( julia.tal ) ( ) ( based on mandelbrot.tal by alderwick and d_m ) ( ) ( uses 4.12 fixed point arithmetic. ) ( SCALE LOGICAL SCREENSIZE ) ( #0001 21x16 42x32 ) ( #0002 42x32 84x64 ) ( #0004 84x64 168x128 ) ( #0008 168x128 336x256 ) ( #0010 336x256 672x512 ) ( #0020 672x512 1344x1024 ) %SCALE { #0009 } ( 32 ) %WIDTH { #0015 } ( 21 ) %HEIGHT { #0010 } ( 16 ) %XMIN { #de69 } ( -8601 => -8601/4096 => -2.100 ) %XMAX { #0b33 } ( 2867 => 2867/4096 => 0.700 ) %YMIN { #ecc7 } ( -4915 => -4915/4096 => -1.200 ) %YMAX { #1333 } ( 4915 => 4915/4096 => 1.200 ) |00 @System &vector $2 &wst $1 &rst $1 &eaddr $2 &ecode $1 &pad $1 &r $2 &g $2 &b $2 &debug $1 &halt $1 |20 @Screen &vector $2 &width $2 &height $2 &auto $1 &pad $1 &x $2 &y $2 &addr $2 &pixel $1 &sprite $1 |0100 ( -> ) ( set colors ) #00ff .System/r DEO2 #0ff0 .System/g DEO2 #0f0f .System/b DEO2 ( set window size ) width #10 SFT2 .Screen/width DEO2 height #10 SFT2 .Screen/height DEO2 ( starting c values ) #0630 ;evaluate/cx STA2 #f5e0 ;evaluate/cy STA2 ;on-screen .Screen/vector DEO2 BRK @on-screen ( -> BRK ) #0000 DUP2 .Screen/x DEO2 .Screen/y DEO2 draw-julia ;evaluate/cx LDA2 DUP2 #2000 LTH2 ?&upx DUP2 #e000 GTH2 ?&upx DUP2 #8000 LTH2 #ff MUL #80 ,&dx STR2 &upx [ LIT2 &dx 0080 ] ADD2 SWP2 STA2 ;evaluate/cy LDA2k DUP2 #2000 LTH2 ?&upy DUP2 #e000 GTH2 ?&upy DUP2 #8000 LTH2 #ff MUL #80 ,&dy STR2 &upy [ LIT2 &dy 0080 ] ADD2 SWP2 STA2 BRK ( logical width ) @width ( -> w* ) WIDTH SCALE MUL2 JMP2r ( logical height ) @height ( -> h* ) HEIGHT SCALE MUL2 JMP2r ( draw the julia set using 4.12 fixed point numbers ) @draw-julia ( -> ) XMAX XMIN SUB2 width DIV2 ,&dx STR2 ( ; &dx<-{xmax-min}/width ) YMAX YMIN SUB2 height DIV2 ,&dy STR2 ( ; &dy<-{ymax-ymin}/height ) [ LIT2 01 -Screen/auto ] DEO ( ; auto<-1 ) LIT2r 8000 ( [8000] ) YMAX YMIN ( ymax* ymin* [8000] ) &yloop ( ymax* y* [8000] ) XMAX XMIN ( ymax* y* xmax* xmin* [8000] ) &xloop ( ymax* y* xmax* x* [8000] ) ROT2k evaluate ( ymax* y* xmax* x* xmax* count^ [8000] ) draw-px POP2 ( ymax* y* xmax* x* [8000] ) [ LIT2 &dx $2 ] ADD2 ( ymax* y* xmax* x+dx* [8000] ) OVR2 STH2kr ADD2 ( ymax* y* xmax* x+dx* 8000+xmax* [8000] ) OVR2 STH2kr ADD2 ( ymax* y* xmax* x+dx* 8000+xmax* 8000+x+dx* [8000] ) GTH2 ?&xloop ( ymax* y* xmax* x+dx* [8000] ) POP2 POP2 ( ymax* y* [8000] ) #0000 .Screen/x DEO2 ( ymax* y* [8000] ; sc/x<-0 ) .Screen/y ;inc2 adjust ( ymax* y* [8000] ; sc/y<-sy+1 ) [ LIT2 &dy $2 ] ADD2 ( ymax* y+dy* [8000] ) OVR2 STH2kr ADD2 ( ymax* y+dy* 8000+ymax* [8000] ) OVR2 STH2kr ADD2 ( ymax* y+dy* 8000+ymax* 8000+y+dy* [8000] ) GTH2 ?&yloop ( ymax* y+dy* [8000] ) POP2 POP2 POP2r JMP2r ( ) ( dithering pattern for 2x2 pixels: ) ( ) ( |o o| -> |x o| -> |x o| -> |x x| -> |x x| ) ( |o o| -> |o o| -> |o x| -> |o x| -> |x x| ) ( ) ( |[p+3]/4 [px+1]/4| ) ( |[p+0]/4 [px+2]/4| ) @draw-px ( px^ -> ) INCk INCk INC ( p+0 p+1 p+3 ) draw-quad draw-quad ( p+0 ; draw NW, NE ) .Screen/y ;inc1 adjust ( ; y<-y+1 ) .Screen/x ;sub2 adjust ( ; x<-x-2 ) INCk INC SWP ( p+2 p+0 ) draw-quad draw-quad ( ; draw SW, SE ) .Screen/y ;sub1 !adjust ( ; y<-y-1 ) ( draw one quadrant of a 2x2 area ) @draw-quad ( p^ -> ) #02 SFT .Screen/pixel DEO JMP2r ( ; pixel<-p/4 ) ( evaluate the julia function at one point ) @evaluate ( x* y* -> count^ ) LIT2r 2000 ( x* y* [20 00] ) ( DUP2 ,&cy STR2 OVR2 ,&cx STR2 ) ( #fa8b ,&cx STR2 #f5e7 ,&cy STR2 ) ,&y1 STR2 ,&x1 STR2 ( [20 00] ; x1<-x, y1<- y ) &loop [ LIT2 &x1 $2 ] ( x1* [20 n^] ) square DUP2 ,&x2 STR2 ( [20 n^] ) [ LIT2 &y1 $2 ] ( x1* [20 n^] ) square DUP2 ,&y2 STR2 ( [20 n^] ) ADD2 #4000 GTH2 ?&end ( [20 n^] ) ,&x1 LDR2 ,&y1 LDR2 ( x1* y1* [20 n^] ) smul2 DUP2 ADD2 ( 2x1y1* [20 n^] ) [ LIT2 &cy $2 ] ADD2 ( 2x1y1+cy* [20 n^] ) ,&y1 STR2 ( [20 n^] ; y1<-2x1y1+cy* ) [ LIT2 &x2 $2 ] ( x2* [20 n^] ) [ LIT2 &y2 $2 ] SUB2 ( x2-y2* [20 n^] ) [ LIT2 &cx $2 ] ADD2 ( x2-y2+cx* [20 n^] ) ,&x1 STR2 ( [20 n^] ; x1<-x2-y2+x* ) INCr GTHkr STHr ?&loop ( [20 n+1*] ) &end ( [20 count^] ) NIPr STHr JMP2r ( count^ ) ( is x a non-negative signed value? ) @non-negative ( x* -> x* x>=0^ ) DUP2 #8000 LTH2 JMP2r ( multiply two signed 4.12 fixed point numbers ) @smul2 ( a* b* -> ab* ) LIT2r 0001 non-negative ?{ negate SWPr } ( a* |b|* [sign*] ) SWP2 non-negative ?{ negate SWPr } ( |b|* |a|* [sign*] ) smul2-pos STHr ?{ negate } POPr JMP2r ( ab* ) ( multiply two non-negative fixed point numbers ) ( ) ( a * b = {a0/16 + a1/4096} * {b0/16 + b1/4096} ) ( = a0b0/256 + a1b0/65536 + a0b1/65536 + a1b1/16777216 ) ( = x + y + z + 0 ; the last term is too small to represent, i.e. zero ) ( ) ( x = a0b0 << 4 ) ( y = a1b0 >> 4 ) ( z = a0b1 >> 4 ) @smul2-pos ( a* b* -> ab* ) aerate ROT2 aerate ( b0* b1* a0* a1* ) STH2 ROT2k STH2 MUL2r ( b0* b1* a0* b1* a0* [a1b0*] ) MUL2 STH2 ADD2r ( b0* b1* a0* [a1b0+a0b1*] ) NIP2 MUL2 #07ff min #40 SFT2 ( a0b0* [y+z*] ) STH2r #04 SFT2 ADD2 ( x* [y+z*] ) #7fff !min ( ab* ) ( equivalent to DUP2 smul2 but faster ) @square ( a* -> aa* ) non-negative ?{ negate } ( |a|* ) aerate ( 00 ahi^ 00 alo^ ) OVR2 MUL2 #03 SFT2 SWP2 ( yz* ahi* ) DUP2 MUL2 #07ff min #40 SFT2 ( x* yz* ) ADD2 #7fff !min ( aa* ) ( update a device d^ given a function f: x* -> f[x]* ) @adjust ( d^ f* -> ) STH2 DEI2k STH2r JSR2 ROT DEO2 JMP2r ( return the minimum of two non-negative numbers. ) @min ( x* y* ) GTH2k [ JMP SWP2 ] NIP2 JMP2r ( convert each byte of a a short into a short ) @aerate ( x* -> 00 xhi^ 00 xlo^ ) SWP #0000 ROT SWP2 SWP JMP2r ( negate a fixed point number. doesn't work for #8000 ) @negate ( x* -> -x* ) DUP2k EOR2 SWP2 SUB2 JMP2r ( useful arithmetic operations ) @inc2 ( n* -> n+2* ) INC2 @inc1 ( n* -> n+1* ) INC2 JMP2r @sub1 ( n* -> n-1* ) #0001 SUB2 JMP2r @sub2 ( n* -> n-2* ) #0002 SUB2 JMP2r