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/*
5.12.91 original date
3.15.96 code last modified
1.29.98 modified
6.28.99 made whichfactor static
3.30.00 added if(looplimit < 5) looplimit = 5
4.6.04 corrected setting of mod11 in get_small_factors at line 192,
added table of primes up to 7907,
corrected return value of get_small_factors, which previously assumed 16-bit digits.
4.15.04 modified get_small_factors to not tack 1 on at the end if 1 is all that's left over.
6.17.04 removed 16-bit conditional compilation
9.2.04 changed includes to eliminate superfluous ones.
*/
#include <assert.h>
#include <math.h>
#include <string.h>
#define BIGNUMS_DLL
#include "export.h"
#include "heap.h"
#include "bignum.h"
static unsigned get_looplimit(bignum);
static int bigtakeout(unsigned,bignum,bignum *);
/* _______________________________________________________________*/
/* The following table can be enlarged if desired but the last entry must
always be congruent to 1 mod 6, not to 5 mod 6.
*/
static unsigned primes[] = {
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, 1009, 1013,
1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583,
1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889,
1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213,
2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531,
2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819,
2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181,
3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,
3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821,
3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139,
4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493,
4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831,
4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003,
5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179,
5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521,
5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693,
5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857,
5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053,
6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221,
6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367,
6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761,
6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917,
6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499,
7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643,
7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829,
7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907
};
/*___________________________________________________________________*/
MEXPORT_BIGNUMS int get_small_factors(bignum x, unsigned *ans, int *n, bignum *rest, unsigned *sofar)
/* Remove all 16-bit factors from bignum x, returning in *rest the
unfactored portion. Return value 0 means x factored completely
as a product of 16-bit integers.
*n is in that case the number of prime factors, and *rest is garbage.
Return value 1 means rest is a 17-to-32-bit prime and *n is 1 + the number of
16-bit factors found. Return value 2 means rest is more than 32 bits,
unknown whether it is prime or not, and *n is 1 + the number of
16-bit factors found.
Return value 3 means the function isn't done yet,
but is just pausing for a report by the caller. The loop will
be started at *sofar, so it should be zero at the initial call.
To use this function, you do the following:
sofar = 0;
while(1)
{ err = get_small_factors(...,&sofar);
if(err != 3)
break; actually finished
Now report the progress using 'sofar', or
allow the user to interrupt, or whatever
}
*/
/* ans is a pre-allocated array to hold the prime factors and their powers;
e.g. for 12 it would be { 2,2,3,1} for 2^2 3^1 */
{ int i,ii;
unsigned j;
static bignum localx; /* static so its value will be correct on re-entry */
static unsigned looplimit; /* ditto */
bignum temp;
int mod5,mod7,mod11;
unsigned short k,exponentofk;
unsigned long y;
digit *saveit;
static int whichfactor;
if(*sofar == 0) /* initial call */
{ whichfactor = 0;
localx.ln = x.ln; /* make a local copy of x */
localx.val = getspace(localx.ln);
saveit = localx.val; /* save it so it can be freed later */
memcpy(localx.val,x.val,localx.ln * sizeof(digit));
/* is x divisible by 2? let i count the factors of 2 */
i=j=0;
while(j < x.ln && x.val[j]==0)
{ i += 8*sizeof(digit);
++j;
}
y = x.val[j];
localx.val += j; /* drop j least significant bignum digits */
localx.ln = (unsigned)(localx.ln - j); /* localx.ln -= j causes a warning
and this generates the same code */
if( (y & 1) == 0)
{ whichfactor = 2;
ans[0] = 2; /* now count how many twos divide y */
ii=0;
while( ((y >> ii) & 1) ==0 )
++ii;
i += ii;
ans[1] = i;
right_shift(localx, ii,&localx);
/* y will not be used again so we don't need: y >>= ii; */
}
else if(j > 0) /* some trailing bignum digits are zero but the least
significant non-zero digit is odd */
{ whichfactor = 2;
ans[0] = 2;
ans[1] = i;
}
if(localx.ln == 1 && localx.val[0] == 1) /* finished, x was a power of 2 */
{ *n = 1;
freespace(saveit);
return 0;
}
/* Now localx is odd and not 1 */
looplimit = get_looplimit(localx);
for(i = 0; ((i < sizeof(primes)/sizeof(unsigned)) && (localx.ln !=1 || localx.val[0] != 1)); i++ )
/* take out primes in the static primes table */
{ k = primes[i];
if(k > looplimit)
break;
exponentofk = bigtakeout(k,localx,&temp); /* is there a factor of k? */
if(!saveit)
{ freespace(saveit);
saveit = NULL;
}
if(exponentofk)
{ ans[whichfactor] = k;
ans[whichfactor + 1] = exponentofk;
whichfactor += 2;
if(!saveit)
freespace(localx.val); /* the 'temp' from last time */
localx = temp;
looplimit = get_looplimit(localx);
}
}
if(k > looplimit)
{ assert(localx.ln == 1);
rest->ln = 1;
rest->val = getspace(1);
rest->val[0] = 1;
if (localx.val[0] != 1)
/* remaining 16-bit unfactored portion is prime */
{ ans[whichfactor] = localx.val[0];
ans[whichfactor+1] = 1;
whichfactor += 2;
}
*n = whichfactor/2;
if(!saveit)
freespace(saveit);
return 0;
}
*sofar = primes[sizeof(primes)/sizeof(unsigned) - 1];
/* now all primes in the static primes table are out, and unless k > looplimit,
*sofar is the last prime checked */
}
/* Now set k to the first integer congruent to 5 mod 6 greater than *sofar */
k = *sofar + 1;
while((k+1)%6)
++k;
mod5 = k % 5; /* these variables record the indicated congruence class of k */
mod7 = k % 7;
mod11 = k % 11;
/* k is already initialized so there's no initialization in the next line */
for(; k < looplimit-5; k +=6) /* k will be congruent to 5 mod 6 */
/* k < looplimit - 5 so if looplimit is 0xffff we WILL stop; 0xffff,
0xfffd, and 0xfffb aren't prime anyway. */
{ if( (mod5!=0) && (mod7!=0) && (mod11!=0) )
{ i = bigtakeout(k,localx,&temp);
if( i > 0)
{ localx = temp;
ans[whichfactor]=k;
ans[whichfactor+1] = i;
whichfactor +=2;
looplimit = get_looplimit(localx);
if(looplimit < 5)
looplimit = 5; /* to prevent wraparound of looplimit-5 in the loop test */
}
}
if((mod5!=3) && (mod7!= -2) && (mod11 != 9))
{ i = bigtakeout(k+2,localx,&temp);
if( i > 0)
{ localx = temp;
ans[whichfactor]=k+2;
ans[whichfactor+1] = i;
whichfactor +=2;
looplimit = get_looplimit(localx);
if(looplimit < 5)
looplimit = 5; /* to prevent wraparound of looplimit-5 in the loop test */
}
}
if( ((k<<6)>>6) < 6 ) /* 1024 <= k < 1030 */
{ *sofar = k;
return 3; /* so caller can display progress */
}
if (mod5==4)
mod5=0;
else
++mod5;
if (mod7== -6)
mod7=0;
else
--mod7;
(mod11 <=4) ? (mod11 +=6) : (mod11 -= 5);
}
/* Now: localx is left over; if it's less than 32 bits it's necessarily
prime. Otherwise we don't know. */
if(localx.ln == 1) /* 32 bits or less, now that digits are 32 bits. Add it to workspace */
{ assert(sizeof(digit)==4);
if(localx.val[0] > 1)
{ ans[whichfactor] = localx.val[0];
ans[whichfactor+1] = 1;
whichfactor += 2;
}
*n = whichfactor/2;
freespace(localx.val-j);
return 0;
}
*rest = localx;
*n = whichfactor/2 + 1;
return 2;
}
/*_______________________________________________________________________*/
static unsigned get_looplimit(bignum x)
{ unsigned long y;
if (x.ln == 1)
{ y = x.val[0];
return (unsigned) sqrt( (double) y) + 1;
}
else
return 0xffff; /* 2^16-1 */
}
/*________________________________________________________________*/
static int bigtakeout(unsigned k,bignum x,bignum *ans)
/* divide x by all powers of k that will go; return the
exponent of k in x, and the quotient in *ans */
{
bignum localx = x;
bignum q;
digit r=0;
int i=0;
while(r==0)
{ divide_by_digit(localx,k,&q,&r);
if(r==0) /* zero remainder */
{ if(i>0)
freespace(localx.val); /* allocated by divide_by_digit previous
time through the loop */
localx = q;
++i;
}
}
freespace(q.val); /* allocated by divide_by_digit last time through */
*ans = localx;
return i;
}
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