 2c 79 2c 77 |..(.fp_sub(0,y,w|
00001410 72 6b 32 29 20 20 20 20 20 20 3b 20 79 2d 30 2e |rk2) ; y-0.|
00001420 38 36 36 30 32 35 34 0d 06 fe 3b a4 66 70 5f 73 |8660254...;.fp_s|
00001430 71 72 28 30 2c 30 29 20 20 20 20 20 20 20 20 20 |qr(0,0) |
00001440 20 20 3b 20 79 72 3d 28 79 2d 30 2e 38 36 36 30 | ; yr=(y-0.8660|
00001450 32 35 34 29 2a 28 79 2d 30 2e 38 36 36 30 32 35 |254)*(y-0.866025|
00001460 34 29 0d 07 08 22 a4 66 70 5f 61 64 64 28 30 2c |4)...".fp_add(0,|
00001470 77 72 6b 31 2c 30 29 20 20 20 20 20 20 3b 20 78 |wrk1,0) ; x|
00001480 72 2b 79 72 0d 07 12 25 43 4d 50 20 52 30 2c 65 |r+yr...%CMP R0,e|
00001490 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | |
000014a0 3b 20 52 6f 6f 74 20 32 3f 0d 07 1c 11 4d 4f 56 |; Root 2?....MOV|
000014b0 4c 54 20 72 6f 6f 74 2c 23 32 0d 07 26 0d 42 4c |LT root,#2..&.BL|
000014c0 54 20 6e 65 78 69 74 0d 07 30 16 3b 20 43 68 65 |T nexit..0.; Che|
000014d0 63 6b 20 66 6f 72 20 72 6f 6f 74 3d 33 0d 07 3a |ck for root=3..:|
000014e0 28 a4 66 70 5f 61 64 64 28 30 2c 79 2c 77 72 6b |(.fp_add(0,y,wrk|
000014f0 32 29 20 20 20 20 20 20 3b 20 79 2b 30 2e 38 36 |2) ; y+0.86|
00001500 36 30 32 35 34 0d 07 44 3b a4 66 70 5f 73 71 72 |60254..D;.fp_sqr|
00001510 28 30 2c 30 29 20 20 20 20 20 20 20 20 20 20 20 |(0,0) |
00001520 3b 20 79 72 3d 28 79 2b 30 2e 38 36 36 30 32 35 |; yr=(y+0.866025|
00001530 34 29 2a 28 79 2b 30 2e 38 36 36 30 32 35 34 29 |4)*(y+0.8660254)|
00001540 0d 07 4e 22 a4 66 70 5f 61 64 64 28 30 2c 77 72 |..N".fp_add(0,wr|
00001550 6b 31 2c 30 29 20 20 20 20 20 20 3b 20 78 72 2b |k1,0) ; xr+|
00001560 79 72 0d 07 58 25 43 4d 50 20 52 30 2c 65 20 20 |yr..X%CMP R0,e |
00001570 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3b 20 | ; |
00001580 52 6f 6f 74 20 33 3f 0d 07 62 11 4d 4f 56 4c 54 |Root 3?..b.MOVLT|
00001590 20 72 6f 6f 74 2c 23 33 0d 07 6c 0d 42 4c 54 20 | root,#3..l.BLT |
000015a0 6e 65 78 69 74 0d 07 76 05 3b 0d 07 80 17 53 55 |nexit..v.;....SU|
000015b0 42 53 20 64 65 70 74 68 2c 64 65 70 74 68 2c 23 |BS depth,depth,#|
000015c0 31 0d 07 8a 0d 42 4e 45 20 6e 6c 6f 6f 70 0d 07 |1....BNE nloop..|
000015d0 94 31 4c 44 52 20 64 65 70 74 68 2c 6e 69 74 65 |.1LDR depth,nite|
000015e0 72 20 20 20 20 20 20 20 20 20 3b 20 4e 6f 20 63 |r ; No c|
000015f0 6f 6c 6f 75 72 20 69 66 20 61 74 20 6d 61 78 0d |olour if at max.|
00001600 07 9e 0a 2e 6e 65 78 69 74 0d 07 a8 10 4c 44 52 |....nexit....LDR|
00001610 20 52 30 2c 6e 69 74 65 72 0d 07 b2 2b 53 55 42 | R0,niter...+SUB|
00001620 20 52 30 2c 52 30 2c 64 65 70 74 68 20 20 20 20 | R0,R0,depth |
00001630 20 20 20 20 20 3b 20 72 65 74 75 72 6e 20 63 6f | ; return co|
00001640 6c 6f 75 72 0d 07 bc 30 41 44 44 20 52 30 2c 52 |lour...0ADD R0,R|
00001650 30 2c 23 31 36 20 20 20 20 20 20 20 20 20 20 20 |0,#16 |
00001660 3b 20 61 76 6f 69 64 20 64 61 72 6b 20 63 6f 6c |; avoid dark col|
00001670 6f 75 72 73 0d 07 c6 22 4c 44 4d 46 44 20 52 31 |ours..."LDMFD R1|
00001680 33 21 2c 7b 50 43 7d 5e 20 20 20 20 20 20 20 20 |3!,{PC}^ |
00001690 3b 20 65 78 69 74 0d 07 d0 05 3b 0d 07 da 23 2e |; exit....;...#.|
000016a0 74 77 6f 74 68 69 72 64 20 a4 66 70 28 22 44 46 |twothird .fp("DF|
000016b0 53 20 30 2e 36 36 36 36 36 36 36 36 22 29 0d 07 |S 0.66666666")..|
000016c0 e4 1f 2e 6e 65 77 74 6f 6e 5f 65 20 a4 66 70 28 |...newton_e .fp(|
000016d0 22 44 46 53 20 30 2e 30 30 32 35 22 29 0d 07 ee |"DFS 0.0025")...|
000016e0 23 2e 6e 65 77 74 6f 6e 5f 72 32 20 a4 66 70 28 |#.newton_r2 .fp(|
000016f0 22 44 46 53 20 30 2e 38 36 36 30 32 35 34 22 29 |"DFS 0.8660254")|
00001700 0d 07 f8 1c 2e 66 70 5f 74 68 72 65 65 20 a4 66 |.....fp_three .f|
00001710 70 28 22 44 46 53 20 33 2e 30 22 29 0d 08 02 1f |p("DFS 3.0")....|
00001720 3b 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |;---------------|
00001730 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0d 08 0c 37 a4 |-----------...7.|
00001740 66 69 6e 74 65 72 66 61 63 65 20 20 20 20 20 20 |finterface |
00001750 20 20 20 20 20 20 3b 20 4e 65 63 65 73 73 61 72 | ; Necessar|
00001760 79 20 43 20 49 6e 74 65 72 66 61 63 65 20 63 6f |y C Interface co|
00001770 64 65 0d 08 16 25 a4 66 70 65 61 73 6d 28 a3 29 |de...%.fpeasm(.)|
00001780 20 20 20 20 20 20 20 20 20 3b 20 46 50 45 20 72 | ; FPE r|
00001790 6f 75 74 69 6e 65 73 0d 08 20 07 5d 3a ed 0d 08 |outines.. .]:...|
000017a0 2a 3a c8 99 20 22 4f 53 5f 46 69 6c 65 22 2c 31 |*:.. "OS_File",1|
000017b0 30 2c 22 3c 46 72 61 63 24 44 69 72 3e 2e 53 61 |0,"<Frac$Dir>.Sa|
000017c0 6d 70 4e 65 77 74 6f 6e 22 2c 26 46 46 41 2c 2c |mpNewton",&FFA,,|
000017d0 63 6f 64 65 25 2c 4f 25 0d 08 34 05 e0 0d ff |code%,O%..4....|
000017df 
.