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
|
#include <tommath.h>
#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
*/
#ifndef NO_FLOATING_POINT
#include <math.h>
#endif
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
{
int res;
mp_int t1,t2;
int i, j, k;
#ifndef NO_FLOATING_POINT
volatile double d;
mp_digit dig;
#endif
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* easy out */
if (mp_iszero(arg) == MP_YES) {
mp_zero(ret);
return MP_OKAY;
}
i = (arg->used / 2) - 1;
j = 2 * i;
if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
for (k = 0; k < i; ++k) {
t1.dp[k] = (mp_digit) 0;
}
#ifndef NO_FLOATING_POINT
/* Estimate the square root using the hardware floating point unit. */
d = 0.0;
for (k = arg->used-1; k >= j; --k) {
d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]);
}
/*
* At this point, d is the nearest floating point number to the most
* significant 1 or 2 mp_digits of arg. Extract its square root.
*/
d = sqrt(d);
/* dig is the most significant mp_digit of the square root */
dig = (mp_digit) ldexp(d, -DIGIT_BIT);
/*
* If the most significant digit is nonzero, find the next digit down
* by subtracting DIGIT_BIT times thie most significant digit.
* Subtract one from the result so that our initial estimate is always
* low.
*/
if (dig) {
t1.used = i+2;
d -= ldexp((double) dig, DIGIT_BIT);
if (d >= 1.0) {
t1.dp[i+1] = dig;
t1.dp[i] = ((mp_digit) d) - 1;
} else {
t1.dp[i+1] = dig-1;
t1.dp[i] = MP_DIGIT_MAX;
}
} else {
t1.used = i+1;
t1.dp[i] = ((mp_digit) d) - 1;
}
#else
/* Estimate the square root as having 1 in the most significant place. */
t1.used = i + 2;
t1.dp[i+1] = (mp_digit) 1;
t1.dp[i] = (mp_digit) 0;
#endif
/* t1 > 0 */
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* And now t1 > sqrt(arg) */
do {
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1,&t2) == MP_GT);
mp_exch(&t1,ret);
E1: mp_clear(&t2);
E2: mp_clear(&t1);
return res;
}
#endif
|
