#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "ptypes.h"
#include "prime_iterator.h"
#if 0
/* Add this to a number and you'll ensure you're on a wheel location */
static const unsigned char distancewheel30[30] =
{1,0,5,4,3,2,1,0,3,2,1,0,1,0,3,2,1,0,1,0,3,2,1,0,5,4,3,2,1,0};
#endif
/* The bit mask within a byte */
static const unsigned char masktab30[30] = {
0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 8, 0,
0, 0, 16, 0, 32, 0, 0, 0, 64, 0, 0, 0, 0, 0,128 };
static const unsigned char nextwheel30[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 };
#if 0
static const unsigned char prevwheel30[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 };
#endif
static INLINE UV next_prime_in_segment( const unsigned char* sieve, UV segment_start, UV segment_bytes, UV p)
{
UV d, m;
if (p < segment_start) return 0;
d = (p-segment_start)/30;
if (d >= segment_bytes) return 0;
m = (p-segment_start) - d*30;
do {
if (m==29) {
d++; m = 1;
if (d >= segment_bytes) return 0;
} else {
m = nextwheel30[m];
}
} while (sieve[d] & masktab30[m]);
return (segment_start + d*30 + m);
}
static INLINE int is_prime_in_segment( const unsigned char* sieve, UV segment_start, UV segment_bytes, UV p)
{
UV d, m, mtab;
if (p < segment_start) return -1;
d = (p-segment_start)/30;
if (d >= segment_bytes) return -1;
m = (p-segment_start) - d*30;
mtab = masktab30[m];
if (mtab == 0) return 0;
return ((sieve[d] & mtab) == 0);
}
#define next_prime_in_sieve(sieve, p) next_prime_in_segment(sieve, 0, UV_MAX, p)
/* 1001 bytes of presieved mod-30 bytes. If the area to be sieved is
* appropriately filled with this data, then 7, 11, and 13 do not have
* to be sieved. It wraps, so multiple memcpy's can be used. Do be
* aware that if you start at 0, you'll have to correct the first byte.
*/
#define PRESIEVE_SIZE (7*11*13)
static const unsigned char presieve13[PRESIEVE_SIZE] =
{ 0x0e,0x20,0x10,0x81,0x49,0x24,0xc2,0x06,0x2a,0x90,0xa1,0x0c,0x14,
0x58,0x02,0x61,0x11,0xc3,0x28,0x0c,0x44,0x22,0xa4,0x10,0x91,0x18,
0x4d,0x40,0x82,0x21,0x58,0xa1,0x28,0x04,0x42,0x92,0x20,0x51,0x91,
0x8a,0x04,0x48,0x03,0x60,0x34,0x81,0x1c,0x06,0xc1,0x02,0xa2,0x10,
0x89,0x08,0x24,0x45,0x42,0x30,0x10,0xc5,0x0a,0x86,0x40,0x0a,0x30,
0x38,0x85,0x08,0x15,0x40,0x63,0x20,0x96,0x83,0x88,0x04,0x60,0x16,
0x28,0x10,0x81,0x49,0x44,0xe2,0x02,0x2c,0x12,0xa1,0x0c,0x04,0x50,
0x0a,0x61,0x10,0x83,0x48,0x2c,0x40,0x26,0x26,0x90,0x91,0x08,0x55,
0x48,0x82,0x20,0x19,0xc1,0x28,0x04,0x44,0x12,0xa0,0x51,0x81,0x9a,
0x0c,0x48,0x02,0x21,0x54,0xa1,0x18,0x04,0x43,0x82,0xa2,0x10,0x99,
0x08,0x24,0x44,0x03,0x70,0x30,0xc1,0x0c,0x86,0xc0,0x0a,0x20,0x30,
0x8d,0x08,0x14,0x41,0x43,0x20,0x92,0x85,0x0a,0x84,0x60,0x06,0x30,
0x18,0x81,0x49,0x05,0xc2,0x22,0x28,0x14,0xa3,0x8c,0x04,0x50,0x12,
0x69,0x10,0x83,0x09,0x4c,0x60,0x22,0x24,0x12,0x91,0x08,0x45,0x50,
0x8a,0x20,0x18,0x81,0x68,0x24,0x40,0x16,0x22,0xd1,0x81,0x8a,0x14,
0x48,0x02,0x20,0x15,0xc1,0x38,0x04,0x45,0x02,0xa2,0x10,0x89,0x18,
0x2c,0x44,0x02,0x31,0x50,0xe1,0x08,0x86,0x42,0x8a,0x20,0x30,0x95,
0x08,0x14,0x40,0x43,0x60,0xb2,0x81,0x0c,0x06,0xe0,0x06,0x20,0x10,
0x89,0x49,0x04,0xc3,0x42,0x28,0x10,0xa5,0x0e,0x84,0x50,0x02,0x71,
0x18,0x83,0x08,0x0d,0x40,0x22,0x24,0x14,0x93,0x88,0x45,0x40,0x92,
0x28,0x18,0x81,0x29,0x44,0x60,0x12,0x24,0x53,0x81,0x8a,0x04,0x58,
0x0a,0x20,0x14,0x81,0x58,0x24,0x41,0x06,0xa2,0x90,0x89,0x08,0x34,
0x4c,0x02,0x30,0x11,0xc1,0x28,0x86,0x44,0x0a,0xa0,0x30,0x85,0x18,
0x1c,0x40,0x43,0x21,0xd2,0xa1,0x08,0x04,0x62,0x86,0x20,0x10,0x91,
0x49,0x04,0xc2,0x03,0x68,0x30,0xa1,0x0c,0x06,0xd0,0x02,0x61,0x10,
0x8b,0x08,0x0c,0x41,0x62,0x24,0x10,0x95,0x0a,0xc5,0x40,0x82,0x30,
0x18,0x81,0x28,0x05,0x40,0x32,0x20,0x55,0x83,0x8a,0x04,0x48,0x12,
0x28,0x14,0x81,0x19,0x44,0x61,0x02,0xa6,0x12,0x89,0x08,0x24,0x54,
0x0a,0x30,0x10,0xc1,0x48,0xa6,0x40,0x0e,0x22,0xb0,0x85,0x08,0x14,
0x48,0x43,0x20,0x93,0xc1,0x28,0x04,0x64,0x06,0xa0,0x10,0x81,0x59,
0x0c,0xc2,0x02,0x29,0x50,0xa1,0x0c,0x04,0x52,0x82,0x61,0x10,0x93,
0x08,0x0c,0x40,0x23,0x64,0x30,0x91,0x0c,0x47,0xc0,0x82,0x20,0x18,
0x89,0x28,0x04,0x41,0x52,0x20,0x51,0x85,0x8a,0x84,0x48,0x02,0x30,
0x1c,0x81,0x18,0x05,0x41,0x22,0xa2,0x14,0x8b,0x88,0x24,0x44,0x12,
0x38,0x10,0xc1,0x09,0xc6,0x60,0x0a,0x24,0x32,0x85,0x08,0x14,0x50,
0x4b,0x20,0x92,0x81,0x48,0x24,0x60,0x06,0x22,0x90,0x81,0x49,0x14,
0xca,0x02,0x28,0x11,0xe1,0x2c,0x04,0x54,0x02,0xe1,0x10,0x83,0x18,
0x0c,0x40,0x22,0x25,0x50,0xb1,0x08,0x45,0x42,0x82,0x20,0x18,0x91,
0x28,0x04,0x40,0x13,0x60,0x71,0x81,0x8e,0x06,0xc8,0x02,0x20,0x14,
0x89,0x18,0x04,0x41,0x42,0xa2,0x10,0x8d,0x0a,0xa4,0x44,0x02,0x30,
0x18,0xc1,0x08,0x87,0x40,0x2a,0x20,0x34,0x87,0x88,0x14,0x40,0x53,
0x28,0x92,0x81,0x09,0x44,0x60,0x06,0x24,0x12,0x81,0x49,0x04,0xd2,
0x0a,0x28,0x10,0xa1,0x4c,0x24,0x50,0x06,0x63,0x90,0x83,0x08,0x1c,
0x48,0x22,0x24,0x11,0xd1,0x28,0x45,0x44,0x82,0xa0,0x18,0x81,0x38,
0x0c,0x40,0x12,0x21,0x51,0xa1,0x8a,0x04,0x4a,0x82,0x20,0x14,0x91,
0x18,0x04,0x41,0x03,0xe2,0x30,0x89,0x0c,0x26,0xc4,0x02,0x30,0x10,
0xc9,0x08,0x86,0x41,0x4a,0x20,0x30,0x85,0x0a,0x94,0x40,0x43,0x30,
0x9a,0x81,0x08,0x05,0x60,0x26,0x20,0x14,0x83,0xc9,0x04,0xc2,0x12,
0x28,0x10,0xa1,0x0d,0x44,0x70,0x02,0x65,0x12,0x83,0x08,0x0c,0x50,
0x2a,0x24,0x10,0x91,0x48,0x65,0x40,0x86,0x22,0x98,0x81,0x28,0x14,
0x48,0x12,0x20,0x51,0xc1,0xaa,0x04,0x4c,0x02,0xa0,0x14,0x81,0x18,
0x0c,0x41,0x02,0xa3,0x50,0xa9,0x08,0x24,0x46,0x82,0x30,0x10,0xd1,
0x08,0x86,0x40,0x0b,0x60,0x30,0x85,0x0c,0x16,0xc0,0x43,0x20,0x92,
0x89,0x08,0x04,0x61,0x46,0x20,0x10,0x85,0x4b,0x84,0xc2,0x02,0x38,
0x18,0xa1,0x0c,0x05,0x50,0x22,0x61,0x14,0x83,0x88,0x0c,0x40,0x32,
0x2c,0x10,0x91,0x09,0x45,0x60,0x82,0x24,0x1a,0x81,0x28,0x04,0x50,
0x1a,0x20,0x51,0x81,0xca,0x24,0x48,0x06,0x22,0x94,0x81,0x18,0x14,
0x49,0x02,0xa2,0x11,0xc9,0x28,0x24,0x44,0x02,0xb0,0x10,0xc1,0x18,
0x8e,0x40,0x0a,0x21,0x70,0xa5,0x08,0x14,0x42,0xc3,0x20,0x92,0x91,
0x08,0x04,0x60,0x07,0x60,0x30,0x81,0x4d,0x06,0xc2,0x02,0x28,0x10,
0xa9,0x0c,0x04,0x51,0x42,0x61,0x10,0x87,0x0a,0x8c,0x40,0x22,0x34,
0x18,0x91,0x08,0x45,0x40,0xa2,0x20,0x1c,0x83,0xa8,0x04,0x40,0x12,
0x28,0x51,0x81,0x8b,0x44,0x68,0x02,0x24,0x16,0x81,0x18,0x04,0x51,
0x0a,0xa2,0x10,0x89,0x48,0x24,0x44,0x06,0x32,0x90,0xc1,0x08,0x96,
0x48,0x0a,0x20,0x31,0xc5,0x28,0x14,0x44,0x43,0xa0,0x92,0x81,0x18,
0x0c,0x60,0x06,0x21,0x50,0xa1,0x49,0x04,0xc2,0x82,0x28,0x10,0xb1,
0x0c,0x04,0x50,0x03,0x61,0x30,0x83,0x0c,0x0e,0xc0,0x22,0x24,0x10,
0x99,0x08,0x45,0x41,0xc2,0x20,0x18,0x85,0x2a,0x84,0x40,0x12,0x30,
0x59,0x81,0x8a,0x05,0x48,0x22,0x20,0x14,0x83,0x98,0x04,0x41,0x12,
0xaa,0x10,0x89,0x09,0x64,0x64,0x02,0x34,0x12,0xc1,0x08,0x86,0x50,
0x0a,0x20,0x30,0x85,0x48,0x34,0x40,0x47,0x22,0x92,0x81,0x08,0x14,
0x68,0x06,0x20,0x11,0xc1,0x69,0x04,0xc6,0x02,0xa8,0x10,0xa1,0x1c,
0x0c,0x50,0x02,0x61,0x50,0xa3,0x08,0x0c,0x42,0xa2,0x24,0x10,0x91,
0x08,0x45,0x40,0x83,0x60,0x38,0x81,0x2c,0x06,0xc0,0x12,0x20,0x51,
0x89,0x8a,0x04,0x49,0x42,0x20,0x14,0x85,0x1a,0x84,0x41,0x02,0xb2,
0x18,0x89,0x08,0x25,0x44,0x22,0x30,0x14,0xc3,0x88,0x86,0x40,0x1a,
0x28,0x30,0x85,0x09,0x54,0x60,0x43,0x24,0x92,0x81,0x08,0x04,0x70};
#define FIND_COMPOSITE_POS(i,j) \
{ \
UV dlast = d; \
do { \
d += dinc; \
m += minc; \
if (m >= 30) { d++; m -= 30; } \
} while ( masktab30[m] == 0 ); \
wdinc[i] = d - dlast; \
wmask[j] = masktab30[m]; \
}
#define FIND_COMPOSITE_POSITIONS(p) \
do { \
FIND_COMPOSITE_POS(0,1) \
FIND_COMPOSITE_POS(1,2) \
FIND_COMPOSITE_POS(2,3) \
FIND_COMPOSITE_POS(3,4) \
FIND_COMPOSITE_POS(4,5) \
FIND_COMPOSITE_POS(5,6) \
FIND_COMPOSITE_POS(6,7) \
FIND_COMPOSITE_POS(7,0) \
d -= p; \
} while (0)
static void sieve_prefill(unsigned char* mem, UV startd, UV endd)
{
UV nbytes = endd - startd + 1;
MPUassert( (mem != 0) && (endd >= startd), "sieve_prefill bad arguments");
/* Walk the memory, tiling in the presieve area using memcpy.
* This is pretty fast, but it might still benefit from using copy
* doubling (where we copy to the memory, then copy memory to memory
* doubling in size each time), as memcpy usually loves big chunks.
*/
while (startd <= endd) {
UV pstartd = startd % PRESIEVE_SIZE;
UV sieve_bytes = PRESIEVE_SIZE - pstartd;
UV bytes = (nbytes > sieve_bytes) ? sieve_bytes : nbytes;
memcpy(mem, presieve13 + pstartd, bytes);
if (startd == 0) mem[0] = 0x01; /* Correct first byte */
startd += bytes;
mem += bytes;
nbytes -= bytes;
}
}
/* Wheel 30 sieve. Ideas from Terje Mathisen and Quesada / Van Pelt. */
static unsigned char* sieve_erat30(UV end)
{
unsigned char* mem;
UV max_buf, limit;
UV prime;
max_buf = (end/30) + ((end%30) != 0);
/* Round up to a word */
max_buf = ((max_buf + sizeof(UV) - 1) / sizeof(UV)) * sizeof(UV);
New(0, mem, max_buf, unsigned char );
if (mem == 0) {
croak("allocation failure in sieve_erat30: could not alloc %"UVuf" bytes", max_buf);
return 0;
}
/* Fill buffer with marked 7, 11, and 13 */
sieve_prefill(mem, 0, max_buf-1);
limit = (UV) sqrt((double) end); /* prime*prime can overflow */
for (prime = 17; prime <= limit; prime = next_prime_in_sieve(mem,prime)) {
UV d = (prime*prime)/30;
UV m = (prime*prime) - d*30;
UV dinc = (2*prime)/30;
UV minc = (2*prime) - dinc*30;
UV wdinc[8];
unsigned char wmask[8];
/* Find the positions of the next composites we will mark */
FIND_COMPOSITE_POSITIONS(prime);
/* Mark the composites (unrolled) */
while (1) {
mem[d] |= wmask[0]; d += wdinc[0]; if (d >= max_buf) break;
mem[d] |= wmask[1]; d += wdinc[1]; if (d >= max_buf) break;
mem[d] |= wmask[2]; d += wdinc[2]; if (d >= max_buf) break;
mem[d] |= wmask[3]; d += wdinc[3]; if (d >= max_buf) break;
mem[d] |= wmask[4]; d += wdinc[4]; if (d >= max_buf) break;
mem[d] |= wmask[5]; d += wdinc[5]; if (d >= max_buf) break;
mem[d] |= wmask[6]; d += wdinc[6]; if (d >= max_buf) break;
mem[d] |= wmask[7]; d += wdinc[7]; if (d >= max_buf) break;
}
}
return mem;
}
static int sieve_segment(unsigned char* mem, UV startd, UV endd,
const unsigned char* prim_sieve, UV prim_limit)
{
const unsigned char* sieve;
UV limit, p;
UV startp = 30*startd;
UV endp = (endd >= (UV_MAX/30)) ? UV_MAX-2 : 30*endd+29;
MPUassert( (mem != 0) && (endd >= startd) && (endp >= startp),
"sieve_segment bad arguments");
/* Fill buffer with marked 7, 11, and 13 */
sieve_prefill(mem, startd, endd);
limit = (UV) sqrt((double) endp);
if (limit*limit < endp) limit++; /* ceil(sqrt(endp)) */
/* printf("segment sieve from %"UVuf" to %"UVuf" (aux sieve to %"UVuf")\n", startp, endp, limit); */
if ( (prim_sieve != 0) && (limit <= prim_limit) ) {
sieve = prim_sieve;
} else {
sieve = sieve_erat30(limit);
}
MPUassert( sieve != 0, "Could not generate base sieve" );
for (p = 17; p <= limit; p = next_prime_in_sieve(sieve,p))
{
/* p increments from 17 to at least sqrt(endp) */
UV p2 = p*p; /* TODO: overflow */
if (p2 > endp) break;
/* Find first multiple of p greater than p*p and larger than startp */
if (p2 < startp) {
p2 = (startp / p) * p;
if (p2 < startp) p2 += p;
}
/* Bump to next multiple that isn't divisible by 2, 3, or 5 */
while (masktab30[p2%30] == 0) { p2 += p; }
/* It is possible we've overflowed p2, so check for that */
if ( (p2 <= endp) && (p2 >= startp) ) {
/* Sieve from startd to endd starting at p2, stepping p */
UV d = (p2)/30;
UV m = (p2) - d*30;
UV dinc = (2*p)/30;
UV minc = (2*p) - dinc*30;
UV wdinc[8];
unsigned char wmask[8];
UV offset_endd = endd - startd;
/* Find the positions of the next composites we will mark */
FIND_COMPOSITE_POSITIONS(p);
d -= startd;
/* Mark composites (unrolled) */
while ( (d+p) <= offset_endd ) {
mem[d] |= wmask[0]; d += wdinc[0];
mem[d] |= wmask[1]; d += wdinc[1];
mem[d] |= wmask[2]; d += wdinc[2];
mem[d] |= wmask[3]; d += wdinc[3];
mem[d] |= wmask[4]; d += wdinc[4];
mem[d] |= wmask[5]; d += wdinc[5];
mem[d] |= wmask[6]; d += wdinc[6];
mem[d] |= wmask[7]; d += wdinc[7];
}
while (1) {
mem[d] |= wmask[0]; d += wdinc[0]; if (d > offset_endd) break;
mem[d] |= wmask[1]; d += wdinc[1]; if (d > offset_endd) break;
mem[d] |= wmask[2]; d += wdinc[2]; if (d > offset_endd) break;
mem[d] |= wmask[3]; d += wdinc[3]; if (d > offset_endd) break;
mem[d] |= wmask[4]; d += wdinc[4]; if (d > offset_endd) break;
mem[d] |= wmask[5]; d += wdinc[5]; if (d > offset_endd) break;
mem[d] |= wmask[6]; d += wdinc[6]; if (d > offset_endd) break;
mem[d] |= wmask[7]; d += wdinc[7]; if (d > offset_endd) break;
}
}
}
if (sieve != prim_sieve) Safefree(sieve);
return 1;
}
/*****************************************************************************/
/* Prime iterator */
/*****************************************************************************/
/* These sizes are a tradeoff. For better memory use I think 16k,4k is good.
* For performance, 32k,16k or 64k,16k is better. To avoid threading hell,
* this is just decided statically. At 24k,16k we handle 736800 numbers in
* the primary sieve and won't redo for segments until after 5*10^11. Each
* segment will store a range of 30*(16384-16) = 491040 numbers.
*/
#define PRIMARY_SIZE (32768-16)
#define SEGMENT_SIZE (24576-16)
#define NSMALL_PRIMES (83970-180)
static const unsigned char* primary_sieve = 0;
static const UV primary_limit = (30 * PRIMARY_SIZE)-1;
static const uint32_t* small_primes = 0;
static UV num_small_primes = 0;
void prime_iterator_global_startup(void)
{
primary_sieve = sieve_erat30(primary_limit);
#ifdef NSMALL_PRIMES
{
UV p;
uint32_t *primes32;
UV *primes64 = sieve_to_n(NSMALL_PRIMES + 180, &num_small_primes);
New(0, primes32, num_small_primes, uint32_t);
for (p = 0; p < num_small_primes; p++) primes32[p] = primes64[p];
Safefree(primes64);
small_primes = primes32;
}
#endif
}
void prime_iterator_global_shutdown(void)
{
if (primary_sieve != 0) Safefree(primary_sieve);
if (small_primes != 0) Safefree(small_primes);
primary_sieve = 0;
small_primes = 0;
}
#if 0
void prime_iterator_init(prime_iterator *iter)
{
iter->p = 2;
iter->segment_start = 0;
iter->segment_bytes = 0;
iter->segment_mem = 0;
}
prime_iterator prime_iterator_default(void)
{
prime_iterator iter = {2, 0, 0, 0};
return iter;
}
#endif
void prime_iterator_destroy(prime_iterator *iter)
{
if (iter->segment_mem != 0) Safefree(iter->segment_mem);
iter->segment_mem = 0;
iter->segment_start = 0;
iter->segment_bytes = 0;
iter->p = 0;
}
#ifdef NSMALL_PRIMES
static UV pcount(UV n)
{
UV lo = 0 + (n >> 4);
UV hi = (n >> 3) - (n >> 6) + ( (n<503) ? 40 : (n<1669) ? 80 : 139 );
if (hi > num_small_primes) hi = num_small_primes;
while (lo < hi) {
UV mid = lo + (hi-lo)/2;
if (small_primes[mid] <= n) lo = mid+1;
else hi = mid;
}
return lo; /* Because 2 is stored at location 0 */
}
#endif
void prime_iterator_setprime(prime_iterator *iter, UV n) {
/* Is it inside the current segment? */
if ( (iter->segment_mem != 0)
&& (n >= iter->segment_start)
&& (n <= iter->segment_start + 30*iter->segment_bytes - 1) ) {
iter->p = n;
return;
}
prime_iterator_destroy(iter);
#ifdef NSMALL_PRIMES
/* In small area? */
if (n < NSMALL_PRIMES) {
UV pc = pcount(n);
iter->segment_start = pc-1;
iter->p = (pc == 0) ? 2 : small_primes[pc-1];
} else
#endif
if (n <= primary_limit) { /* Is it inside the primary cache range? */
iter->p = n;
} else { /* Sieve this range */
UV lod, hid;
lod = n/30;
hid = lod + SEGMENT_SIZE;
New(0, iter->segment_mem, SEGMENT_SIZE, unsigned char );
iter->segment_start = lod * 30;
iter->segment_bytes = SEGMENT_SIZE;
if (!sieve_segment((unsigned char*)iter->segment_mem, lod, hid, primary_sieve, primary_limit))
croak("Could not segment sieve");
iter->p = n;
}
}
UV prime_iterator_next(prime_iterator *iter)
{
UV lod, hid, seg_beg, seg_end;
const unsigned char* sieve;
UV n = iter->p;
#ifdef NSMALL_PRIMES
if (n < NSMALL_PRIMES) {
iter->p = small_primes[++iter->segment_start];
return iter->p;
}
#else
if (n < 11) {
switch (n) {
case 0: case 1: iter->p = 2; break;
case 2: iter->p = 3; break;
case 3: case 4: iter->p = 5; break;
case 5: case 6: iter->p = 7; break;
default: iter->p = 11; break;
}
return iter->p;
}
#endif
/* Primary sieve */
if (primary_sieve != 0 && n < 30*PRIMARY_SIZE) {
n = next_prime_in_segment(primary_sieve, 0, PRIMARY_SIZE, iter->p);
if (n > 0) {
iter->p = n;
return n;
}
}
sieve = iter->segment_mem;
/* Current segment */
if (sieve != 0) {
seg_beg = iter->segment_start;
seg_end = iter->segment_start + 30*iter->segment_bytes - 1;
n = next_prime_in_segment(sieve, seg_beg, iter->segment_bytes, iter->p);
if (n > 0) {
iter->p = n;
return n;
}
/* Not found in this segment */
lod = (seg_end+1)/30;
} else {
lod = PRIMARY_SIZE;
New(0, sieve, SEGMENT_SIZE, unsigned char );
}
hid = lod + SEGMENT_SIZE - 1;
iter->segment_start = lod * 30;
iter->segment_bytes = SEGMENT_SIZE;
seg_beg = iter->segment_start;
seg_end = iter->segment_start + 30*iter->segment_bytes - 1;
if (!sieve_segment((unsigned char*)sieve, lod, hid, primary_sieve, primary_limit))
croak("Could not segment sieve from %"UVuf" to %"UVuf, seg_beg, seg_end);
iter->segment_mem = sieve;
n = next_prime_in_segment(sieve, seg_beg, iter->segment_bytes, seg_beg);
if (n > 0) {
iter->p = n;
return n;
}
croak("MPU: segment size too small, could not find prime\n");
}
static int _is_trial_prime(UV n)
{
UV i = 7;
UV limit = (UV)sqrt(n);
while (1) { /* trial division, skipping multiples of 2/3/5 */
if (i > limit) break; if ((n % i) == 0) return 0; i += 4;
if (i > limit) break; if ((n % i) == 0) return 0; i += 2;
if (i > limit) break; if ((n % i) == 0) return 0; i += 4;
if (i > limit) break; if ((n % i) == 0) return 0; i += 2;
if (i > limit) break; if ((n % i) == 0) return 0; i += 4;
if (i > limit) break; if ((n % i) == 0) return 0; i += 6;
if (i > limit) break; if ((n % i) == 0) return 0; i += 2;
if (i > limit) break; if ((n % i) == 0) return 0; i += 6;
}
return 1;
}
int prime_iterator_isprime(prime_iterator *iter, UV n)
{
if (n < 11) {
switch (n) {
case 2: case 3: case 5: case 7: return 1; break;
default: break;
}
return 0;
}
/* Primary sieve */
if (primary_sieve != 0 && n <= primary_limit) {
UV d = n/30;
UV m = n - d*30;
unsigned char mtab = masktab30[m];
return mtab && !(primary_sieve[d] & mtab);
}
/* Current segment */
if (iter->segment_mem != 0) {
int isp = is_prime_in_segment(iter->segment_mem, iter->segment_start, iter->segment_bytes, n);
if (isp >= 0) return isp;
}
/* Out of segment range, can't answer. Try simple divisibility */
{
UV d = n/30;
UV m = n - d*30;
unsigned char mtab = masktab30[m];
if (mtab == 0) return 0;
return _is_trial_prime(n);
}
}
UV* sieve_to_n(UV n, UV* count)
{
UV pi_max, max_buf, i, p, pi;
const unsigned char* sieve;
UV* primes;
#ifdef NSMALL_PRIMES
if (small_primes != 0 && n < NSMALL_PRIMES) {
pi = pcount(n);
New(0, primes, pi, UV);
for (i = 0; i < pi; i++) primes[i] = small_primes[i];
if (count != 0) *count = pi;
return primes;
}
#endif
pi_max = (n < 67) ? 18
: (n < 355991) ? 15+(n/(log(n)-1.09))
: (n/log(n)) * (1.0+1.0/log(n)+2.51/(log(n)*log(n)));
New(0, primes, pi_max + 10, UV);
pi = 0;
primes[pi++] = 2; primes[pi++] = 3; primes[pi++] = 5; primes[pi++] = 7;
primes[pi++] = 11; primes[pi++] = 13; primes[pi++] = 17; primes[pi++] = 19;
primes[pi++] = 23; primes[pi++] = 29;
if (primary_sieve != 0 && n < 30*PRIMARY_SIZE)
sieve = primary_sieve;
else
sieve = sieve_erat30(n);
max_buf = (n/30) + ((n%30) != 0);
for (i = 1, p = 30; i < max_buf; i++, p += 30) {
UV c = sieve[i];
if (!(c & 1)) primes[pi++] = p+ 1;
if (!(c & 2)) primes[pi++] = p+ 7;
if (!(c & 4)) primes[pi++] = p+11;
if (!(c & 8)) primes[pi++] = p+13;
if (!(c & 16)) primes[pi++] = p+17;
if (!(c & 32)) primes[pi++] = p+19;
if (!(c & 64)) primes[pi++] = p+23;
if (!(c & 128)) primes[pi++] = p+29;
}
while (pi > 0 && primes[pi-1] > n) pi--;
if (sieve != primary_sieve) Safefree(sieve);
if (count != 0) *count = pi;
return primes;
}