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Assembly Source File | 1994-09-18 | 7KB | 318 lines

; ROOTS Copyright (C) 1992-1994 by Celso Minnitti Jr. All Rights Reserved. ; ; Version: 0.2 (September-18-1994) ; ; Compile: TASM /m2 example ; TLINK /t /3 /x example ; ; I just wrote this program because I found quite interesting two new ; algorithms that developed to find N^2 and N^3 only using additions. ; To compute N^2 we need two registers and two ADDs. ; To compute N^3 we need three registers and three ADDs. ; ; Please note that: ; ; 1 4 9 16 25 36 49 ; \-/ \-/ \-/ \-/ \-/ \-/ ; 3 5 7 9 11 13 (subtract 4-1, 9-4,...) ; \-/ \-/ \-/ \-/ \-/ ; 2 2 2 2 2 (2!) 2 factorial... ; ; ; 1 8 27 64 125 216 ; \-/ \-/ \-/ \-/ \-/ ; 7 19 37 61 91 7 = 8-1 19 = 27-8 37 = 64-27 ; \-/ \-/ \-/ \-/ ; 12 18 24 30 12=19-7 18 = 37-19 30 = 91-61 ; \-/ \-/ \-/ ; 6 6 6 (3!) 3 factorial... ; ; N^4 will require 4 additions and the constant to add is 24 (4!)... ; N^5 will require 5 additions and the constant to add is 120 (5!)... ; N^6 will require 6 additions and the constant to add is 720 (6!)...etc... ; ; If you find these algorithms interesting please let me know... If you ; have any questions or comments, please contact me at: ; ; Celso Minnitti Jr ; 139 Linden St ; Wellesley, MA 02181 ; Home phone #: 617-235-4018 ; email: celsomj@world.std.com _TEXT segment byte public 'CODE' assume cs:_TEXT, ds:_TEXT org 100h .386 ANY_NUMBER = 10000 ;can be any number from ;1 to 429101525 (0FFC3B3C9h) start: mov ax,13h ;320x200x256 int 10h cld ;just to be safe... mov es,[vidseg] ;A000 mov di,150*320+10 ;x = 10, y = 150 mov al,1 ;color = blue mov bx,140 ;draw 140 pixels draw_x1: mov es:[di],al ;draw y = x sub di,319 dec bx jnz draw_x1 call getch ;wait for a key mov si,1 mov dx,1 mov bx,17 ;draw 17 segments... mov al,2 ;color = green mov di,150*320+10 ;x = 10, y = 155 draw_x2: mov cx,si rep stosb ;draw y = x^2 add si,2 ;si=1,3,5,7,9... sub di,320 dec bx jnz draw_x2 call getch mov dx,1 ; mov si,6 ;3 factorial... mov bx,6 ;draw 6 segments mov al,3 ;color = cyan mov di,150*320+10 ;x = 10, y = 160 draw_x3: mov cx,dx ; rep stosb ;draw y = x^3 add dx,si ;dx=1,7,19,37,61... add si,6 sub di,320 dec bx jnz draw_x3 call getch mov ax,3 ;return to 80x25 int 10h mov si,offset copyRight call prints mov si,offset message_1 call prints mov eax,ANY_NUMBER call print2d mov si,offset message_11 call prints call root22 ;eax = sqrt, edx = reminder call print2d mov si,offset message_12 call prints mov eax,edx call print2d call print_crlf mov si,offset message_2 call prints mov eax,ANY_NUMBER call print2d mov si,offset message_21 call prints call root32 ;eax = cubic_rt, edx = reminder call print2d mov si,offset message_22 call prints mov eax,edx call print2d int 20h ;exit to DOS ;************************************************************************** ; ROOT22 ; enter: EAX = 1 - 0FFFE0001h (4294836225=65535*65535) ; return: EAX = square root ; EDX = reminder ;************************************************************************** root22 proc near push ecx push ebx xor ecx,ecx inc cx mov edx,ecx mov ebx,ecx ;ecx=edx=ebx=1 root22_loop: cmp edx,eax je short root22_ret ja short root22_ret0 add ebx,2 ;ebx=1,3,5,7 ,9 ,11,13... add edx,ebx ;edx=1,4,9,16,25,36,49... inc ecx ;ecx=1,2,3,4 ,5 ,6 ,7 ... jmp short root22_loop root22_ret0: dec ecx sub edx,ebx root22_ret: sub edx,eax neg edx mov eax,ecx pop ebx pop ecx ret root22 endp ;************************************************************************** ; ROOT32 ; enter: EAX = 1 - 0FFC3B3C9h (4291015625=1625*1625*1625) ; return: EAX = cubic root ; EDX = reminder ;************************************************************************** root32 proc near push ecx push ebx push esi xor ecx,ecx inc cx mov edx,ecx mov ebx,ecx ;ecx=edx=ebx=1 mov esi,6 root32_loop: cmp edx,eax je short root32_ret ja short root32_ret0 add ebx,esi ;ebx=7 ,19,37,61... add esi,6 ;esi=12,18,24,30... add edx,ebx ;edx=8 ,27,64,125... inc ecx ;ecx=2 , 3, 4, 5 jmp root32_loop root32_ret0: dec ecx sub edx,ebx root32_ret: sub edx,eax neg edx mov eax,ecx pop esi pop ebx pop ecx ret root32 endp ;************************************************************************** ; PRINT2D ; enter: EAX = # to print in decimal ;************************************************************************** print2d proc near push eax push cx push edx push ebx push si xor cx,cx mov si,offset pbuff mov ebx,10 pri21d: xor edx,edx div ebx add dl,30h mov [si],dl inc si inc cx or eax,eax jnz short pri21d pri22d: dec si mov al,[si] call putchar dec cx jnz pri22d pop si pop ebx pop edx pop cx pop eax ret print2d endp ;************************************************************************** ; PRINTS ; enter: DS:SI = address of string ;************************************************************************** prints proc near push ax push si prints1: mov al,[si] inc si or al,al jz prints_ret call putchar jmp prints1 prints_ret: pop si pop ax ret prints endp ;************************************************************************** ; PUTCHAR ; enter: AL = character to write ;************************************************************************** putchar proc near push ax push cx push bx mov ah,0eh ;Teletype Output mov cx,1 ;# times mov bh,0 ;page number int 10h pop bx pop cx pop ax ret putchar endp ;************************************************************************** ; GETCH ; return: AH = scancode ; AL = character ;************************************************************************** getch proc near mov ah,0 int 16h ret getch endp print_crlf: mov si,offset crlf call prints ret copyRight db 'ROOTS 0.2 (C) Copyright 1994 Celso Minnitti Jr',13,10,10,0 message_1 db 'The square root of ',0 message_11 db ' is: ',0 message_12 db ' .Reminder = ',0 message_2 db 'The cubic root of ',0 message_21 db ' is: ',0 message_22 db ' .Reminder = ',0 crlf db 13,10,0 vidseg dw 0a000h pbuff label byte _TEXT ends end start