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/*
* Copyright (C) 2017 Denys Vlasenko <vda.linux@googlemail.com>
*
* Licensed under GPLv2, see file LICENSE in this source tree.
*/
//config:config FACTOR
//config: bool "factor"
//config: default y
//config: help
//config: factor factorizes integers
//applet:IF_FACTOR(APPLET(factor, BB_DIR_USR_BIN, BB_SUID_DROP))
//kbuild:lib-$(CONFIG_FACTOR) += factor.o
//usage:#define factor_trivial_usage
//usage: "NUMBER..."
//usage:#define factor_full_usage "\n\n"
//usage: "Print prime factors"
#include "libbb.h"
#if 0
# define dbg(...) bb_error_msg(__VA_ARGS__)
#else
# define dbg(...) ((void)0)
#endif
typedef unsigned long long wide_t;
#define WIDE_BITS (unsigned)(sizeof(wide_t)*8)
#define TOPMOST_WIDE_BIT ((wide_t)1 << (WIDE_BITS-1))
#if ULLONG_MAX == (UINT_MAX * UINT_MAX + 2 * UINT_MAX)
/* "unsigned" is half as wide as ullong */
typedef unsigned half_t;
#define HALF_MAX UINT_MAX
#define HALF_FMT ""
#elif ULLONG_MAX == (ULONG_MAX * ULONG_MAX + 2 * ULONG_MAX)
/* long is half as wide as ullong */
typedef unsigned long half_t;
#define HALF_MAX ULONG_MAX
#define HALF_FMT "l"
#else
#error Cant find an integer type which is half as wide as ullong
#endif
/* Returns such x that x+1 > sqrt(N) */
static inline half_t isqrt(wide_t N)
{
wide_t mask_2bits;
half_t x;
// Never called with N < 1
// if (N == 0)
// return 0;
/* First approximation of x+1 > sqrt(N) - all-ones, half as many bits:
* 1xxxxx -> 111 (six bits to three)
* 01xxxx -> 111
* 001xxx -> 011
* 0001xx -> 011 and so on.
*/
x = HALF_MAX;
mask_2bits = TOPMOST_WIDE_BIT | (TOPMOST_WIDE_BIT >> 1);
while (!(N & mask_2bits)) {
x >>= 1;
mask_2bits >>= 2;
}
dbg("x:%"HALF_FMT"x", x);
for (;;) {
half_t y = (x + N/x) / 2;
dbg("y:%x y^2:%llx", y, (wide_t)y * y);
/*
* "real" y may be one bit wider: 0x100000000 and get truncated to 0.
* In this case, "real" y is > x. The first check below is for this case:
*/
if (y == 0 || y >= x) {
dbg("isqrt(%llx)=%"HALF_FMT"x", N, x);
return x;
}
x = y;
}
}
static NOINLINE half_t isqrt_odd(wide_t N)
{
half_t s = isqrt(N);
/* Subtract 1 from even s, odd s won't change: */
/* (doesnt work for zero, but we know that s != 0 here) */
s = (s - 1) | 1;
return s;
}
static NOINLINE void factorize(wide_t N)
{
half_t factor;
half_t max_factor;
unsigned count3;
unsigned count5;
unsigned count7;
if (N < 4)
goto end;
while (!(N & 1)) {
printf(" 2");
N >>= 1;
}
/* The code needs to be optimized for the case where
* there are large prime factors. For example,
* this is not hard:
* 8262075252869367027 = 3 7 17 23 47 101 113 127 131 137 823
* (the largest factor to test is only ~sqrt(823) = 28)
* but this is:
* 18446744073709551601 = 53 348051774975651917
* the last factor requires testing up to
* 589959129 - about 100 million iterations.
*/
max_factor = isqrt_odd(N);
count3 = 3;
count5 = 6;
count7 = 9;
factor = 3;
for (;;) {
/* The division is the most costly part of the loop.
* On 64bit CPUs, takes at best 12 cycles, often ~20.
*/
while ((N % factor) == 0) { /* not likely */
N = N / factor;
printf(" %"HALF_FMT"u", factor);
max_factor = isqrt_odd(N);
}
next_factor:
if (factor >= max_factor)
break;
factor += 2;
/* Rudimentary wheel sieving: skip multiples of 3, 5 and 7:
* Every third odd number is divisible by three and thus isn't a prime:
* 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47...
* ^ ^ ^ ^ ^ ^ ^ _ ^ ^ _ ^ ^ ^ ^
* (^ = primes, _ = would-be-primes-if-not-divisible-by-5)
* The numbers with space under them are excluded by sieve 3.
*/
count7--;
count5--;
count3--;
if (count3 && count5 && count7)
continue;
/*
* "factor" is multiple of 3 33% of the time (count3 reached 0),
* else, multiple of 5 13% of the time,
* else, multiple of 7 7.6% of the time.
* Cumulatively, with 3,5,7 sieving we are here 54.3% of the time.
*/
if (count3 == 0) {
count3 = 3;
}
if (count5 == 0) {
count5 = 5;
}
if (count7 == 0) {
count7 = 7;
}
goto next_factor;
}
end:
if (N > 1)
printf(" %llu", N);
bb_putchar('\n');
}
int factor_main(int argc, char **argv) MAIN_EXTERNALLY_VISIBLE;
int factor_main(int argc UNUSED_PARAM, char **argv)
{
//// coreutils has undocumented option ---debug (three dashes)
//getopt32(argv, "");
//argv += optind;
argv++;
if (!*argv)
//TODO: read from stdin
bb_show_usage();
do {
wide_t N;
const char *numstr;
/* Coreutils compat */
numstr = skip_whitespace(*argv);
if (*numstr == '+')
numstr++;
N = bb_strtoull(numstr, NULL, 10);
if (errno)
bb_show_usage();
printf("%llu:", N);
factorize(N);
} while (*++argv);
return EXIT_SUCCESS;
}
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