#include <string.h>
#include <time.h>
#include <gmp.h>
#include "ptypes.h"
#include "gmp_main.h"
#include "primality.h"
#include "prime_iterator.h"
#include "ecpp.h"
#include "factor.h"
#define FUNC_gcd_ui 1
#include "utility.h"
static mpz_t _bgcd;
static mpz_t _bgcd2;
static mpz_t _bgcd3;
#define BGCD_PRIMES 168
#define BGCD_LASTPRIME 997
#define BGCD_NEXTPRIME 1009
#define BGCD2_PRIMES 1229
#define BGCD2_NEXTPRIME 10007
#define BGCD3_PRIMES 4203
#define BGCD3_NEXTPRIME 40009
#define NSMALLPRIMES 168
static const unsigned short sprimes[NSMALLPRIMES] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997};
#define TSTAVAL(arr, val) (arr[(val) >> 6] & (1U << (((val)>>1) & 0x1F)))
#define SETAVAL(arr, val) arr[(val) >> 6] |= 1U << (((val)>>1) & 0x1F)
void _GMP_init(void)
{
/* We should not use this random number system for crypto, so
* using this lousy seed is ok. We just would like something a
* bit different every run. Using Perl_seed(aTHX) would be better. */
unsigned long seed = time(NULL);
init_randstate(seed);
prime_iterator_global_startup();
mpz_init(_bgcd);
_GMP_pn_primorial(_bgcd, BGCD_PRIMES); /* mpz_primorial_ui(_bgcd, 1000) */
mpz_init_set_ui(_bgcd2, 0);
mpz_init_set_ui(_bgcd3, 0);
_init_factor();
}
void _GMP_destroy(void)
{
prime_iterator_global_shutdown();
clear_randstate();
mpz_clear(_bgcd);
mpz_clear(_bgcd2);
mpz_clear(_bgcd3);
destroy_ecpp_gcds();
}
static const unsigned char next_wheel[30] =
{1,7,7,7,7,7,7,11,11,11,11,13,13,17,17,17,17,19,19,23,23,23,23,29,29,29,29,29,29,1};
static const unsigned char prev_wheel[30] =
{29,29,1,1,1,1,1,1,7,7,7,7,11,11,13,13,13,13,17,17,19,19,19,19,23,23,23,23,23,23};
static const unsigned char wheel_advance[30] =
{1,6,5,4,3,2,1,4,3,2,1,2,1,4,3,2,1,2,1,4,3,2,1,6,5,4,3,2,1,2};
static const unsigned char wheel_retreat[30] =
{1,2,1,2,3,4,5,6,1,2,3,4,1,2,1,2,3,4,1,2,1,2,3,4,1,2,3,4,5,6};
/*****************************************************************************/
int primality_pretest(mpz_t n)
{
/* If less than 1009, make trial factor handle it. */
if (mpz_cmp_ui(n, BGCD_NEXTPRIME) < 0)
return _GMP_trial_factor(n, 2, BGCD_LASTPRIME) ? 0 : 2;
/* Check for tiny divisors */
if (mpz_even_p(n)) return 0;
if (sizeof(unsigned long) < 8) {
if (mpz_gcd_ui(NULL, n, 3234846615UL) != 1) return 0; /* 3-29 */
} else {
if (mpz_gcd_ui(NULL, n, 4127218095UL*3948078067UL)!=1) return 0;/* 3-53 */
if (mpz_gcd_ui(NULL, n, 4269855901UL*1673450759UL)!=1) return 0;/* 59-101 */
}
{
UV log2n = mpz_sizeinbase(n,2);
mpz_t t;
mpz_init(t);
/* Do a GCD with all primes < 1009 */
mpz_gcd(t, n, _bgcd);
if (mpz_cmp_ui(t, 1))
{ mpz_clear(t); return 0; }
/* No divisors under 1009 */
if (mpz_cmp_ui(n, BGCD_NEXTPRIME*BGCD_NEXTPRIME) < 0)
{ mpz_clear(t); return 2; }
/* If we're reasonably large, do a gcd with more primes */
if (log2n > 700) {
if (mpz_sgn(_bgcd3) == 0) {
_GMP_pn_primorial(_bgcd3, BGCD3_PRIMES);
mpz_divexact(_bgcd3, _bgcd3, _bgcd);
}
mpz_gcd(t, n, _bgcd3);
if (mpz_cmp_ui(t, 1))
{ mpz_clear(t); return 0; }
} else if (log2n > 300) {
if (mpz_sgn(_bgcd2) == 0) {
_GMP_pn_primorial(_bgcd2, BGCD2_PRIMES);
mpz_divexact(_bgcd2, _bgcd2, _bgcd);
}
mpz_gcd(t, n, _bgcd2);
if (mpz_cmp_ui(t, 1))
{ mpz_clear(t); return 0; }
}
mpz_clear(t);
/* Do more trial division if we think we should.
* According to Menezes (section 4.45) as well as Park (ISPEC 2005),
* we want to select a trial limit B such that B = E/D where E is the
* time for our primality test (one M-R test) and D is the time for
* one trial division. Example times on my machine came out to
* log2n = 840375, E= 6514005000 uS, D=1.45 uS, E/D = 0.006 * log2n
* log2n = 465618, E= 1815000000 uS, D=1.05 uS, E/D = 0.008 * log2n
* log2n = 199353, E= 287282000 uS, D=0.70 uS, E/D = 0.01 * log2n
* log2n = 99678, E= 56956000 uS, D=0.55 uS, E/D = 0.01 * log2n
* log2n = 33412, E= 4289000 uS, D=0.30 uS, E/D = 0.013 * log2n
* log2n = 13484, E= 470000 uS, D=0.21 uS, E/D = 0.012 * log2n
* Our trial division could also be further improved for large inputs.
*/
if (log2n > 16000) {
double dB = (double)log2n * (double)log2n * 0.005;
if (BITS_PER_WORD == 32 && dB > 4200000000.0) dB = 4200000000.0;
if (_GMP_trial_factor(n, BGCD3_NEXTPRIME, (UV)dB)) return 0;
} else if (log2n > 4000) {
if (_GMP_trial_factor(n, BGCD3_NEXTPRIME, 80*log2n)) return 0;
} else if (log2n > 1600) {
if (_GMP_trial_factor(n, BGCD3_NEXTPRIME, 30*log2n)) return 0;
}
}
return 1;
}
/*****************************************************************************/
/* Controls how many numbers to sieve. Little time impact. */
#define NPS_MERIT 30.0
/* Controls how many primes to use. Big time impact. */
#define NPS_DEPTH(log2n, log2log2n) \
(log2n < 100) ? 1000 : \
(BITS_PER_WORD == 32 && log2n > 9000U) ? UVCONST(2500000000) : \
(BITS_PER_WORD == 64 && log2n > 4294967294U) ? UVCONST(9300000000000000000) :\
((log2n * (log2n >> 5) * log2log2n) >> 1)
static void next_prime_with_sieve(mpz_t n) {
UV i, log2n, log2log2n, width, depth;
uint32_t* comp;
mpz_t t, base;
log2n = mpz_sizeinbase(n, 2);
for (log2log2n = 1, i = log2n; i >>= 1; ) log2log2n++;
width = (UV) (NPS_MERIT/1.4427 * (double)log2n + 0.5);
depth = NPS_DEPTH(log2n, log2log2n);
if (width & 1) width++; /* Make width even */
mpz_add_ui(n, n, mpz_even_p(n) ? 1 : 2); /* Set n to next odd */
mpz_init(t); mpz_init(base);
while (1) {
mpz_set(base, n);
comp = partial_sieve(base, width, depth); /* sieve range to depth */
for (i = 1; i <= width; i += 2) {
if (!TSTAVAL(comp, i)) {
mpz_add_ui(t, base, i); /* We found a candidate */
if (_GMP_BPSW(t)) {
mpz_set(n, t);
mpz_clear(t); mpz_clear(base);
Safefree(comp);
return;
}
}
}
Safefree(comp); /* A huge gap found, so sieve another range */
mpz_add_ui(n, n, width);
}
}
static void prev_prime_with_sieve(mpz_t n) {
UV i, j, log2n, log2log2n, width, depth;
uint32_t* comp;
mpz_t t, base;
log2n = mpz_sizeinbase(n, 2);
for (log2log2n = 1, i = log2n; i >>= 1; ) log2log2n++;
width = (UV) (NPS_MERIT/1.4427 * (double)log2n + 0.5);
depth = NPS_DEPTH(log2n, log2log2n);
mpz_sub_ui(n, n, mpz_even_p(n) ? 1 : 2); /* Set n to prev odd */
width = 64 * ((width+63)/64); /* Round up to next 64 */
mpz_init(t); mpz_init(base);
while (1) {
mpz_sub_ui(base, n, width-2);
/* gmp_printf("sieve from %Zd to %Zd width %lu\n", base, n, width); */
comp = partial_sieve(base, width, depth); /* sieve range to depth */
/* if (mpz_odd_p(base)) croak("base off after partial");
if (width & 1) croak("width is odd after partial"); */
for (j = 1; j < width; j += 2) {
i = width - j;
if (!TSTAVAL(comp, i)) {
mpz_add_ui(t, base, i); /* We found a candidate */
if (_GMP_BPSW(t)) {
mpz_set(n, t);
mpz_clear(t); mpz_clear(base);
Safefree(comp);
return;
}
}
}
Safefree(comp); /* A huge gap found, so sieve another range */
mpz_sub_ui(n, n, width);
}
}
/* Modifies argument */
void _GMP_next_prime(mpz_t n)
{
if (mpz_cmp_ui(n, 29) < 0) { /* small inputs */
UV m = mpz_get_ui(n);
m = (m < 2) ? 2 : (m < 3) ? 3 : (m < 5) ? 5 : next_wheel[m];
mpz_set_ui(n, m);
} else if (mpz_sizeinbase(n,2) > 120) {
next_prime_with_sieve(n);
} else {
UV m23 = mpz_fdiv_ui(n, 223092870UL); /* 2*3*5*7*11*13*17*19*23 */
UV m = m23 % 30;
do {
UV skip = wheel_advance[m];
mpz_add_ui(n, n, skip);
m23 += skip;
m = next_wheel[m];
} while ( !(m23% 7) || !(m23%11) || !(m23%13) || !(m23%17) ||
!(m23%19) || !(m23%23) || !_GMP_is_prob_prime(n) );
}
}
/* Modifies argument */
void _GMP_prev_prime(mpz_t n)
{
UV m, m23;
if (mpz_cmp_ui(n, 29) <= 0) { /* small inputs */
m = mpz_get_ui(n);
m = (m < 3) ? 0 : (m < 4) ? 2 : (m < 6) ? 3 : (m < 8) ? 5 : prev_wheel[m];
mpz_set_ui(n, m);
} else if (mpz_sizeinbase(n,2) > 200) {
prev_prime_with_sieve(n);
} else {
m23 = mpz_fdiv_ui(n, 223092870UL); /* 2*3*5*7*11*13*17*19*23 */
m = m23 % 30;
m23 += 223092870UL; /* No need to re-mod inside the loop */
do {
UV skip = wheel_retreat[m];
mpz_sub_ui(n, n, skip);
m23 -= skip;
m = prev_wheel[m];
} while ( !(m23% 7) || !(m23%11) || !(m23%13) || !(m23%17) ||
!(m23%19) || !(m23%23) || !_GMP_is_prob_prime(n) );
}
}
/*****************************************************************************/
#define LAST_TRIPLE_PROD \
((ULONG_MAX <= 4294967295UL) ? UVCONST(1619) : UVCONST(2642231))
#define LAST_DOUBLE_PROD \
((ULONG_MAX <= 4294967295UL) ? UVCONST(65521) : UVCONST(4294967291))
void _GMP_pn_primorial(mpz_t prim, UV n)
{
UV i = 0, al = 0, p = 2;
mpz_t* A;
if (n <= 4) { /* tiny input */
p = (n == 0) ? 1 : (n == 1) ? 2 : (n == 2) ? 6 : (n == 3) ? 30 : 210;
mpz_set_ui(prim, p);
} else if (n < 200) { /* simple linear multiply */
PRIME_ITERATOR(iter);
mpz_set_ui(prim, 1);
while (n-- > 0) {
if (n > 0) { p *= prime_iterator_next(&iter); n--; }
mpz_mul_ui(prim, prim, p);
p = prime_iterator_next(&iter);
}
prime_iterator_destroy(&iter);
} else { /* tree mult array of products of 8 UVs */
PRIME_ITERATOR(iter);
New(0, A, n, mpz_t);
while (n-- > 0) {
if (p <= LAST_TRIPLE_PROD && n > 0)
{ p *= prime_iterator_next(&iter); n--; }
if (p <= LAST_DOUBLE_PROD && n > 0)
{ p *= prime_iterator_next(&iter); n--; }
/* each array entry holds the product of 8 UVs */
if ((i & 7) == 0) mpz_init_set_ui( A[al++], p );
else mpz_mul_ui(A[al-1],A[al-1], p );
i++;
p = prime_iterator_next(&iter);
}
mpz_product(A, 0, al-1);
mpz_set(prim, A[0]);
for (i = 0; i < al; i++) mpz_clear(A[i]);
Safefree(A);
prime_iterator_destroy(&iter);
}
}
void _GMP_primorial(mpz_t prim, UV n)
{
#if (__GNU_MP_VERSION > 5) || (__GNU_MP_VERSION == 5 && __GNU_MP_VERSION_MINOR >= 1)
mpz_primorial_ui(prim, n);
#else
if (n <= 4) {
UV p = (n == 0) ? 1 : (n == 1) ? 1 : (n == 2) ? 2 : (n == 3) ? 6 : 6;
mpz_set_ui(prim, p);
} else {
mpz_t *A;
UV nprimes, i, al;
UV *primes = sieve_to_n(n, &nprimes);
/* Multiply native pairs until we overflow the native type */
while (nprimes > 1 && ULONG_MAX/primes[0] > primes[nprimes-1]) {
i = 0;
while (nprimes > i+1 && ULONG_MAX/primes[i] > primes[nprimes-1])
primes[i++] *= primes[--nprimes];
}
if (nprimes <= 8) {
/* Just multiply if there are only a few native values left */
mpz_set_ui(prim, primes[0]);
for (i = 1; i < nprimes; i++)
mpz_mul_ui(prim, prim, primes[i]);
} else {
/* Create n/4 4-way products, then use product tree */
New(0, A, nprimes/4 + 1, mpz_t);
for (i = 0, al = 0; i < nprimes; al++) {
mpz_init_set_ui(A[al], primes[i++]);
if (i < nprimes) mpz_mul_ui(A[al], A[al], primes[i++]);
if (i < nprimes) mpz_mul_ui(A[al], A[al], primes[i++]);
if (i < nprimes) mpz_mul_ui(A[al], A[al], primes[i++]);
}
mpz_product(A, 0, al-1);
mpz_set(prim, A[0]);
for (i = 0; i < al; i++) mpz_clear(A[i]);
Safefree(A);
}
Safefree(primes);
}
#endif
}
/* Luschny's version of the "Brent-Harvey" method */
void bernfrac(mpz_t num, mpz_t den, mpz_t zn)
{
UV k, j, n = mpz_get_ui(zn);
mpz_t* T;
mpz_t t;
if (n == 0) { mpz_set_ui(num, 1); mpz_set_ui(den, 1); return; }
else if (n == 1) { mpz_set_ui(num, 1); mpz_set_ui(den, 2); return; }
else if (n & 1) { mpz_set_ui(num, 0); mpz_set_ui(den, 1); return; }
n >>= 1;
New(0, T, n+1, mpz_t);
for (k = 1; k <= n; k++) mpz_init(T[k]);
mpz_set_ui(T[1], 1);
mpz_init(t);
for (k = 2; k <= n; k++)
mpz_mul_ui(T[k], T[k-1], k-1);
for (k = 2; k <= n; k++) {
for (j = k; j <= n; j++) {
mpz_mul_ui(t, T[j], j-k+2);
mpz_mul_ui(T[j], T[j-1], j-k);
mpz_add(T[j], T[j], t);
}
}
mpz_mul_ui(num, T[n], n);
mpz_mul_si(num, num, (n & 1) ? 2 : -2);
mpz_set_ui(t, 1);
mpz_mul_2exp(den, t, 2*n); /* den = U = 1 << 2n */
mpz_sub_ui(t, den, 1); /* t = U-1 */
mpz_mul(den, den, t); /* den = U*(U-1) */
mpz_gcd(t, num, den);
mpz_divexact(num, num, t);
mpz_divexact(den, den, t);
mpz_clear(t);
for (k = 1; k <= n; k++) mpz_clear(T[k]);
Safefree(T);
}
static void _harmonic(mpz_t a, mpz_t b, mpz_t t) {
mpz_sub(t, b, a);
if (mpz_cmp_ui(t, 1) == 0) {
mpz_set(b, a);
mpz_set_ui(a, 1);
} else {
mpz_t q, r;
mpz_add(t, a, b);
mpz_tdiv_q_2exp(t, t, 1);
mpz_init_set(q, t); mpz_init_set(r, t);
_harmonic(a, q, t);
_harmonic(r, b, t);
mpz_mul(a, a, b);
mpz_mul(t, q, r);
mpz_add(a, a, t);
mpz_mul(b, b, q);
mpz_clear(q); mpz_clear(r);
}
}
void harmfrac(mpz_t num, mpz_t den, mpz_t zn)
{
mpz_t t;
mpz_init(t);
mpz_add_ui(den, zn, 1);
mpz_set_ui(num, 1);
_harmonic(num, den, t);
mpz_gcd(t, num, den);
mpz_divexact(num, num, t);
mpz_divexact(den, den, t);
mpz_clear(t);
}
char* harmreal(mpz_t zn, unsigned long prec) {
char* out;
mpz_t num, den;
mpf_t fnum, fden, res;
unsigned long numsize, densize;
mpz_init(num); mpz_init(den);
harmfrac(num, den, zn);
numsize = mpz_sizeinbase(num, 10);
densize = mpz_sizeinbase(den, 10);
mpf_init2(fnum, 1 + mpz_sizeinbase(num,2));
mpf_init2(fden, 1 + mpz_sizeinbase(den,2));
mpf_set_z(fnum, num); mpf_set_z(fden, den);
mpz_clear(den); mpz_clear(num);
mpf_init2(res, (unsigned long) (8+prec*3.4) );
mpf_div(res, fnum, fden);
mpf_clear(fnum); mpf_clear(fden);
New(0, out, (10+numsize-densize)+prec, char);
gmp_sprintf(out, "%.*Ff", (int)(prec), res);
mpf_clear(res);
return out;
}
void stirling(mpz_t r, unsigned long n, unsigned long m, UV type)
{
mpz_t t, t2;
unsigned long j;
if (type < 1 || type > 3) croak("stirling type must be 1, 2, or 3");
if (n == m) {
mpz_set_ui(r, 1);
} else if (n == 0 || m == 0 || m > n) {
mpz_set_ui(r,0);
} else if (m == 1) {
switch (type) {
case 1: mpz_fac_ui(r, n-1); if (!(n&1)) mpz_neg(r, r); break;
case 2: mpz_set_ui(r, 1); break;
case 3:
default: mpz_fac_ui(r, n); break;
}
} else {
mpz_init(t); mpz_init(t2);
mpz_set_ui(r,0);
if (type == 3) {
mpz_bin_uiui(t, n-1, m-1);
mpz_fac_ui(t2, n);
mpz_mul(r, t, t2);
mpz_fac_ui(t2, m);
mpz_divexact(r, r, t2);
} else if (type == 2) {
for (j = 1; j <= m; j++) {
mpz_bin_uiui(t, m, j);
mpz_ui_pow_ui(t2, j, n);
mpz_mul(t, t, t2);
if ((m-j) & 1) mpz_sub(r, r, t);
else mpz_add(r, r, t);
}
mpz_fac_ui(t, m);
mpz_divexact(r, r, t);
} else {
for (j = 1; j <= n-m; j++) {
mpz_bin_uiui(t, n+j-1, n+j-m);
mpz_bin_uiui(t2, n+n-m, n-j-m);
mpz_mul(t, t, t2);
stirling(t2, n+j-m, j, 2);
mpz_mul(t, t, t2);
if (j & 1) mpz_sub(r, r, t);
else mpz_add(r, r, t);
}
}
mpz_clear(t2); mpz_clear(t);
}
}
/* Goetgheluck method. Also thanks to Peter Luschny */
void binomial(mpz_t r, UV n, UV k)
{
UV fi, nk, sqrtn, piN, prime, i, j;
UV* primes;
mpz_t* mprimes;
if (k > n) { mpz_set_ui(r, 0); return; }
if (k == 0 || k == n) { mpz_set_ui(r, 1); return; }
if (k > n/2) k = n-k;
sqrtn = (UV) (sqrt((double)n));
fi = 0;
nk = n-k;
primes = sieve_to_n(n, &piN);
#define PUSHP(p) \
do { \
if ((j++ % 8) == 0) mpz_init_set_ui(mprimes[fi++], p); \
else mpz_mul_ui(mprimes[fi-1], mprimes[fi-1], p); \
} while (0)
New(0, mprimes, (piN+7)/8, mpz_t);
for (i = 0, j = 0; i < piN; i++) {
prime = primes[i];
if (prime > nk) {
PUSHP(prime);
} else if (prime > n/2) {
/* nothing */
} else if (prime > sqrtn) {
if (n % prime < k % prime)
PUSHP(prime);
} else {
UV N = n, K = k, p = 1, s = 0;
while (N > 0) {
s = (N % prime) < (K % prime + s) ? 1 : 0;
if (s == 1) p *= prime;
N /= prime;
K /= prime;
}
if (p > 1)
PUSHP(p);
}
}
Safefree(primes);
mpz_product(mprimes, 0, fi-1);
mpz_set(r, mprimes[0]);
for (i = 0; i < fi; i++)
mpz_clear(mprimes[i]);
Safefree(mprimes);
}
void _GMP_lcm_of_consecutive_integers(UV B, mpz_t m)
{
UV i, p, p_power, pmin;
mpz_t t[8];
PRIME_ITERATOR(iter);
/* Create eight sub-products to combine at the end. */
for (i = 0; i < 8; i++) mpz_init_set_ui(t[i], 1);
i = 0;
/* For each prime, multiply m by p^floor(log B / log p), which means
* raise p to the largest power e such that p^e <= B.
*/
if (B >= 2) {
p_power = 2;
while (p_power <= B/2)
p_power *= 2;
mpz_mul_ui(t[i&7], t[i&7], p_power); i++;
}
p = prime_iterator_next(&iter);
while (p <= B) {
pmin = B/p;
if (p > pmin)
break;
p_power = p*p;
while (p_power <= pmin)
p_power *= p;
mpz_mul_ui(t[i&7], t[i&7], p_power); i++;
p = prime_iterator_next(&iter);
}
while (p <= B) {
mpz_mul_ui(t[i&7], t[i&7], p); i++;
p = prime_iterator_next(&iter);
}
/* combine the eight sub-products */
for (i = 0; i < 4; i++) mpz_mul(t[i], t[2*i], t[2*i+1]);
for (i = 0; i < 2; i++) mpz_mul(t[i], t[2*i], t[2*i+1]);
mpz_mul(m, t[0], t[1]);
for (i = 0; i < 8; i++) mpz_clear(t[i]);
prime_iterator_destroy(&iter);
}
/* a=0, return power. a>1, return bool if an a-th power */
UV is_power(mpz_t n, UV a)
{
if (mpz_cmp_ui(n,3) <= 0)
return 0;
else if (a == 1)
return 1;
else if (a == 2)
return mpz_perfect_square_p(n);
else {
UV result;
mpz_t t;
mpz_init(t);
result = (a == 0) ? power_factor(n, t) : (UV)mpz_root(t, n, a);
mpz_clear(t);
return result;
}
}
void exp_mangoldt(mpz_t res, mpz_t n)
{
UV k;
mpz_set_ui(res, 1);
if (mpz_cmp_ui(n, 1) <= 0)
return;
k = mpz_scan1(n, 0);
if (k > 0) {
if (k+1 == mpz_sizeinbase(n, 2))
mpz_set_ui(res, 2);
return;
}
if (_GMP_is_prob_prime(n)) {
mpz_set(res, n);
return;
}
k = power_factor(n, res);
if (k > 1 && _GMP_is_prob_prime(res))
return;
mpz_set_ui(res, 1);
}
static void word_tile(uint32_t* source, uint32_t from, uint32_t to) {
while (from < to) {
uint32_t words = (2*from > to) ? to-from : from;
memcpy(source+from, source, sizeof(uint32_t)*words);
from += words;
}
}
static void sievep(uint32_t* comp, mpz_t start, UV p, UV len) {
UV pos = p - mpz_fdiv_ui(start,p); /* First multiple of p after start */
if (!(pos & 1)) pos += p; /* Make sure it is odd. */
for ( ; pos < len; pos += 2*p )
SETAVAL(comp, pos);
}
static void sievep_ui(uint32_t* comp, UV pos, UV p, UV len) {
if (!(pos & 1)) pos += p;
for ( ; pos < len; pos += 2*p )
SETAVAL(comp, pos);
}
uint32_t* partial_sieve(mpz_t start, UV length, UV maxprime)
{
uint32_t* comp;
UV p, wlen, pwlen;
PRIME_ITERATOR(iter);
/* mpz_init(t);
mpz_add_ui(t, start, (length & 1) ? length-1 : length-2);
gmp_printf("partial sieve start %Zd length %lu mark %Zd to %Zd\n", start, length, start, t); */
MPUassert(mpz_odd_p(start), "partial sieve given even start");
MPUassert(length > 0, "partial sieve given zero length");
mpz_sub_ui(start, start, 1);
if (length & 1) length++;
/* Allocate odds-only array in uint32_t units */
wlen = (length+63)/64;
New(0, comp, wlen, uint32_t);
p = prime_iterator_next(&iter);
/* Mark 3, 5, ... by tiling as long as we can. */
pwlen = (wlen < 3) ? wlen : 3;
memset(comp, 0x00, pwlen*sizeof(uint32_t));
while (p <= maxprime) {
sievep(comp, start, p, pwlen*64);
p = prime_iterator_next(&iter);
if (pwlen*p >= wlen) break;
word_tile(comp, pwlen, pwlen*p);
pwlen *= p;
}
word_tile(comp, pwlen, wlen);
/* Sieve up to their limit.
*
* Simple code for this:
* for ( ; p <= maxprime; p = prime_iterator_next(&iter))
* sievep(comp, start, p, length);
* We'll save some time for large start values by doubling up primes.
*/
{
UV p1, p2;
UV doublelim = (1UL << (sizeof(unsigned long) * 4)) - 1;
UV ulim = (maxprime > ULONG_MAX) ? ULONG_MAX : maxprime;
if (doublelim > maxprime) doublelim = maxprime;
/* Do 2 primes at a time. Fewer mpz remainders. */
for ( p1 = p, p2 = prime_iterator_next(&iter);
p2 <= doublelim;
p1 = prime_iterator_next(&iter), p2 = prime_iterator_next(&iter) ) {
UV p1p2 = p1 * p2;
UV ddiv = mpz_fdiv_ui(start, p1p2);
sievep_ui(comp, p1 - (ddiv % p1), p1, length);
sievep_ui(comp, p2 - (ddiv % p2), p2, length);
}
if (p1 <= maxprime) sievep(comp, start, p1, length);
for (p = p2; p <= ulim; p = prime_iterator_next(&iter))
sievep(comp, start, p, length);
if (p < maxprime) {
/* UV is 64-bit, GMP's ui functions are 32-bit. Sigh. */
UV lastp, pos;
mpz_t mp, rem;
mpz_init(rem);
mpz_init_set_ui(mp, p >> 32);
mpz_mul_2exp(mp, mp, 32);
mpz_add_ui(mp, mp, p & 0xFFFFFFFFUL);
for (lastp = p; p <= maxprime; lastp=p, p=prime_iterator_next(&iter)) {
mpz_add_ui(mp, mp, p-lastp); /* Calc mp = p */
mpz_fdiv_r(rem, start, mp); /* Calc start % mp */
if (mpz_cmp_ui(rem, ULONG_MAX) <= 0) { /* pos = p - (start % p) */
pos = p - mpz_get_ui(rem);
} else {
p1 = mpz_fdiv_q_ui(rem, rem, 2147483648UL);
p1 += ((UV)mpz_get_ui(rem)) << 31;
pos = p - p1;
}
sievep_ui(comp, pos, p, length);
}
mpz_clear(mp);
mpz_clear(rem);
}
}
prime_iterator_destroy(&iter);
return comp;
}
char* pidigits(UV n) {
char* out;
New(0, out, n+4, char);
out[0] = '3'; out[1] = '\0';
if (n <= 1)
return out;
#if 0
/* Spigot method.
* ~40x slower than the Machin formulas, 2x slower than spigot in plain C */
{
mpz_t t1, t2, acc, den, num;
UV i, k, d, d2;
mpz_init(t1); mpz_init(t2);
mpz_init_set_ui(acc, 0);
mpz_init_set_ui(den, 1);
mpz_init_set_ui(num, 1);
n++; /* rounding */
for (i = k = 0; i < n; ) {
{
UV k2 = ++k * 2 + 1;
mpz_mul_2exp(t1, num, 1);
mpz_add(acc, acc, t1);
mpz_mul_ui(acc, acc, k2);
mpz_mul_ui(den, den, k2);
mpz_mul_ui(num, num, k);
}
if (mpz_cmp(num, acc) > 0) continue;
{
mpz_mul_ui(t1, num, 3);
mpz_add(t2, t1, acc);
mpz_tdiv_q(t1, t2, den);
d = mpz_get_ui(t1);
}
{
mpz_mul_ui(t1, num, 4);
mpz_add(t2, t1, acc);
mpz_tdiv_q(t1, t2, den);
d2 = mpz_get_ui(t1);
}
if (d != d2) continue;
out[++i] = '0' + d;
{
mpz_submul_ui(acc, den, d);
mpz_mul_ui(acc, acc, 10);
mpz_mul_ui(num, num, 10);
}
}
mpz_clear(num); mpz_clear(den); mpz_clear(acc); mpz_clear(t2);mpz_clear(t1);
if (out[n] >= '5') out[n-1]++; /* Round */
for (i = n-1; out[i] == '9'+1; i--) /* Keep rounding */
{ out[i] = '0'; out[i-1]++; }
n--; /* Undo the extra digit we used for rounding */
out[1] = '.';
out[n+1] = '\0';
}
#elif 0
/* https://en.wikipedia.org/wiki/Machin-like_formula
* Thanks to Ledrug from RosettaCode for the simple code for base 10.
* Pretty fast, but growth is a lot slower than AGM. */
{
mpz_t t1, t2, term1, term2, pows;
UV i, k;
mpz_init(t1); mpz_init(t2); mpz_init(term1); mpz_init(term2); mpz_init(pows);
n++; /* rounding */
mpz_ui_pow_ui(pows, 10, n+20);
#if 0
/* Machin 1706 */
mpz_arctan(term1, 5, pows, t1, t2); mpz_mul_ui(term1, term1, 4);
mpz_arctan(term2, 239, pows, t1, t2);
mpz_sub(term1, term1, term2);
#elif 0
/* Störmer 1896 */
mpz_arctan(term1, 57, pows, t1, t2); mpz_mul_ui(term1, term1, 44);
mpz_arctan(term2, 239, pows, t1, t2); mpz_mul_ui(term2, term2, 7);
mpz_add(term1, term1, term2);
mpz_arctan(term2, 682, pows, t1, t2); mpz_mul_ui(term2, term2, 12);
mpz_sub(term1, term1, term2);
mpz_arctan(term2, 12943, pows, t1, t2); mpz_mul_ui(term2, term2, 24);
mpz_add(term1, term1, term2);
#else
/* Chien-Lih 1997 */
mpz_arctan(term1, 239, pows, t1, t2); mpz_mul_ui(term1, term1, 183);
mpz_arctan(term2, 1023, pows, t1, t2); mpz_mul_ui(term2, term2, 32);
mpz_add(term1, term1, term2);
mpz_arctan(term2, 5832, pows, t1, t2); mpz_mul_ui(term2, term2, 68);
mpz_sub(term1, term1, term2);
mpz_arctan(term2, 110443, pows, t1, t2); mpz_mul_ui(term2, term2, 12);
mpz_add(term1, term1, term2);
mpz_arctan(term2, 4841182, pows, t1, t2); mpz_mul_ui(term2, term2, 12);
mpz_sub(term1, term1, term2);
mpz_arctan(term2, 6826318, pows, t1, t2); mpz_mul_ui(term2, term2, 100);
mpz_sub(term1, term1, term2);
#endif
mpz_mul_ui(term1, term1, 4);
mpz_ui_pow_ui(pows, 10, 20);
mpz_tdiv_q(term1, term1, pows);
mpz_clear(t1); mpz_clear(t2); mpz_clear(term2); mpz_clear(pows);
k = mpz_sizeinbase(term1, 10); /* Copy result to out string */
while (k > n+1) { /* making sure we don't overflow */
mpz_tdiv_q_ui(term1, term1, 10);
k = mpz_sizeinbase(term1, 10);
}
(void) mpz_get_str(out+1, 10, term1);
mpz_clear(term1);
if (out[n] >= '5') out[n-1]++; /* Round */
for (i = n-1; out[i] == '9'+1; i--) /* Keep rounding */
{ out[i] = '0'; out[i-1]++; }
n--; /* Undo the extra digit we used for rounding */
out[1] = '.';
out[n+1] = '\0';
}
#else
/* AGM using GMP's floating point. Fast and very good growth. */
{
mpf_t t, an, bn, tn, prev_an;
UV k = 0;
unsigned long oldprec = mpf_get_default_prec();
mpf_set_default_prec(10 + n * 3.322);
mpf_init(t); mpf_init(prev_an);
mpf_init_set_d(an, 1); mpf_init_set_d(bn, 0.5); mpf_init_set_d(tn, 0.25);
mpf_sqrt(bn, bn);
while ((n >> k) > 0) {
mpf_set(prev_an, an);
mpf_add(t, an, bn);
mpf_div_ui(an, t, 2);
mpf_mul(t, bn, prev_an);
mpf_sqrt(bn, t);
mpf_sub(prev_an, prev_an, an);
mpf_mul(t, prev_an, prev_an);
mpf_mul_2exp(t, t, k);
mpf_sub(tn, tn, t);
k++;
}
mpf_add(t, an, bn);
mpf_mul(an, t, t);
mpf_mul_2exp(t, tn, 2);
mpf_div(bn, an, t);
gmp_sprintf(out, "%.*Ff", (int)(n-1), bn);
mpf_clear(tn); mpf_clear(bn); mpf_clear(an);
mpf_clear(prev_an); mpf_clear(t);
mpf_set_default_prec(oldprec);
}
#endif
return out;
}
typedef struct {
uint32_t nmax;
uint32_t nsize;
UV* list;
} vlist;
#define INIT_VLIST(v) \
v.nsize = 0; \
v.nmax = 1024; \
New(0, v.list, v.nmax, UV);
#define RESIZE_VLIST(v, size) \
do { if (v.nmax < size) Renew(v.list, v.nmax = size, UV); } while (0)
#define PUSH_VLIST(v, n) \
do { \
if (v.nsize >= v.nmax) \
Renew(v.list, v.nmax += 1024, UV); \
v.list[v.nsize++] = n; \
} while (0)
#define ADDVAL32(v, n, max, val) \
do { if (n >= max) Renew(v, max += 1024, UV); v[n++] = val; } while (0)
#define SWAPL32(l1, n1, m1, l2, n2, m2) \
{ UV t_, *u_ = l1; l1 = l2; l2 = u_; \
t_ = n1; n1 = n2; n2 = t_; \
t_ = m1; m1 = m2; m2 = t_; }
UV* sieve_primes(mpz_t inlow, mpz_t high, UV k, UV *rn) {
mpz_t t, low;
int test_primality = 0, k_primality = 0;
uint32_t* comp;
vlist retlist;
if (mpz_cmp_ui(inlow, 2) < 0) mpz_set_ui(inlow, 2);
if (mpz_cmp(inlow, high) > 0) { *rn = 0; return 0; }
mpz_init(t);
mpz_sqrt(t, high); /* No need for k to be > sqrt(high) */
/* If auto-setting k or k >= sqrt(n), pick a good depth and test primality */
if (k == 0 || mpz_cmp_ui(t, k) <= 0) {
/* TODO: We need to take into account the sieve width */
UV hbits = mpz_sizeinbase(high,2);
test_primality = 1;
k = (hbits < 100) ? 50000000 : hbits*500000;
}
/* If k >= sqrtn, sieving is enough. Use k=sqrtn, turn off post-sieve test */
if (mpz_cmp_ui(t, k) <= 0) {
k = mpz_get_ui(t);
k_primality = 1; /* Our sieve is complete */
test_primality = 0; /* Don't run BPSW */
}
INIT_VLIST(retlist);
/* If we want small primes, do it quickly */
if ( (k_primality || test_primality) && mpz_cmp_ui(high,2000000000U) <= 0 ) {
UV ulow = mpz_get_ui(inlow), uhigh = mpz_get_ui(high);
if (uhigh < 1000000U || uhigh/ulow >= 4) {
UV n, Pi, *primes;
primes = sieve_to_n(mpz_get_ui(high), &Pi);
RESIZE_VLIST(retlist, Pi);
for (n = 0; n < Pi; n++) {
if (primes[n] >= ulow)
PUSH_VLIST(retlist, primes[n]-ulow);
}
Safefree(primes);
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}
}
mpz_init_set(low, inlow);
if (k < 2) k = 2; /* Should have been handled by quick return */
/* Include all primes up to k, since they will get filtered */
if (mpz_cmp_ui(low, k) <= 0) {
UV n, Pi, *primes, ulow = mpz_get_ui(low);
primes = sieve_to_n(k, &Pi);
RESIZE_VLIST(retlist, Pi);
for (n = 0; n < Pi; n++) {
if (primes[n] >= ulow)
PUSH_VLIST(retlist, primes[n]-ulow);
}
Safefree(primes);
}
if (mpz_even_p(low)) mpz_add_ui(low, low, 1);
if (mpz_even_p(high)) mpz_sub_ui(high, high, 1);
if (mpz_cmp(low, high) <= 0) {
UV i, length, offset;
mpz_sub(t, high, low); length = mpz_get_ui(t) + 1;
/* Get bit array of odds marked with composites(k) marked with 1 */
comp = partial_sieve(low, length, k);
mpz_sub(t, low, inlow); offset = mpz_get_ui(t);
for (i = 1; i <= length; i += 2) {
if (!TSTAVAL(comp, i)) {
if (!test_primality || (mpz_add_ui(t,low,i),_GMP_BPSW(t)))
PUSH_VLIST(retlist, i - offset);
}
}
Safefree(comp);
}
mpz_clear(low);
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}
UV* sieve_twin_primes(mpz_t low, mpz_t high, UV twin, UV *rn) {
mpz_t t;
UV i, length, k, starti = 1, skipi = 2;
uint32_t* comp;
vlist retlist;
/* Twin offset will always be even, so we will never return 2 */
MPUassert( !(twin & 1), "twin prime offset is even" );
if (mpz_cmp_ui(low, 3) <= 0) mpz_set_ui(low, 3);
if (mpz_even_p(low)) mpz_add_ui(low, low, 1);
if (mpz_even_p(high)) mpz_sub_ui(high, high, 1);
i = twin % 6;
if (i == 2 || i == 4) { skipi = 6; starti = ((twin%6)==2) ? 5 : 1; }
/* If no way to return any more results, leave now */
if (mpz_cmp(low, high) > 0 || (i == 1 || i == 3 || i == 5))
{ *rn = 0; return 0; }
INIT_VLIST(retlist);
mpz_init(t);
/* Use a much higher k value than we do for primes */
k = 80000 * mpz_sizeinbase(high,2);
/* No need for k to be > sqrt(high) */
mpz_sqrt(t, high);
if (mpz_cmp_ui(t, k) < 0)
k = mpz_get_ui(t);
/* Handle small primes that will get sieved out */
if (mpz_cmp_ui(low, k) <= 0) {
UV p, ulow = mpz_get_ui(low);
PRIME_ITERATOR(iter);
for (p = 2; p <= k; p = prime_iterator_next(&iter)) {
if (p < ulow) continue;
if (mpz_set_ui(t, p+twin), _GMP_BPSW(t))
PUSH_VLIST(retlist, p-ulow+1);
}
prime_iterator_destroy(&iter);
}
mpz_sub(t, high, low);
length = mpz_get_ui(t) + 1;
starti = ((starti+skipi) - mpz_fdiv_ui(low,skipi) + 1) % skipi;
/* Get bit array of odds marked with composites(k) marked with 1 */
comp = partial_sieve(low, length + twin, k);
for (i = starti; i <= length; i += skipi) {
if (!TSTAVAL(comp, i) && !TSTAVAL(comp, i+twin)) {
mpz_add_ui(t, low, i);
if (_GMP_BPSW(t)) {
mpz_add_ui(t, t, twin);
if (_GMP_BPSW(t)) {
PUSH_VLIST(retlist, i);
}
}
}
}
Safefree(comp);
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}
#define addmodded(r,a,b,n) do { r = a + b; if (r >= n) r -= n; } while(0)
UV* sieve_cluster(mpz_t low, mpz_t high, uint32_t* cl, UV nc, UV *rn) {
mpz_t t, savelow;
vlist retlist;
UV i, ppr, nres, allocres;
uint32_t const targres = 4000000;
uint32_t const maxpi = 168;
UV *residues, *cres;
uint32_t pp_0, pp_1, pp_2, *resmod_0, *resmod_1, *resmod_2;
uint32_t rem_0, rem_1, rem_2, remadd_0, remadd_1, remadd_2;
uint32_t pi, startpi = 1;
uint32_t lastspr = sprimes[maxpi-1];
uint32_t c, smallnc;
UV ibase = 0, nprps = 0;
char crem_0[53*59], crem_1[61*67], crem_2[71*73], *VPrem;
int run_pretests = 0;
int _verbose = get_verbose_level();
if (nc == 1) return sieve_primes(low, high, 0, rn);
if (nc == 2) return sieve_twin_primes(low, high, cl[1], rn);
if (mpz_even_p(low)) mpz_add_ui(low, low, 1);
if (mpz_even_p(high)) mpz_sub_ui(high, high, 1);
if (mpz_cmp(low, high) > 0) { *rn = 0; return 0; }
INIT_VLIST(retlist);
mpz_init(t);
/* Handle small values that would get sieved away */
if (mpz_cmp_ui(low, lastspr) <= 0) {
UV ui_low = mpz_get_ui(low);
UV ui_high = (mpz_cmp_ui(high,lastspr) > 0) ? lastspr : mpz_get_ui(high);
for (pi = 0; pi < maxpi; pi++) {
UV p = sprimes[pi];
if (p > ui_high) break;
if (p < ui_low) continue;
for (c = 1; c < nc; c++)
if (!(mpz_set_ui(t, p+cl[c]), _GMP_is_prob_prime(t))) break;
if (c == nc)
PUSH_VLIST(retlist, p-ui_low+1);
}
}
if (mpz_odd_p(low)) mpz_sub_ui(low, low, 1);
if (mpz_cmp_ui(high, lastspr) <= 0) {
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}
/* Determine the primorial size and acceptable residues */
New(0, residues, allocres = 1024, UV);
{
UV remr, *res2, allocres2, nres2, maxppr;
/* Calculate residues for a small primorial */
for (pi = 2, ppr = 1, i = 0; i <= pi; i++) ppr *= sprimes[i];
remr = mpz_fdiv_ui(low, ppr);
nres = 0;
for (i = 1; i <= ppr; i += 2) {
UV remi = remr + i;
for (c = 0; c < nc; c++) {
if (gcd_ui(remi + cl[c], ppr) != 1) break;
}
if (c == nc)
ADDVAL32(residues, nres, allocres, i);
}
/* Raise primorial size until we have plenty of residues */
New(0, res2, allocres2 = 1024, UV);
mpz_sub(t, high, low);
maxppr = (mpz_sizeinbase(t,2) >= BITS_PER_WORD) ? UV_MAX : (UVCONST(1) << mpz_sizeinbase(t,2));
#if BITS_PER_WORD == 64
while (pi++ < 14) {
#else
while (pi++ < 8) {
#endif
uint32_t j, p = sprimes[pi];
UV r, newppr = ppr * p;
if (nres == 0 || nres > targres/(p/2) || newppr > maxppr) break;
if (_verbose > 1) printf("cluster sieve found %"UVuf" residues mod %"UVuf"\n", nres, ppr);
remr = mpz_fdiv_ui(low, newppr);
nres2 = 0;
for (i = 0; i < p; i++) {
for (j = 0; j < nres; j++) {
r = i*ppr + residues[j];
for (c = 0; c < nc; c++) {
UV v = remr + r + cl[c];
if ((v % p) == 0) break;
}
if (c == nc)
ADDVAL32(res2, nres2, allocres2, r);
}
}
ppr = newppr;
SWAPL32(residues, nres, allocres, res2, nres2, allocres2);
}
startpi = pi;
Safefree(res2);
}
if (_verbose) printf("cluster sieve using %"UVuf" residues mod %"UVuf"\n", nres, ppr);
/* Return if not admissible, maybe with a single small value */
if (nres == 0) {
Safefree(residues);
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}
mpz_init_set(savelow, low);
if (mpz_sizeinbase(low, 2) > 260) run_pretests = 1;
if (run_pretests && mpz_sgn(_bgcd2) == 0) {
_GMP_pn_primorial(_bgcd2, BGCD2_PRIMES);
mpz_divexact(_bgcd2, _bgcd2, _bgcd);
}
/* Pre-mod the residues with first two primes for fewer modulos every chunk */
{
uint32_t p1 = sprimes[startpi+0], p2 = sprimes[startpi+1];
uint32_t p3 = sprimes[startpi+2], p4 = sprimes[startpi+3];
uint32_t p5 = sprimes[startpi+4], p6 = sprimes[startpi+5];
pp_0 = p1*p2; pp_1 = p3*p4; pp_2 = p5*p6;
memset(crem_0, 1, pp_0);
memset(crem_1, 1, pp_1);
memset(crem_2, 1, pp_2);
/* Mark remainders that indicate a composite for this residue. */
for (i = 0; i < p1; i++) { crem_0[i*p1]=0; crem_0[i*p2]=0; }
for ( ; i < p2; i++) { crem_0[i*p1]=0; }
for (i = 0; i < p3; i++) { crem_1[i*p3]=0; crem_1[i*p4]=0; }
for ( ; i < p4; i++) { crem_1[i*p3]=0; }
for (i = 0; i < p5; i++) { crem_2[i*p5]=0; crem_2[i*p6]=0; }
for ( ; i < p6; i++) { crem_2[i*p5]=0; }
for (c = 1; c < nc; c++) {
uint32_t c1=cl[c], c2=cl[c], c3=cl[c], c4=cl[c], c5=cl[c], c6=cl[c];
if (c1 >= p1) c1 %= p1;
if (c2 >= p2) c2 %= p2;
for (i = 1; i <= p1; i++) { crem_0[i*p1-c1]=0; crem_0[i*p2-c2]=0; }
for ( ; i <= p2; i++) { crem_0[i*p1-c1]=0; }
if (c3 >= p3) c3 %= p3;
if (c4 >= p4) c4 %= p4;
for (i = 1; i <= p3; i++) { crem_1[i*p3-c3]=0; crem_1[i*p4-c4]=0; }
for ( ; i <= p4; i++) { crem_1[i*p3-c3]=0; }
if (c5 >= p5) c5 %= p5;
if (c6 >= p6) c6 %= p6;
for (i = 1; i <= p5; i++) { crem_2[i*p5-c5]=0; crem_2[i*p6-c6]=0; }
for ( ; i <= p6; i++) { crem_2[i*p5-c5]=0; }
}
New(0, resmod_0, nres, uint32_t);
New(0, resmod_1, nres, uint32_t);
New(0, resmod_2, nres, uint32_t);
for (i = 0; i < nres; i++) {
resmod_0[i] = residues[i] % pp_0;
resmod_1[i] = residues[i] % pp_1;
resmod_2[i] = residues[i] % pp_2;
}
}
/* Precalculate acceptable residues for more primes */
MPUassert( lastspr <= 1024, "cluster sieve internal" );
New(0, VPrem, maxpi * 1024, char);
memset(VPrem, 1, maxpi * 1024);
for (pi = startpi+6; pi < maxpi; pi++)
VPrem[pi*1024] = 0;
for (pi = startpi+6, smallnc = 0; pi < maxpi; pi++) {
uint32_t p = sprimes[pi];
char* prem = VPrem + pi*1024;
while (smallnc < nc && cl[smallnc] < p) smallnc++;
for (c = 1; c < smallnc; c++) prem[p-cl[c]] = 0;
for ( ; c < nc; c++) prem[p-(cl[c]%p)] = 0;
}
New(0, cres, nres, UV);
rem_0 = mpz_fdiv_ui(low,pp_0); remadd_0 = ppr % pp_0;
rem_1 = mpz_fdiv_ui(low,pp_1); remadd_1 = ppr % pp_1;
rem_2 = mpz_fdiv_ui(low,pp_2); remadd_2 = ppr % pp_2;
/* Loop over their range in chunks of size 'ppr' */
while (mpz_cmp(low, high) <= 0) {
uint32_t r, nr, remr, ncres;
unsigned long ui_low = (mpz_sizeinbase(low,2) > 8*sizeof(unsigned long)) ? 0 : mpz_get_ui(low);
/* Reduce the allowed residues for this chunk using more primes */
{ /* Start making a list of this chunk's residues using three pairs */
for (r = 0, ncres = 0; r < nres; r++) {
addmodded(remr, rem_0, resmod_0[r], pp_0);
if (crem_0[remr]) {
addmodded(remr, rem_1, resmod_1[r], pp_1);
if (crem_1[remr]) {
addmodded(remr, rem_2, resmod_2[r], pp_2);
if (crem_2[remr]) {
cres[ncres++] = residues[r];
}
}
}
}
addmodded(rem_0, rem_0, remadd_0, pp_0);
addmodded(rem_1, rem_1, remadd_1, pp_1);
addmodded(rem_2, rem_2, remadd_2, pp_2);
}
/* Sieve through more primes one at a time, removing residues. */
for (pi = startpi+6; pi < maxpi && ncres > 0; pi++) {
uint32_t p = sprimes[pi];
uint32_t rem = (ui_low) ? (ui_low % p) : mpz_fdiv_ui(low,p);
char* prem = VPrem + pi*1024;
/* Check divisibility of each remaining residue with this p */
if (startpi <= 9 || cres[ncres-1] < 4294967295U) { /* Residues are 32-bit */
for (r = 0, nr = 0; r < ncres; r++) {
if (prem[ (rem+(uint32_t)cres[r]) % p ])
cres[nr++] = cres[r];
}
} else { /* Residues are 64-bit */
for (r = 0, nr = 0; r < ncres; r++) {
if (prem[ (rem+cres[r]) % p ])
cres[nr++] = cres[r];
}
}
ncres = nr;
}
if (_verbose > 2) printf("cluster sieve range has %u residues left\n", ncres);
/* Now check each of the remaining residues for inclusion */
for (r = 0; r < ncres; r++) {
i = cres[r];
mpz_add_ui(t, low, i);
if (mpz_cmp(t, high) > 0) break;
/* Pretest each element if the input is large enough */
if (run_pretests) {
for (c = 0; c < nc; c++)
if (mpz_add_ui(t, low, i+cl[c]), mpz_gcd(t,t,_bgcd2), mpz_cmp_ui(t,1)) break;
if (c != nc) continue;
}
/* PRP test */
for (c = 0; c < nc; c++)
if (! (mpz_add_ui(t, low, i+cl[c]), nprps++, _GMP_BPSW(t)) ) break;
if (c != nc) continue;
PUSH_VLIST(retlist, ibase + i);
}
ibase += ppr;
mpz_add_ui(low, low, ppr);
}
if (_verbose) printf("cluster sieve ran %"UVuf" BPSW tests (pretests %s)\n", nprps, run_pretests ? "on" : "off");
mpz_set(low, savelow);
Safefree(cres);
Safefree(VPrem);
Safefree(resmod_0);
Safefree(resmod_1);
Safefree(resmod_2);
Safefree(residues);
mpz_clear(savelow);
mpz_clear(t);
*rn = retlist.nsize;
return retlist.list;
}