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src/ltm/mp_prime_strong_lucas_selfridge.c  view on Meta::CPAN

   if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY)          goto LBL_LS_ERR;
   /* We must now compute U_d and V_d. Since d is odd, the accumulated
      values U and V are initialized to U_1 and V_1 (if the target
      index were even, U and V would be initialized instead to U_0=0
      and V_0=2). The values of U_2m and V_2m are also initialized to
      U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
      U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
      (1, 2, 3, ...) of t are on (the zero bit having been accounted
      for in the initialization of U and V), these values are then
      combined with the previous totals for U and V, using the
      composition formulas for addition of indices. */

   mp_set(&Uz, 1uL);    /* U=U_1 */
   mp_set(&Vz, (mp_digit)P);    /* V=V_1 */
   mp_set(&U2mz, 1uL);  /* U_1 */
   mp_set(&V2mz, (mp_digit)P);  /* V_1 */

   mp_set_i32(&Qmz, Q);
   if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY)                  goto LBL_LS_ERR;
   /* Initializes calculation of Q^d */
   mp_set_i32(&Qkdz, Q);

src/ltm/mp_prime_strong_lucas_selfridge.c  view on Meta::CPAN

      goto LBL_LS_ERR;
   }

   /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
      1995/6) omits the condition V0 on p.142, but includes it on
      p. 130. The condition is NECESSARY; otherwise the test will
      return MP_NO negatives---e.g., the primes 29 and 2000029 will be
      returned as composite. */

   /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
      by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
      these are congruent to 0 mod N, then N is a prime or a strong
      Lucas pseudoprime. */

   /* Initialize 2*Q^(d*2^r) for V_2m */
   if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY)                goto LBL_LS_ERR;

   for (r = 1; r < s; r++) {
      if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY)                    goto LBL_LS_ERR;
      if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY)            goto LBL_LS_ERR;
      if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY)                 goto LBL_LS_ERR;

src/ltm/s_mp_mul_toom.c  view on Meta::CPAN

*/

/*
   This file contains code from J. Arndt's book  "Matters Computational"
   and the accompanying FXT-library with permission of the author.
*/

/*
   Setup from

     Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
     18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.

   The interpolation from above needed one temporary variable more
   than the interpolation here:

     Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
     Centro Vito Volterra Universita di Roma Tor Vergata (2006)
*/

mp_err s_mp_mul_toom(const mp_int *a, const mp_int *b, mp_int *c)

src/ltm/s_mp_sqr_toom.c  view on Meta::CPAN

/*
   This file contains code from J. Arndt's book  "Matters Computational"
   and the accompanying FXT-library with permission of the author.
*/

/* squaring using Toom-Cook 3-way algorithm */
/*
   Setup and interpolation from algorithm SQR_3 in

     Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
     18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.

*/
mp_err s_mp_sqr_toom(const mp_int *a, mp_int *b)
{
   mp_int S0, a0, a1, a2;
   int B;
   mp_err err;

   /* init temps */