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annotate libtommath/bn_s_mp_toom_sqr.c @ 1692:1051e4eea25a

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Update LibTomMath to 1.2.0 (#84) * update C files * update other files * update headers * update makefiles * remove mp_set/get_double() * use ltm 1.2.0 API * update ltm_desc * use bundled tommath if system-tommath is too old * XMALLOC etc. were changed to MP_MALLOC etc.
author Steffen Jaeckel <s@jaeckel.eu>
date Tue, 26 May 2020 17:36:47 +0200
parents
children
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1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
1 #include "tommath_private.h"
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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2 #ifdef BN_S_MP_TOOM_SQR_C
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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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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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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6 /* squaring using Toom-Cook 3-way algorithm */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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7
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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8 /*
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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9 This file contains code from J. Arndt's book "Matters Computational"
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
10 and the accompanying FXT-library with permission of the author.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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11 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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12
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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13 /* squaring using Toom-Cook 3-way algorithm */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
14 /*
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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15 Setup and interpolation from algorithm SQR_3 in
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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16
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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17 Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
18 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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19
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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20 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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21 mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b)
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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22 {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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23 mp_int S0, a0, a1, a2;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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24 mp_digit *tmpa, *tmpc;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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25 int B, count;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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26 mp_err err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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27
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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28
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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29 /* init temps */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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30 if ((err = mp_init(&S0)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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31 return err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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32 }
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33
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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34 /* B */
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35 B = a->used / 3;
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36
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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37 /** a = a2 * x^2 + a1 * x + a0; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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38 if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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39
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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40 a0.used = B;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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41 if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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42 a1.used = B;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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43 if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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44
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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45 tmpa = a->dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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46 tmpc = a0.dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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47 for (count = 0; count < B; count++) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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48 *tmpc++ = *tmpa++;
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)
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50 tmpc = a1.dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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51 for (; count < (2 * B); count++) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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52 *tmpc++ = *tmpa++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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53 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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54 tmpc = a2.dp;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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55 for (; count < a->used; count++) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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56 *tmpc++ = *tmpa++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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57 a2.used++;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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58 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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59 mp_clamp(&a0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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60 mp_clamp(&a1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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61 mp_clamp(&a2);
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62
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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63 /** S0 = a0^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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64 if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
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65
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
66 /** \\S1 = (a2 + a1 + a0)^2 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
67 /** \\S2 = (a2 - a1 + a0)^2 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
68 /** \\S1 = a0 + a2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
69 /** a0 = a0 + a2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
70 if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
71 /** \\S2 = S1 - a1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
72 /** b = a0 - a1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
73 if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
74 /** \\S1 = S1 + a1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
75 /** a0 = a0 + a1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
76 if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
77 /** \\S1 = S1^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
78 /** a0 = a0^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
79 if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
80 /** \\S2 = S2^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
81 /** b = b^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
82 if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
83
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
84 /** \\ S3 = 2 * a1 * a2 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
85 /** \\S3 = a1 * a2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
86 /** a1 = a1 * a2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
87 if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
88 /** \\S3 = S3 << 1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
89 /** a1 = a1 << 1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
90 if ((err = mp_mul_2(&a1, &a1)) != 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 /** \\S4 = a2^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
93 /** a2 = a2^2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
94 if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
95
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
96 /** \\ tmp = (S1 + S2)/2 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
97 /** \\tmp = S1 + S2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
98 /** b = a0 + b; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
99 if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
100 /** \\tmp = tmp >> 1; */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
101 /** b = b >> 1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
102 if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
103
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
104 /** \\ S1 = S1 - tmp - S3 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
105 /** \\S1 = S1 - tmp; */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
106 /** a0 = a0 - b; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
107 if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
108 /** \\S1 = S1 - S3; */
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Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
109 /** a0 = a0 - a1; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
110 if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
111
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
112 /** \\S2 = tmp - S4 -S0 */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
113 /** \\S2 = tmp - S4; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
114 /** b = b - a2; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
115 if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
116 /** \\S2 = S2 - S0; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
117 /** b = b - S0; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
118 if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
119
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
120
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
121 /** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
122 /** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents:
diff changeset
123
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
124 if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
125 if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
126 if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
127 if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
128 if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
129 if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
130 if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
131 if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
132 /** a^2 - P */
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
133
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
134
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
135 LBL_ERR:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
136 mp_clear(&a2);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
137 LBL_ERRa2:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
138 mp_clear(&a1);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
139 LBL_ERRa1:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
140 mp_clear(&a0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
141 LBL_ERRa0:
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
142 mp_clear(&S0);
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
143
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
144 return err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
145 }
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
146
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
diff changeset
147 #endif