#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define FUNC_next_prime_in_sieve
#include "sieve.h"
#include "ptypes.h"
#include "cache.h"
#include "util.h"
/* 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. */
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 = isqrt(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);
#if 0
assert(d == ((prime*prime)/30));
assert(d < max_buf);
assert(prime = (wdinc[0]+wdinc[1]+wdinc[2]+wdinc[3]+wdinc[4]+wdinc[5]+wdinc[6]+wdinc[7]));
#endif
/* Regular code to mark composites:
* i = 0;
* do {mem[d] |= wmask[i]; d += wdinc[i]; i = (i+1)&7;} while (d < max_buf);
* Unrolled version: */
while ( (d+prime) < max_buf ) {
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 >= 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;
}
int sieve_segment(unsigned char* mem, UV startd, UV endd)
{
const unsigned char* sieve;
UV limit;
UV pcsize;
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 = isqrt(endp);
if (limit*limit < endp) limit++; /* ceil(sqrt(endp)) */
/* printf("segment sieve from %"UVuf" to %"UVuf" (aux sieve to %"UVuf")\n", startp, endp, limit); */
pcsize = get_prime_cache(limit, &sieve);
if (pcsize < limit) {
release_prime_cache(sieve);
return 0;
}
START_DO_FOR_EACH_SIEVE_PRIME(sieve, 17, pcsize)
{
/* p increments from 17 to at least sqrt(endp). Note on overflow:
* 32-bit: limit= 65535, max p = 65521, p*p = ~0-1965854
* 64-bit: limit=4294967295, max p = 4294967291, p*p = ~0-42949672934
* No overflow here, but possible after the incrementing below. */
UV p2 = p*p;
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; } */
p2 += p * primestepadvance30[m_>>1][p2%30];
/* 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 */
#if 0
/* Basic sieve */
do {
mem[(p2 - startp)/30] |= masktab30[p2%30];
do { p2 += 2*p; } while (masktab30[p2%30] == 0);
} while ( (p2 <= endp) && (p2 >= startp) );
#else
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;
/* Unrolled inner loop for marking composites */
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;
}
#endif
}
}
END_DO_FOR_EACH_SIEVE_PRIME;
release_prime_cache(sieve);
return 1;
}
/**************************************************************************/
typedef struct {
UV lod;
UV hid;
UV low;
UV high;
UV endp;
UV segment_size;
unsigned char* segment;
unsigned char* base;
} segment_context_t;
/*
* unsigned char* segment;
* UV seg_base, seg_low, seg_high;
* void* ctx = start_segment_primes(low, high, &segment);
* while (beg < 7) {
* beg = (beg <= 2) ? 2 : (beg <= 3) ? 3 : 5;
* .... with beg ....
* beg += 1 + (beg > 2);
* }
* while (next_segment_primes(ctx, &seg_base, &seg_low, &seg_high)) {
* START_DO_FOR_EACH_SIEVE_PRIME( segment, seg_low - seg_base, seg_high - seg_base )
* .... with seg_base + p ....
* END_DO_FOR_EACH_SIEVE_PRIME
* }
* end_segment_primes(ctx);
*/
void* start_segment_primes(UV low, UV high, unsigned char** segmentmem)
{
segment_context_t* ctx;
MPUassert( high >= low, "start_segment_primes bad arguments");
New(0, ctx, 1, segment_context_t);
ctx->low = low;
ctx->high = high;
ctx->lod = low / 30;
ctx->hid = high / 30;
ctx->endp = (ctx->hid >= (UV_MAX/30)) ? UV_MAX-2 : 30*ctx->hid+29;
ctx->segment = get_prime_segment( &(ctx->segment_size) );
if (ctx->segment == 0)
croak("start_segment_primes: Could not get segment");
*segmentmem = ctx->segment;
ctx->base = sieve_erat30( isqrt(ctx->endp)+1 );
if (ctx->base == 0)
croak("start_segment_primes: Could not get base");
return (void*) ctx;
}
int next_segment_primes(void* vctx, UV* base, UV* low, UV* high)
{
UV seghigh_d, range_d;
segment_context_t* ctx = (segment_context_t*) vctx;
if (ctx->lod > ctx->hid) return 0;
seghigh_d = ((ctx->hid - ctx->lod) < ctx->segment_size)
? ctx->hid
: (ctx->lod + ctx->segment_size - 1);
range_d = seghigh_d - ctx->lod + 1;
*low = ctx->low;
*high = (seghigh_d == ctx->hid) ? ctx->high : (seghigh_d*30 + 29);
*base = ctx->lod * 30;
MPUassert( seghigh_d >= ctx->lod, "next_segment_primes: highd < lowd");
MPUassert( range_d <= ctx->segment_size, "next_segment_primes: range > segment size");
if (sieve_segment(ctx->segment, ctx->lod, seghigh_d) == 0) {
croak("Could not segment sieve from %"UVuf" to %"UVuf, *base+1, *high);
}
ctx->lod += range_d;
ctx->low = *high + 2;
return 1;
}
void end_segment_primes(void* vctx)
{
segment_context_t* ctx = (segment_context_t*) vctx;
MPUassert(ctx != 0, "end_segment_primes given a null pointer");
if (ctx->segment != 0) {
release_prime_segment(ctx->segment);
ctx->segment = 0;
}
if (ctx->base != 0) {
Safefree(ctx->base);
ctx->base = 0;
}
Safefree(ctx);
}