/*
 * 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 (2.6 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"

#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

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)
{
        half_t factor;
        half_t max_factor;
        // 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;

        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.
         * The slowest case (largest prime) for N < 2^64 is
         * factor 18446744073709551557 (0xffffffffffffffc5).
         */
        max_factor = isqrt_odd(N);
        // 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.
                 * 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;
                sieve_word += INCREMENT_EACH;
                if (!(sieve_word & MULTIPLE_DETECTED))
                        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 (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:
        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)
{
        //// 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;
}