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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 (2.7 kb)"
//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"
#include "common_bufsiz.h"
#if 0
# define dbg(...) bb_error_msg(__VA_ARGS__)
#else
# define dbg(...) ((void)0)
#endif
typedef unsigned long long wide_t;
#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
/* The trial divisor increment wheel. Use it to skip over divisors that
* are composites of 2, 3, 5, 7, or 11.
* Larger wheels improve sieving only slightly, but quickly grow in size
* (adding just one prime, 13, results in 5766 element sieve).
*/
#define R(a,b,c,d,e,f,g,h,i,j,A,B,C,D,E,F,G,H,I,J) \
(((uint64_t)(a<<0) | (b<<3) | (c<<6) | (d<<9) | (e<<12) | (f<<15) | (g<<18) | (h<<21) | (i<<24) | (j<<27)) ) | \
(((uint64_t)(A<<0) | (B<<3) | (C<<6) | (D<<9) | (E<<12) | (F<<15) | (G<<18) | (H<<21) | (I<<24) | (J<<27)) << 30) | \
(((uint64_t)7 << 60))
#define P(a,b,c,d,e,f,g,h,i,j,A,B,C,D,E,F,G,H,I,J) \
R( (a/2-1),(b/2-1),(c/2-1),(d/2-1),(e/2-1),(f/2-1),(g/2-1),(h/2-1),(i/2-1),(j/2-1), \
(A/2-1),(B/2-1),(C/2-1),(D/2-1),(E/2-1),(F/2-1),(G/2-1),(H/2-1),(I/2-1),(J/2-1) )
static const uint64_t packed_wheel[] = {
/*1, 2, 2, 4, 2,*/
P( 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4), //01
P( 2, 4, 2, 4,14, 4, 6, 2,10, 2, 6, 6, 4, 2, 4, 6, 2,10, 2, 4), //02
P( 2,12,10, 2, 4, 2, 4, 6, 2, 6, 4, 6, 6, 6, 2, 6, 4, 2, 6, 4), //03
P( 6, 8, 4, 2, 4, 6, 8, 6,10, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2), //04
P( 6, 4, 2, 6,10, 2,10, 2, 4, 2, 4, 6, 8, 4, 2, 4,12, 2, 6, 4), //05
P( 2, 6, 4, 6,12, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6,10, 2), //06
P( 4, 6, 2, 6, 4, 2, 4, 2,10, 2,10, 2, 4, 6, 6, 2, 6, 6, 4, 6), //07
P( 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 6, 4, 8, 6, 4, 6, 2, 4, 6), //08
P( 8, 6, 4, 2,10, 2, 6, 4, 2, 4, 2,10, 2,10, 2, 4, 2, 4, 8, 6), //09
P( 4, 2, 4, 6, 6, 2, 6, 4, 8, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4), //10
P( 6, 6, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2,10, 2,10, 2), //11
P( 6, 4, 6, 2, 6, 4, 2, 4, 6, 6, 8, 4, 2, 6,10, 8, 4, 2, 4, 2), //12
P( 4, 8,10, 6, 2, 4, 8, 6, 6, 4, 2, 4, 6, 2, 6, 4, 6, 2,10, 2), //13
P(10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 6, 6, 4, 6, 8), //14
P( 4, 2, 4, 2, 4, 8, 6, 4, 8, 4, 6, 2, 6, 6, 4, 2, 4, 6, 8, 4), //15
P( 2, 4, 2,10, 2,10, 2, 4, 2, 4, 6, 2,10, 2, 4, 6, 8, 6, 4, 2), //16
P( 6, 4, 6, 8, 4, 6, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 6), //17
P( 6, 2, 6, 6, 4, 2,10, 2,10, 2, 4, 2, 4, 6, 2, 6, 4, 2,10, 6), //18
P( 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2,12, 6, 4, 6, 2, 4, 6, 2), //19
P(12, 4, 2, 4, 8, 6, 4, 2, 4, 2,10, 2,10, 6, 2, 4, 6, 2, 6, 4), //20
P( 2, 4, 6, 6, 2, 6, 4, 2,10, 6, 8, 6, 4, 2, 4, 8, 6, 4, 6, 2), //21
P( 4, 6, 2, 6, 6, 6, 4, 6, 2, 6, 4, 2, 4, 2,10,12, 2, 4, 2,10), //22
P( 2, 6, 4, 2, 4, 6, 6, 2,10, 2, 6, 4,14, 4, 2, 4, 2, 4, 8, 6), //23
P( 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4,12, 2,12), //24
};
#undef P
#undef r
#define WHEEL_START 5
#define WHEEL_SIZE (5 + 24 * 20)
#define wheel_tab ((uint8_t*)&bb_common_bufsiz1)
/*
* Why, you ask?
* plain byte array:
* function old new delta
* wheel_tab - 485 +485
* 3-bit-packed insanity:
* packed_wheel - 192 +192
* factor_main 108 176 +68
*/
static void unpack_wheel(void)
{
int i;
uint8_t *p;
setup_common_bufsiz();
wheel_tab[0] = 1;
wheel_tab[1] = 2;
wheel_tab[2] = 2;
wheel_tab[3] = 4;
wheel_tab[4] = 2;
p = &wheel_tab[5];
for (i = 0; i < ARRAY_SIZE(packed_wheel); i++) {
uint64_t v = packed_wheel[i];
do {
*p = ((unsigned)(v & 7) + 1) * 2;
//printf("%2u,", *p);
p++;
v >>= 3;
} while ((unsigned)v != 7);
//printf("\n");
}
}
static 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)
{
unsigned w;
half_t factor;
half_t max_factor;
if (N < 4)
goto end;
/* 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 divisor to test for largest factor 823
* is only ~sqrt(823) = 28, the entire factorization needs
* only ~33 trial divisions)
* but this is:
* 18446744073709551601 = 53 348051774975651917
* the last factor requires testing up to
* 589959129 - about 100 million iterations.
* The slowest case (largest prime) for N < 2^64 is
* factor 18446744073709551557 (0xffffffffffffffc5).
*/
max_factor = isqrt_odd(N);
factor = 2;
w = 0;
for (;;) {
half_t fw;
/* 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);
}
if (factor >= max_factor)
break;
fw = factor + wheel_tab[w];
if (fw < factor)
break; /* overflow */
factor = fw;
w++;
if (w < WHEEL_SIZE)
continue;
w = WHEEL_START;
}
end:
if (N > 1)
printf(" %llu", N);
bb_putchar('\n');
}
static void factorize_numstr(const char *numstr)
{
wide_t N;
/* Leading + is ok (coreutils compat) */
if (*numstr == '+')
numstr++;
N = bb_strtoull(numstr, NULL, 10);
if (errno)
bb_show_usage();
printf("%llu:", N);
factorize(N);
}
int factor_main(int argc, char **argv) MAIN_EXTERNALLY_VISIBLE;
int factor_main(int argc UNUSED_PARAM, char **argv)
{
unpack_wheel();
//// coreutils has undocumented option ---debug (three dashes)
//getopt32(argv, "");
//argv += optind;
argv++;
if (!*argv) {
/* Read from stdin, several numbers per line are accepted */
for (;;) {
char *numstr, *line;
line = xmalloc_fgetline(stdin);
if (!line)
return EXIT_SUCCESS;
numstr = line;
for (;;) {
char *end;
numstr = skip_whitespace(numstr);
if (!numstr[0])
break;
end = skip_non_whitespace(numstr);
if (*end != '\0')
*end++ = '\0';
factorize_numstr(numstr);
numstr = end;
}
free(line);
}
}
do {
/* Leading spaces are ok (coreutils compat) */
factorize_numstr(skip_whitespace(*argv));
} while (*++argv);
return EXIT_SUCCESS;
}
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