?? div.asm
字號:
;******************************************************************************
;* *
;* Functions for arithmetic and number theory with large integers in C *
;* Software supplement to the book "Cryptography in C and C++" *
;* by Michael Welschenbach *
;* *
;* Module div.asm Revision: 18.12.2000 *
;* *
;* Copyright (C) 1998-2005 by Michael Welschenbach *
;* Copyright (C) 2001-2005 by Springer-Verlag Berlin, Heidelberg *
;* Copyright (C) 2001-2005 by Apress L.P., Berkeley, CA *
;* Copyright (C) 2002-2005 by Wydawnictwa MIKOM, Poland *
;* Copyright (C) 2002-2005 by PHEI, P.R.China *
;* Copyright (C) 2002-2005 by InfoBook, Korea *
;* Copyright (C) 2002-2005 by Triumph Publishing, Russia *
;* *
;* All Rights Reserved *
;* *
;* The software may be used for noncommercial purposes and may be altered, *
;* as long as the following conditions are accepted without any *
;* qualification: *
;* *
;* (1) All changes to the sources must be identified in such a way that the *
;* changed software cannot be misinterpreted as the original software. *
;* *
;* (2) The statements of copyright may not be removed or altered. *
;* *
;* (3) The following DISCLAIMER is accepted: *
;* *
;* DISCLAIMER: *
;* *
;* There is no warranty for the software contained in this distribution, to *
;* the extent permitted by applicable law. The copyright holders provide the *
;* software `as is' without warranty of any kind, either expressed or *
;* implied, including, but not limited to, the implied warranty of fitness *
;* for a particular purpose. The entire risk as to the quality and *
;* performance of the program is with you. *
;* *
;* In no event unless required by applicable law or agreed to in writing *
;* will the copyright holders, or any of the individual authors named in *
;* the source files, be liable to you for damages, including any general, *
;* special, incidental or consequential damages arising out of any use of *
;* the software or out of inability to use the software (including but not *
;* limited to any financial losses, loss of data or data being rendered *
;* inaccurate or losses sustained by you or by third parties as a result of *
;* a failure of the software to operate with any other programs), even if *
;* such holder or other party has been advised of the possibility of such *
;* damages. *
;* *
;******************************************************************************
;* *
;* Division, interface compatible with C-function div_l() *
;* *
;* Quotient := Dividend div Divisor *
;* Remainder := Dividend mod Divisor *
;* *
;* Stack on calling of div_l: SP+16 ---> Offset remainder *
;* SP+12 ---> Offset quotient *
;* SP+ 8 ---> Offset divisor *
;* SP+ 4 ---> Offset dividend *
;* SP ---> Return address *
;* *
;* Return Value: ax = -1 if divisor = 0 *
;* ax = 0 else *
;* *
;******************************************************************************
PUBLIC div_l
.386
.MODEL FLAT
.CODE
div_l proc near
;
a equ 0 ; Dividend (working copy)
b equ 1030 ; Divisor (working copy)
q equ 1546 ; Quotient qhat (working memory)
q1 equ 2566 ; High-order digit of divisor (normalized)
v1 equ 2570 ; 2nd digit of divisor (normalized)
v2 equ 2574 ; Exponent for normalization
d equ 2578 ; uj+1 (normalized)
uj1 equ 2582 ; uj+2 (normalized)
uj2 equ 2586
;
_dvd equ [ebp+8] ; Dividend (parameter)
_dvs equ [ebp+12] ; Divisor (parameter)
_qot equ [ebp+16] ; Quotient (parameter)
_rst equ [ebp+20] ; Remainder (parameter)
;
WORKSP equ 2600 ; Working memory in stack area
;
divs: push ebp ; Store value for calling procedure
mov ebp,esp
sub esp,WORKSP ; Local memory
mov eax,esp
push ebx
push edi
push esi
mov ebx,eax ; Store start address of local memory
;
mov esi,_dvd ; Offset of variable a
mov edi,_dvs ; Offset of variable b
mov ax,[esi] ; length(a)
mov dx,[edi] ; length(b)
cmp dx,0 ; b = 0 ?
jne @F
jmp divbyz ; Division by zero!
;
;>>>>>> Load Operands
;
@@: push edi ; Store Seg:Offs b
lea edi,a[ebx] ; destination offset is a[bx]
xor ecx,ecx
mov cx,ax ; l(a) in cx
shr cx,1
jnc @F
inc cx
@@: cld
rep movsd ; Load a as ULONG
movsw ; plus one USHORT
mov cx,ax
shl cx,1
lea edi,a[ebx+ecx+2]
mov word ptr [edi],0
;
pop esi ; Get Seg:Offs of b
lea edi,b[ebx] ; Destination offset is b[bx]
xor ecx,ecx
mov cx,dx ; l(b) in cx
shr cx,1
jnc @F
inc cx
@@: cld
rep movsd ; Load b as ULONG
movsw ; plus one USHORT
mov cx,dx
shl cx,1
lea edi,b[ebx+ecx+2]
mov word ptr [edi],0
;
;>>>>>> Prepare access to local memory
;
push ebp ; Save bp
mov ebp,ebx ; Indexed addressing based on ss
;
;>>>>>> Remove leading zeros from operands
;
xor eax,eax
xor ecx,ecx
mov ax,a[ebp] ; #USHORTs into ax
cmp ax,0
je next1
shl eax,1 ; Index to low-order byte
; of high-order digit
mov esi,eax
@@: cmp word ptr a[ebp][esi],0 ; Digit = 0 ?
jne @F ; No, then we're done
sub esi,2 ; Else: step back one digit
cmp esi,0 ; Index = 0?
je mazer1 ; Then argument = 0
jmp @B ; Next comparison
@@: ; Length found
mazer1: shr esi,1 ; #Digits
mov eax,esi ; Store number of digits
mov word ptr a[ebp],ax
;Operand2
next1: mov ax,b[ebp] ; #USHORTs in ax
cmp ax,0
je end1
shl eax,1 ; #Bytes, index to low-order byte
; of high-order digit
mov esi,eax
@@: cmp word ptr b[ebp][esi],0 ; Digit = 0 ?
jne @F ; If not, we're done
sub esi,2 ; Else: step back one digit
cmp esi,0 ; Index = 0?
je mazer2 ; Then argument = 0
jmp @B ; Next comparison
@@: ; Length found
mazer2: shr esi,1 ; #Digits
mov eax,esi ; Store number of digits
mov b[ebp],ax
end1: cmp ax,0
jne @F
pop ebp
jmp divbyz
@@: cmp word ptr a[ebp],0
jne @F
pop ebp
jmp divz
;
;>>>>>> Test a < b ?
;
@@: mov ecx,0
mov cx,a[ebp]
cmp cx,b[ebp] ; l(a) - l(b)
jnc div03
jmp dra
div03: jne div05 ; Compare digits
mov eax,ecx ; cl = l(a) = l(b)
shl eax,1
lea esi,a[ebp]
lea edi,b[ebp]
add esi,eax ; si points to high-order digit of a
add edi,eax ; di points to high-order digit of b
std
repe cmpsw
cld
jnc div05 ; If no carry occurs, q is positive
jmp dra ; Else q := 0 and r := a
div05: mov ax,b[ebp]
shr ax,1
jnc div05a
inc ax
div05a: cmp ax,1 ; Test if length l(b) = 1
jne dstart
jmp dshort ; Then go to short division
;
;>>>>>> Beginn der Division
;
dstart: mov eax,0
mov ax,b[ebp]
shr ax,1
jnc dm0
inc ax
dm0: mov esi,eax
shl esi,2
sub esi,2 ; Pointer to low byte of b[l(b)]
; (pointer to high-order ULONG)
cmp esi,10 ; Does divisor have 3 or more digits?
jb dm1a ; Two digits are present at mininum!
mov ebx,b[ebp][esi] ; b[l(b)] in bx
mov eax,b[ebp][esi-4]
mov edx,b[ebp][esi-8]
;
mov ecx,0 ; Prepare counter
;
@@: cmp ebx,080000000h ; v1 >= 2^31 ?
jae dm2 ; If not...
inc cx
clc
rcl edx,1
rcl eax,1
rcl ebx,1 ; v1 = v1 * 2
jmp short @B ; until v1 >= 2^31
dm1a: mov ebx,b[ebp][esi] ; b[l(b)] in bx
mov eax,b[ebp][esi-4]
;
mov ecx,0 ; Prepare counter
;
@@: cmp ebx,080000000h ; v1 >= 2^31 ?
jae dm2 ; If not...
inc cx
clc
rcl eax,1
rcl ebx,1 ; v1 = v1 * 2
jmp short @B ; until v1 >= 2^31
;
dm2: mov d[ebp],cx ; Store exponent
mov v1[ebp],ebx ; v1
mov v2[ebp],eax ; v2
dm3: inc word ptr a[ebp] ; l(a) = l(a) + 2
inc word ptr a[ebp]
mov eax,0
mov ax,a[ebp]
shr ax,1
jnc dm3a
inc ax
dm3a: mov esi,eax
shl esi,2
sub esi,2
mov dword ptr a[ebp][esi],0 ; a[l(a)] = 0
;
d2: mov eax,0
mov ax,b[ebp]
shr ax,1
jnc d2a
inc ax
d2a: mov esi,eax
shl esi,2
sub esi,2 ; si points to low-order byte of b[l(b)]
;
mov ecx,0
mov cx,a[ebp]
shr cx,1
jnc d2b
inc cx
d2b: mov edi,ecx
shl edi,2
sub edi,2 ; di points to low-order byte of a[l(a)]
push edi
sub edi,esi
inc edi ; di points to high-order byte of a[l(a)-l(b)]
mov ecx,edi
shr ecx,2 ; Counter in cx
pop esi ; si points to low-order byte of a[l(a)] (j+l(b))
sub edi,3 ; di points to low-order byte of a[l(a)-l(b)] (j)
push edi ; Possible length of q
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