;THE COMPUTER CODE CONTAINED HEREIN IS THE SOLE PROPERTY OF PARALLAX ;SOFTWARE CORPORATION ("PARALLAX"). PARALLAX, IN DISTRIBUTING THE CODE TO ;END-USERS, AND SUBJECT TO ALL OF THE TERMS AND CONDITIONS HEREIN, GRANTS A ;ROYALTY-FREE, PERPETUAL LICENSE TO SUCH END-USERS FOR USE BY SUCH END-USERS ;IN USING, DISPLAYING, AND CREATING DERIVATIVE WORKS THEREOF, SO LONG AS ;SUCH USE, DISPLAY OR CREATION IS FOR NON-COMMERCIAL, ROYALTY OR REVENUE ;FREE PURPOSES. IN NO EVENT SHALL THE END-USER USE THE COMPUTER CODE ;CONTAINED HEREIN FOR REVENUE-BEARING PURPOSES. THE END-USER UNDERSTANDS ;AND AGREES TO THE TERMS HEREIN AND ACCEPTS THE SAME BY USE OF THIS FILE. ;COPYRIGHT 1993-1998 PARALLAX SOFTWARE CORPORATION. ALL RIGHTS RESERVED. ; ; $Source: f:/miner/source/fix/rcs/fix.asm $ ; $Revision: 1.16 $ ; $Author: mike $ ; $Date: 1994/11/30 00:59:40 $ ; ; Fixed-point rotines ; ; $Log: fix.asm $ ; Revision 1.16 1994/11/30 00:59:40 mike ; optimizations. ; ; Revision 1.15 1994/11/16 18:05:01 matt ; Added error checking to atan2 ; ; Revision 1.14 1994/10/21 12:14:26 matt ; For acos & asin, saturate at 1 instead of generate error ; ; Revision 1.13 1994/05/18 17:15:56 matt ; Allow sin & cos ptrs in C sincos func to be null ; ; Revision 1.12 1994/02/10 21:23:08 matt ; Changed 'if DEBUG_ON' to 'ifndef NDEBUG' ; ; Revision 1.11 1994/01/19 23:11:26 matt ; Made fix_atan2() left-handed, like our coordinate system ; ; Revision 1.10 1993/10/26 18:51:49 matt ; Fixed register trash in fix_atan2() ; ; Revision 1.9 1993/10/20 01:09:01 matt ; Add fix_asin(), improved fix_atan2() ; ; Revision 1.8 1993/10/19 23:53:48 matt ; Added fix_atan2() ; ; Revision 1.7 1993/10/19 22:22:34 matt ; Added fix_acos() ; ; Revision 1.6 1993/09/10 19:13:44 matt ; Fixed problem with quad_sqrt() when edx==0 and high bit of eax set ; ; Revision 1.5 1993/08/24 13:00:17 matt ; Adopted new standard, and made assembly-callable routines not trash any regs ; ; Revision 1.4 1993/08/12 14:43:34 matt ; Added rcsid ; ; Revision 1.3 1993/08/06 15:59:49 matt ; Added check for high bit of low longword set in quad_sqrt ; Changed long_sqrt to do longword moves and save the override ; ; Revision 1.2 1993/08/04 19:56:03 matt ; Fixed mistake in quad_sqrt first quess code ; ; Revision 1.1 1993/08/03 17:45:26 matt ; Initial revision ; ; ; .386 option oldstructs .nolist include types.inc include psmacros.inc include fix.inc .list assume cs:_TEXT,ds:_DATA _DATA segment dword public USE32 'DATA' rcsid db "$Id: fix.asm 1.16 1994/11/30 00:59:40 mike Exp $" sin_table dw 0 dw 402 dw 804 dw 1205 dw 1606 dw 2006 dw 2404 dw 2801 dw 3196 dw 3590 dw 3981 dw 4370 dw 4756 dw 5139 dw 5520 dw 5897 dw 6270 dw 6639 dw 7005 dw 7366 dw 7723 dw 8076 dw 8423 dw 8765 dw 9102 dw 9434 dw 9760 dw 10080 dw 10394 dw 10702 dw 11003 dw 11297 dw 11585 dw 11866 dw 12140 dw 12406 dw 12665 dw 12916 dw 13160 dw 13395 dw 13623 dw 13842 dw 14053 dw 14256 dw 14449 dw 14635 dw 14811 dw 14978 dw 15137 dw 15286 dw 15426 dw 15557 dw 15679 dw 15791 dw 15893 dw 15986 dw 16069 dw 16143 dw 16207 dw 16261 dw 16305 dw 16340 dw 16364 dw 16379 cos_table dw 16384 dw 16379 dw 16364 dw 16340 dw 16305 dw 16261 dw 16207 dw 16143 dw 16069 dw 15986 dw 15893 dw 15791 dw 15679 dw 15557 dw 15426 dw 15286 dw 15137 dw 14978 dw 14811 dw 14635 dw 14449 dw 14256 dw 14053 dw 13842 dw 13623 dw 13395 dw 13160 dw 12916 dw 12665 dw 12406 dw 12140 dw 11866 dw 11585 dw 11297 dw 11003 dw 10702 dw 10394 dw 10080 dw 9760 dw 9434 dw 9102 dw 8765 dw 8423 dw 8076 dw 7723 dw 7366 dw 7005 dw 6639 dw 6270 dw 5897 dw 5520 dw 5139 dw 4756 dw 4370 dw 3981 dw 3590 dw 3196 dw 2801 dw 2404 dw 2006 dw 1606 dw 1205 dw 804 dw 402 dw 0 dw -402 dw -804 dw -1205 dw -1606 dw -2006 dw -2404 dw -2801 dw -3196 dw -3590 dw -3981 dw -4370 dw -4756 dw -5139 dw -5520 dw -5897 dw -6270 dw -6639 dw -7005 dw -7366 dw -7723 dw -8076 dw -8423 dw -8765 dw -9102 dw -9434 dw -9760 dw -10080 dw -10394 dw -10702 dw -11003 dw -11297 dw -11585 dw -11866 dw -12140 dw -12406 dw -12665 dw -12916 dw -13160 dw -13395 dw -13623 dw -13842 dw -14053 dw -14256 dw -14449 dw -14635 dw -14811 dw -14978 dw -15137 dw -15286 dw -15426 dw -15557 dw -15679 dw -15791 dw -15893 dw -15986 dw -16069 dw -16143 dw -16207 dw -16261 dw -16305 dw -16340 dw -16364 dw -16379 dw -16384 dw -16379 dw -16364 dw -16340 dw -16305 dw -16261 dw -16207 dw -16143 dw -16069 dw -15986 dw -15893 dw -15791 dw -15679 dw -15557 dw -15426 dw -15286 dw -15137 dw -14978 dw -14811 dw -14635 dw -14449 dw -14256 dw -14053 dw -13842 dw -13623 dw -13395 dw -13160 dw -12916 dw -12665 dw -12406 dw -12140 dw -11866 dw -11585 dw -11297 dw -11003 dw -10702 dw -10394 dw -10080 dw -9760 dw -9434 dw -9102 dw -8765 dw -8423 dw -8076 dw -7723 dw -7366 dw -7005 dw -6639 dw -6270 dw -5897 dw -5520 dw -5139 dw -4756 dw -4370 dw -3981 dw -3590 dw -3196 dw -2801 dw -2404 dw -2006 dw -1606 dw -1205 dw -804 dw -402 dw 0 dw 402 dw 804 dw 1205 dw 1606 dw 2006 dw 2404 dw 2801 dw 3196 dw 3590 dw 3981 dw 4370 dw 4756 dw 5139 dw 5520 dw 5897 dw 6270 dw 6639 dw 7005 dw 7366 dw 7723 dw 8076 dw 8423 dw 8765 dw 9102 dw 9434 dw 9760 dw 10080 dw 10394 dw 10702 dw 11003 dw 11297 dw 11585 dw 11866 dw 12140 dw 12406 dw 12665 dw 12916 dw 13160 dw 13395 dw 13623 dw 13842 dw 14053 dw 14256 dw 14449 dw 14635 dw 14811 dw 14978 dw 15137 dw 15286 dw 15426 dw 15557 dw 15679 dw 15791 dw 15893 dw 15986 dw 16069 dw 16143 dw 16207 dw 16261 dw 16305 dw 16340 dw 16364 dw 16379 dw 16384 asin_table dw 0 dw 41 dw 81 dw 122 dw 163 dw 204 dw 244 dw 285 dw 326 dw 367 dw 408 dw 448 dw 489 dw 530 dw 571 dw 612 dw 652 dw 693 dw 734 dw 775 dw 816 dw 857 dw 897 dw 938 dw 979 dw 1020 dw 1061 dw 1102 dw 1143 dw 1184 dw 1225 dw 1266 dw 1307 dw 1348 dw 1389 dw 1431 dw 1472 dw 1513 dw 1554 dw 1595 dw 1636 dw 1678 dw 1719 dw 1760 dw 1802 dw 1843 dw 1884 dw 1926 dw 1967 dw 2009 dw 2050 dw 2092 dw 2134 dw 2175 dw 2217 dw 2259 dw 2300 dw 2342 dw 2384 dw 2426 dw 2468 dw 2510 dw 2551 dw 2593 dw 2636 dw 2678 dw 2720 dw 2762 dw 2804 dw 2847 dw 2889 dw 2931 dw 2974 dw 3016 dw 3059 dw 3101 dw 3144 dw 3187 dw 3229 dw 3272 dw 3315 dw 3358 dw 3401 dw 3444 dw 3487 dw 3530 dw 3573 dw 3617 dw 3660 dw 3704 dw 3747 dw 3791 dw 3834 dw 3878 dw 3922 dw 3965 dw 4009 dw 4053 dw 4097 dw 4142 dw 4186 dw 4230 dw 4275 dw 4319 dw 4364 dw 4408 dw 4453 dw 4498 dw 4543 dw 4588 dw 4633 dw 4678 dw 4723 dw 4768 dw 4814 dw 4859 dw 4905 dw 4951 dw 4997 dw 5043 dw 5089 dw 5135 dw 5181 dw 5228 dw 5274 dw 5321 dw 5367 dw 5414 dw 5461 dw 5508 dw 5556 dw 5603 dw 5651 dw 5698 dw 5746 dw 5794 dw 5842 dw 5890 dw 5938 dw 5987 dw 6035 dw 6084 dw 6133 dw 6182 dw 6231 dw 6281 dw 6330 dw 6380 dw 6430 dw 6480 dw 6530 dw 6580 dw 6631 dw 6681 dw 6732 dw 6783 dw 6835 dw 6886 dw 6938 dw 6990 dw 7042 dw 7094 dw 7147 dw 7199 dw 7252 dw 7306 dw 7359 dw 7413 dw 7466 dw 7521 dw 7575 dw 7630 dw 7684 dw 7740 dw 7795 dw 7851 dw 7907 dw 7963 dw 8019 dw 8076 dw 8133 dw 8191 dw 8249 dw 8307 dw 8365 dw 8424 dw 8483 dw 8543 dw 8602 dw 8663 dw 8723 dw 8784 dw 8846 dw 8907 dw 8970 dw 9032 dw 9095 dw 9159 dw 9223 dw 9288 dw 9353 dw 9418 dw 9484 dw 9551 dw 9618 dw 9686 dw 9754 dw 9823 dw 9892 dw 9963 dw 10034 dw 10105 dw 10177 dw 10251 dw 10324 dw 10399 dw 10475 dw 10551 dw 10628 dw 10706 dw 10785 dw 10866 dw 10947 dw 11029 dw 11113 dw 11198 dw 11284 dw 11371 dw 11460 dw 11550 dw 11642 dw 11736 dw 11831 dw 11929 dw 12028 dw 12130 dw 12234 dw 12340 dw 12449 dw 12561 dw 12677 dw 12796 dw 12919 dw 13046 dw 13178 dw 13315 dw 13459 dw 13610 dw 13770 dw 13939 dw 14121 dw 14319 dw 14538 dw 14786 dw 15079 dw 15462 dw 16384 dw 16384 ;extra for when exacty 1 acos_table dw 16384 dw 16343 dw 16303 dw 16262 dw 16221 dw 16180 dw 16140 dw 16099 dw 16058 dw 16017 dw 15976 dw 15936 dw 15895 dw 15854 dw 15813 dw 15772 dw 15732 dw 15691 dw 15650 dw 15609 dw 15568 dw 15527 dw 15487 dw 15446 dw 15405 dw 15364 dw 15323 dw 15282 dw 15241 dw 15200 dw 15159 dw 15118 dw 15077 dw 15036 dw 14995 dw 14953 dw 14912 dw 14871 dw 14830 dw 14789 dw 14748 dw 14706 dw 14665 dw 14624 dw 14582 dw 14541 dw 14500 dw 14458 dw 14417 dw 14375 dw 14334 dw 14292 dw 14250 dw 14209 dw 14167 dw 14125 dw 14084 dw 14042 dw 14000 dw 13958 dw 13916 dw 13874 dw 13833 dw 13791 dw 13748 dw 13706 dw 13664 dw 13622 dw 13580 dw 13537 dw 13495 dw 13453 dw 13410 dw 13368 dw 13325 dw 13283 dw 13240 dw 13197 dw 13155 dw 13112 dw 13069 dw 13026 dw 12983 dw 12940 dw 12897 dw 12854 dw 12811 dw 12767 dw 12724 dw 12680 dw 12637 dw 12593 dw 12550 dw 12506 dw 12462 dw 12419 dw 12375 dw 12331 dw 12287 dw 12242 dw 12198 dw 12154 dw 12109 dw 12065 dw 12020 dw 11976 dw 11931 dw 11886 dw 11841 dw 11796 dw 11751 dw 11706 dw 11661 dw 11616 dw 11570 dw 11525 dw 11479 dw 11433 dw 11387 dw 11341 dw 11295 dw 11249 dw 11203 dw 11156 dw 11110 dw 11063 dw 11017 dw 10970 dw 10923 dw 10876 dw 10828 dw 10781 dw 10733 dw 10686 dw 10638 dw 10590 dw 10542 dw 10494 dw 10446 dw 10397 dw 10349 dw 10300 dw 10251 dw 10202 dw 10153 dw 10103 dw 10054 dw 10004 dw 9954 dw 9904 dw 9854 dw 9804 dw 9753 dw 9703 dw 9652 dw 9601 dw 9549 dw 9498 dw 9446 dw 9394 dw 9342 dw 9290 dw 9237 dw 9185 dw 9132 dw 9078 dw 9025 dw 8971 dw 8918 dw 8863 dw 8809 dw 8754 dw 8700 dw 8644 dw 8589 dw 8533 dw 8477 dw 8421 dw 8365 dw 8308 dw 8251 dw 8193 dw 8135 dw 8077 dw 8019 dw 7960 dw 7901 dw 7841 dw 7782 dw 7721 dw 7661 dw 7600 dw 7538 dw 7477 dw 7414 dw 7352 dw 7289 dw 7225 dw 7161 dw 7096 dw 7031 dw 6966 dw 6900 dw 6833 dw 6766 dw 6698 dw 6630 dw 6561 dw 6492 dw 6421 dw 6350 dw 6279 dw 6207 dw 6133 dw 6060 dw 5985 dw 5909 dw 5833 dw 5756 dw 5678 dw 5599 dw 5518 dw 5437 dw 5355 dw 5271 dw 5186 dw 5100 dw 5013 dw 4924 dw 4834 dw 4742 dw 4648 dw 4553 dw 4455 dw 4356 dw 4254 dw 4150 dw 4044 dw 3935 dw 3823 dw 3707 dw 3588 dw 3465 dw 3338 dw 3206 dw 3069 dw 2925 dw 2774 dw 2614 dw 2445 dw 2263 dw 2065 dw 1846 dw 1598 dw 1305 dw 922 dw 0 dw 0 ;extra for when exacty 1 ;values for first guess in square root routines. Note that the first entry ;is useful in quad_sqrt when edx=0 and high bit of eax is set. guess_table db 1 dup (1) ;0 db 3 dup (1) ;1..3 db 5 dup (2) ;4..8 db 7 dup (3) ;9..15 db 9 dup (4) ;16..24 db 11 dup (5) ;25..35 db 13 dup (6) ;36..48 db 15 dup (7) ;49..63 db 17 dup (8) ;64..80 db 19 dup (9) ;81..99 db 21 dup (10) ;100..120 db 23 dup (11) ;121..143 db 25 dup (12) ;144..168 db 27 dup (13) ;169..195 db 29 dup (14) ;196..224 db 31 dup (15) ;225..255 _DATA ends _TEXT segment para public USE32 'CODE' ;the sincos functions have two varients: the C version is passed pointer ;to variables for sin & cos, and the assembly version returns the values ;in two registers ;takes ax=angle, returns eax=sin, ebx=cos. fix_fastsincos: movzx eax,ah ;get high byte movsx ebx,cos_table[eax*2] sal ebx,2 ;make a fix movsx eax,sin_table[eax*2] sal eax,2 ;make a fix ret ;takes ax=angle, returns eax=sin, ebx=cos. fix_sincos: pushm ecx,edx xor edx, edx xor ecx, ecx mov dl, ah ;get high byte mov cl, al ;save low byte shl edx, 1 movsx eax,sin_table[edx] movsx ebx,sin_table+2[edx] sub ebx,eax imul ebx,ecx ;mul by fraction sar ebx,8 add eax,ebx ;add in frac part sal eax,2 ;make a fix movsx ebx,cos_table[edx] movsx edx,cos_table+2[edx] sub edx,ebx imul edx,ecx ;mul by fraction sar edx,8 add ebx,edx ;add in frac part sal ebx,2 ;make a fix popm ecx,edx ret align 16 ;takes eax=cos angle, returns ax=angle fix_acos: pushm ebx,ecx,edx abs_eax ;get abs value push edx ;save sign cmp eax,10000h jle no_acos_oflow mov eax,10000h no_acos_oflow: movzx ecx,al ;save low byte (fraction) mov edx,eax sar edx,8 ;get high byte (+1 bit) movsx eax,acos_table[edx*2] movsx ebx,acos_table+2[edx*2] sub ebx,eax imul ebx,ecx ;mul by fraction sar ebx,8 add eax,ebx ;add in frac part pop edx ;get sign back xor eax,edx sub eax,edx ;make correct sign and edx,8000h ;zero or 1/2 add eax,edx popm ebx,ecx,edx ret ;takes eax=sin angle, returns ax=angle fix_asin: pushm ebx,ecx,edx abs_eax ;get abs value push edx ;save sign cmp eax,10000h jle no_asin_oflow mov eax,10000h no_asin_oflow: movzx ecx,al ;save low byte (fraction) mov edx,eax sar edx,8 ;get high byte (+1 bit) movsx eax,asin_table[edx*2] movsx ebx,asin_table+2[edx*2] sub ebx,eax imul ebx,ecx ;mul by fraction sar ebx,8 add eax,ebx ;add in frac part pop edx ;get sign back xor eax,edx ;make sign correct sub eax,edx popm ebx,ecx,edx ret ;given cos & sin of an angle, return that angle. takes eax=cos,ebx=sin. ;returns ax. parms need not be normalized, that is, the ratio eax/ebx must ;equal the ratio cos/sin, but the parms need not be the actual cos & sin. ;NOTE: this is different from the standard C atan2, since it is left-handed. ;trashes ebx ;uses either asin or acos, to get better precision fix_atan2: pushm ecx,edx ifndef NDEBUG mov edx,eax or edx,ebx break_if z,'Both parms to atan2 are zero!' endif push ebx push eax ;find smaller of two pushm eax,ebx ;save abs_eax xchg eax,ebx abs_eax cmp ebx,eax ;compare x to y popm eax,ebx jl use_cos ;sin is smaller, use arcsin imul eax xchg eax,ebx mov ecx,edx imul eax add eax,ebx adc edx,ecx call quad_sqrt mov ecx,eax ;ecx = mag pop ebx ;get cos, save in ebx pop eax ;get sin jecxz sign_ok ;abort! fixdiv ecx ;normalize it call fix_asin ;get angle or ebx,ebx ;check sign of cos jns sign_ok sub eax,8000h ;adjust neg eax sign_ok: popm ecx,edx ret ;cos is smaller, use arccos use_cos: imul eax xchg eax,ebx mov ecx,edx imul eax add eax,ebx adc edx,ecx call quad_sqrt mov ecx,eax pop eax ;get cos fixdiv ecx ;normalize it call fix_acos ;get angle mov ebx,eax ;save in ebx pop eax ;get sin cdq ;get sign of sin mov eax,ebx ;get cos back xor eax,edx sub eax,edx ;make sign correct popm ecx,edx ret public fix_fastsincos_,fix_sincos_ ;C version - takes ax=angle, esi,edi=*sin,*cos. fills in sin&cos. ;either (or both) pointers can be null ;trashes eax,ebx fix_fastsincos_: call fix_fastsincos or esi,esi jz no_sin mov [esi],eax no_sin: or edi,edi jz no_cos mov [edi],ebx no_cos: ret ;C version - takes ax=angle, esi,edi=*sin,*cos. fills in sin&cos. ;trashes eax,ebx ;either (or both) pointers can be null fix_sincos_: call fix_sincos or esi,esi jz no_sin mov [esi],eax or edi,edi jz no_cos mov [edi],ebx ret ;standard Newtonian-iteration square root routine. takes eax, returns ax ;trashes eax,ebx,ecx,edx,esi,edi long_sqrt: or eax,eax ;check sign jle error ;zero or negative pushm ebx,ecx,edx,esi,edi mov edx,eax shr edx,16 ;split eax -> dx:ax ;get a good first quess by checking which byte most significant bit is in xor ebx,ebx ;clear high bytes for index or dh,dh ;highest byte jz not_dh mov bl,dh ;get value for lookup mov cl,12 jmp got_guess not_dh: or dl,dl jz not_dl mov bl,dl ;get value for lookup mov cl,8 jmp got_guess not_dl: or ah,ah jz not_ah mov bl,ah ;get value for lookup mov cl,4 jmp got_guess not_ah: mov bl,al ;get value for lookup mov cl,0 got_guess: movzx ebx,guess_table[ebx] ;get byte guess sal ebx,cl ;get in right place mov ecx,eax mov esi,edx ;save dx:ax ;the loop nearly always executes 3 times, so we'll unroll it 2 times and ;not do any checking until after the third time. By my calcutations, the ;loop is executed 2 times in 99.97% of cases, 3 times in 93.65% of cases, ;four times in 16.18% of cases, and five times in 0.44% of cases. It never ;executes more than five times. By timing, I determined that is is faster ;to always execute three times and not check for termination the first two ;times through. This means that in 93.65% of cases, we save 6 cmp/jcc pairs, ;and in 6.35% of cases we do an extra divide. In real life, these numbers ;might not be the same. ;newt_loop: rept 2 mov eax,ecx mov edx,esi ;restore dx:ax div bx ;dx:ax / bx mov edi,ebx ;save for compare add bx,ax rcr bx,1 ;next guess = (d + q)/2 endm newt_loop: mov ax,cx mov dx,si ;restore dx:ax div bx ;dx:ax / bx cmp ax,bx ;correct? je got_it ;..yep mov di,bx ;save for compare add bx,ax rcr bx,1 ;next guess = (d + q)/2 cmp bx,ax je almost_got_it cmp bx,di jne newt_loop almost_got_it: mov ax,bx or dx,dx ;check remainder jz got_it inc ax got_it: popm ebx,ecx,edx,esi,edi ret ;sqrt called with zero or negative input. return zero error: xor eax,eax ret ;call the longword square root for quad with high longword equal zero call_long: call long_sqrt movzx eax,ax ;return longword result ret ;standard Newtonian-iteration square root routine. takes edx:eax, returns eax quad_sqrt: or edx,edx ;check sign js error ;can't do negative number! jnz must_do_quad ;we really must do 64/32 div or eax,eax ;check high bit of low longword jns call_long ;we can use longword version must_do_quad: pushm ebx,ecx,edx,esi,edi ;get a good first quess by checking which byte most significant bit is in xor ebx,ebx ;clear high bytes for index ror edx,16 ;get high 2 bytes or dh,dh jz q_not_dh mov bl,dh ;get value for lookup mov cl,12+16 ror edx,16 ;restore edx jmp q_got_guess q_not_dh: or dl,dl jz q_not_dl mov bl,dl ;get value for lookup mov cl,8+16 ror edx,16 ;restore edx jmp q_got_guess q_not_dl: ror edx,16 ;restore edx or dh,dh jz q_not_ah mov bl,dh ;get value for lookup mov cl,4+16 jmp q_got_guess q_not_ah: mov bl,dl ;get value for lookup mov cl,0+16 q_got_guess: movzx ebx,guess_table[ebx] ;get byte guess sal ebx,cl ;get in right place q_really_got_guess: mov ecx,eax mov esi,edx ;save edx:eax ;quad loop usually executes 4 times ;q_newt_loop: rept 3 mov eax,ecx mov edx,esi ;restore dx:ax div ebx ;dx:ax / bx mov edi,ebx ;save for compare add ebx,eax rcr ebx,1 ;next guess = (d + q)/2 endm q_newt_loop: mov eax,ecx mov edx,esi ;restore dx:ax div ebx ;dx:ax / bx cmp eax,ebx ;correct? je q_got_it ;..yep mov edi,ebx ;save for compare add ebx,eax rcr ebx,1 ;next guess = (d + q)/2 cmp ebx,eax je q_almost_got_it cmp ebx,edi jne q_newt_loop q_almost_got_it: mov eax,ebx or edx,edx ;check remainder jz q_got_it inc eax q_got_it: popm ebx,ecx,edx,esi,edi ret ;fixed-point square root fix_sqrt: call long_sqrt movzx eax,ax sal eax,8 ret _TEXT ends end