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Assembly Source File | 1990-09-11 | 24.8 KB | 841 lines

; CALCMAND.ASM - Mandelbrot/Julia Set calculation Routines ; This module runs as part of an overlay with calcfrac.c. ; It must not be called from anywhere other than calcfrac. ; The routines in this code perform Mandelbrot and Julia set ; calculations using 32-bit integer math as opposed to the ; "traditional" floating-point approach. ; This code relies on several tricks to run as quickly as it does. ; One can fake floating point arithmetic by using integer ; arithmetic and keeping track of the implied decimal point ; if things are reasonable -- and in this case, they are. ; I replaced code that looked like: z = x*y with code that ; looks like: ; ix = x * ifudge (outside the loops) ; iy = y * ifudge ; .... ; iz = (ix * iy) / ifudge (inside the loops) ; (and keep remembering that all the integers are "ifudged" bigger) ; The 386 has native 32-bit integer arithmetic, and (briefly) keeps ; 64-bit values around after 32-bit multiplies. If the result is ; divided down right away, you've got 64-bit arithmetic. You just ; have to ensure that the result after the divide is <= 32 bits long. ; CPUs predating the 386 have to emulate 32-bit arithmetic using ; 16-bit arithmetic, which is significantly slower. ; Dividing is slow -- but shifting is fast, and we can select our ; "fudge factor" to be a power of two, permitting us to use that ; method instead. In addition, the 386 can perform 32-bit wide ; shifting -- and even 64-bit shifts with the following logic: ; shdr eax,edx,cl ; shr edx,cl ; so we make sure that our "fudge factor" is a power of 2 and shift ; it down that way. ; Calcmand is hardcoded for a fudge factor of 2**29. ; Bert Tyler ; required for compatibility if Turbo ASM IFDEF ??version MASM51 QUIRKS ENDIF .MODEL medium,c DGROUP group _DATA,_DATA2 .8086 ; these must NOT be in any segment!! ; this get's rid of TURBO-C fixup errors extrn keypressed:far ; this routine is in 'general.asm' extrn getakey:far ; this routine is in 'general.asm' extrn iplot_orbit:far ; this routine is in 'calcfrac.c' extrn scrub_orbit:far ; this routine is in 'calcfrac.c' _DATA2 segment DWORD PUBLIC 'DATA' FUDGEFACTOR equ 29 ; default (non-potential) fudgefactor ; ************************ External variables ***************************** extrn fractype:word ; == 0 if Mandelbrot set, else Julia extrn inside:word ; "inside" color, normally 1 (blue) extrn creal:dword, cimag:dword ; Julia Set Constant extrn delmin:dword ; min increment - precision required extrn maxit:word ; maximum iterations extrn lm:dword ; magnitude bailout limit extrn row:word, col:word ; current pixel to calc extrn color:word ; color calculated for the pixel extrn reset_periodicity:word ; nonzero if to be reset extrn kbdcount:word ; keyboard counter extrn cpu:word ; cpu type: 86, 186, 286, or 386 extrn show_orbit:word ; "show-orbit" flag extrn orbit_ptr:word ; "orbit pointer" flag extrn periodicitycheck:word ; no periodicity if zero public linitx,linity ; caller sets these public savedmask ; caller sets this ; ************************ Internal variables ***************************** align 4 x dd 0 ; temp value: x y dd 0 ; temp value: y absx dd 0 ; temp value: abs(x) linitx dd 0 ; initial value, set by calcfrac linity dd 0 ; initial value, set by calcfrac savedmask dd 0 ; saved values mask savedx dd 0 ; saved values of X and Y iterations savedy dd 0 ; (for periodicity checks) k dw 0 ; iteration countdown counter oldcolor dw 0 ; prior pixel's escape time k value savedand dw 0 ; AND value for periodicity checks savedincr dw 0 ; flag for incrementing AND value period db 0 ; periodicity, if in the lake _DATA2 ends .CODE ; ***************** Function calcmandasm() ********************************** public calcmandasm calcmandasm proc uses di si sub ax,ax ; clear ax cmp periodicitycheck,ax ; periodicity checking disabled? je initoldcolor ; yup, set oldcolor 0 to disable it cmp reset_periodicity,ax ; periodicity reset? je short initparms ; inherit oldcolor from prior invocation mov ax,maxit ; yup. reset oldcolor to maxit-250 sub ax,250 ; (avoids slowness at high maxits) initoldcolor: mov oldcolor,ax ; reset oldcolor initparms: mov ax,word ptr creal ; initialize x == creal mov dx,word ptr creal+2 ; ... mov word ptr x,ax ; ... mov word ptr x+2,dx ; ... mov ax,word ptr cimag ; initialize y == cimag mov dx,word ptr cimag+2 ; ... mov word ptr y,ax ; ... mov word ptr y+2,dx ; ... mov ax,maxit ; setup k = maxit inc ax ; (+ 1) mov k,ax ; (decrementing to 0 is faster) cmp fractype,1 ; julia or mandelbrot set? je short dojulia ; julia set - go there ; (Tim wants this code changed so that, for the Mandelbrot, ; Z(1) = (x + iy) + (a + ib). Affects only "fudged" Mandelbrots. ; (for the "normal" case, a = b = 0, and this works, too) ; cmp word ptr x,0 ; Mandelbrot shortcut: ; jne short doeither ; if creal = cimag = 0, ; cmp word ptr x+2,0 ; the first iteration can be emulated. ; jne short doeither ; ... ; cmp word ptr y,0 ; ... ; jne short doeither ; ... ; cmp word ptr y+2,0 ; ... ; jne short doeither ; ... ; dec k ; we know the first iteration passed ; mov dx,word ptr linitx+2 ; copy x = linitx ; mov ax,word ptr linitx ; ... ; mov word ptr x+2,dx ; ... ; mov word ptr x,ax ; ... ; mov dx,word ptr linity+2 ; copy y = linity ; mov ax,word ptr linity ; ... ; mov word ptr y+2,dx ; ... ; mov word ptr y,ax ; ... dec k ; we know the first iteration passed mov dx,word ptr linitx+2 ; add x += linitx mov ax,word ptr linitx ; ... add word ptr x,ax ; ... adc word ptr x+2,dx ; ... mov dx,word ptr linity+2 ; add y += linity mov ax,word ptr linity ; ... add word ptr y,ax ; ... adc word ptr y+2,dx ; ... jmp short doeither ; branch around the julia switch dojulia: ; Julia Set initialization ; "fudge" Mandelbrot start-up values mov ax,word ptr x ; switch x with linitx mov dx,word ptr x+2 ; ... mov bx,word ptr linitx ; ... mov cx,word ptr linitx+2 ; ... mov word ptr x,bx ; ... mov word ptr x+2,cx ; ... mov word ptr linitx,ax ; ... mov word ptr linitx+2,dx ; ... mov ax,word ptr y ; switch y with linity mov dx,word ptr y+2 ; ... mov bx,word ptr linity ; ... mov cx,word ptr linity+2 ; ... mov word ptr y,bx ; ... mov word ptr y+2,cx ; ... mov word ptr linity,ax ; ... mov word ptr linity+2,dx ; ... doeither: ; common Mandelbrot, Julia set code mov period,0 ; claim periodicity of 1 mov savedand,1 ; initial periodicity check mov savedincr,1 ; flag for incrementing periodicity mov word ptr savedx+2,0ffffh; impossible value of "old" x mov word ptr savedy+2,0ffffh; impossible value of "old" y mov orbit_ptr,0 ; clear orbits dec kbdcount ; decrement the keyboard counter jns short nokey ; skip keyboard test if still positive mov kbdcount,10 ; stuff in a low kbd count cmp show_orbit,0 ; are we showing orbits? jne quickkbd ; yup. leave it that way. mov kbdcount,5000 ; else, stuff an appropriate count val cmp cpu,386 ; ("appropriate" to the CPU) je short quickkbd ; ... cmp word ptr delmin+2,1 ; is 16-bit math good enough? ja quickkbd ; yes. test less often mov kbdcount,500 ; no. test more often quickkbd: call far ptr keypressed ; has a key been pressed? cmp ax,0 ; ... je nokey ; nope. proceed cmp ax,'o' ; orbit toggle hit? je orbitkey ; yup. show orbits cmp ax,'O' ; orbit toggle hit? jne keyhit ; nope. normal key. orbitkey: call far ptr getakey ; read the key for real mov ax,1 ; reset orbittoggle = 1 - orbittoggle sub ax,show_orbit ; ... mov show_orbit,ax ; ... mov kbdcount,10 ; adjust the keyboard jmp short nokey ; pretend no key was hit keyhit: mov ax,-1 ; return with -1 mov color,ax ; set color to -1 ret ; bail out! nokey: cmp show_orbit,0 ; is orbiting on? jne no16bitcode ; yup. slow down. cmp cpu,386 ; are we on a 386? je short code386bit ; YAY!! 386-class speed! cmp word ptr delmin+2,1 ; OK, we're desperate. 16 bits OK? ja yes16bitcode ; YAY! 16-bit speed! no16bitcode: call near ptr code32bit ; BOO!! nap time. Full 32 bit math jmp kloopend ; bypass the 386-specific code. yes16bitcode: call near ptr code16bit ; invoke the 16-bit version jmp kloopend ; bypass the 386-specific code. .386 ; 386-specific code starts here code386bit: cmp word ptr delmin+2,3 ; is 16-bit math good enough? jbe code386_32 ; nope, go do 32 bit stuff IFDEF ??version jmp code386_32 ; TASM screws up IMUL EBX,EBX!! ENDIF ; 16 bit on 386, now we are really gonna move movsx esi,word ptr x+2 ; use SI for X movsx edi,word ptr y+2 ; use DI for Y push ebp mov ebp,-1 shl ebp,FUDGEFACTOR-1 mov cx,FUDGEFACTOR-16 kloop386_16: ; cx=bitshift-16, ebp=overflow.mask mov ebx,esi ; compute (x * x) imul ebx,ebx ; ... test ebx,ebp ; say, did we overflow? <V20-compat> jnz short end386_16 ; (oops. We done.) shr ebx,cl ; get result down to 16 bits mov edx,edi ; compute (y * y) imul edx,edx ; ... test edx,ebp ; say, did we overflow? <V20-compat> jnz short end386_16 ; (oops. We done.) shr edx,cl ; get result down to 16 bits mov ax,bx ; compute (x*x - y*y) / fudge sub bx,dx ; for the next iteration add ax,dx ; compute (x*x + y*y) / fudge cmp ax,word ptr lm+2 ; while (xx+yy < lm) jae short end386_16 ; ... imul edi,esi ; compute (y * x) shl edi,1 ; ( * 2 / fudge) sar edi,cl add di,word ptr linity+2 ; (2*y*x) / fudge + linity movsx edi,di ; save as y add bx,word ptr linitx+2 ; (from above) (x*x - y*y)/fudge + linitx movsx esi,bx ; save as x mov ax,oldcolor ; recall the old color cmp ax,k ; check it against this iter jge short chkpd386_16 ; yup. do periodicity check. nonmax386_16: dec k ; while (k < maxit) jnz short kloop386_16 ; try, try again end386_16: pop ebp jmp kloopend ; we done chkpd386_16: mov ax,k ; set up to test for save-time test ax,savedand ; save on 0, check on anything else jz short chksv386_16 ; time to save a new "old" value mov ax,si ; load up x xor ax,word ptr savedx+2 ; does X match? test ax,word ptr savedmask+2 ; truncate to appropriate precision jne short nonmax386_16 ; nope. forget it. mov ax,di ; now test y xor ax,word ptr savedy+2 ; does Y match? test ax,word ptr savedmask+2 ; truncate to appropriate precision jne short nonmax386_16 ; nope. forget it. mov period,1 ; note that we have found periodicity mov k,0 ; pretend maxit reached jmp short end386_16 chksv386_16: mov word ptr savedx+2,si ; save x mov word ptr savedy+2,di ; save y dec savedincr ; time to change the periodicity? jnz short nonmax386_16 ; nope. shl savedand,1 ; well then, let's try this one! inc savedand ; (2**n -1) mov savedincr,4 ; and reset the increment flag jmp short nonmax386_16 ; 32bit on 386: code386_32: mov esi,x ; use ESI for X mov edi,y ; use EDI for Y ; This is the main processing loop. Here, every T-state counts... kloop: ; for (k = 0; k <= maxit; k++) mov eax,esi ; compute (x * x) imul esi ; ... shrd eax,edx,FUDGEFACTOR ; ( / fudge) shr edx,FUDGEFACTOR-1 ; (complete 64-bit shift and check jne short kloopend1 ; bail out if too high mov ebx,eax ; save this for below mov eax,edi ; compute (y * y) imul edi ; ... shrd eax,edx,FUDGEFACTOR ; ( / fudge) shr edx,FUDGEFACTOR-1 ; (complete 64-bit shift and check jne short kloopend1 ; bail out if too high mov ecx,ebx ; compute (x*x - y*y) / fudge sub ebx,eax ; for the next iteration add ecx,eax ; compute (x*x + y*y) / fudge cmp ecx,lm ; while (lr < lm) jae short kloopend1 ; ... mov eax,edi ; compute (y * x) imul esi ; ... shrd eax,edx,FUDGEFACTOR-1 ; ( * 2 / fudge) add eax,linity ; (above) + linity mov edi,eax ; save this as y ; (from the earlier code) ; compute (x*x - y*y) / fudge add ebx,linitx ; + linitx mov esi,ebx ; save this as x mov ax,oldcolor ; recall the old color cmp ax,k ; check it against this iter jge short chkperiod1 nonmax1: dec k ; while (k < maxit) (dec to 0 is faster) jnz short kloop ; while (k < maxit) ... kloopend1: jmp short kloopend32 ; we done. chkperiod1: mov eax,esi xor eax,savedx test eax,savedmask jnz short chksave1 mov eax,edi xor eax,savedy test eax,savedmask jnz short chksave1 mov period,1 ; note that we have found periodicity mov k,0 ; pretend maxit reached jmp short kloopend1 chksave1: mov ax,k test ax,savedand jne short nonmax1 mov savedx,esi mov savedy,edi dec savedincr ; time to change the periodicity? jnz short nonmax1 ; nope. shl savedand,1 ; well then, let's try this one! inc savedand ; (2**n -1) mov savedincr,4 ; and reset the increment flag jmp short nonmax1 kloopend32: .8086 ; 386-specific code ends here kloopend: cmp orbit_ptr,0 ; any orbits to clear? je noorbit2 ; nope. call far ptr scrub_orbit ; clear out any old orbits noorbit2: mov ax,k ; set old color sub ax,10 ; minus 10, for safety mov oldcolor,ax ; and save it as the "old" color mov ax,maxit ; compute color sub ax,k ; (first, re-compute "k") sub kbdcount,ax ; adjust the keyboard count cmp ax,1 ; convert any "outlier" region jge short coloradjust1 ; (where abs(x) > 2 or abs(y) > 2) mov ax,1 ; to look like we ran through coloradjust1: ; at least one loop. cmp ax,maxit ; did we max out on iterations? jne short wedone ; nope. mov oldcolor,ax ; set "oldcolor" to maximum cmp inside,0 ; is "inside" >= 0? jl wedone ; nope. leave it at "maxit" mov ax,inside ; reset max-out color to default cmp periodicitycheck,0 ; show periodicity matches? jge wedone ; nope. mov al,period ; reset color to periodicity flag wedone: ; mov color,ax ; save the color result ret ; and return with color calcmandasm endp ; ******************** Function code16bit() ***************************** ; ; Performs "short-cut" 16-bit math where we can get away with it. ; code16bit proc near mov si,word ptr x+2 ; use SI for X mov di,word ptr y+2 ; use DI for Y start16bit: mov ax,si ; compute (x * x) imul si ; ... cmp dx,0 ; say, did we overflow? <V20-compat> jl end16bit ; (oops. We done.) mov cx,32-FUDGEFACTOR ; ( / fudge) loop16bit1: shl ax,1 ; ... rcl dx,1 ; ... jo end16bit ; (oops. overflow) loop loop16bit1 ; ... mov bx,dx ; save this for a tad mov ax,di ; compute (y * y) imul di ; ... cmp dx,0 ; say, did we overflow? <V20-compat> jl end16bit ; (oops. We done.) mov cx,32-FUDGEFACTOR ; ( / fudge) loop16bit2: shl ax,1 ; ... rcl dx,1 ; ... jo end16bit ; (oops. overflow) loop loop16bit2 ; ... mov cx,bx ; compute (x*x - y*y) / fudge sub bx,dx ; for the next iteration add cx,dx ; compute (x*x + y*y) / fudge jo end16bit ; bail out if too high js end16bit ; ... cmp cx,word ptr lm+2 ; while (xx+yy < lm) jae end16bit ; ... mov ax,di ; compute (y * x) imul si ; ... mov cx,33-FUDGEFACTOR ; ( * 2 / fudge) loop16bit3: shl ax,1 ; ... rcl dx,1 ; ... loop loop16bit3 ; ... add dx,word ptr linity+2 ; (2*y*x) / fudge + linity mov di,dx ; save as y add bx,word ptr linitx+2 ; (from above) (x*x - y*y)/fudge + linitx mov si,bx ; save as x mov ax,oldcolor ; recall the old color cmp ax,k ; check it against this iter jl short nonmax3 ; nope. bypass periodicity check. mov word ptr x+2,si ; save x for periodicity check mov word ptr y+2,di ; save y for periodicity check call checkperiod ; check for periodicity nonmax3: dec k ; while (k < maxit) jz end16bit ; we done. jmp start16bit ; try, try again. end16bit: ; we done. ret code16bit endp ; The following routine checks for periodic loops (a known ; method of decay inside "Mandelbrot Lake", and an easy way to ; bail out of "lake" points quickly). For speed, only the ; high-order sixteen bits of X and Y are checked for periodicity. ; For accuracy, this routine is only fired up if the previous pixel ; was in the lake (which means that the FIRST "wet" pixel was ; detected by the dull-normal maximum iteration process). checkperiod proc near ; periodicity check mov ax,k ; set up to test for save-time test ax,savedand ; save on 0, check on anything else jz checksave ; time to save a new "old" value mov dx,word ptr x+2 ; load up x and dx,word ptr savedmask+2 ; truncate to appropriate precision cmp dx,word ptr savedx+2 ; does X match? jne checkdone ; nope. forget it. mov ax,word ptr x ; load up x and ax,word ptr savedmask ; truncate to appropriate precision cmp ax,word ptr savedx ; does X match? jne checkdone ; nope. forget it. mov dx,word ptr y+2 ; now test y and dx,word ptr savedmask+2 ; truncate to appropriate precision cmp dx,word ptr savedy+2 ; does Y match? jne checkdone ; nope. forget it. mov ax,word ptr y ; load up y and ax,word ptr savedmask ; truncate to appropriate precision cmp ax,word ptr savedy ; does Y match? jne checkdone ; nope. forget it. mov period,1 ; note that we have found periodicity mov k,1 ; pretend maxit reached checksave: mov dx,word ptr x+2 ; load up x and dx,word ptr savedmask+2 ; truncate to appropriate precision mov word ptr savedx+2,dx ; and save it mov ax,word ptr x ; load up x and ax,word ptr savedmask ; truncate to appropriate precision mov word ptr savedx,ax ; and save it mov dx,word ptr y+2 ; load up y and dx,word ptr savedmask+2 ; truncate to appropriate precision mov word ptr savedy+2,dx ; and save it mov ax,word ptr y ; load up y and ax,word ptr savedmask ; truncate to appropriate precision mov word ptr savedy,ax ; and save it dec savedincr ; time to change the periodicity? jnz checkdone ; nope. shl savedand,1 ; well then, let's try this one! inc savedand ; (2**n -1) mov savedincr,4 ; and reset the increment flag checkdone: ret ; we done. checkperiod endp ; ******************** Function code32bit() ***************************** ; ; Perform the 32-bit logic required using 16-bit logic ; ; New twice as fast logic, ; Courtesy of Bill Townsend and Mike Gelvin (CIS:73337,520) square macro doneaddr local donejp,skip1y,skip2y,squrey,allzero sub bh,bh sub cx,cx mov bp,cx or ax,ax ;GET LOW HWORD jz skip1y ;LOW HWORD IS ZERO, ONLY DO HIGH HWORD mov si,ax mul ax ;SQUARE LOW HWORD - B*B mov bh,dh or di,di ;TEST HIGH HWORD jz squrey ;HIGH HWORD ZERO, SKIP THE FOLLOWING mov ax,di mul si ;GET MIDDLE PART - A*B add bh,ah ;add adc cx,dx ; A*B adc bp,0 ; twice add bh,ah ; - adc cx,dx ; - adc bp,0 ; SI,CX,BH = 2(A*B)+(B*B) jmp short skip2y donejp: JMP doneaddr ;M0=DONEJP skip1y: or di,di ;M1=SKIP1Y jz allzero skip2y: mov ax,di ;M2=SKIP2Y mul ax ;SQUARE HIGH HWORD - A*A add cx,ax adc bp,dx squrey: shl bh,1 ;M3=SQUREY rcl cx,1 rcl bp,1 ; jo donejp ; squaring a +ve, top bit known off shl bh,1 rcl cx,1 rcl bp,1 ; jo donejp ; squaring a +ve, 2nd bit known off shl bh,1 rcl cx,1 rcl bp,1 jo donejp add bp,0 js donejp ; if went neg have overflow also allzero: endm ;#EM code32bit proc near ; ; BL IS USED FOR THE FLAGS,TWO LOW ORDER BITS ARE "NEGSWT", THIRD BIT IS XSIGN ; XSIGN IS ONE IF THE SIGN OF THE NEW "X" IS NEGATIVE ; NEGSWT IS ONE IF EITHER "X" OR "Y" ARE NEGATIVE, BUT NOT BOTH NEGATIVE ; xsign equ 00000100b negswt equ 00000001b push bp sub si,si ; make a zero __________ mov bx,si ; BOTH XSIGN & NEGSWT START OFF ZERO mov di,1 ; MAKE A ONE mov cx,word ptr y ; cx=y mov bp,word ptr y+2 ; bp=y+2 cmp bp,si ; y>0? jns qnotng ; yup not cx ; nope, negate it not bp ; ... add cx,di ; ... adc bp,si ; ... inc bl ; INCREMENT negswt qnotng: mov ax,word ptr x mov dx,word ptr x+2 cmp dx,si ; x>0? jns pnotng ; yup not ax ; nope, negate it not dx ; ... add ax,di ; ... adc dx,si ; ... inc bl ; INCREMENT negswt pnotng: mov word ptr absx,ax ; save unsigned x mov word ptr absx+2,dx ; ... ; iteration loop nextit: push bp ; save y on stack push cx ; ... mov ax,cx ; load y for squaring mov di,bp ; ... square done2 ; square di,ax & br to jmp_done2 if overflow push cx ; return results in bp,cx push bp ; save y*y on stack mov ax,word ptr absx ; load x for squaring mov di,word ptr absx+2 ; ... square done ; square di,ax & br to done if overflow mov di,bp ; return results in bp,cx mov si,cx ; save x*x in di,si pop dx ; unstack y*y into dx,ax pop ax ; ... ADD cx,ax ; calc y*y + x*x ADC bp,dx ; ... jo done2 ; overflow? js done2 ; overflow? cmp bp,word ptr lm+2 ; while (lr < lm) jb short nextxy ; keep going jmp short done2 ; magnitude is past limit, bailout done: add sp,4 ; discard saved value of "y*y" done2: add sp,4 ; discard saved value of "y" xydone: pop bp ; restore saved bp ret ;--------------------------------------------------------------------------- ;y=nz, x=nz, x+2=z x2is0: pop ax ; get old y+2 or ax,ax ; test y+2 jz jgotxy mul si ; do y+2(ax)*x(si) add bh,ah adc cx,dx adc bp,0 jgotxy: jmp gotxy ;x=z xis0: or di,di ; test x+2 jz popy_2 ; zero all done, around again please mul di ; do y(ax)*x+2(di) add bh,ah adc cx,dx adc bp,0 pop ax ; get old y+2 or ax,ax jz gotxy mulxyj: jmp mulxy2 ;x=z, x+2=z popy_2: pop ax ; discard old y+2 sub cx,cx ; x==0, so x*y is zero mov bp,cx ; ... jmp signok ; go add b and store new y nextxy: sub si,ax ; subtract y*y from x*x sbb di,dx ; ... add si,word ptr linitx ; add "A" adc di,word ptr linitx+2 ; ... mov word ptr x,si ; store new x = x*x+y*y+a mov word ptr x+2,di ; ... jns swtxxx ; NO SIGN, NOT NEG or bl,xsign ; REMEMBER THE NEW "X" IS NEGATIVE not si ; make it positive in register not di ; ... add si,1 ; ... adc di,0 ; ... swtxxx: xchg di,word ptr absx+2 ; save the new x, load the old xchg si,word ptr absx ; ... ; now calculate x*y sub bh,bh ; zero some registers sub cx,cx ; ... mov bp,cx ; ... pop ax ; get old "y" or ax,ax ; test "y" jz yis0 ; br if "y" is zero or si,si ; test old "x" jz xis0 ; br if "x" is zero mov bp,ax ; save old "y" mul si ; do y(ax)*x(si) mov ax,bp ; get old "y" again mov bp,cx ; RE-ZERO BP mov bh,dh ; save/set low hword(bx) or di,di ; test old "x+2" jz x2is0 mul di ; do y(ax)*x+2(di) add bh,ah adc cx,dx adc bp,0 yis0: pop ax ; get old "y+2" or ax,ax ; test y+2 jz gotxy ; br if y+2 is zero mov dx,si ; dx="x" mov si,ax ; si=save "y+2" mul dx ; do y+2(ax)*x(dx)--(si) add bh,ah adc cx,dx adc bp,0 mov ax,si ; get old "y+2" mulxy2: mul di ; do y+2(ax)*x+2(di) add cx,ax adc bp,dx gotxy: shl bh,1 rcl cx,1 ; bp,cx,bx rcl bp,1 jo jmpxydone shl bh,1 rcl cx,1 rcl bp,1 jo jmpxydone shl bh,1 rcl cx,1 rcl bp,1 jo jmpxydone add bp,0 js jmpxydone ; if went neg have overflow also test bl,negswt ; ZERO IF NONE OR BOTH X , Y NEG jz signok ; ONE IF ONLY ONE OF X OR Y IS NEG not cx ; negate result not bp ; ... add cx,1 ; ... adc bp,0 ; ... signok: shr bl,1 shr bl,1 ;MOVE "XSIGN"(X=NEG) DOWN TO "NEGSWT" add cx,cx ;bp,CX = 2(X*Y) adc bp,bp add cx,word ptr linity adc bp,word ptr linity+2 ; BP,CX = 2(X*Y)+B mov word ptr y,cx ; save the new value of y mov word ptr y+2,bp ; ... jns jmpnit ; NO SIGN, NOT NEG inc bl ; INCREMENT NEGSWT not cx ; negate not bp ; ... add cx,1 ; ... adc bp,0 ; ... jmpnit: mov ax,oldcolor ; recall the old color cmp ax,k ; check it against this iter jl short chkmaxit ; nope. bypass periodicity check. call checkperiod ; check for periodicity chkmaxit: dec k ; while (k < maxit) jz jmpxydone ; we done. cmp show_orbit,0 ; orbiting on? jne horbit ; yep. jmp nextit ;go around again jmpxydone: jmp xydone ; DOES [(X*X)-(Y*Y)+P] BEFORE THE DEC. horbit: push bx ; save my flags push bp ; and registers push cx ; ... mov ax,-1 ; color for plot orbit push ax ; ... push word ptr y+2 ; co-ordinates for plot orbit push word ptr y ; ... push word ptr x+2 ; ... push word ptr x ; ... call far ptr iplot_orbit ; display the orbit add sp,5*2 ; clear out the parameters pop cx ; restore registers pop bp ; ... pop bx ; and flags jmp nextit ; go around again code32bit endp calcmand_TEXT ends end