calc/cal/toomcook.cal

/*
 * toomcook - implementation of Toom-Cook(3,4) multiplication algorithm
 *
 * Copyright (C) 2013,2021 Christoph Zurnieden
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc 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 Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * Under source code control:   2013/08/11 01:31:28
 * File existed as early as:    2013
 */

/*
 * hide internal function from resource debugging
 */
static resource_debug_level;
resource_debug_level = config("resource_debug", 0);


/* */
define toomcook3(a,b){
  local alen blen  a0 a1 a2  b0 b1 b2 m ret sign mask;
  local S0 S1 S2 S3 S4 T1 T2;

  if(!isint(a) || !isint(b))
      return newerror("toomcook3(a,b): a and/or b is not an integer");

  alen = digits(a,2);
  blen = digits(b,2);

  sign = sgn(a) * sgn(b);
  /* sgn(x) returns 0 if x = 0 */
  if(sign == 0) return 0;

  m = min(alen,blen)//3;
  mask = ~-(1<<m);

  /*
    Cut-off at about 4,000 dec. digits
    TODO: check
  */
  if(isdefined("test8900")){
    if(m < 20) return a*b;
  }
  else{
    if(m < 4096 ) return a*b;
  }
  a = abs(a);
  b = abs(b);

  a0 = a & mask;
  a1 = (a>>m) & mask;
  a2 = (a>>(2*m));

  b0 =  b         & mask;
  b1 = (b>>m)     & mask;
  b2 = (b>>(2*m));

  /*
    Zimmermann
  */

  S0 = toomcook3(a0 , b0);
  S1 = toomcook3((a2+a1+a0) , (b2+b1+b0));
  S2 = toomcook3(((a2<<2)+(a1<<1)+a0) , ((b2<<2)+(b1<<1)+b0));
  S3 = toomcook3((a2-a1+a0) , (b2-b1+b0));
  S4 = toomcook3(a2,b2);
  T1 = (S3<<1) + S2;
  T1 /= 3;
  T1 += S0;
  T1 >>= 1;
  T1 -= S4<<1;
  T2 = (S1 + S3)>>1;
  S1 -= T1;
  S2 = T2 - S0 - S4;
  S3 = T1 - T2;

  ret =  (S4<<(4*m)) + (S3<<(3*m)) + (S2<<(2*m)) + (S1<<(1*m)) + S0;


  ret = sign *ret;

  return ret;
}

define toomcook3square(a){
  local alen  a0 a1 a2  m tmp tmp2 ret sign S0 S1 S2 S3 S4 T1 mask;

  if(!isint(a))return newerror("toomcook3square(a): a is not integer");

  alen = digits(a,2);

  sign = sgn(a) * sgn(a);
  if(sign == 0) return 0;

  m = alen//3;
  mask = ~-(1<<m);
  /*
    Cut-off at about 5,000 dec. digits
    TODO: check
  */

  if(isdefined("test8900")){
    if(m < 20) return a^2;
  }
  else{
    if(m < 5000 ) return a^2;
  }

  a = abs(a);

  a0 = a & mask;
  a1 = (a>>m) & mask;
  a2 = (a>>(2*m));

  /*
   Bodrato/Zanoni
   */
  S0 = toomcook3square(a0);
  S1 = toomcook3square(a2+a1+a0);
  S2 = toomcook3square(a2-a1+a0);
  S3 = toomcook3(a1<<1,a2);
  S4 = toomcook3square(a2);

  T1 = (S1 + S2)>>1;
  S1 = S1 - T1 - S3;
  S2 = T1 - S4 -S0;


  S1 = S1<<(1*m);
  S2 = S2<<(2*m);
  S3 = S3<<(3*m);
  S4 = S4<<(4*m);

  ret = S0 + S1 + S2 + S3 + S4;
  ret = sign *ret;

  return ret;
}

define toomcook4(a,b)
{

  local  a0 a1 a2 a3 b0 b1 b2 b3 b4 ret tmp tmp2 tmp3 sign;
  local  m alen blen mask;
  local w1, w2, w3, w4, w5, w6, w7;

  if(!isint(a) || !isint(b))
    return newerror("toomcook4(a,b): a and/or b is not integer");

  alen = digits(a,2);
  blen = digits(b,2);

  sign = sgn(a) * sgn(b);

  if(sign == 0) return 0;

  m = min(alen//4,blen//4);
  mask = ~-(1<<m);

  if(isdefined("test8900")){
    if(m < 100) return toomcook3(a,b);
  }
  else{
    if(m < 256*3072) return toomcook3(a,b);
  }

  a = abs(a);
  b = abs(b);


  a0 = a & mask;
  a1 = (a>>m) & mask;
  a2 = (a>>(2*m)) & mask;
  a3 = (a>>(3*m));

  b0 =  b         & mask;
  b1 = (b>>m)     & mask;
  b2 = (b>>(2*m)) & mask;
  b3 = (b>>(3*m));

  /*
    Bodrato / Zanoni
  */

  w3 = a3 + (a1 + (a2 + a0));
  w7 = b3 + (b1 + (b2 + b0));

  w4 = -a3 + (-a1 + (a2 + a0));
  w5 = -b3 + (-b1 + (b2 + b0));

  w3 = toomcook4(w3, w7);
  w4 = toomcook4(w4, w5);

  w5 = a3 + ((a1<<2) + ((a2<<1) + (a0<<3)));
  w2 = b3 + ((b1<<2) + ((b2<<1) + (b0<<3)));

  w6 = -a3 + (-(a1<<2) + ((a2<<1) + (a0<<3)));
  w7 = -b3 + (-(b1<<2) + ((b2<<1) + (b0<<3)));

  w5 = toomcook4(w5, w2);
  w6 = toomcook4(w6, w7);


  w2 = (a3<<3) + ((a1<<1) + ((a2<<2) + a0));
  w7 = (b3<<3) + ((b1<<1) + ((b2<<2) + b0));


  w2 = toomcook4(w2, w7);

  w1 = toomcook4(a3, b3);
  w7 = toomcook4(a0, b0);

  w2 = w2 + w5;
  w6 = w5 - w6;
  w4 = w3 - w4;
  w5 = w5 - w1;
  w5 -= w7 << 6;
  w4 = w4>>1;
  w3 = w3 - w4;
  w5 = w5<<1;
  w5 = w5 - w6;
  w2 -= w3 * 65;
  w3 = w3 - w7;
  w3 = w3 - w1;
  w2 += w3 * 45;
  w5 -= w3<<3;
  w5 = w5//24;
  w6 =  w6 - w2;
  w2 -= w4<<4;
  w2 = w2//18;
  w3 = w3 - w5;
  w4 = w4 - w2;
  w6 += w2 * 30;
  w6 = w6//60;
  w2 = w2 - w6;


  ret = w7 + (w6<<m) + (w5<<(2*m)) + (w4<<(3*m))+ (w3<<(4*m))+
        (w2<<(5*m))+ (w1<<(6*m));

  ret = sign *ret;

  return ret;
}

define toomcook4square(a){
  local  a0 a1 a2 a3 ret S0 S1 S2 S3 S4 S5 S6 S7 tmp tmp2 tmp3;
  local  sign m alen mask;
  local T0 T1 T2 T3 T4 T5 T6 T7 T8;

  if(!isint(a) )return newerror("toomcook3square(a): a is not integer");

  alen = digits(a,2);

  sign = sgn(a) * sgn(a);
  /* sgn(x) returns 0 if x = 0 */
  if(sign == 0) return 0;

  m = (alen)//4;
  mask = ~-( 1 << m );

  /*
    cut-off at about 2 mio. dec. digits
    TODO: check!
  */

  if(isdefined("test8900")){
    if(m < 100) return toomcook3square(a);
  }
  else{
    if(m < 512*3072) return toomcook3square(a);
  }

  a = abs(a);

  a0 = a          & mask;
  a1 = (a>>m)     & mask;
  a2 = (a>>(2*m)) & mask;
  a3 = (a>>(3*m)) ;

  /*
    Bodrato / Zanoni
  */

  S1 = toomcook4square(a0);
  S2 = toomcook4(a0<<1,a1);
  S3 = toomcook4((a0 + a1 - a2 - a3 ) , (a0 - a1 - a2 + a3 ));
  S4 = toomcook4square(a0 + a1 + a2 + a3 );
  S5 = toomcook4( (a0 - a2 )<<1 , (a1 - a3 ));
  S6 = toomcook4(a3<<1 , a2);
  S7 = toomcook4square(a3);

  T1 = S3 + S4;
  T2 = (T1 + S5 )>>1;
  T3 = S2 + S6;
  T4 = T2 - T3;
  T5 = T3 - S5;
  T6 = T4 - S3;
  T7 = T4 - S1;
  T8 = T6 - S7;

  ret =   (S7<<(6*m)) + (S6<<(5*m)) + (T7<<(4*m))
        + (T5<<(3*m)) + (T8<<(2*m)) + (S2<<(1*m))  + S1;

  ret = sign *ret;

  return ret;
}

/*
 * TODO: Implement the asymmetric variations
 */

/*
 * produce_long_random_number(n) returns large pseudo-random numbers.
 * Really large numbers, e.g.:
 *     produce_long_random_number(16)
 * is ca 4,128,561 bits (ca 1,242,821 dec. digits) large. Exact length is not
 * pre-determinable because of the chaotic output of the function random().
 */
define __CZ__produce_long_random_number(n)
{
  local ret k;
  ret = 1;
  if(!isint(n) || n<1)
    return newerror("__CZ__produce_long_random_number(n): "
                    "n is not an integer >=1");
  for(k=0;k<n;k++){
    ret += random();
    ret  = toomcook4square(ret);
  }
  return ret;
}


/*
 * restore internal function from resource debugging
 * report important interface functions
 */
config("resource_debug", resource_debug_level),;
if (config("resource_debug") & 3) {
    print "toomcook3(a,b)";
    print "toomcook3square(a)";
    print "toomcook4(a,b)";
    print "toomcook4square(a)";
}