diff --git a/projects/examples/demos/mandelbrot.tal b/projects/examples/demos/mandelbrot.tal index 0ed83c5..cc3d18b 100644 --- a/projects/examples/demos/mandelbrot.tal +++ b/projects/examples/demos/mandelbrot.tal @@ -1,4 +1,6 @@ -( mandelbrot ) +( mandelbrot.tal ) +( ) +( by alderwick and d_m ) %WIDTH { #02a0 } %HEIGHT { #0200 } @@ -17,88 +19,106 @@ #0ff0 .System/g DEO2 #00ff .System/b DEO2 - WIDTH .Screen/width DEO2 ( 640 ) - HEIGHT .Screen/height DEO2 ( 480 ) + ( size ) + WIDTH .Screen/width DEO2 + HEIGHT .Screen/height DEO2 + ( run ) draw-mandel + BRK -BRK +( draw the mandelbrot set using 4.12 fixed point numbers ) +@draw-mandel ( -> ) + 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] ) + .Screen/pixel DEO 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 DEI2k ( ymax* y* d^ sy* [8000] ) + INC2 ROT DEO2 ( 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 ( ) -@draw-mandel ( -- ) +@evaluate ( x* y* -> count^ ) + #0000 DUP2 ,&x1 STR2 ( x* y* ; x1<-0 ) + DUP2 ,&y1 STR2 ( x* y* ; y1<-0 ) + DUP2 ,&x2 STR2 ( x* y* ; x2<-0 ) + ,&y2 STR2 ( x* y* ; y2<-0 ) + LIT2r 2000 ( x* y* [20 00] ) + &loop ( x* y* [20 n^] ) + [ LIT2 &x1 $2 ] ( x* y* x1* [20 n^] ) + [ LIT2 &y1 $2 ] ( x* y* x1* y1* [20 n^] ) + smul2 DUP2 ADD2 ( x* y* 2x1y1* [20 n^] ) + OVR2 ADD2 ,&y1 STR2 ( x* y* [20 n^] ; y1<-2x1y1+y* ) + SWP2 [ LIT2 &x2 $2 ] ( y* x* x2* [20 n^] ) + [ LIT2 &y2 $2 ] SUB2 ( y* x* x2-y2* [20 n^] ) + OVR2 ADD2 ,&x1 STR2 SWP2 ( x* y* [20 n^] ; x1<-x2-y2+x* ) + ,&x1 LDR2 square ( x* y* x1^2* [20 n^] ) + DUP2 ,&x2 STR2 ( x* y* x1^2* [20 n^] ; x2<-x1^2* ) + ,&y1 LDR2 square ( x* y* x1^2* y1^2* [20 n^] ) + DUP2 ,&y2 STR2 ( x* y* x1^2* y1^2* [20 n^] ; y2<-y1^2* ) + ADD2 #4000 GTH2 ?&end ( x* y* [20 n^] ) + INCr GTHkr STHr ?&loop ( x* y* [20 n+1*] ) + &end ( x* y* [20 count^] ) + POP2 POP2 NIPr STHr JMP2r ( count^ ) - XMAX XMIN SUB2 WIDTH DIV2 ;&dx STA2 - YMAX YMIN SUB2 HEIGHT DIV2 ;&dy STA2 - [ LIT2 01 -Screen/auto ] DEO - YMAX YMIN - &ver - DUP2 ,&y STR2 - XMAX XMIN - &hor - DUP2 ,&x STR2 - #0000 - DUP2 ,&x1 STR2 - DUP2 ,&y1 STR2 - DUP2 ,&x2 STR2 - ,&y2 STR2 - ( pixel ) - #2000 - &loop - [ LIT2 &x1 $2 ] [ LIT2 &y1 $2 ] smul2 DUP2 ADD2 - [ LIT2 &y $2 ] ADD2 ,&y1 STR2 - [ LIT2 &x2 $2 ] [ LIT2 &y2 $2 ] SUB2 - [ LIT2 &x $2 ] ADD2 ,&x1 STR2 - ,&x1 LDR2 DUP2 smul2 - DUP2 ,&x2 STR2 - ,&y1 LDR2 DUP2 smul2 - DUP2 ,&y2 STR2 - ADD2 #4000 GTH2 ?&end - INC GTHk ?&loop - &end - NIP .Screen/pixel DEO - ( done. ) - [ LIT2 &dx $2 ] ADD2 OVR2 #8000 ADD2 OVR2 #8000 ADD2 SWP2 LTH2 ?&hor - POP2 POP2 - #0000 .Screen/x DEO2 - .Screen/y DEI2k INC2 ROT DEO2 - [ LIT2 &dy $2 ] ADD2 OVR2 #8000 ADD2 OVR2 #8000 ADD2 SWP2 LTH2 ?&ver - POP2 POP2 +( multiply two signed 4.12 fixed point numbers ) +@smul2 ( a* b* -> ab* ) + LIT2r 0001 DUP2 #8000 LTH2 ?&bpos negate SWPr ( a* |b|* [sign*] ) + &bpos SWP2 DUP2 #8000 LTH2 ?&apos negate SWPr ( |b|* |a|* [sign*] ) + &apos smul2-pos STHr ?&abpos negate ( ab* [scrap^] ) + &abpos POPr JMP2r ( ab* ) -JMP2r +( 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 ( b0* b1* a0* b1* a0* b0* [a1*] ) + 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* ) -@smul2 ( a* b* -- c* ) - LITr 00 - DUP2 #8000 LTH2 ?&b-positive - INCr DUP2k EOR2 SWP2 SUB2 - &b-positive - SWP2 - DUP2 #8000 LTH2 ?&a-positive - INCr DUP2k EOR2 SWP2 SUB2 - &a-positive - ( ahi alo bhi blo ) - LITr 00 STH ( ahi alo bhi / blo* ) - OVRr STH ( ahi alo / blo* bhi* ) - OVRr STH ( ahi / blo* bhi* alo* ) - OVRr STH ( asign / blo* bhi* alo* ahi* ) - ROT2r MUL2kr STH2r ( asign ahi-bhi* / blo* alo* ahi* bhi* ) - ROT2r MUL2kr STH2r ( asign ahi-bhi* alo-bhi* / blo* ahi* bhi* alo* ) - NIP2r ( asign ahi-bhi* alo-bhi* / blo* ahi* alo* ) - ROT2r MUL2kr STH2r ( asign ahi-bhi* alo-bhi* alo-blo* / ahi* alo* blo* ) - ROT2r MUL2r STH2r POP2r ( asign ahi-bhi* alo-bhi* alo-blo* ahi-blo* ) - SWP2 ( asign ahi-bhi* alo-bhi* ahi-blo* alo-blo* ) - ( 32-bit result is [ r3 r2 r1 r0 ] ) - POP #00 SWP ( asign ahi-bhi* alo-bhi* ahi-blo* r21* ) - ( r21 max is 00fe, ahi-blo max is 7e81, max sum is 7f7f ) - ADD2 ( asign ahi-bhi* alo-bhi* r21'* ) - ( r21' max is 7f7f, alo-bhi max is 7e81, max sum is fe00 ) - ADD2 ( asign ahi-bhi* r21"* ) - ( The result we want is bits 27-12 due to the fixed point representation we use. ) - #04 SFT2 SWP2 #07ff min #40 SFT2 ADD2 - ( saturate to +/-7.fff ) - #7fff min - STHr #01 NEQ ?&result-positive - DUP2k EOR2 SWP2 SUB2 - &result-positive -JMP2r +( equivalent to DUP2 smul2 but faster ) +@square ( a* -> aa* ) + DUP2 #8000 LTH2 ?&pos negate &pos -@min ( x* y* -- min* ) - GTH2k [ JMP SWP2 NIP2 ] JMP2r +( >> ) + +( equivalent to DUP2 smul2-pos but faster ) +@square-pos ( a* -> aa* ) + aerate ( 00 ahi^ 00 alo^ ) + OVR2 MUL2 #03 SFT2 SWP2 ( yz* ahi* ) + DUP2 MUL2 #07ff min #40 SFT2 ( x* yz* ) + ADD2 #7fff !min ( aa* ) + +( 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 + +( return the minimum of two non-negative numbers. ) +@min ( x* y* ) GTH2k [ JMP SWP2 ] NIP2 JMP2r