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#include "Diffusion.h"
#include "Types.h"
#include <memory.h>
//-----------------------------------------------------------------------------
// check invertibility of diffusion matrix
void TestDiffusionMatrix ( void )
{
//int m[4] = { 3, 1, 1, 3 };
int tab[65536];
memset(tab,0,sizeof(tab));
for(int i = 0; i < 65536; i++)
{
uint8_t a1 = (uint8_t)i;
uint8_t a2 = (uint8_t)(i >> 8);
//uint8_t b1 = uint8_t(a1 * m[0]) + uint8_t(a2*m[1]);
//uint8_t b2 = uint8_t(a1 * m[2]) + uint8_t(a2*m[3]);
uint8_t b1 = a1;
uint8_t b2 = a2;
b1 += b2;
b2 += b1;
int index = (int(b1) << 8) + b2;
tab[index]++;
}
int missing = 0;
for(int i = 0; i < 65536; i++)
{
if(tab[i] == 0) missing++;
}
printf("missing - %d\n",missing);
}
//-----------------------------------------------------------------------------
void add_row ( int m[16], int a, int b )
{
for(int i = 0; i < 4; i++)
{
m[4*a+i] += m[4*b+i];
}
}
void sub_row ( int m[16], int a, int b )
{
for(int i = 0; i < 4; i++)
{
m[4*a+i] -= m[4*b+i];
}
}
//-----------------------------------------------------------------------------
// search through diffusion matrices computable in N operations, find ones
// with a maximal number of odd terms
bool check ( const int m[16], std::vector<int> & dst, std::vector<int> & src )
{
static int best = 0;
int c = 0;
int s = 0;
if(abs(m[0]+m[4]+m[8]+m[12]) > 2) return false;
if(abs(m[1]+m[5]+m[9]+m[13]) > 2) return false;
if(abs(m[2]+m[6]+m[10]+m[14]) > 2) return false;
if(abs(m[3]+m[7]+m[11]+m[15]) > 2) return false;
for(int i = 0; i < 16; i++)
{
if(m[i] == 0) return false;
int d = abs(m[i]);
c += (d & 1);
if(m[i] < 0) s++;
}
if((c == 13) && (s == 8))
{
std::string g[4];
g[0] = "A";
g[1] = "B";
g[2] = "C";
g[3] = "D";
printf("----------\n");
for(int i = 0; i < (int)dst.size(); i++)
{
int d = dst[i];
int s = src[i];
std::string tmp;
tmp += g[d-1];
tmp += (s < 0) ? "-" : "+";
tmp += "(";
tmp += g[abs(s)-1];
tmp += ")";
g[d-1] = tmp;
}
printf("A : %s\n",g[0].c_str());
printf("B : %s\n",g[1].c_str());
printf("C : %s\n",g[2].c_str());
printf("D : %s\n",g[3].c_str());
for(int i = 0; i < (int)dst.size(); i++)
{
int d = dst[i];
int s = src[i];
if(s < 0)
{
printf("h[%1d] -= h[%1d];\n",d,-s);
}
else
{
printf("h[%1d] += h[%1d];\n",d,s);
}
}
printf("----------\n");
}
return c == 16;
}
bool difrecurse ( const int m[16], int depth, int maxdepth, int last, std::vector<int> & dst, std::vector<int> & src )
{
if(depth == maxdepth)
{
return check(m,dst,src);
}
for(int i = 0; i < 4; i++)
{
dst.push_back(i+1);
for(int j = 0; j < 4; j++)
{
if(i == j) continue;
if(i == last) continue;
if(j == last) continue;
int n[16];
memcpy(n,m,sizeof(n));
src.push_back(j+1);
add_row(n,i,j);
difrecurse(n,depth+1,maxdepth,i,dst,src);
sub_row(n,i,j);
src.pop_back();
src.push_back(-(j+1));
sub_row(n,i,j);
difrecurse(n,depth+1,maxdepth,i,dst,src);
add_row(n,i,j);
src.pop_back();
}
dst.pop_back();
}
return false;
}
void findDiffuse ( void )
{
int m[16];
memset(m,0,sizeof(m));
m[4*0 + 0] = 1;
m[4*1 + 1] = 1;
m[4*2 + 2] = 1;
m[4*3 + 3] = 1;
std::vector<int> dst;
std::vector<int> src;
difrecurse(m,0,7,-1,dst,src);
printf("\n");
}
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