arithmetic.cpp
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/* Copyright (C) 2010-2012 kaosu (qiupf2000@gmail.com)
* This file is part of the Interactive Text Hooker.
* Interactive Text Hooker is free software: you can redistribute it and/or
* modify it under the terms of the GNU General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <intrin.h>
#include "arithmetic.h"
int count;
u32 next_pow2(u32 n)
{
if (n == 0) return 1;
n--;
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
n++;
return n;
}
void mulasm(unsigned int* dest,unsigned int* left,unsigned int* right,unsigned int bit_size)
{
__asm
{
cmp bit_size,64
jbe _small
xor eax,eax
mov ebx,bit_size
mov ecx,ebx
sub esp,ecx
mov edi,esp
shr ecx,2
rep stos dword ptr [edi]
mov edi,esp
mov ecx,ebx
shr ecx,1
push ecx
mov eax,left ;left low
push eax
mov eax,right ;right low
push eax
push edi
call mulasm ;left low*right lwo, z0
add esp,0x10
mov ecx,ebx
shr ecx,1
push ecx
shr ecx,3
lea edi,[edi+ecx*2]
mov eax,left
add eax,ecx ;left high
push eax
mov eax,right
add eax,ecx ;right high
push eax
push edi
call mulasm ;left high*right high; z2
add esp,0x10
xor edx,edx
shr ebx,3
add edi,ebx
mov esi,left
shr ebx,1
mov ecx,ebx
add ebx,esi
push 0
_add_left:
mov eax,[esi+ecx]
add eax,edx
movs dword ptr [edi]
adc [edi-4],eax
setc dl
cmp esi,ebx
jne _add_left
or [esp],dl
mov esi,right
mov ebx,esi
add ebx,ecx
xor edx,edx
_add_right:
mov eax,[esi+ecx]
add eax,edx
movs dword ptr [edi]
adc [edi-4],eax
setc dl
cmp esi,ebx
jne _add_right
add edx,edx
or [esp],edx
mov ebx,bit_size
shr ebx,1
push ebx
mov eax,edi
sub eax,ecx
push eax
sub eax,ecx
push eax
push edi
call mulasm ;(left low+left high)*(right low+right high);
add esp,0x10
mov ecx,bit_size
shr ecx,4
mov esi,edi
sub esi,ecx
sub esi,ecx
add edi,ecx
mov ebx,edi
add ebx,ecx
mov edx,[esp]
mov eax,edx
and eax,2
shr eax,1
sub eax,1
not eax
push eax
mov eax,edx
and eax,1
sub eax,1
not eax
push eax
push 0
xor edx,edx
_carry_mul_add:
mov eax,[esi]
and eax,[esp+8]
add eax,edx
adc dh,0
mov [esp],eax
mov eax,[esi+ecx]
and eax,[esp+4]
add eax,[esp]
adc dh,0
add [edi],eax
adc dh,0
shr edx,8
add esi,4
add edi,4
cmp ebx,edi
jne _carry_mul_add
add esp,0xC
bt dword ptr [esp],1
setc al
and al,[esp]
add dl,al
mov [esp],edx
lea esi,[esp+4]
shl ecx,1
lea ebx,[edi+ecx]
xor edx,edx
_add_z0_z2:
mov eax,[esi+ecx]
add eax,edx
movs dword ptr [edi]
adc [edi-4],eax
setc dl
cmp edi,ebx
jne _add_z0_z2
sub [esp],edx
lea esi,[esi+2*ecx]
mov ebx,edi
sub edi,ecx
xor edx,edx
_form_z1:
mov eax,[edi]
bt edx,0
sbb [esi],eax
setc dl
add esi,4
add edi,4
cmp edi,ebx
jne _form_z1
sub [esp],edx
sub ebx,ecx
sub esi,ecx
shr ecx,1
lea edi, [esp+ecx+4]
xor edx,edx
_final_pack:
lods dword ptr [esi]
bt edx,0
adc [edi],eax
setc dl
add edi,4
cmp esi,ebx
jne _final_pack
add edx,[esp]
_add_carry:
add [edi],edx
setc dl
add edi,4
test dl,dl
jne _add_carry
pop eax
mov esi,esp
mov edi,dest
rep movs dword ptr [edi]
add esp,bit_size
jmp _final
_small:
mov esi,left
mov edi,right
mov ebx,dest
mov eax,[esi]
mov ecx,[edi]
mul ecx
mov [ebx],eax
mov [ebx+4],edx
mov eax,[esi+4]
mul ecx
add [ebx+4],eax
adc edx,0
mov [ebx+8],edx
mov ecx,[edi+4]
mov eax,[esi]
mul ecx
add [ebx+4],eax
adc [ebx+8],edx
push 0
setc [esp]
mov eax,[esi+4]
mul ecx
add [ebx+8],eax
adc edx,[esp]
mov [ebx+0xC],edx
pop eax
_final:
}
}
/*void __declspec(naked) mulmnu_asm(u8* w, u8* u, u8* v, u32 m)
{
__asm
{
push ebx
push ebp
push esi
push edi
mov ecx,[esp+0x20] ; mov ecx,m
shr ecx,1
xor eax,eax
mov edi,[esp+0x14] ; mov edi,w
rep stos ; memset(w,0,2*m);
xor ebx,ebx; i
xor ebp,ebp; j
mov esi,[esp+0x18] ; mov esi,u
mov edi,[esp+0x1C] ; mov edi,v
xor edx,edx
push 0
_mul_outer_loop:
xor ebp,ebp
mov [esp],ebp
_mul_inner_loop:
mov eax, [esi+ebx]
mul dword ptr [edi+ebp]
add dword ptr [ecx+ebp],eax
adc dword ptr [ecx+ebp+4],edx
adc dword ptr [ecx+ebp+8],0
mov eax, [esi+ebx]
mul dword ptr [edi+ebp+4]
add edx, [esp]
add dword ptr [ecx+ebp+4],eax
adc dword ptr [ecx+ebp+8],edx
setc [esp]
add ebp,8
cmp ebp,[esp+0x24]
jne _mul_inner_loop
bt [esp],0
adc [ecx+ebp+4],0
add ebx,4
add ecx,4
cmp ebx,[esp+0x24]
jne _mul_outer_loop
pop eax
pop edi
pop esi
pop ebp
pop ebx
retn
}
}*/
void mulmnu(u16 w[], u16 u[], u16 v[], int m, int n)
{
unsigned int k, t;
int i, j;
for (i = 0; i < m; i++)
w[i] = 0;
for (j = 0; j < n; j++)
{
k = 0;
for (i = 0; i < m; i++)
{
t = u[i]*v[j] + w[i + j] + k;
w[i + j] = t; // (I.e., t & 0xFFFF).
k = t >> 16;
}
w[j + m] = k;
}
return;
}
int mulmnu(u8 w[], u8 u[], u8 v[], int m, int n)
{
//mulmnu((u16*)w,(u16*)u,(u16*)v,m/2,n/2);
//__asm int 3
for (m--;m>=0 && u[m] == 0;m--);
for (n--;n>=0 && v[n] == 0;n--);
m = next_pow2(m);
n = next_pow2(n);
m = m > n ? m : n;
mulasm((u32*)w,(u32*)u,(u32*)v,m << 3);
return 0;
}
int nlz(unsigned x) {
int n;
if (x == 0) return(32);
n = 0;
if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
if (x <= 0x7FFFFFFF) {n = n + 1;}
return n;
}
unsigned char nlz_table[0x100] =
{
8,7,6,6, 5,5,5,5, 4,4,4,4, 4,4,4,4,
3,3,3,3, 3,3,3,3, 3,3,3,3, 3,3,3,3,
2,2,2,2, 2,2,2,2, 2,2,2,2, 2,2,2,2,
2,2,2,2, 2,2,2,2, 2,2,2,2, 2,2,2,2,
1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1,
1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1,
1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1,
1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1
};
__declspec(naked) int divasm(void* q, void* r, const void* u, const void* v, unsigned int m, unsigned int n)
{
__asm
{
push ebp
mov ebp,esp
push esi
push edi
push ebx
std
mov edx,n
mov esi,v
lea esi,[esi+edx-4]
mov eax,[esi]
xor ecx,ecx
test eax,0xFFFF0000
jne _nlz1
add ecx,0x10
shl eax,0x10
_nlz1:
test eax,0xFF000000
jne _nlz2
add ecx,8
shl eax,8
_nlz2:
shr eax,24
add cl,byte ptr [nlz_table+eax]
push ecx
lea edi,[esp-4]
sub esp,edx
lodsd
mov edx,eax
_normalize:
lodsd
shld edx,eax,cl
xchg edx,eax
stosd
cmp esi,v
jae _normalize
mov eax,edx
shl eax, cl
stosd
mov esi,u
mov edx,m
sub esp,edx
sub esp,4
lea esi,[esi+edx-4]
xor edx,edx
_normalize2:
lodsd
shld edx,eax,cl
xchg edx,eax
stosd
cmp esi,u
jae _normalize2
shl edx, cl
mov [edi],edx
cld
sub esp, 0xC
mov ecx, n
mov ebx, m
lea esi, [ebx+edi+4] ; v
sub ebx, ecx
mov [esp], ebx
xor eax,eax
mov [esp+4],eax
mov [esp+8],eax
_div_test:
mov ebx, [esp]; j
mov ecx, n
add ebx, ecx
mov edx, [edi + ebx] ; u(j+n)
mov eax, [edi + ebx - 4]; u(j+n-1)
mov ebx, [esi + ecx - 4]; v(n-1)
cmp edx, ebx ;q >= b?
setae cl
jb _no_over_div
sub edx, ebx ;q = b + q`
_no_over_div:
div ebx
mov [esp + 4], eax ;q`
mov [esp + 8], edx ;r
test cl,cl; cl: q >= b
jz _test_qob
_dec_quo:
sub dword ptr [esp + 4], 1 ; q--
mov ecx, n
mov ebx, [esi + ecx - 4]
jnc _qob
add [esp + 8], ebx
jmp _mul_sub
_qob:
add [esp + 8], ebx ;r += v(n-1) > b (c) ?
jc _mul_sub
_test_qob:
mov eax, [esp + 4]
mov ecx, n
mul dword ptr [esi + ecx - 8]
mov ebx, [esp]
add ebx, ecx
sub eax, [edi + ebx - 8]
sbb edx, [esp + 8] ; q*v(n-2) > b*r + u(j+n-2) (a)?
ja _dec_quo ; _dec_quo : $
_mul_sub:
xor ebx, ebx
mov ecx, [esp]
add ecx, edi
push 0
_mul_sub_loop:
mov eax, [esp + 8] ; q
mul dword ptr [esi + ebx]
sub [ecx], eax
sbb [ecx + 4], edx
mov edx, [esp]
setc byte ptr [esp]
sub [ecx + 4], edx
adc byte ptr [esp],0
add ecx, 4
add ebx, 4
cmp ebx, n
jb _mul_sub_loop
pop eax
test eax,eax
jz _loop_on_j
xor ecx,ecx
xor ebx,ebx
mov edx, [esp]
add edx, edi
_add_back:
mov eax,[esi + ecx]
bt ebx,0
adc [edx], eax
setc bl
add ecx,4
add edx,4
cmp ecx,n
jb _add_back
add [edx], ebx
dec dword ptr [esp + 4]
_loop_on_j:
mov eax, [esp]
mov edx, q
mov ecx, [esp + 4]
mov [edx + eax], ecx
sub eax, 4
mov [esp], eax
jae _div_test
add esp,0x10
add esp,m
add esp,n
pop ecx
mov esi, edi
mov edi, r
mov ebx, n
add ebx, esi
xor edx,edx
lodsd
mov edx,eax
_unnormalize:
lodsd
shrd edx,eax,cl
xchg edx,eax
stosd
cmp esi, ebx
jb _unnormalize
shr edx, cl
mov [edi],edx
pop ebx
pop edi
pop esi
mov esp,ebp
pop ebp
retn
}
};
__declspec(naked) int divasm_s(void* q, void* r, const void* u, unsigned int v, unsigned int m)
{
__asm
{
push ebp
mov ebp,esp
push esi
push edi
push ebx
std
mov ebx, m
mov esi, u
mov edi, q
lea esi, [esi + ebx - 4]
lea edi, [edi + ebx - 4]
shr ebx, 4
mov ecx, v
xor edx,edx
test ebx,ebx
jz _remain
_div_loop:
lodsd
div ecx
stosd
lodsd
div ecx
stosd
lodsd
div ecx
stosd
lodsd
div ecx
stosd
dec ebx
jne _div_loop
_remain:
mov ebx, m
shr ebx, 2
and ebx, 3
jz _div_no_single
dec ebx
jz _div_one_single
dec ebx
jz _div_two_single
lodsd
div ecx
stosd
_div_two_single:
lodsd
div ecx
stosd
_div_one_single:
lodsd
div ecx
stosd
_div_no_single:
mov ebx, r
mov [ebx], edx
cld
pop ebx
pop edi
pop esi
pop ebp
retn
}
}
int div_long(void* q, void* r, const void* u, const void* v, unsigned m, unsigned n)
{
if ((m|n)&3) return 1; //align 4 byte
unsigned int *pu, *pv;
unsigned int m1,n1;
pu = (unsigned int*)u;
pv = (unsigned int*)v;
m1 = m / 4 - 1;
n1 = n / 4 - 1;
while (m1 && pu[m1] == 0) m1--;
while (n1 && pv[n1] == 0) n1--;
if (n1 == 0 && pv[0]) divasm_s(q,r,u,pv[0], (m1+1) << 2);
else
{
divasm(q,r,u,v,(m1+1)*4,(n1+1)*4);
}
return 0;
}
int divmnu(u8 q[], u8 r[], const u8 u[], const u8 v[], int m, int n)
{
return div_long(q,r,u,v,m<<1,n<<1);
/*
//m=(m+3)/4;n=(n+3)/4;
//return divmnu32((u32*)q,(u32*)r,(u32*)u,(u32*)v,m,n);
if ((m|n)&3) return 1;
u8* u_copy = alloca(m+n);
u8* v_copy = u_copy + m;
memcpy(u_copy, u, m);
memcpy(v_copy, v, n);
divasm(q,r,u_copy,v_copy,m,n);
return 0;*/
//return divmnu((u16*)q,(u16*)r,(u16*)u,(u16*)v,m/2,n/2);
}
void exp_mod(u8* base, u8* exp, u8* mod,u8* res, u32 base_size, u32 exp_size, u32 mod_size)
{
int i,j,exp_head;
u8 t=0x80;
for (exp_head=exp_size-1;exp_head>=0&&exp[exp_head]==0;exp_head--);
if (exp_head<0) return;
u8 *block;
u8 *result[2];
u8 *new_base[2];
u8 *quotient;//=(u8 *)alloca(base_size*2);
u8 *remainder;//=(u8 *)alloca(mod_size*2);
block=(u8*)alloca(base_size*12);
quotient=block;
remainder=block+base_size*2;
result[0]=block+base_size*4;
result[1]=block+base_size*6;
new_base[0]=block+base_size*8;
new_base[1]=block+base_size*10;
memset(block,0,base_size*8);
memcpy(new_base[0],base,base_size);//memset(new_base[0]+base_size,0,base_size);
memcpy(new_base[1],base,base_size);//memset(new_base[1]+base_size,0,base_size);
result[0][0]=1;
for (i=0;i<exp_head;i++)
{
t=1;
for (j=0;j<8;j++)
{
if (exp[i]&t)
{
mulmnu(result[1],result[0],new_base[0],base_size,base_size);
//divmnu((u16*)quotient,(u16*)result[0],(u16*)result[1],(u16*)mod,base_size,mod_size/2);
div_long(quotient,result[0],result[1],mod,base_size*2,mod_size);
}
mulmnu(new_base[1],new_base[0],new_base[0],base_size,base_size);
//divmnu((u16*)quotient,(u16*)new_base[0],(u16*)new_base[1],(u16*)mod,base_size,mod_size/2);
div_long(quotient,new_base[0],new_base[1],mod,base_size*2,mod_size);
t<<=1;
}
}
for (t=exp[exp_head]; t; t>>=1)
{
if (t&1)
{
mulmnu(result[1],result[0],new_base[0],base_size,base_size);
//divmnu((u16*)quotient,(u16*)result[0],(u16*)result[1],(u16*)mod,base_size,mod_size/2);
div_long(quotient,result[0],result[1],mod,base_size*2,mod_size);
}
mulmnu(new_base[1],new_base[0],new_base[0],base_size,base_size);
//divmnu((u16*)quotient,(u16*)new_base[0],(u16*)new_base[1],(u16*)mod,base_size,mod_size/2);
div_long(quotient,new_base[0],new_base[1],mod,base_size*2,mod_size);
}
memcpy(res,result[0],mod_size);
}