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annotate 3rdparty/libtommath/bn_mp_montgomery_setup.c @ 0:2cf249471370

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author Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
date Tue, 08 May 2018 16:09:12 +0900
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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1 #include <tommath_private.h>
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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2 #ifdef BN_MP_MONTGOMERY_SETUP_C
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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4 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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5 * LibTomMath is a library that provides multiple-precision
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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6 * integer arithmetic as well as number theoretic functionality.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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7 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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8 * The library was designed directly after the MPI library by
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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9 * Michael Fromberger but has been written from scratch with
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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10 * additional optimizations in place.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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11 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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12 * The library is free for all purposes without any express
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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13 * guarantee it works.
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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14 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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16 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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17
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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18 /* setups the montgomery reduction stuff */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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19 int
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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20 mp_montgomery_setup (mp_int * n, mp_digit * rho)
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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21 {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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22 mp_digit x, b;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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23
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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24 /* fast inversion mod 2**k
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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25 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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26 * Based on the fact that
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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27 *
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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28 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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29 * => 2*X*A - X*X*A*A = 1
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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30 * => 2*(1) - (1) = 1
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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31 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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32 b = n->dp[0];
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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33
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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34 if ((b & 1) == 0) {
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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35 return MP_VAL;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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36 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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37
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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38 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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39 x *= 2 - (b * x); /* here x*a==1 mod 2**8 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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40 #if !defined(MP_8BIT)
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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41 x *= 2 - (b * x); /* here x*a==1 mod 2**16 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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42 #endif
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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43 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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44 x *= 2 - (b * x); /* here x*a==1 mod 2**32 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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45 #endif
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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46 #ifdef MP_64BIT
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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47 x *= 2 - (b * x); /* here x*a==1 mod 2**64 */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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48 #endif
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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49
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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50 /* rho = -1/m mod b */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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51 *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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52
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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53 return MP_OKAY;
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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54 }
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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55 #endif
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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56
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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57 /* $Source$ */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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58 /* $Revision$ */
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Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
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59 /* $Date$ */