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
|
/*
* 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 (;;) {
while ((N % factor) == 0) {
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...
* ^ ^ ^ ^ ^ ^ ^ _ ^ ^ _ ^
* (^ = 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;
}
|
