* Licensed under GPLv2, see file LICENSE in this source tree.
*/
//config:config FACTOR
-//config: bool "factor"
+//config: bool "factor (2.6 kb)"
//config: default y
//config: help
-//config: factor factorizes integers
+//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: "[NUMBER]..."
//usage:#define factor_full_usage "\n\n"
//usage: "Print prime factors"
#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 */
#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 x > sqrt(N) - 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 (mask_2bits && !(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)
+static half_t isqrt_odd(wide_t N)
{
half_t s = isqrt(N);
- if (s && !(s & 1)) /* even? */
- s--;
+ /* 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;
}
{
half_t factor;
half_t max_factor;
- unsigned count3;
- unsigned count5;
- unsigned count7;
+ // unsigned count3;
+ // unsigned count5;
+ // unsigned count7;
+ // ^^^^^^^^^^^^^^^ commented-out simple sieving code (easier to grasp).
+ // Faster sieving, using one word for potentially up to 6 counters:
+ // count upwards in each mask, counter "triggers" when it sets its mask to "100[0]..."
+ // 10987654321098765432109876543210 - bits 31-0 in 32-bit word
+ // 17777713333311111777775555333 - bit masks for counters for primes 3,5,7,11,13,17
+ // 100000100001000010001001 - value for adding 1 to each mask
+ // 10000010000010000100001000100 - value for checking that any mask reached msb
+ enum {
+ SHIFT_3 = 1 << 0,
+ SHIFT_5 = 1 << 3,
+ SHIFT_7 = 1 << 7,
+ INCREMENT_EACH = SHIFT_3 | SHIFT_5 | SHIFT_7,
+ MULTIPLE_OF_3 = 1 << 2,
+ MULTIPLE_OF_5 = 1 << 6,
+ MULTIPLE_OF_7 = 1 << 11,
+ MULTIPLE_DETECTED = MULTIPLE_OF_3 | MULTIPLE_OF_5 | MULTIPLE_OF_7,
+ };
+ unsigned sieve_word;
if (N < 4)
goto end;
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.
+ * The slowest case (largest prime) for N < 2^64 is
+ * factor 18446744073709551557 (0xffffffffffffffc5).
+ */
max_factor = isqrt_odd(N);
- count3 = 3;
- count5 = 6;
- count7 = 9;
+ // count3 = 3;
+ // count5 = 6;
+ // count7 = 9;
+ sieve_word = 0
+ /* initial count for SHIFT_n is (n-1)/2*3: */
+ + (MULTIPLE_OF_3 - 3 * SHIFT_3)
+ + (MULTIPLE_OF_5 - 6 * SHIFT_5)
+ + (MULTIPLE_OF_7 - 9 * SHIFT_7)
+ //+ (MULTIPLE_OF_11 - 15 * SHIFT_11)
+ //+ (MULTIPLE_OF_13 - 18 * SHIFT_13)
+ //+ (MULTIPLE_OF_17 - 24 * SHIFT_17)
+ ;
factor = 3;
for (;;) {
/* The division is the most costly part of the loop.
*/
while ((N % factor) == 0) { /* not likely */
N = N / factor;
- printf(" %u"HALF_FMT, 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:
+ /* 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)
+ // count7--;
+ // count5--;
+ // count3--;
+ // if (count3 && count5 && count7)
+ // continue;
+ sieve_word += INCREMENT_EACH;
+ if (!(sieve_word & MULTIPLE_DETECTED))
continue;
- if (count3 == 0)
- count3 = 3;
- if (count5 == 0)
- count5 = 5;
- if (count7 == 0)
- count7 = 7;
+ /*
+ * "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 (sieve_word & MULTIPLE_OF_3)
+ sieve_word -= SHIFT_3 * 3;
+ // if (count5 == 0)
+ // count5 = 5;
+ if (sieve_word & MULTIPLE_OF_5)
+ sieve_word -= SHIFT_5 * 5;
+ // if (count7 == 0)
+ // count7 = 7;
+ if (sieve_word & MULTIPLE_OF_7)
+ sieve_word -= SHIFT_7 * 7;
goto next_factor;
}
end:
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)
{
//argv += optind;
argv++;
- if (!*argv)
- //TODO: read from stdin
- bb_show_usage();
+ 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 {
- 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);
+ /* Leading spaces are ok (coreutils compat) */
+ factorize_numstr(skip_whitespace(*argv));
} while (*++argv);
return EXIT_SUCCESS;
projects / oweals / busybox.git / blobdiff