gf2x.cpp

数值算法库for Windows

   hl2[2] = hl2[2] ^ c[2];
   hl2[3] = hl2[3] ^ c[3];
   
   c[2] ^= hl2[0];
   c[3] ^= hl2[1];
   c[4] ^= hl2[2];
   c[5] ^= hl2[3];
}

static
void mul4(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b)
{
   _ntl_ulong hs0[2], hs1[2];
   _ntl_ulong hl2[4];

   hs0[0] = a[0] ^ a[2];
   hs0[1] = a[1] ^ a[3];
   hs1[0] = b[0] ^ b[2];
   hs1[1] = b[1] ^ b[3];

   mul2(c, a, b);
   mul2(c+4, a+2, b+2); 
   mul2(hl2, hs0, hs1);

   hl2[0] = hl2[0] ^ c[0] ^ c[4];
   hl2[1] = hl2[1] ^ c[1] ^ c[5];
   hl2[2] = hl2[2] ^ c[2] ^ c[6];
   hl2[3] = hl2[3] ^ c[3] ^ c[7];
   
   c[2] ^= hl2[0];
   c[3] ^= hl2[1];
   c[4] ^= hl2[2];
   c[5] ^= hl2[3];
}

static
void mul5 (_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b)
{
   _ntl_ulong hs0[3], hs1[3];
   _ntl_ulong hl2[6];

   hs0[0] = a[0] ^ a[3]; 
   hs0[1] = a[1] ^ a[4];
   hs0[2] = a[2];
   hs1[0] = b[0] ^ b[3]; 
   hs1[1] = b[1] ^ b[4];
   hs1[2] = b[2];

   mul3(c, a, b); 
   mul2(c+6, a+3, b+3); 
   mul3(hl2, hs0, hs1);

   hl2[0] = hl2[0] ^ c[0] ^ c[6]; 
   hl2[1] = hl2[1] ^ c[1] ^ c[7];
   hl2[2] = hl2[2] ^ c[2] ^ c[8];
   hl2[3] = hl2[3] ^ c[3] ^ c[9];
   hl2[4] = hl2[4] ^ c[4];
   hl2[5] = hl2[5] ^ c[5];

  
   c[3] ^= hl2[0];
   c[4] ^= hl2[1];
   c[5] ^= hl2[2];
   c[6] ^= hl2[3];
   c[7] ^= hl2[4];
   c[8] ^= hl2[5];
}

static
void mul6(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b)
{
   _ntl_ulong hs0[3], hs1[3];
   _ntl_ulong hl2[6];

   hs0[0] = a[0] ^ a[3];   
   hs0[1] = a[1] ^ a[4];
   hs0[2] = a[2] ^ a[5];
   hs1[0] = b[0] ^ b[3];   
   hs1[1] = b[1] ^ b[4];
   hs1[2] = b[2] ^ b[5];

   mul3(c, a, b);   
   mul3(c+6, a+3, b+3); 
   mul3(hl2, hs0, hs1);  

   hl2[0] = hl2[0] ^ c[0] ^ c[6];
   hl2[1] = hl2[1] ^ c[1] ^ c[7];
   hl2[2] = hl2[2] ^ c[2] ^ c[8];
   hl2[3] = hl2[3] ^ c[3] ^ c[9];
   hl2[4] = hl2[4] ^ c[4] ^ c[10];
   hl2[5] = hl2[5] ^ c[5] ^ c[11];
   
   c[3] ^= hl2[0];
   c[4] ^= hl2[1];
   c[5] ^= hl2[2];
   c[6] ^= hl2[3];
   c[7] ^= hl2[4];
   c[8] ^= hl2[5];
}

static
void mul7(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b)
{
   _ntl_ulong hs0[4], hs1[4];
   _ntl_ulong hl2[8];

   hs0[0] = a[0] ^ a[4]; 
   hs0[1] = a[1] ^ a[5];
   hs0[2] = a[2] ^ a[6];
   hs0[3] = a[3];
   hs1[0] = b[0] ^ b[4]; 
   hs1[1] = b[1] ^ b[5];
   hs1[2] = b[2] ^ b[6];
   hs1[3] = b[3];

   mul4(c, a, b); 
   mul3(c+8, a+4, b+4); 
   mul4(hl2, hs0, hs1);

   hl2[0] = hl2[0] ^ c[0] ^ c[8];
   hl2[1] = hl2[1] ^ c[1] ^ c[9];
   hl2[2] = hl2[2] ^ c[2] ^ c[10];
   hl2[3] = hl2[3] ^ c[3] ^ c[11];
   hl2[4] = hl2[4] ^ c[4] ^ c[12];
   hl2[5] = hl2[5] ^ c[5] ^ c[13];
   hl2[6] = hl2[6] ^ c[6];
   hl2[7] = hl2[7] ^ c[7];
   
   c[4]  ^= hl2[0];
   c[5]  ^= hl2[1];
   c[6]  ^= hl2[2];
   c[7]  ^= hl2[3];
   c[8]  ^= hl2[4];
   c[9]  ^= hl2[5];
   c[10] ^= hl2[6];
   c[11] ^= hl2[7];
}

static
void mul8(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b)
{
   _ntl_ulong hs0[4], hs1[4];
   _ntl_ulong hl2[8];

   hs0[0] = a[0] ^ a[4]; 
   hs0[1] = a[1] ^ a[5];
   hs0[2] = a[2] ^ a[6];
   hs0[3] = a[3] ^ a[7];
   hs1[0] = b[0] ^ b[4]; 
   hs1[1] = b[1] ^ b[5];
   hs1[2] = b[2] ^ b[6];
   hs1[3] = b[3] ^ b[7];

   mul4(c, a, b); 
   mul4(c+8, a+4, b+4);
   mul4(hl2, hs0, hs1); 

   hl2[0] = hl2[0] ^ c[0] ^ c[8];
   hl2[1] = hl2[1] ^ c[1] ^ c[9];
   hl2[2] = hl2[2] ^ c[2] ^ c[10];
   hl2[3] = hl2[3] ^ c[3] ^ c[11];
   hl2[4] = hl2[4] ^ c[4] ^ c[12];
   hl2[5] = hl2[5] ^ c[5] ^ c[13];
   hl2[6] = hl2[6] ^ c[6] ^ c[14];
   hl2[7] = hl2[7] ^ c[7] ^ c[15];
   
   c[4]  ^= hl2[0];
   c[5]  ^= hl2[1];
   c[6]  ^= hl2[2];
   c[7]  ^= hl2[3];
   c[8]  ^= hl2[4];
   c[9]  ^= hl2[5];
   c[10] ^= hl2[6];
   c[11] ^= hl2[7];
}

static
void KarMul(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b, long len, _ntl_ulong *stk)
{
   if (len <= 8) {
      switch (len) {
         case 1: mul1(c, a[0], b[0]); break;
         case 2: mul2(c, a, b); break;
         case 3: mul3(c, a, b); break;
         case 4: mul4(c, a, b); break;
         case 5: mul5(c, a, b); break;
         case 6: mul6(c, a, b); break;
         case 7: mul7(c, a, b); break;
         case 8: mul8(c, a, b); break;
      }

      return;
   }

   long ll, lh, i, ll2, lh2;
   const _ntl_ulong *a0, *a1, *b0, *b1;
   _ntl_ulong *a01, *b01, *h;

   lh = len >> 1;
   ll = (len+1) >> 1;

   ll2 = ll << 1;
   lh2 = lh << 1;

   a01 = stk;  stk += ll+1;
   b01 = stk;  stk += ll+1;
   h = stk; stk += ll2+1;

   a0 = a;
   a1 = a+ll;
   b0 = b;
   b1 = b+ll;

   KarMul(c, a0, b0, ll, stk);
   KarMul(c+ll2, a1, b1, lh, stk);

   for (i = 0; i < lh; i++) {
      a01[i] = a[i] ^ a[i+ll];
      b01[i] = b[i] ^ b[i+ll];
   }

   if (lh < ll) {
      a01[lh] = a[lh];
      b01[lh] = b[lh];
   }

   KarMul(h, a01, b01, ll, stk);

   for (i = 0; i < ll2; i++)
      h[i] ^= c[i];

   for (i = 0; i < lh2; i++)
      h[i] ^= c[i+ll2];

   for (i = 0; i < ll2; i++)
      c[i+ll] ^= h[i];
}


void mul(GF2X& c, const GF2X& a, const GF2X& b)
{
   long sa = a.xrep.length();
   long sb = b.xrep.length();

   if (sa <= 0 || sb <= 0) {
      clear(c);
      return;
   }
 
   _ntl_ulong a0 = a.xrep[0];
   _ntl_ulong b0 = b.xrep[0];

   if (sb == 1 && b0 == 1) {
      c = a;
      return;
   }

   if (sa == 1 && a0 == 1) {
      c = b;
      return;
   }

   if (&a == &b) {
      sqr(c, a);
      return;
   }

   if (sa == sb && sa <= 8) {
      // we treat these cases specially for efficiency reasons

      switch (sa) {
         case 1: {
            _ntl_ulong v[2];
            if (!(a0 >> NTL_BITS_PER_LONG/2))
               mul_half(v, b0, a0);
            else if (!(b0 >> NTL_BITS_PER_LONG/2))
               mul_half(v, a0, b0);
            else
               mul1(v, a0, b0);

            if (v[1]) {
               c.xrep.SetLength(2);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
            }
            else {
               c.xrep.SetLength(1);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
            }
         }
         return;

         case 2: {
            _ntl_ulong v[4];
            mul2(v, &a.xrep[0], &b.xrep[0]);
            if (v[3]) {
               c.xrep.SetLength(4);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
            }
            else {
               c.xrep.SetLength(3);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
            }
         }
         return;

         case 3: {
            _ntl_ulong v[6];
            mul3(v, &a.xrep[0], &b.xrep[0]);
            if (v[5]) {
               c.xrep.SetLength(6);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
            }
            else {
               c.xrep.SetLength(5);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
            }
         }
         return;

         case 4: {
            _ntl_ulong v[8];
            mul4(v, &a.xrep[0], &b.xrep[0]);
            if (v[7]) {
               c.xrep.SetLength(8);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
            }
            else {
               c.xrep.SetLength(7);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
            }
         }
         return;

         case 5: {
            _ntl_ulong v[10];
            mul5(v, &a.xrep[0], &b.xrep[0]);
            if (v[9]) {
               c.xrep.SetLength(10);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
            }
            else {
               c.xrep.SetLength(9);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
            }
         }
         return;

         case 6: {
            _ntl_ulong v[12];
            mul6(v, &a.xrep[0], &b.xrep[0]);
            if (v[11]) {
               c.xrep.SetLength(12);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
               cp[11] = v[11];
            }
            else {
               c.xrep.SetLength(11);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
            }
         }
         return; 

         case 7: {
            _ntl_ulong v[14];
            mul7(v, &a.xrep[0], &b.xrep[0]);
            if (v[13]) {
               c.xrep.SetLength(14);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
               cp[11] = v[11];
               cp[12] = v[12];
               cp[13] = v[13];
            }
            else {
               c.xrep.SetLength(13);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
               cp[11] = v[11];
               cp[12] = v[12];
            }
         }
         return; 

         case 8: {
            _ntl_ulong v[16];
            mul8(v, &a.xrep[0], &b.xrep[0]);
            if (v[15]) {
               c.xrep.SetLength(16);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
               cp[11] = v[11];
               cp[12] = v[12];
               cp[13] = v[13];
               cp[14] = v[14];
               cp[15] = v[15];
            }
            else {
               c.xrep.SetLength(15);
               _ntl_ulong *cp = &c.xrep[0];
               cp[0] = v[0];
               cp[1] = v[1];
               cp[2] = v[2];
               cp[3] = v[3];
               cp[4] = v[4];
               cp[5] = v[5];
               cp[6] = v[6];
               cp[7] = v[7];
               cp[8] = v[8];
               cp[9] = v[9];
               cp[10] = v[10];
               cp[11] = v[11];
               cp[12] = v[12];
               cp[13] = v[13];
               cp[14] = v[14];
            }
         }
         return; 

      }
   }

   // another special case:  one of the two inputs
   // has length 1 (and maybe 1/2).

   if (sa == 1) {
      c.xrep.SetLength(sb + 1);
      _ntl_ulong *cp = c.xrep.elts();
      const _ntl_ulong *bp = b.xrep.elts();

      long i;
      _ntl_ulong carry;
      _ntl_ulong v[2];

      carry = 0;

      if (a0 >> NTL_BITS_PER_LONG/2) {
         for (i = 0; i < sb; i++) {
            mul1(v, bp[i], a0);
            cp[i] = carry ^ v[0];
            carry = v[1];
         }
      }
      else {
         for (i = 0; i < sb; i++) {
            mul_half(v, bp[i], a0);
            cp[i] = carry ^ v[0];
            carry = v[1];
         }
      }

      cp[sb] = carry;
      c.normalize();
      return;
   }

   if (sb == 1) {
      c.xrep.SetLength(sa + 1);
      _ntl_ulong *cp = c.xrep.elts();
      const _ntl_ulong *ap = a.xrep.elts();

      long i;
      _ntl_ulong carry;
      _ntl_ulong v[2];

      carry = 0;

      if (b0 >> NTL_BITS_PER_LONG/2) {
         for (i = 0; i < sa; i++) {
            mul1(v, ap[i], b0);
            cp[i] = carry ^ v[0];
            carry = v[1];
         }
      }
      else {
         for (i = 0; i < sa; i++) {
            mul_half(v, ap[i], b0);
            cp[i] = carry ^ v[0];
            carry = v[1];
         }
      }

      cp[sa] = carry;
      c.normalize();
      return;
   }

   // finally: the general case

   
   static WordVector mem;
   static WordVector stk;
   static WordVector vec;

   const _ntl_ulong *ap, *bp;
   _ntl_ulong *cp;


   long sc = sa + sb;
   long in_mem = 0;

   if (&a == &c || &b == &c) {
      mem.SetLength(sc);
      cp = mem.elts();