1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
|
/*
* 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;
#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_3_5_7 = 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
+ (MULTIPLE_OF_3 - 3 * SHIFT_3)
+ (MULTIPLE_OF_5 - 6 * SHIFT_5)
+ (MULTIPLE_OF_7 - 9 * SHIFT_7)
;
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_3_5_7))
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');
}
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;
}
|
