int sg_big_float_floor(sg_big_float_t* dst, const sg_big_float_t* src)
{
if (!dst || !src)
return -1;
mpf_floor(dst->mpf, src->mpf);
return 0;
}
/**
* rasqal_xsd_decimal_round:
* @result: result variable
* @a: argment decimal
*
* Return the number with no fractional part closes to argument for an XSD Decimal
*
* Return value: non-0 on failure
**/
int
rasqal_xsd_decimal_round(rasqal_xsd_decimal* result, rasqal_xsd_decimal* a)
{
int rc = 0;
#ifdef RASQAL_DECIMAL_GMP
mpf_t b;
mpf_t c;
#endif
rasqal_xsd_decimal_clear_string(result);
#if defined(RASQAL_DECIMAL_C99) || defined(RASQAL_DECIMAL_NONE)
result->raw = round(a->raw);
#endif
#ifdef RASQAL_DECIMAL_MPFR
mpfr_round(result->raw, a->raw);
#endif
#ifdef RASQAL_DECIMAL_GMP
/* GMP has no mpf_round so use result := floor(a + 0.5) */
mpf_init2(b, a->precision_bits);
mpf_init2(c, a->precision_bits);
mpf_set_d(b, 0.5);
mpf_add(c, a->raw, b);
mpf_floor(result->raw, c);
mpf_clear(b);
mpf_clear(c);
#endif
return rc;
}
/* ceil function: floor(a) + 1 */
int mpf_ceil(mp_float * a, mp_float * b)
{
int err;
if ((err = mpf_floor(a, b)) != MP_OKAY) {
return err;
}
if ((err = mpf_add_d(b, 1, b)) != MP_OKAY) {
return err;
}
return MP_OKAY;
}
void my_out_str_raw(FILE *fp, unsigned long digits, mpf_t f, unsigned long offset)
{
unsigned long d;
if (digits <= LINE_SIZE*NUM_BLOCKS) {
unsigned long cursor = offset % LINE_SIZE;
for (d = 0; d < digits; ) {
mpf_set_prec_raw(f, (int)((digits-d)*BITS_PER_DIGIT+1));
mpf_mul_ui(f, f, UNIT_MOD);
unsigned long i = mpf_get_ui(f);
mpf_sub_ui(f, f, i);
utoa(i, UNIT_SIZE);
*out_ptr++ = ' ';
d += UNIT_SIZE;
cursor += UNIT_SIZE;
if (cursor == LINE_SIZE) {
cursor = 0;
*out_ptr++ = ':';
*out_ptr++ = ' ';
utoa(offset + d, 0);
*out_ptr++ = '\n';
if ((offset + d) % (LINE_SIZE*10) == 0)
flush_out(fp);
}
}
} else {
mpf_t block, mod;
unsigned long num_units = (digits + UNIT_SIZE-1)/UNIT_SIZE;
unsigned long block_size = (num_units + NUM_BLOCKS-1)/NUM_BLOCKS*UNIT_SIZE;
mpf_set_default_prec((int)(block_size*BITS_PER_DIGIT+1));
mpf_init(block);
mpf_init_set_ui(mod, 10);
mpf_pow_ui(mod, mod, block_size);
for (d = 0; d < digits; d += block_size) {
unsigned long size = block_size < digits - d ? block_size : digits - d;
mpf_set_prec_raw(block, (int)(size*BITS_PER_DIGIT+1));
mpf_set(block, f);
my_out_str_raw(fp, size, block, offset+d);
if (block_size < digits - d) {
mpf_set_prec_raw(f, (int)((digits-d)*BITS_PER_DIGIT+1));
mpf_mul(f, f, mod);
mpf_floor(trunk, f);
mpf_sub(f, f, trunk);
}
}
mpf_clear(block);
mpf_clear(mod);
}
}
/**
* rasqal_xsd_decimal_floor:
* @result: result variable
* @a: argment decimal
*
* Return the number with no fractional part closes to argument for an XSD Decimal
*
* Return value: non-0 on failure
**/
int
rasqal_xsd_decimal_floor(rasqal_xsd_decimal* result, rasqal_xsd_decimal* a)
{
int rc = 0;
rasqal_xsd_decimal_clear_string(result);
#if defined(RASQAL_DECIMAL_C99) || defined(RASQAL_DECIMAL_NONE)
result->raw = floor(a->raw);
#endif
#ifdef RASQAL_DECIMAL_MPFR
mpfr_floor(result->raw, a->raw);
#endif
#ifdef RASQAL_DECIMAL_GMP
mpf_floor(result->raw, a->raw);
#endif
return rc;
}
void
mpc_mod (mpc_t *rop, mpc_t op1, mpc_t op2)
{
/* I am 90% sure that this doesn't work. However, it works for
* integers, so I'll put off fixing it for a little while.
*/
mpf_t hold_op1;
mpf_t hold_op2;
mpf_t hold_res;
unsigned int prec;
mpf_init (hold_op1);
mpf_init (hold_op2);
mpf_init (hold_res);
mpf_set_z (hold_op1, op1.object);
mpf_set_z (hold_op2, op2.object);
// Get the largest precision.
prec = (op1.precision > op2.precision) ? op1.precision : op2.precision;
// Set the scalar values
while (op1.precision-- > 0)
mpf_div_ui (hold_op1, hold_op1, 10);
while (op2.precision-- > 0)
mpf_div_ui (hold_op2, hold_op2, 10);
// Get the value
mpf_div (hold_res, hold_op1, hold_op2);
mpf_floor (hold_res, hold_res);
mpf_mul (hold_res, hold_res, hold_op2);
mpf_sub (hold_res, hold_op1, hold_res);
for (rop->precision = prec; prec > 0; prec--)
mpf_mul_ui (hold_res, hold_res, 10);
mpz_set_f (rop->object, hold_res);
}
//Le but de la fonction est de calculer le développement en fractions continue jusqu'à un certain rang de racine carrée de kN et de stocker les couples (A_n-1,Q_n) comme décrit dans la section (à venir)
cfrac expand(const mpz_t N, const long long unsigned int rang, const mpz_t k)
{
cfrac res; //Contient l'ensemble des A_n-1 et l'ensemble Q_n
mpz_inits(res.N, res.k, res.g, NULL);
//Initialisation des variables
mpz_t* A = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Le tableau contenant les A_n-1
mpz_t* Q = (mpz_t*)malloc((rang+2)*sizeof(mpz_t)); //Le tableau contenant les Q_n
mpz_t* P = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Éléments reliés au Q_n
mpz_t* r = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Interviennent dans le calcul des A_n-1 & Q_n
mpz_t* q = (mpz_t*)malloc(rang*sizeof(mpz_t)); //Idem
mpz_t g, tempz; //Idem, tempz = variable à tout faire
mpf_t sqrtkN, tempf, tempf2; //sqrtkN = sqrt(k*N), tempf = variable à tout faire
//Valeurs d'initialisation de la boucle
mpz_inits(g, A[0], Q[0], r[0], tempz, NULL);
mpf_inits(tempf, sqrtkN, tempf2, NULL);
//Initialisation des différentes valeurs "indépendantes"
mpz_set(tempz, N);
mpz_mul(tempz, tempz, k);
mpf_set_z(sqrtkN, tempz);
mpf_sqrt(sqrtkN, sqrtkN);
mpf_floor(tempf, sqrtkN);
mpz_set_f(g, tempf); //g = [sqrt(kN)]
mpz_set(Q[0], k);
mpz_mul(Q[0], Q[0], N); //Q_-1 = kN = Q[0]
mpz_set(r[0], g); //r_-1 = r[0]
mpz_set_ui(A[0], 1); //A_-1 = A[0]
//Calcul de P_0 & Q_0
mpz_init_set_ui(Q[1], 1); //Q_0 = Q[1]
mpz_init_set_ui(P[0], 0); //P_0 = P[0]
for(long long int i = 0; i < rang; i++)
{
switch(i)
{
case 0:
//Calcul de q_0
mpz_init_set(q[0], g); //q_0 = [(sqrt(kN) + P_0)/Q_0] avec P_0 = 0 et Q_0 = 1
//Calcul de A_0
mpz_init_set(A[1],A[0]);
mpz_mul(A[1], A[1], q[0]); //A_0 = q_0*A_-1
mpz_mod(A[1], A[1], N); //On réduit mod N
//Calcul de r_0
mpz_init_set_ui(r[1], 0); //r_0 = P_0 + g - q_0.Q_0 = 0 + g - g.1 = 0
//Calcul de P_1
mpz_init_set(P[1], g); //P_1 = g - r_0 = g - 0 = g
//Calcul de Q_1 = Q[2]
mpz_init_set(Q[2], r[1]);
mpz_sub(Q[2], Q[2], r[0]);
mpz_mul(Q[2], Q[2], q[0]);
mpz_add(Q[2], Q[2], Q[0]);
break;
default:
//Calcul q_i
mpz_init(q[i]);
mpf_set_z(tempf, P[i]);
mpf_set_z(tempf2, Q[i+1]);
mpf_add(tempf, tempf, sqrtkN); //sqrt(kN) + P_i
mpf_div(tempf, tempf, tempf2);
mpf_floor(tempf, tempf); //floor((sqrt(kN) + P_i)/Q_i)
mpz_set_f(q[i], tempf);
//Calcul de r_n = r[n+1]
mpz_init(r[i+1]);
mpz_submul(r[i+1], q[i], Q[i+1]);
mpz_add(r[i+1], r[i+1], P[i]);
mpz_add(r[i+1], r[i+1], g);
//Calcul de A_n = A[n+1]
mpz_init_set(A[i+1],A[i]);
mpz_mul(A[i+1], A[i+1], q[i]); //A_i-1*q_i
mpz_add(A[i+1], A[i+1], A[i-1]); //A_i-1*q_i + A_i-2
mpz_mod(A[i+1], A[i+1], N); //réduction modulo N
//Calcul P_n+1
mpz_init_set(P[i+1], g);
mpz_sub(P[i+1], P[i+1], r[i+1]); //P[n+1] = g - r_n = g - r[n+1]
//Calcul Q_n+1 = Q[n+2]
mpz_init_set(Q[i+2], r[i+1]);
mpz_sub(Q[i+2], Q[i+2], r[i]); //(r_n - r_n-1)
mpz_mul(Q[i+2], Q[i+2], q[i]); //q_n(r_n - r_n-1)
mpz_add(Q[i+2], Q[i+2], Q[i]); //Q_n-1 + q_n(r_n - r_n-1)
break;
}
}
//Test de routine pour voir si le développement de la fraction continue s'est bien passé
mpz_t tempsqrt;
mpz_init(tempsqrt);
mpz_set(tempsqrt, k);
mpz_mul(tempsqrt, tempsqrt, N);
mpz_sqrt(tempsqrt, tempsqrt);
mpz_mul_ui(tempsqrt, tempsqrt, 2);
for(int i = 1; i < rang; i++) //Éviter de commencer à i = 0 puisque cela représente Q_-1 qui n'intervient uniquement dans l'algo et non dans le développement en fraction continue
{
if(mpz_cmp(Q[i], tempsqrt) >= 0) //Si Q_n >= 2sqrt(kN)
{
res.rang = 0;
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
}
//Assignation des tableaux dans le résultat
res.A = A;
res.Q = Q;
res.r = r;
res.q = q;
res.P = P;
mpz_set(res.N, N);
mpz_set(res.k, k);
res.rang = rang;
mpz_set(res.g, g);
//Libération de mémoire
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
void series(bool const & abortTask, mpf_t & rop, unsigned long m,
mpz_t * const & tmpI, mpf_t * const & tmpF,
mpz_t const & sixteen, mpz_t const & digit, mpf_t const & epsilon)
{
// temporary local variables
mpf_t & tmp1 = tmpF[0];
mpf_t & t = tmpF[1];
mpz_t & tmp2 = tmpI[0];
mpz_t & k = tmpI[1];
mpz_t & p = tmpI[2];
mpz_t & ak = tmpI[3];
mpf_set_ui(rop, 0);
mpz_set_ui(k, 0);
while (mpz_cmp(k, digit) < 0) // k < digit
{
// p = id - k;
mpz_sub(p, digit, k);
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = expm (p, ak);
mpz_powm(tmp2, sixteen, p, ak);
mpf_set_z(t, tmp2);
// s = s + t / ak;
mpf_set_z(tmp1, ak);
mpf_div(tmp1, t, tmp1);
mpf_add(rop, rop, tmp1);
// s = s - (int) s;
mpf_floor(tmp1, rop);
mpf_sub(rop, rop, tmp1);
// k++
mpz_add_ui(k, k, 1);
if (abortTask)
return;
}
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = pow (16., (double) (id - k)) / ak;
mpf_set_z(tmp1, ak);
mpf_ui_div(t, 1, tmp1);
while (mpf_cmp(t, epsilon) >= 0) // t >= epsilon
{
// s = s + t;
mpf_add(rop, rop, t);
// s = s - (int) s;
mpf_floor(tmp1, rop);
mpf_sub(rop, rop, tmp1);
// k++
mpz_add_ui(k, k, 1);
// p = id - k;
mpz_sub(p, digit, k);
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = pow (16., (double) (id - k)) / ak;
mpz_pow_ui(tmp2, sixteen, mpz_get_ui(p));
mpz_mul(tmp2, tmp2, ak);
mpf_set_z(t, tmp2);
mpf_ui_div(t, 1, t);
if (abortTask)
return;
}
}
bool bbp_pi(bool const & abortTask,
std::string const & digitIndex,
uint32_t const digitStep,
std::string & piSequence)
{
unsigned long const mantissa_bits = 132;
unsigned long const count_offset = 7;
// settings above gives 32 hexadecimal digits
unsigned long count = static_cast<unsigned long>(
floor(log10(pow(2.0, static_cast<double>(mantissa_bits)))));
count -= count_offset;
// starting digit
mpz_t digit;
mpz_init(digit);
if (mpz_set_str(digit, digitIndex.c_str(), 10) < 0)
return false;
mpz_sub_ui(digit, digit, 1); // subtract the 3 digit
mpz_add_ui(digit, digit, digitStep);
mpz_t tmpI[TEMPORARY_INTEGERS];
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_init(tmpI[i]);
mpf_t tmpF[TEMPORARY_FLOATS];
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_init2(tmpF[i], mantissa_bits);
// determine epsilon based on the number of digits required
mpf_t epsilon;
mpf_init2(epsilon, mantissa_bits);
mpf_set_ui(epsilon, 10);
mpf_pow_ui(epsilon, epsilon, count + count_offset);
mpf_ui_div(epsilon, 1, epsilon);
// integer constant
mpz_t sixteen;
mpz_init(sixteen);
mpz_set_ui(sixteen, 16);
// determine the series
mpf_t s1, s2, s3, s4;
mpf_init2(s1, mantissa_bits);
mpf_init2(s2, mantissa_bits);
mpf_init2(s3, mantissa_bits);
mpf_init2(s4, mantissa_bits);
series(abortTask, s1, 1, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s2, 4, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s3, 5, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s4, 6, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
// pid = 4. * s1 - 2. * s2 - s3 - s4;
mpf_mul_ui(s1, s1, 4);
mpf_mul_ui(s2, s2, 2);
mpf_t result;
mpf_init2(result, mantissa_bits);
mpf_sub(result, s1, s2);
mpf_sub(result, result, s3);
mpf_sub(result, result, s4);
// pid = pid - (int) pid + 1.;
mpf_t & tmp1 = tmpF[0];
mpf_floor(tmp1, result);
mpf_sub(result, result, tmp1);
mpf_add_ui(result, result, 1);
mpf_abs(result, result);
// output the result
char resultStr[256];
mp_exp_t exponent;
mpf_get_str(resultStr, &exponent, 16, 254, result);
resultStr[count + 1] = '\0'; // cut off any erroneous bits
piSequence.assign(&resultStr[1]);
// cleanup
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_clear(tmpI[i]);
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_clear(tmpF[i]);
mpz_clear(digit);
mpf_clear(epsilon);
mpz_clear(sixteen);
mpf_clear(s1);
mpf_clear(s2);
mpf_clear(s3);
mpf_clear(s4);
mpf_clear(result);
return true;
}
int
aks (mpz_t n)
{
mpz_t r;
mpz_t a;
mpz_t max_a;
mpz_t gcd_rslt;
mpz_t totient_r;
mpf_t ftotient_r;
mpf_t sqrt_rslt;
mpf_t sqrt_rslt2;
mpf_t temp;
mpf_t temp2;
sli_t logn;
/* For the sake of maple kernel */
int argc = 0;
char **argv;
char err[2048];
mpz_init (r);
mpz_init (a);
mpz_init (max_a);
mpz_init (gcd_rslt);
mpz_init (totient_r);
mpf_init (ftotient_r);
mpf_init (sqrt_rslt);
mpf_init (sqrt_rslt2);
mpf_init (temp);
mpf_init (temp2);
/* 1. If (n = a^k for a in N and b > 1) output COMPOSITE */
if (mpz_perfect_power_p (n) != 0)
{
printf ("Step 1 detected composite\n");
return FALSE;
}
/* 2. Find the smallest r such that or(n) > 4(log n)^2 */
find_smallest_r (r, n);
gmp_printf ("good r seems to be %Zd\n", r);
/* 3. If 1 < gcd(a, n) < n for some a <= r, output COMPOSITE */
/* for (a = 1; a <= r; a++) {
* gcd_rslt = gcd(a, n);
* if (gcd_rslt > 1 && gcd_rslt < n) {
* return FALSE;
* }
* }
*/
for (mpz_set_ui (a, 1);
mpz_cmp (a, r) < 0 || mpz_cmp (a, r) == 0; mpz_add_ui (a, a, 1))
{
mpz_gcd (gcd_rslt, a, n);
if (mpz_cmp_ui (gcd_rslt, 1) > 0 && mpz_cmp (gcd_rslt, n) < 0)
{
printf ("Step 3 detected composite\n");
return FALSE;
}
}
/* 4. If n <= r, output PRIME */
if (mpz_cmp (n, r) < 0 || mpz_cmp (n, r) == 0)
{
printf ("Step 4 detected prime\n");
return TRUE;
}
/* 5. For a = 1 to floor(2*sqrt(totient(r))*(log n)
* if ( (X+a)^n != X^n + a (mod X^r-1, n) ), output COMPOSITE
*
* Choices of implementation to evaluate the polynomial equality:
* (1) Implement powermodreduce on polynomial ourselves (tough manly way)
* (2) Use MAPLE (not so manly, but less painful)
*/
/* Compute totient(r), since r is prime, this is simply r-1 */
mpz_sub_ui (totient_r, r, 1);
/* Compute log n (ceilinged) */
mpz_logbase2cl (&logn, n);
/* Compute sqrt(totient(r)) */
mpf_set_z (ftotient_r, totient_r);
mpf_sqrt (sqrt_rslt, ftotient_r);
/* Compute 2*sqrt(totient(r)) */
mpf_mul_ui (sqrt_rslt2, sqrt_rslt, 2);
/* Compute 2*sqrt(totient(r))*(log n) */
mpf_set (temp, sqrt_rslt2);
mpf_set_si (temp2, logn);
mpf_mul (temp, temp, temp2);
/* Finally, compute max_a, after lots of singing and dancing */
mpf_floor (temp, temp);
mpz_set_f (max_a, temp);
gmp_printf ("max_a = %Zd\n", max_a);
/* Now evaluate the polynomial equality with the help of maple kernel */
/* Set up maple kernel incantations */
MKernelVector kv;
MCallBackVectorDesc cb = { textCallBack,
0, /* errorCallBack not used */
0, /* statusCallBack not used */
0, /* readLineCallBack not used */
0, /* redirectCallBack not used */
0, /* streamCallBack not used */
0, /* queryInterrupt not used */
0 /* callBackCallBack not used */
};
/* Initialize Maple */
if ((kv = StartMaple (argc, argv, &cb, NULL, NULL, err)) == NULL)
{
printf ("Could not start Maple, %s\n", err);
exit (666);
}
/* Here comes the complexity and bottleneck */
/* for (a = 1; a <= max_a; a++) {
* if (!poly_eq_holds(kv, a, n, r)) {
* return FALSE;
* }
* }
*/
/* Make max_a only up to 5 */
mpz_set_ui (max_a, 5);
for (mpz_set_ui (a, 1);
mpz_cmp (a, max_a) < 0 || mpz_cmp (a, max_a) == 0;
mpz_add_ui (a, a, 1))
{
if (!poly_eq_holds (kv, a, n, r))
{
printf ("Step 5 detected composite\n");
return FALSE;
}
}
/* 6. Output PRIME */
printf ("Step 6 detected prime\n");
return TRUE;
}