(mandelbrot) Improved speed
This commit is contained in:
Devine Lu Linvega
parent
8ae1c191d7
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497b01fcfb
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@ -1,4 +1,6 @@
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( mandelbrot )
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( mandelbrot.tal )
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( )
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( by alderwick and d_m )
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%WIDTH { #02a0 }
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%WIDTH { #02a0 }
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%HEIGHT { #0200 }
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%HEIGHT { #0200 }
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@ -17,88 +19,106 @@
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#0ff0 .System/g DEO2
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#0ff0 .System/g DEO2
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#00ff .System/b DEO2
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#00ff .System/b DEO2
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WIDTH .Screen/width DEO2 ( 640 )
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( size )
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HEIGHT .Screen/height DEO2 ( 480 )
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WIDTH .Screen/width DEO2
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HEIGHT .Screen/height DEO2
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( run )
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draw-mandel
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draw-mandel
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BRK
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BRK
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( draw the mandelbrot set using 4.12 fixed point numbers )
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@draw-mandel ( -> )
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XMAX XMIN SUB2 WIDTH DIV2 ,&dx STR2 ( ; &dx<-{xmax-min}/width )
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YMAX YMIN SUB2 HEIGHT DIV2 ,&dy STR2 ( ; &dy<-{ymax-ymin}/height )
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[ LIT2 01 -Screen/auto ] DEO ( ; auto<-1 )
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LIT2r 8000 ( [8000] )
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YMAX YMIN ( ymax* ymin* [8000] )
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&yloop ( ymax* y* [8000] )
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XMAX XMIN ( ymax* y* xmax* xmin* [8000] )
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&xloop ( ymax* y* xmax* x* [8000] )
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ROT2k evaluate ( ymax* y* xmax* x* xmax* count^ [8000] )
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.Screen/pixel DEO POP2 ( ymax* y* xmax* x* [8000] )
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[ LIT2 &dx $2 ] ADD2 ( ymax* y* xmax* x+dx* [8000] )
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OVR2 STH2kr ADD2 ( ymax* y* xmax* x+dx* 8000+xmax* [8000] )
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OVR2 STH2kr ADD2 ( ymax* y* xmax* x+dx* 8000+xmax* 8000+x+dx* [8000] )
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GTH2 ?&xloop ( ymax* y* xmax* x+dx* [8000] )
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POP2 POP2 ( ymax* y* [8000] )
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#0000 .Screen/x DEO2 ( ymax* y* [8000] ; sc/x<-0 )
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.Screen/y DEI2k ( ymax* y* d^ sy* [8000] )
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INC2 ROT DEO2 ( ymax* y* [8000] ; sc/y<-sy+1 )
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[ LIT2 &dy $2 ] ADD2 ( ymax* y+dy* [8000] )
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OVR2 STH2kr ADD2 ( ymax* y+dy* 8000+ymax* [8000] )
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OVR2 STH2kr ADD2 ( ymax* y+dy* 8000+ymax* 8000+y+dy* [8000] )
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GTH2 ?&yloop ( ymax* y+dy* [8000] )
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POP2 POP2 POP2r JMP2r ( )
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@draw-mandel ( -- )
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@evaluate ( x* y* -> count^ )
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#0000 DUP2 ,&x1 STR2 ( x* y* ; x1<-0 )
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DUP2 ,&y1 STR2 ( x* y* ; y1<-0 )
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DUP2 ,&x2 STR2 ( x* y* ; x2<-0 )
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,&y2 STR2 ( x* y* ; y2<-0 )
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LIT2r 2000 ( x* y* [20 00] )
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&loop ( x* y* [20 n^] )
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[ LIT2 &x1 $2 ] ( x* y* x1* [20 n^] )
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[ LIT2 &y1 $2 ] ( x* y* x1* y1* [20 n^] )
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smul2 DUP2 ADD2 ( x* y* 2x1y1* [20 n^] )
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OVR2 ADD2 ,&y1 STR2 ( x* y* [20 n^] ; y1<-2x1y1+y* )
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SWP2 [ LIT2 &x2 $2 ] ( y* x* x2* [20 n^] )
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[ LIT2 &y2 $2 ] SUB2 ( y* x* x2-y2* [20 n^] )
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OVR2 ADD2 ,&x1 STR2 SWP2 ( x* y* [20 n^] ; x1<-x2-y2+x* )
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,&x1 LDR2 square ( x* y* x1^2* [20 n^] )
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DUP2 ,&x2 STR2 ( x* y* x1^2* [20 n^] ; x2<-x1^2* )
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,&y1 LDR2 square ( x* y* x1^2* y1^2* [20 n^] )
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DUP2 ,&y2 STR2 ( x* y* x1^2* y1^2* [20 n^] ; y2<-y1^2* )
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ADD2 #4000 GTH2 ?&end ( x* y* [20 n^] )
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INCr GTHkr STHr ?&loop ( x* y* [20 n+1*] )
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&end ( x* y* [20 count^] )
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POP2 POP2 NIPr STHr JMP2r ( count^ )
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XMAX XMIN SUB2 WIDTH DIV2 ;&dx STA2
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( multiply two signed 4.12 fixed point numbers )
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YMAX YMIN SUB2 HEIGHT DIV2 ;&dy STA2
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@smul2 ( a* b* -> ab* )
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[ LIT2 01 -Screen/auto ] DEO
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LIT2r 0001 DUP2 #8000 LTH2 ?&bpos negate SWPr ( a* |b|* [sign*] )
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YMAX YMIN
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&bpos SWP2 DUP2 #8000 LTH2 ?&apos negate SWPr ( |b|* |a|* [sign*] )
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&ver
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&apos smul2-pos STHr ?&abpos negate ( ab* [scrap^] )
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DUP2 ,&y STR2
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&abpos POPr JMP2r ( ab* )
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XMAX XMIN
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&hor
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DUP2 ,&x STR2
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#0000
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DUP2 ,&x1 STR2
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DUP2 ,&y1 STR2
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DUP2 ,&x2 STR2
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,&y2 STR2
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( pixel )
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#2000
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&loop
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[ LIT2 &x1 $2 ] [ LIT2 &y1 $2 ] smul2 DUP2 ADD2
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[ LIT2 &y $2 ] ADD2 ,&y1 STR2
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[ LIT2 &x2 $2 ] [ LIT2 &y2 $2 ] SUB2
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[ LIT2 &x $2 ] ADD2 ,&x1 STR2
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,&x1 LDR2 DUP2 smul2
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DUP2 ,&x2 STR2
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,&y1 LDR2 DUP2 smul2
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DUP2 ,&y2 STR2
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ADD2 #4000 GTH2 ?&end
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INC GTHk ?&loop
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&end
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NIP .Screen/pixel DEO
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( done. )
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[ LIT2 &dx $2 ] ADD2 OVR2 #8000 ADD2 OVR2 #8000 ADD2 SWP2 LTH2 ?&hor
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POP2 POP2
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#0000 .Screen/x DEO2
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.Screen/y DEI2k INC2 ROT DEO2
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[ LIT2 &dy $2 ] ADD2 OVR2 #8000 ADD2 OVR2 #8000 ADD2 SWP2 LTH2 ?&ver
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POP2 POP2
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JMP2r
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( multiply two non-negative fixed point numbers )
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( )
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( a * b = {a0/16 + a1/4096} * {b0/16 + b1/4096} )
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( = a0b0/256 + a1b0/65536 + a0b1/65536 + a1b1/16777216 )
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( = x + y + z + 0 ; the last term is too small to represent, i.e. zero )
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( )
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( x = a0b0 << 4 )
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( y = a1b0 >> 4 )
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( z = a0b1 >> 4 )
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@smul2-pos ( a* b* -> ab* )
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aerate ROT2 aerate ( b0* b1* a0* a1* )
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STH2 ROT2k ( b0* b1* a0* b1* a0* b0* [a1*] )
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STH2 MUL2r ( b0* b1* a0* b1* a0* [a1b0*] )
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MUL2 STH2 ADD2r ( b0* b1* a0* [a1b0+a0b1*] )
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NIP2 MUL2 #07ff min #40 SFT2 ( a0b0* [y+z*] )
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STH2r #04 SFT2 ADD2 ( x* [y+z*] )
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#7fff !min ( ab* )
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@smul2 ( a* b* -- c* )
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( equivalent to DUP2 smul2 but faster )
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LITr 00
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@square ( a* -> aa* )
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DUP2 #8000 LTH2 ?&b-positive
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DUP2 #8000 LTH2 ?&pos negate &pos
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INCr DUP2k EOR2 SWP2 SUB2
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&b-positive
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SWP2
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DUP2 #8000 LTH2 ?&a-positive
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INCr DUP2k EOR2 SWP2 SUB2
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&a-positive
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( ahi alo bhi blo )
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LITr 00 STH ( ahi alo bhi / blo* )
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OVRr STH ( ahi alo / blo* bhi* )
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OVRr STH ( ahi / blo* bhi* alo* )
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OVRr STH ( asign / blo* bhi* alo* ahi* )
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ROT2r MUL2kr STH2r ( asign ahi-bhi* / blo* alo* ahi* bhi* )
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ROT2r MUL2kr STH2r ( asign ahi-bhi* alo-bhi* / blo* ahi* bhi* alo* )
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NIP2r ( asign ahi-bhi* alo-bhi* / blo* ahi* alo* )
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ROT2r MUL2kr STH2r ( asign ahi-bhi* alo-bhi* alo-blo* / ahi* alo* blo* )
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ROT2r MUL2r STH2r POP2r ( asign ahi-bhi* alo-bhi* alo-blo* ahi-blo* )
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SWP2 ( asign ahi-bhi* alo-bhi* ahi-blo* alo-blo* )
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( 32-bit result is [ r3 r2 r1 r0 ] )
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POP #00 SWP ( asign ahi-bhi* alo-bhi* ahi-blo* r21* )
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( r21 max is 00fe, ahi-blo max is 7e81, max sum is 7f7f )
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ADD2 ( asign ahi-bhi* alo-bhi* r21'* )
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( r21' max is 7f7f, alo-bhi max is 7e81, max sum is fe00 )
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ADD2 ( asign ahi-bhi* r21"* )
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( The result we want is bits 27-12 due to the fixed point representation we use. )
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#04 SFT2 SWP2 #07ff min #40 SFT2 ADD2
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( saturate to +/-7.fff )
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#7fff min
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STHr #01 NEQ ?&result-positive
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DUP2k EOR2 SWP2 SUB2
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&result-positive
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JMP2r
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@min ( x* y* -- min* )
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( >> )
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GTH2k [ JMP SWP2 NIP2 ] JMP2r
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( equivalent to DUP2 smul2-pos but faster )
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@square-pos ( a* -> aa* )
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aerate ( 00 ahi^ 00 alo^ )
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OVR2 MUL2 #03 SFT2 SWP2 ( yz* ahi* )
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DUP2 MUL2 #07ff min #40 SFT2 ( x* yz* )
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ADD2 #7fff !min ( aa* )
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( convert each byte of a a short into a short )
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@aerate ( x* -> 00 xhi^ 00 xlo^ ) SWP #0000 ROT SWP2 SWP JMP2r
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( negate a fixed point number. doesn't work for #8000 )
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@negate ( x* -> -x* ) DUP2k EOR2 SWP2 SUB2 JMP2r
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( return the minimum of two non-negative numbers. )
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@min ( x* y* ) GTH2k [ JMP SWP2 ] NIP2 JMP2r
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