This x86 assembly language program uses the Sieve of Eratosthenes to generate a list of all the prime numbers starting from 3 that are less than 65536. It was written using FASM – the Flat Assembler.
The algorithm used by the program is as follows:
- An array of 4096 bytes is used to represent all of the odd numbers from 1 to 65535.
- Each bit in the array represents an odd number.
- The bits in the array are indexed from 0 up to 32767.
- The numerical value associated with each bit is calculated as:
number = 1 + (2 x bit_index)
- All of the bits in the array are initialised to 0.
- Then the first bit in the array (representing the number 1) is set to 1.
- Each subsequent bit in the array represents a potential prime number p.
- For each p, all of the bits that represent multiples of p (2p, 3p, 4p etc) are set to 1.
- At the end of the process, those bits which are still 0 represent prime numbers.
- Pseudo-code:
for(bit_index = 1 up to bit_index = 32767)
{
p = 1 + (2 x bit_index)
composite = 2 x p
while(composite is less than 65536)
{
set_bit(composite)
composite += p
}
}
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The x86 Source Code
; -------------------------------------------------------------------------------------
format PE GUI 4.0
entry start
include 'win32a.inc'
; -------------------------------------------------------------------------------------
IDD_THE_DIALOG = 102
IDC_OUTPUT = 1000
IDC_BTN_CALC = 1001
IDC_BTN_RESET = 1002
; -------------------------------------------------------------------------------------
section '.code' code readable executable
start:
invoke GetModuleHandle,0
invoke DialogBoxParam,eax,IDD_THE_DIALOG,0,DialogProc,0
exit:
invoke ExitProcess,0
; -------------------------------------------------------------------------------------
proc DialogProc uses esi edi ebx,hwnddlg,msg,wparam,lparam
cmp [msg],WM_INITDIALOG
je .wminitdialog
cmp [msg],WM_COMMAND
je .wmcommand
cmp [msg],WM_CLOSE
je .wmclose
xor eax,eax
jmp .quit
.wminitdialog:
invoke SetDlgItemText,[hwnddlg],IDC_OUTPUT,""
jmp .done
.wmcommand:
cmp [wparam], BN_CLICKED shl 16 + IDC_BTN_CALC
je .CALC
cmp [wparam], BN_CLICKED shl 16 + IDC_BTN_RESET
je .RESET
jmp .done
.CALC:
stdcall CalcSieve
stdcall PrintPrimes
invoke SetDlgItemText,[hwnddlg],IDC_OUTPUT,bfDisplay
jmp .done
.RESET:
invoke SetDlgItemText,[hwnddlg],IDC_OUTPUT,""
jmp .done
.wmclose:
invoke EndDialog,[hwnddlg],0
.done:
mov eax,1
.quit:
ret
endp
; -------------------------------------------------------------------------------------
proc CalcSieve uses esi edi ebx ecx
; generate the prime number sieve
lea esi,[FactorBase]
lea edi,[FactorBase]
xor ecx,ecx
.CLEAR:
mov [edi+ecx],byte 0
inc cx
cmp cx,4096
jl .CLEAR
; Factor Base array: 4096 bytes = 32768 bits
; all the odd numbers from 1 to 65535
; bit_index = 0 to 32767
; 1 at bit_index 0 divides everything:
mov [edi],byte 1
; EBX = bit_index
; number = 1 + (2 x bit_index)
xor ebx,ebx
; start at bit_index = 1 (3)
inc ebx
.SIEVE:
mov edx,ebx
; EAX = 1 + (bit_index x 2)
mov eax,ebx
shl eax,1
inc eax
.SET_1:
; mark as composite by setting the bit to 1
add edx,eax
cmp edx,32767
jg .NEXT
; EDX gives the bit index, set the bit at this index to 1
; get the byte index
mov ecx,edx
shr ecx,3
mov edi,esi
add edi,ecx
; get the bit index
mov ecx,edx
and ecx,7
mov ch,1
shl ch,cl
; set the bit
or [edi],ch
jmp .SET_1
.NEXT:
inc ebx
cmp ebx,32767
jl .SIEVE
ret
endp
; -------------------------------------------------------------------------------------
proc PrintPrimes uses esi edi ecx
; identify all of the numbers in FactorBase that are prime and print them
locals
bit db 0
bit_index dw 0
endl
lea esi,[FactorBase]
lea edi,[bfDisplay]
xor ecx,ecx
.NEXT:
; get the byte
mov dl,[esi+ecx]
.PRINT:
; test each bit in the byte
shr dl,1
jc .NEXT_BIT
; the bit is 0, so print the number
; number = 1 + (2 x bit_index)
xor eax,eax
mov ax,[bit_index]
shl eax,1
inc eax
; print as a decimal number
stdcall HexToDec
.NEXT_BIT:
; get the next bit
inc word [bit_index]
inc byte [bit]
cmp [bit],8
jl .PRINT
.NEXT_BYTE:
mov [bit],byte 0
inc cx
cmp cx,4096
jl .NEXT
.DONE:
mov [edi],byte 0
ret
endp
; -------------------------------------------------------------------------------------
proc HexToDec uses ecx edx
; convert the hex number in AX to a decimal string
; EDI is the destination string
; EDI is set outside of this procedure
locals
power db 4
digit db 0
endl
; the largest number that AX can hold is 65536
; so start with 10 to the power of 4
.CONVERT:
xor cx,cx
mov cl,[power]
stdcall Power_of_Ten
mov [digit],byte 0
.SUB:
; subtract powers of ten to get the left most decimal digit
cmp eax,edx
jl .NEXT
sub eax,edx
inc [digit]
jmp .SUB
.NEXT:
; add the digit to the output string
mov bl,[digit]
mov [edi],bl
add [edi],byte 48
inc edi
dec [power]
cmp [power],0
jge .CONVERT
mov [edi],byte 32
inc edi
ret
endp
; -------------------------------------------------------------------------------------
proc Power_of_Ten
; the power of ten is in CL
mov edx,1
.x10:
cmp cx,0
je .DONE
; multiply EDX by 10
mov ebx,edx
shl edx,3
shl ebx,1
add edx,ebx
dec cx
jmp .x10
.DONE:
ret
endp
; -------------------------------------------------------------------------------------
section '.idata' import data readable writeable
library kernel,'KERNEL32.DLL',\
user,'USER32.DLL'
import kernel,\
GetModuleHandle,'GetModuleHandleA',\
ExitProcess,'ExitProcess'
import user,\
DialogBoxParam,'DialogBoxParamA',\
SetDlgItemText,'SetDlgItemTextA',\
EndDialog,'EndDialog'
; -------------------------------------------------------------------------------------
section '.data' readable writeable
bfDisplay rb 64000
FactorBase rb 4096
; -------------------------------------------------------------------------------------
section '.rc' resource data readable
directory RT_DIALOG,dialogs
resource dialogs,IDD_THE_DIALOG,LANG_ENGLISH+SUBLANG_DEFAULT,the_dialog
dialog the_dialog,\
'Prime Number Sieve',50,50,360,396,\
DS_MODALFRAME+WS_MINIMIZEBOX+WS_POPUP+WS_VISIBLE+WS_CAPTION+WS_SYSMENU,\
0,0,"Lucida Console",11
dialogitem 'BUTTON',"Output",-1,7,7,346,360,BS_GROUPBOX+WS_VISIBLE,0
dialogitem 'EDIT',0,IDC_OUTPUT,13,18,335,340,ES_MULTILINE+ES_AUTOVSCROLL+ES_WANTRETURN+WS_VSCROLL+WS_BORDER+WS_VISIBLE,0
dialogitem 'BUTTON',"CALC",IDC_BTN_CALC,7,375,80,14,BS_PUSHBUTTON+WS_VISIBLE,0
dialogitem 'BUTTON',"RESET",IDC_BTN_RESET,89,375,80,14,BS_PUSHBUTTON+WS_VISIBLE,0
enddialog
; -------------------------------------------------------------------------------------
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