Stable version

1 files changed, 301 insertions, 0 deletions

diff --git a/kara.c b/kara.c
new file mode 100644
index 0000000..2898e63
--- /dev/null
+++ b/kara.c
@@ -0,0 +1,301 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <string.h>
+
+typedef uint8_t leg_t;
+typedef uint16_t dleg_t;
+
+enum { g_legs = 256 };
+
+#define dump_int(A,B,C) dump_int2(A,B,C)
+static void dump_int2( uint8_t const * p, int l, int nl )
+{
+  while( l-- )
+   printf( "%02X", *(p++) );
+  if( nl ) putchar( 10 );
+}
+
+//#define printf(...)
+//#define putchar(A)
+
+static int mp_cmp( leg_t const *a, leg_t const *b, int legs )
+{
+  int leg;
+  for( leg=0; leg<legs; ++leg )
+  {
+    if( a[leg] < b[leg] ) return -1;
+    if( a[leg] > b[leg] ) return  1;
+  }
+  return 0;
+}
+
+static void add( leg_t *oper, leg_t const *oper2, int legs )
+{
+  dleg_t acc = 0;
+  while( legs-- > 0 )
+  {
+    acc += oper[legs] + oper2[legs];
+    oper[legs] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+  while( acc )
+  {
+    acc += oper[legs];
+    oper[legs--] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+}
+
+static void adm( leg_t *oper, leg_t const *oper2, int legs, int flegs )
+{
+  dleg_t acc = 0;
+  while( legs-- > 0 )
+  {
+    acc += oper[legs] + oper2[legs];
+    oper[legs] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+  while( acc && flegs-- )
+  {
+    acc += oper[legs];
+    oper[legs--] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+}
+
+static void sub( leg_t *oper, leg_t const *oper2, int legs )
+{
+  int borrow = 0, borrow_temp;
+  while( legs-- )
+  {
+    leg_t temp = oper[legs] - oper2[legs];
+    borrow_temp = temp > oper[legs];
+    oper[legs] = temp - borrow;
+    borrow = borrow_temp | ( oper[legs] > temp );
+  }
+  while( borrow )
+  {
+    leg_t temp = oper[legs] - borrow;
+    borrow = temp > oper[legs];
+    oper[legs--] = temp;
+  }
+printf( "sub: %d\n", legs );
+}
+
+/* result is guaranteed to be initialized with enough legs prepended to take the carry */
+static void mp_mul_uint_add( leg_t *result, leg_t const *oper, leg_t fac, int legs )
+{
+  dleg_t acc = 0;
+  while( legs-- )
+  {
+    acc += (dleg_t)result[legs] + (dleg_t)oper[legs] * (dleg_t)fac;
+    result[legs] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+  while( acc )
+  {
+    acc += result[legs];
+    result[legs--] = (leg_t)acc;
+    acc >>= 8*sizeof(leg_t);
+  }
+}
+
+static void mul( leg_t * result, leg_t const *oper, leg_t const *oper2, int legs )
+{
+  int leg = legs;
+  while( leg-- )
+    mp_mul_uint_add( result + 1 + leg, oper, oper2[leg], legs );
+}
+
+static int sub_mod( leg_t * result, leg_t const *a, leg_t const * b, int legs )
+{
+  int borrow = 0, borrow_temp;
+  while( legs-- )
+  {
+    leg_t temp = a[legs] - b[legs];
+    borrow_temp = temp > a[legs];
+    result[legs] = temp - borrow;
+    borrow = borrow_temp | (result[legs] > temp );
+  }
+  return borrow;
+}
+
+static void negate( leg_t * p, int legs )
+{
+  while( legs && !p[legs-1] ) p[legs--]^=(leg_t)-1;
+  if( !legs ) return;
+  p[legs-1]--;
+  while( legs--) p[legs]^=(leg_t)-1;
+}
+
+void kara2( leg_t* p, leg_t *a, leg_t *b, int len )
+{
+printf( "L%d karaloop: a*b ", len ); dump_int( a, len, 0 ); putchar('*'); dump_int( b, len, 1 );
+  memset( p, 0, 2 * len * sizeof( leg_t ));
+  if( len == 2 )
+  {
+    mul( p, a, b, len );
+    printf( "L%d p:", len ); dump_int( p, len*2, 1 );
+  }
+  else
+  {
+    leg_t  scratch[len];
+    int    sign = 0, n = len / 2;
+
+    if( mp_cmp( a, a + n, n ) > 0 )
+      sub_mod( scratch, a, a + n, n );
+    else
+    {
+      sub_mod( scratch, a + n, a, n );
+      sign = 1;
+    }
+
+    if( mp_cmp( b, b + n, n ) > 0 )
+      sub_mod( scratch + n, b, b + n, n );
+    else
+    {
+      sub_mod( scratch + n, b + n, b, n );
+      sign ^= 1;
+    }
+
+printf( "L%d (x0-x1)*(y1-y0)=", len ); dump_int( scratch, n, 0 ); putchar('*'); dump_int( scratch + n, n, 0 ); printf( "(sign = %d)\n", sign );
+
+    kara2( p + n, scratch, scratch + n, n );
+    if( !sign )
+      negate( p, len + n );
+
+printf( "L%d psub:", len ); dump_int( p, len*2, 1 );
+
+    kara2( scratch, a + n, b + n, n );
+    adm( p + len, scratch, len, len );
+    adm( p + n, scratch, len, n );
+
+    kara2( scratch, a, b, n );
+    adm( p + n, scratch, len, n );
+    adm( p, scratch, len, 0 );
+printf( "L%d p:", len ); dump_int( p, len*2, 1 );
+  }
+}
+
+void kara( uint8_t* p, uint8_t *a, uint8_t *b, int len )
+{
+  int i;
+memset( p, 0, 2 * len * sizeof(leg_t ) );
+  if( len <= 3 )
+  {
+printf( "L%d karaend:  a*b ", len ); dump_int( a, len, 0 ); putchar('*'); dump_int( b, len, 1 );
+    mul( p, a, b, len );
+printf( "L%d result:\n", len ); dump_int( p, len*2, 1 );
+  }
+  else {
+    int     n  = len / 2;
+    int     l  = ( len + 1 ) / 2;
+    int     o  = l - n;
+    int     sh = l + 1;
+    uint8_t scratch[2*sh];
+    uint8_t *midpoint = p + len * 2 - n;
+
+printf( "L%d karaloop: a*b ", len ); dump_int( a, len, 0 ); putchar('*'); dump_int( b, len, 1 );
+printf( "Values n: %d l: %d o: %d sh: %d\n", n, l, o, sh );
+
+    memset( scratch, 0, sizeof(scratch));
+    memcpy( scratch + 1      , a, l );
+    memcpy( scratch + 1 + sh , b, l );
+
+    /* P3 = (a1+a2)*(b1+b2) */
+    add( scratch +      1 + o, a + l, n );
+    add( scratch + sh + 1 + o, b + l, n );
+
+    printf( "L%d a1+a2: \n", len ); dump_int( scratch, sh, 1 );
+    printf( "L%d b1+b2: \n", len ); dump_int( scratch+sh, sh, 1 );
+
+    kara( midpoint - 2 * sh, scratch, scratch + sh, sh );
+
+    printf( "L%d (a1+a2)*(b1+b2)<<n: \n", len ); dump_int( p, len*2, 1 );
+
+    /* P2 = a2*b2 */
+    kara( scratch, a + l, b + l, n );
+
+    printf( "L%d a2*b2: \n", len ); dump_int( scratch, n*2, 1 );
+
+    /* P = ( P3 - P2 ) * 2^n + P2 ... and later: + P1 * 2^(2*n) - P1 * 2^n*/
+    add( midpoint - n, scratch, n * 2 );
+
+    printf( "L%d p + p2: \n", len ); dump_int( p, len*2, 1 );
+
+    sub( midpoint - n * 2, scratch, n * 2 );
+
+    printf( "L%d p - p2<<n: \n", len ); dump_int( p, len*2, 1 );
+
+    /* now + P1 * 2^(2*n) - P1 * 2^n*/
+    kara( scratch, a, b, l );
+
+    printf( "L%d a1*b1: \n", len ); dump_int( scratch, l*2, 1 );
+
+    sub( midpoint - l * 2, scratch, l * 2 );
+
+    printf( "L%d p - p1<<n: \n", len ); dump_int( p, len*2, 1 );
+
+    add( midpoint - n - l * 2, scratch, l * 2 );
+
+    printf( "L%d p + p1<<n^2: \n", len ); dump_int( p, len*2, 1 );
+  }
+}
+
+#undef putchar
+int main() {
+  uint8_t a[] = { 0x99,0xf3,0x0a,0x3d,0x8a,0xdd,0x2d,0x1f };
+  uint8_t b[] = { 0xf1,0x48,0x71,0x4b,0xf7,0xb1,0x9a,0x30 };
+
+//  uint8_t a[g_legs], b[g_legs];
+//  uint8_t p[2*g_legs];
+
+/*
+static const leg_t b[] = {
+    0x3D, 0xA9, 0x76, 0x59, 0xE2, 0x80, 0xDB, 0x0B, 0xE6, 0x5B, 0xCC, 0x3A, 0xB7, 0x8F, 0xDA, 0xA9, 0xB7, 0xB7, 0x68, 0xC8, 0x99, 0x31, 0xD7, 0x8D, 0xF8, 0xB1, 0x17, 0x25, 0x33, 0x9E, 0xBC, 0x93,
+    0xAA, 0x7F, 0xBD, 0x95, 0x62, 0x05, 0x9F, 0x1F, 0x4C, 0x2D, 0xE6, 0x7D, 0xAD, 0x47, 0x52, 0x7E, 0x52, 0x6A, 0x65, 0x3A, 0x7A, 0x67, 0x4B, 0xD5, 0x54, 0x01, 0xEA, 0x4F, 0x3E, 0xD7, 0x3A, 0x2F,
+    0x70, 0xB5, 0x6F, 0x52, 0x7F, 0x6F, 0x60, 0x4F, 0xF3, 0xE5, 0x6C, 0xC2, 0xBD, 0x9F, 0x04, 0x8C, 0xFE, 0xA8, 0x0D, 0x9A, 0x6E, 0xC9, 0xFC, 0xD3, 0x3A, 0xD3, 0x6F, 0xD8, 0x22, 0xC3, 0x9F, 0x34,
+    0x91, 0xF3, 0x0C, 0x52, 0xF7, 0x98, 0xDA, 0x6A, 0x18, 0xC3, 0xDC, 0xE2, 0x01, 0x88, 0xD8, 0x4C, 0xCB, 0x22, 0x51, 0x76, 0x25, 0x9E, 0x08, 0x0F, 0xA8, 0x9D, 0x1D, 0xCD, 0x9D, 0x38, 0x1C, 0xC5,
+    0xBE, 0xAC, 0xD4, 0x6F, 0x3C, 0xDD, 0x11, 0x96, 0x91, 0xA4, 0xF5, 0x57, 0x29, 0x29, 0xB9, 0x0C, 0x67, 0xDE, 0x8F, 0xA0, 0x23, 0x86, 0x47, 0x14, 0xC2, 0x8A, 0x61, 0xD4, 0x74, 0x11, 0x40, 0x2D,
+    0x6C, 0x09, 0x06, 0x0D, 0x41, 0x05, 0x86, 0x39, 0xE4, 0xFC, 0xCF, 0x1D, 0x63, 0x8F, 0x45, 0x66, 0x9E, 0x10, 0xFD, 0xE2, 0x8E, 0x54, 0x80, 0x6B, 0xF1, 0xD2, 0x7D, 0x0B, 0x5C, 0x7D, 0xC9, 0xC2,
+    0xB6, 0x16, 0xD6, 0xFA, 0x8B, 0xE2, 0xC9, 0x1D, 0xE8, 0x10, 0x54, 0x64, 0xE9, 0xF8, 0x0A, 0x5F, 0x34, 0x72, 0x08, 0x69, 0x90, 0xDA, 0xCF, 0x1A, 0x7E, 0x2C, 0x75, 0xA5, 0x8E, 0x25, 0xF1, 0x42,
+    0x8F, 0xB4, 0x83, 0x2E, 0xF8, 0x27, 0xDE, 0x84, 0xCA, 0x06, 0xDA, 0x91, 0xC2, 0xB3, 0xE7, 0xE2, 0x4F, 0x02, 0x41, 0x93, 0x78, 0x7A, 0x82, 0x78, 0x8B, 0xD7, 0x05, 0x62, 0xDA, 0x60, 0xE3, 0x92,
+    0x46, 0xBD, 0xB7, 0x33, 0x6E, 0x84, 0x52, 0xD9, 0x1D, 0x7D, 0x37, 0xA2, 0x3F, 0xB8, 0xCF, 0x61, 0xB1, 0x8A, 0x9E, 0xF1, 0x50, 0xC8, 0x95, 0x3A, 0xC9, 0x39, 0x19, 0xD1, 0x2A, 0x4B, 0x1A, 0x67,
+    0xFD, 0xC6, 0x5A, 0x26, 0x9B, 0x51, 0xC1, 0xEF, 0x09, 0x95, 0x48, 0x43, 0x20, 0xE7, 0x39, 0xF4, 0x6C, 0x79, 0x51, 0xA5, 0x23, 0xCE, 0xF7, 0x85, 0xE6, 0x0C, 0x6E, 0xFD, 0xFF, 0xB7, 0xA9, 0xA9,
+    0x5F, 0x66, 0x61, 0x46, 0xCB, 0x44, 0x1F, 0x59, 0xAE, 0x01, 0xE0, 0xF3, 0x63, 0xA9, 0x31, 0x5D, 0x04, 0xBA, 0x04, 0x4A, 0xEB, 0x4E, 0xEF, 0xD4, 0x85, 0x63, 0x21, 0x5F, 0x72, 0xC8, 0xD9, 0x89,
+    0x62, 0xD2, 0x18, 0x77, 0x12, 0x96, 0xEF, 0x6A, 0x20, 0xBD, 0x72, 0xB9, 0xB2, 0x1E, 0x6B, 0x3D, 0x53, 0xC4, 0x4F, 0xAB, 0x73, 0x48, 0x10, 0xF7, 0xD2, 0x03, 0xA9, 0xE0, 0xD7, 0xCE, 0x25, 0xD0,
+    0x2E, 0x52, 0x98, 0x9E, 0xCC, 0xF8, 0x5F, 0x34, 0x91, 0x2A, 0x04, 0x91, 0x3E, 0x9E, 0xBD, 0x87, 0x82, 0x67, 0x53, 0x7D, 0x4A, 0x61, 0x2A, 0x18, 0x51, 0xE7, 0x5D, 0x99, 0x98, 0xF0, 0x01, 0xDB,
+    0xC9, 0xC7, 0x7F, 0x0C, 0x35, 0x2D, 0x40, 0x8C, 0xA7, 0x96, 0xD1, 0x82, 0x04, 0xA6, 0x36, 0xF7, 0xE4, 0x40, 0x40, 0x92, 0x1C, 0x1E, 0x46, 0x7C, 0x52, 0x4E, 0x7C, 0x7A, 0x7E, 0xD3, 0x6C, 0x41,
+    0x2A, 0x43, 0x4C, 0xEB, 0x23, 0x0B, 0x2D, 0xFE, 0x35, 0x49, 0xC5, 0x77, 0x7A, 0x17, 0xFB, 0x04, 0xB8, 0x50, 0xDE, 0x95, 0xD9, 0x7A, 0xC4, 0x0A, 0x55, 0xEA, 0x6F, 0x75, 0x41, 0xC4, 0xF8, 0x2B,
+    0x37, 0xBF, 0x90, 0xFE, 0x52, 0x07, 0x4F, 0x19, 0xFA, 0x8F, 0x75, 0xF0, 0x06, 0x7E, 0x82, 0xB1, 0x8A, 0x1A, 0xC0, 0x24, 0xB3, 0x0E, 0x9B, 0x12, 0xC1, 0x4A, 0xB0, 0xDD, 0xCC, 0x03, 0xAA, 0x20
+};
+  uint8_t a[sizeof(b)];
+*/
+
+  uint8_t p[2*sizeof(b)];
+  int i;
+
+  srandomdev();
+
+//  while( 1 )
+  {
+//    memset( a, 0, sizeof(a) );
+//    a[sizeof(b)-1]=2;
+/*
+    memset( b, 0, sizeof(b) );
+    a[g_legs-1] = random() & 0xff;
+    for( i=g_legs/2; i<sizeof(a); ++i )
+    {
+      b[i] = random() & 0xff;
+    }
+*/
+    kara2( p, a, b, sizeof(b));
+
+    dump_int2( a, sizeof(a), 0 );
+    putchar( '*' );
+    dump_int2( b, sizeof(b), 0 );
+    putchar( '-' );
+    dump_int2( p, sizeof(p), 1 );
+  }
+  return 0;
+}