Mercurial > dropbear

annotate libtommath/bn_mp_root_u32.c @ 1909:43ebe0028187

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Add tests for dropbearconvert
author Matt Johnston <matt@ucc.asn.au>
date Tue, 29 Mar 2022 22:29:17 +0800
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
1 #include "tommath_private.h"
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
2 #ifdef BN_MP_ROOT_U32_C
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
4 /* SPDX-License-Identifier: Unlicense */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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5
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
6 /* find the n'th root of an integer
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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7 *
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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8 * Result found such that (c)**b <= a and (c+1)**b > a
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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9 *
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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10 * This algorithm uses Newton's approximation
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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11 * x[i+1] = x[i] - f(x[i])/f'(x[i])
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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12 * which will find the root in log(N) time where
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
13 * each step involves a fair bit.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
14 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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15 mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c)
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
16 {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
17 mp_int t1, t2, t3, a_;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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18 mp_ord cmp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
19 int ilog2;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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20 mp_err err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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21
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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22 /* input must be positive if b is even */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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23 if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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24 return MP_VAL;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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25 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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26
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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27 if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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28 return err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
29 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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30
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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31 /* if a is negative fudge the sign but keep track */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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32 a_ = *a;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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33 a_.sign = MP_ZPOS;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
34
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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35 /* Compute seed: 2^(log_2(n)/b + 2)*/
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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36 ilog2 = mp_count_bits(a);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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37
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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38 /*
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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39 If "b" is larger than INT_MAX it is also larger than
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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40 log_2(n) because the bit-length of the "n" is measured
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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41 with an int and hence the root is always < 2 (two).
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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42 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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43 if (b > (uint32_t)(INT_MAX/2)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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44 mp_set(c, 1uL);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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45 c->sign = a->sign;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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46 err = MP_OKAY;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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47 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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48 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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49
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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50 /* "b" is smaller than INT_MAX, we can cast safely */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
51 if (ilog2 < (int)b) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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52 mp_set(c, 1uL);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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53 c->sign = a->sign;
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Steffen Jaeckel <s@jaeckel.eu>
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54 err = MP_OKAY;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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55 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
56 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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57 ilog2 = ilog2 / ((int)b);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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58 if (ilog2 == 0) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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59 mp_set(c, 1uL);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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60 c->sign = a->sign;
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Steffen Jaeckel <s@jaeckel.eu>
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61 err = MP_OKAY;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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62 goto LBL_ERR;
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Steffen Jaeckel <s@jaeckel.eu>
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63 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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64 /* Start value must be larger than root */
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65 ilog2 += 2;
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Steffen Jaeckel <s@jaeckel.eu>
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66 if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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67 do {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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68 /* t1 = t2 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
69 if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
70
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
71 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
72
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
73 /* t3 = t1**(b-1) */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
74 if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
75
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
76 /* numerator */
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
77 /* t2 = t1**b */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
78 if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
79
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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80 /* t2 = t1**b - a */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
81 if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
82
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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83 /* denominator */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
84 /* t3 = t1**(b-1) * b */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
85 if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
86
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
88 if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
89
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
90 if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
91
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
92 /*
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
93 Number of rounds is at most log_2(root). If it is more it
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
94 got stuck, so break out of the loop and do the rest manually.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
95 */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
96 if (ilog2-- == 0) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
97 break;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
98 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
99 } while (mp_cmp(&t1, &t2) != MP_EQ);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
100
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
101 /* result can be off by a few so check */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
102 /* Loop beneath can overshoot by one if found root is smaller than actual root */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
103 for (;;) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
104 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
105 cmp = mp_cmp(&t2, &a_);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
106 if (cmp == MP_EQ) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
107 err = MP_OKAY;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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108 goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
109 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
110 if (cmp == MP_LT) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
111 if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
112 } else {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
113 break;
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
114 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
115 }
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
116 /* correct overshoot from above or from recurrence */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
117 for (;;) {
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
118 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
119 if (mp_cmp(&t2, &a_) == MP_GT) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
120 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
121 } else {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
122 break;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
123 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
124 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
125
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
126 /* set the result */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
127 mp_exch(&t1, c);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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128
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129 /* set the sign of the result */
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130 c->sign = a->sign;
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131
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132 err = MP_OKAY;
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133
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134 LBL_ERR:
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135 mp_clear_multi(&t1, &t2, &t3, NULL);
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136 return err;
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137 }
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138
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139 #endif