252 lines
9.0 KiB
Tal
252 lines
9.0 KiB
Tal
( graph.tal )
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( )
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( graphing calculator )
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( EXPRESSIONS )
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( )
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( expressions use one byte for an id, and )
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( zero or more bytes for data. )
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( )
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( ID NAME DATA DESCRIPTION )
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( 00 var variable x )
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( 01 lit const* literal value )
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( 02 neg e1* -e1 )
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( 03 pow e* k^ e^k )
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( 04 add e1* e2* e1 + e2 )
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( 05 sub e1* e2* e1 - e2 )
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( 06 mul e1* e2* e1 * e2 )
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( 07 div e1* e2* e1 / e2 )
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( )
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( const* is a fixed point value )
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( e*, e1*, and e2* are addresses of expressions. )
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( k^ is an unsigned integer )
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|00 @System &vect $2 &wst $1 &rst $1 &eaddr $2 &ecode $1 &pad $1 &r $2 &g $2 &b $2 &debug $1 &halt $1
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|20 @Screen &vect $2 &w $2 &h $2 &auto $1 &pad $1 &x $2 &y $2 &addr $2 &pixel $1 &sprite $1
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|0000
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( set up variables used to configure graphing )
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@width $2 ( screen width in pixels )
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@height $2 ( screen height in pixels )
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@epsilon $2 ( graph value per pixel )
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@xmin $2 ( min x graph coord )
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@xmax $2 ( max x graph coord )
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@ymin $2 ( min y graph coord )
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@ymax $2 ( max y graph coord )
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( we really want (xmax-xmin)*epsilon to exactly equal width )
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( and similarly (ymax-ymin)*epsilon to exactly equal height )
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( )
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( this implies a square screen. for non-square screens we'll )
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( need separate epsilons for x and y. )
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( )
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( variables used during graphing )
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@step $2 ( current step size for drawing )
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@expr $2 ( current equation being graphed )
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@x0 $2 ( lower bound of x )
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@x1 $2 ( upper bound of x )
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@y0 $2 ( lower bound of y )
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@y1 $2 ( upper bound of y )
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|0100
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( screen size )
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#0200 .width STZ2
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#0200 .height STZ2
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( colors )
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#0f0f .System/r DEO2
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#0ff0 .System/g DEO2
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#00ff .System/b DEO2
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( set up screen device )
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.width LDZ2 .Screen/w DEO2
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.height LDZ2 .Screen/h DEO2
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( default settings: -4.0 to +4.0 )
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( #fc00 DUP2 .xmin STZ2 .ymin STZ2
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#0400 DUP2 .xmax STZ2 .ymax STZ2 )
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#0400
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DUP2 .xmax STZ2 DUP2 .ymax STZ2
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#0000 SWP2 SUB2
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DUP2 .xmin STZ2 .ymin STZ2
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( TODO: we probably want separate epsilons for x and y )
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( TODO: validate that (xmax-xmin)*eps = width exactly )
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x-range .width LDZ2 DIV2 .epsilon STZ2
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( draw x and y axis on background )
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draw-y-axis draw-x-axis
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( prepare equation )
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;x^3-2x+1 .expr STZ2
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( ;0.5x^2-6 .expr STZ2 )
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( set up starting parameters )
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.xmin LDZ2 .ymin LDZ2 x-range
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( graph the equation )
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draw BRK
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@x-range ( -> x-range* ) .xmax LDZ2 .xmin LDZ2 SUB2 JMP2r
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@y-range ( -> y-range* ) .ymax LDZ2 .ymin LDZ2 SUB2 JMP2r
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@hline ( x1* x2* y* )
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#01 .Screen/auto DEO .Screen/y DEO2 OVR2 .Screen/x DEO2
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SUB2 &xloop #02 .Screen/pixel DEO INC2 ORAk ?&xloop POP2 JMP2r
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@vline ( y1* y2* x* )
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#02 .Screen/auto DEO .Screen/x DEO2 OVR2 .Screen/y DEO2
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SUB2 &yloop #02 .Screen/pixel DEO INC2 ORAk ?&yloop POP2 JMP2r
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@center-x ( -> cx* ) .width LDZ2 #01 SFT2 JMP2r
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@center-y ( -> cx* ) .height LDZ2 #01 SFT2 JMP2r
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( TODO: gets weird with non-powers-of-2 )
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@draw-y-axis ( -> )
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#0000 .height LDZ2 center-x vline ( )
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center-x #0010 SUB2k ,&lmid STR2 ( )
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ADD2 ,&rmid STR2 ( )
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.height LDZ2 STH2 ( [h*] )
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#0100 .epsilon LDZ2 DIV2 ,&vstep STR2 ( [h*] )
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,&vstep LDR2 STH2 ( [h* step*] )
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&vloop ( [h* pos*] )
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[ LIT2 &lmid $2 ] ( lmid* [h* pos*] )
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[ LIT2 &rmid $2 ] ( lmid* rmid* [h* pos*] )
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STH2kr vline ( [h* pos*] )
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[ LIT2r &vstep $2 ] ADD2r ( [h* pos+step*] )
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GTH2kr STHr ?&vloop ( [h* pos+step*] )
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POP2r POP2r JMP2r ( )
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( TODO: gets weird with non-powers-of-2 )
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@draw-x-axis ( -> )
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#0000 .width LDZ2 center-y hline ( )
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center-y #0010 SUB2k ,&lmid STR2 ( )
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ADD2 ,&rmid STR2 ( )
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.width LDZ2 STH2 ( [w*] )
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#0100 .epsilon LDZ2 DIV2 ,&hstep STR2 ( [w*] )
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,&hstep LDR2 STH2 ( [h* step*] )
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&hloop ( [w* pos*] )
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[ LIT2 &lmid $2 ] ( lmid* [w* pos*] )
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[ LIT2 &rmid $2 ] ( lmid* rmid* [w* pos*] )
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STH2kr hline ( [w* pos*] )
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[ LIT2r &hstep $2 ] ADD2r ( [w* pos+step*] )
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GTH2kr STHr ?&hloop ( [w* pos+step*] )
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POP2r POP2r JMP2r ( )
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( recursive drawing procedure )
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( )
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( this draws the area [x,y] to [x+s,y+s]. )
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( first it checks whether that area contains a point. )
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( next it checks if s=1: )
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( - if so we draw that point )
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( - if not, we split into a 2x2 grid and recurse )
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@draw ( x* y* s* -> )
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STH2k .step STZ2 ( x* y* [s*] ; step<-s )
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OVR2 OVR2 evaluate ?&hit ( x* y* [s*] )
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POP2 POP2 POP2r JMP2r ( ; miss )
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&hit ( x* y* [s*] )
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STH2kr #0001 EQU2 ?&term ( x* y* [s*] )
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( STH2kr .epsilon LDZ2 LTH2 ?&term ( x* y* [s*] ) )
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LITr 01 SFT2r ( x* y* [h=s/2*] )
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OVR2 OVR2 ( x* y* x* y* h* [h*] )
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STH2kr draw ( x* y* [h*] ; south west )
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OVR2 OVR2 STH2kr ADD2 ( x* y* x* y+h* [h*] )
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STH2kr draw ( x* y* [h*] ; north west )
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OVR2 STH2kr ADD2 OVR2 ( x* y* x+h* y* [h*] )
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STH2kr draw ( x+h* y* [h*] ; south east )
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STH2kr ADD2 SWP2 STH2kr ADD2 SWP2 ( x+h* y+h* [h*] )
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STH2r draw ( ; upper-right )
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JMP2r ( )
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&term ( x* y* [s*] )
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POP2r ( x* y* )
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.ymax LDZ2 SWP2 SUB2 ( x* ymax-y* )
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.epsilon LDZ2 SUB2 ( x* ymax-y-e* )
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.epsilon LDZ2 DIV2 ( x* sy=(ymax-y-e)/e* )
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.Screen/y DEO2 ( x* ; screen/y<-sy )
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.xmin LDZ2 SUB2 ( x-xmin* )
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.epsilon LDZ2 DIV2 ( x* sx=(x-xmin)/e* )
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.Screen/x DEO2 ( ; screen/x<-sx )
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#41 .Screen/pixel DEO ( ; screen/pixel<-41 )
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JMP2r ( )
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( determine if the given x and y intervals intersect )
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( if they do, at least one point of the graph is in this region )
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( if not, the entire region is empty. )
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@evaluate ( x* y* -> bool^ )
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( store epsilon and x/y intervals )
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LITr -step LDZ2r ( x* y* [e*] )
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DUP2 .y0 STZ2 ( x* y* [e*] ; y0<-y )
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STH2kr x16-add .y1 STZ2 ( x* [e*] ; y1<-y+e )
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DUP2 .x0 STZ2 ( x* [e*] ; x0<-x )
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STH2r x16-add .x1 STZ2 ( ; x1<-x+e )
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( evaluate our equation )
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.expr LDZ2 eval ( x-iv** )
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.y0 LDZ2 .y1 LDZ2 ( x-iv** y-iv** )
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!iv-intersects ( result^ )
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( requires .x0 and .x1 to already be set )
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@eval ( expr* -> interval** )
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LDAk #00 NEQ ?&o1 ( var ) POP2 .x0 LDZ2 .x1 LDZ2 JMP2r
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&o1 LDAk #01 NEQ ?&o2 ( lit ) INC2 LDA2 DUP2 JMP2r
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&o2 LDAk #02 NEQ ?&o3 ( neg ) INC2 LDA2 eval !iv-negate
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&o3 LDAk #03 NEQ ?&o4 ( pow ) INC2 STH2k LDA2 eval STH2r INC2 INC2 LDA !iv-pow
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&o4 LDAk #04 NEQ ?&o5 ( add ) ;iv-add !binop
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&o5 LDAk #05 NEQ ?&o6 ( sub ) ;iv-sub !binop
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&o6 LDAk #06 NEQ ?&o7 ( mul ) ;iv-mul !binop
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&o7 #0000 DIV ( TODO: div )
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@binop ( addr* op* -> interval** )
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STH2 INC2 STH2k ( addr+1* [op* addr+1*] )
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LDA2 eval ( lhs** [op* addr+1*] )
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STH2r INC2 INC2 LDA2 eval ( lhs** rhs** [op*] )
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STH2r JMP2 ( result** )
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@clear ( -> )
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#0000 ;expr STA2
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;arena ;next STA2
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JMP2r
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@alloc ( id^ size* -> addr* )
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;next LDA2k STH2k ( id^ size* next* addr* [addr*] )
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ROT2 ADD2 SWP2 STA2 ( id^ [addr*] ; next<-addr+size )
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STH2kr STA ( [addr*] ; addr<-id )
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STH2r JMP2r ( addr* )
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@alloc-const ( const* -> e* )
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#01 #0003 alloc ( const* addr* )
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STH2k INC2 STA2 ( [addr*] ; addr+1<-const )
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STH2r JMP2r ( addr* )
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@alloc-lit ( const* -> e* )
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#01 #0003 alloc ( const* addr* )
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STH2k INC2 STA2 ( [addr*] ; addr+1<-const )
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STH2r JMP2r ( addr* )
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@alloc-neg ( e0* -> e* )
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#02 #0003 alloc ( e0 addr* )
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STH2k INC2 STA2 ( [addr*] ; addr+1<-e0* )
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STH2r JMP2r ( addr* )
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@0.5x^2-6 05 =0.5x^2 =six
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@0.5x^2 06 =x^2 =0.5
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@x^2 03 =x 02
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@0.5 01 0080
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@six 01 0600
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@x^3-2x+1 04 =x^3-2x =one
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@x^3-2x 05 =x^3 =2x
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@one 01 0100
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@x^3 03 =x 03
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@2x 06 =x =two
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@two 01 0200
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~interval.tal
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@x 00
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@next :arena
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@arena $1000
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