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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 x;
unsigned c;
// Never called with N < 1
// if (N == 0)
// return 0;
//
/* Count leading zeros */
c = 0;
while (!(N & TOPMOST_WIDE_BIT)) {
c++;
N <<= 1;
}
N >>= c;
/* Make x > sqrt(n) */
x = (wide_t)1 << ((WIDE_BITS + 1 - c) / 2);
dbg("x:%llx", x);
for (;;) {
wide_t y = (x + N/x) / 2;
dbg("y:%llx y^2:%llx (y+1)^2:%llx]", y, y*y, (y+1)*(y+1));
if (y >= x) {
/* Handle degenerate case N = 0xffffffffff...fffffff */
if (y == (wide_t)HALF_MAX + 1)
y--;
dbg("isqrt(%llx)=%llx"HALF_FMT, N, y);
return y;
}
x = y;
}
}
static NOINLINE half_t isqrt_odd(wide_t N)
{
half_t s = isqrt(N);
if (s && !(s & 1)) /* even? */
s--;
return s;
}
static NOINLINE void factorize(wide_t N)
{
wide_t factor2;
half_t factor;
half_t max_factor;
unsigned count3;
if (N < 4)
goto end;
while (!(N & 1)) {
printf(" 2");
N >>= 1;
}
max_factor = isqrt_odd(N);
count3 = 3;
factor = 3;
factor2 = 3 * 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(" %u"HALF_FMT, factor);
max_factor = isqrt_odd(N);
}
next_factor:
if (factor >= max_factor)
break;
/* (f + 2)^2 = f^2 + 4*f + 4 = f^2 + 4*(f+1) */
factor2 = factor2 + 4 * (factor + 1);
/* overflow is impossible due to max_factor check */
/* (factor2 > N) is impossible due to max_factor check */
factor += 2;
/* Rudimentary wheel sieving: skip multiples of 3:
* 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)
*/
--count3;
if (count3 == 0) {
count3 = 3;
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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