/*
* compute X = (a * X + c) MOD m where c = a
*/
void m_apm_get_random(M_APM mrnd)
{
if (M_firsttime2) /* use the system time as the initial seed value */
{
M_firsttime2 = FALSE;
M_rnd_aa = m_apm_init();
M_rnd_XX = m_apm_init();
M_rnd_mm = m_apm_init();
M_rtmp0 = m_apm_init();
M_rtmp1 = m_apm_init();
/* set the multiplier M_rnd_aa and M_rnd_mm */
m_apm_set_string(M_rnd_aa, "716805947629621");
m_apm_set_string(M_rnd_mm, "1.0E15");
M_get_rnd_seed(M_rnd_XX);
}
m_apm_multiply(M_rtmp0, M_rnd_XX, M_rnd_aa);
m_apm_add(M_rtmp1, M_rtmp0, M_rnd_aa);
m_apm_integer_div_rem(M_rtmp0, M_rnd_XX, M_rtmp1, M_rnd_mm);
m_apm_copy(mrnd, M_rnd_XX);
mrnd->m_apm_exponent -= 15;
}
/*
* From Knuth, The Art of Computer Programming:
*
* To compute GCD(u,v)
*
* A1:
* if (v == 0) return (u)
* A2:
* t = u mod v
* u = v
* v = t
* goto A1
*/
void m_apm_gcd_traditional(M_APM r, M_APM u, M_APM v)
{
M_APM tmpD, tmpN, tmpU, tmpV;
tmpD = M_get_stack_var();
tmpN = M_get_stack_var();
tmpU = M_get_stack_var();
tmpV = M_get_stack_var();
m_apm_absolute_value(tmpU, u);
m_apm_absolute_value(tmpV, v);
while (TRUE)
{
if (tmpV->m_apm_sign == 0)
break;
m_apm_integer_div_rem(tmpD, tmpN, tmpU, tmpV);
m_apm_copy(tmpU, tmpV);
m_apm_copy(tmpV, tmpN);
}
m_apm_copy(r, tmpU);
M_restore_stack(4);
}
static int Bidiv(lua_State *L) /** idiv(x,y) */
{
M_APM a=Bget(L,1);
M_APM b=Bget(L,2);
M_APM q=Bnew(L);
M_APM r=Bnew(L);
m_apm_integer_div_rem(q,r,a,b);
return 2;
}
/*
* functions returns TRUE if the M_APM input number is prime
* FALSE if it is not
*/
int is_number_prime(M_APM input)
{
int ii, ret, index;
char sbuf[32];
/*
* for reference:
*
* table size of 2 to filter multiples of 2 and 3
* table size of 8 to filter multiples of 2, 3 and 5
* table size of 480 to filter multiples of 2,3,5,7, and 11
*
* this increment table will filter out all numbers
* that are multiples of 2,3,5 and 7.
*/
static char incr_table[48] = {
2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2,
6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6,
2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10 };
/*
* since the real algorithm starts at 11 (to syncronize
* with the increment table), we will cheat for numbers < 10.
*/
if (m_apm_compare(input, MM_Ten) <= 0)
{
m_apm_to_integer_string(sbuf, input);
ii = atoi(sbuf);
if (ii == 2 || ii == 3 || ii == 5 || ii == 7)
return(TRUE);
else
return(FALSE);
}
ret = FALSE;
index = 0;
/*
* see if the input number is a
* multiple of 3, 5, or 7.
*/
m_apm_integer_div_rem(M_quot, M_rem, input, MM_Three);
if (m_apm_sign(M_rem) == 0) /* remainder == 0 */
return(ret);
m_apm_integer_div_rem(M_quot, M_rem, input, MM_Five);
if (m_apm_sign(M_rem) == 0)
return(ret);
m_apm_set_long(M_digit, 7L);
m_apm_integer_div_rem(M_quot, M_rem, input, M_digit);
if (m_apm_sign(M_rem) == 0)
return(ret);
ii = m_apm_exponent(input) + 16;
m_apm_sqrt(M_tmp1, ii, input);
m_apm_add(M_limit, MM_Two, M_tmp1);
m_apm_set_long(M_digit, 11L); /* now start at '11' to check */
while (TRUE)
{
if (m_apm_compare(M_digit, M_limit) >= 0)
{
ret = TRUE;
break;
}
m_apm_integer_div_rem(M_quot, M_rem, input, M_digit);
if (m_apm_sign(M_rem) == 0) /* remainder == 0 */
break;
m_apm_set_long(M_tmp1, (long)incr_table[index]);
m_apm_add(M_tmp0, M_digit, M_tmp1);
m_apm_copy(M_digit, M_tmp0);
if (++index == 48)
index = 0;
}
return(ret);
}
void m_apm_integer_div_rem_mt(M_APM qq, M_APM rr, M_APM aa, M_APM bb)
{
m_apm_enter();
m_apm_integer_div_rem(qq,rr,aa,bb);
m_apm_leave();
}
