--- /dev/null
+/* mpn_powm -- Compute R = U^E mod M.
+
+Copyright 2007, 2008, 2009 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
+
+
+/*
+ BASIC ALGORITHM, Compute b^e mod n, where n is odd.
+
+ 1. w <- b
+
+ 2. While w^2 < n (and there are more bits in e)
+ w <- power left-to-right base-2 without reduction
+
+ 3. t <- (B^n * b) / n Convert to REDC form
+
+ 4. Compute power table of e-dependent size
+
+ 5. While there are more bits in e
+ w <- power left-to-right base-k with reduction
+
+
+ TODO:
+
+ * Make getbits a macro, thereby allowing it to update the index operand.
+ That will simplify the code using getbits. (Perhaps make getbits' sibling
+ getbit then have similar form, for symmetry.)
+
+ * Write an itch function.
+
+ * Choose window size without looping. (Superoptimize or think(tm).)
+
+ * How do we handle small bases?
+
+ * This is slower than old mpz code, in particular if we base it on redc_1
+ (use: #undef HAVE_NATIVE_mpn_addmul_2). Why?
+
+ * Make it sub-quadratic.
+
+ * Call new division functions, not mpn_tdiv_qr.
+
+ * Is redc obsolete with improved SB division?
+
+ * Consider special code for one-limb M.
+
+ * CRT for N = odd*2^t:
+ Using Newton's method and 2-adic arithmetic:
+ m1_inv_m2 = 1/odd mod 2^t
+ Plain 2-adic (REDC) modexp:
+ r1 = a ^ b mod odd
+ Mullo+sqrlo-based modexp:
+ r2 = a ^ b mod 2^t
+ mullo, mul, add:
+ r = ((r2 - r1) * m1_i_m2 mod 2^t) * odd + r1
+
+ * How should we handle the redc1/redc2/redc2/redc4/redc_subquad choice?
+ - redc1: T(binvert_1limb) + e * (n) * (T(mullo1x1) + n*T(addmul_1))
+ - redc2: T(binvert_2limbs) + e * (n/2) * (T(mullo2x2) + n*T(addmul_2))
+ - redc3: T(binvert_3limbs) + e * (n/3) * (T(mullo3x3) + n*T(addmul_3))
+ This disregards the addmul_N constant term, but we could think of
+ that as part of the respective mulloNxN.
+*/
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+
+#define getbit(p,bi) \
+ ((p[(bi - 1) / GMP_LIMB_BITS] >> (bi - 1) % GMP_LIMB_BITS) & 1)
+
+static inline mp_limb_t
+getbits (const mp_limb_t *p, unsigned long bi, int nbits)
+{
+ int nbits_in_r;
+ mp_limb_t r;
+ mp_size_t i;
+
+ if (bi < nbits)
+ {
+ return p[0] & (((mp_limb_t) 1 << bi) - 1);
+ }
+ else
+ {
+ bi -= nbits; /* bit index of low bit to extract */
+ i = bi / GMP_LIMB_BITS; /* word index of low bit to extract */
+ bi %= GMP_LIMB_BITS; /* bit index in low word */
+ r = p[i] >> bi; /* extract (low) bits */
+ nbits_in_r = GMP_LIMB_BITS - bi; /* number of bits now in r */
+ if (nbits_in_r < nbits) /* did we get enough bits? */
+ r += p[i + 1] << nbits_in_r; /* prepend bits from higher word */
+ return r & (((mp_limb_t ) 1 << nbits) - 1);
+ }
+}
+
+#undef HAVE_NATIVE_mpn_addmul_2
+
+#ifndef HAVE_NATIVE_mpn_addmul_2
+#define REDC_2_THRESHOLD MP_SIZE_T_MAX
+#endif
+
+#ifndef REDC_2_THRESHOLD
+#define REDC_2_THRESHOLD 4
+#endif
+
+static void mpn_redc_n () {ASSERT_ALWAYS(0);}
+
+static inline int
+win_size (unsigned long eb)
+{
+ int k;
+ static unsigned long x[] = {1,7,25,81,241,673,1793,4609,11521,28161,~0ul};
+ for (k = 0; eb > x[k]; k++)
+ ;
+ return k;
+}
+
+#define MPN_REDC_X(rp, tp, mp, n, mip) \
+ do { \
+ if (redc_x == 1) \
+ mpn_redc_1 (rp, tp, mp, n, mip[0]); \
+ else if (redc_x == 2) \
+ mpn_redc_2 (rp, tp, mp, n, mip); \
+ else \
+ mpn_redc_n (rp, tp, mp, n, mip); \
+ } while (0)
+
+ /* Convert U to REDC form, U_r = B^n * U mod M */
+static void
+redcify (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr mp, mp_size_t n)
+{
+ mp_ptr tp, qp;
+ TMP_DECL;
+ TMP_MARK;
+
+ tp = TMP_ALLOC_LIMBS (un + n);
+ qp = TMP_ALLOC_LIMBS (un + 1); /* FIXME: Put at tp+? */
+
+ MPN_ZERO (tp, n);
+ MPN_COPY (tp + n, up, un);
+ mpn_tdiv_qr (qp, rp, 0L, tp, un + n, mp, n);
+ TMP_FREE;
+}
+
+/* rp[n-1..0] = bp[bn-1..0] ^ ep[en-1..0] mod mp[n-1..0]
+ Requires that mp[n-1..0] is odd.
+ Requires that ep[en-1..0] is > 1.
+ Uses scratch space tp[3n..0], i.e., 3n+1 words. */
+void
+mpn_powm (mp_ptr rp, mp_srcptr bp, mp_size_t bn,
+ mp_srcptr ep, mp_size_t en,
+ mp_srcptr mp, mp_size_t n, mp_ptr tp)
+{
+ mp_limb_t mip[2];
+ int cnt;
+ long ebi;
+ int windowsize, this_windowsize;
+ mp_limb_t expbits;
+ mp_ptr pp, this_pp, last_pp;
+ mp_ptr b2p;
+ long i;
+ int redc_x;
+ TMP_DECL;
+
+ ASSERT (en > 1 || (en == 1 && ep[0] > 1));
+ ASSERT (n >= 1 && ((mp[0] & 1) != 0));
+
+ TMP_MARK;
+
+ count_leading_zeros (cnt, ep[en - 1]);
+ ebi = en * GMP_LIMB_BITS - cnt;
+
+#if 0
+ if (bn < n)
+ {
+ /* Do the first few exponent bits without mod reductions,
+ until the result is greater than the mod argument. */
+ for (;;)
+ {
+ mpn_sqr_n (tp, this_pp, tn);
+ tn = tn * 2 - 1, tn += tp[tn] != 0;
+ if (getbit (ep, ebi) != 0)
+ mpn_mul (..., tp, tn, bp, bn);
+ ebi--;
+ }
+ }
+#endif
+
+ windowsize = win_size (ebi);
+
+ if (BELOW_THRESHOLD (n, REDC_2_THRESHOLD))
+ {
+ binvert_limb (mip[0], mp[0]);
+ mip[0] = -mip[0];
+ redc_x = 1;
+ }
+#if defined (HAVE_NATIVE_mpn_addmul_2)
+ else
+ {
+ mpn_binvert (mip, mp, 2, tp);
+ mip[0] = -mip[0]; mip[1] = ~mip[1];
+ redc_x = 2;
+ }
+#endif
+#if 0
+ mpn_binvert (mip, mp, n, tp);
+ redc_x = 0;
+#endif
+
+ pp = TMP_ALLOC_LIMBS (n << (windowsize - 1));
+
+ this_pp = pp;
+ redcify (this_pp, bp, bn, mp, n);
+
+ b2p = tp + 2*n;
+
+ /* Store b^2 in b2. */
+ mpn_sqr_n (tp, this_pp, n);
+ MPN_REDC_X (b2p, tp, mp, n, mip);
+
+ /* Precompute odd powers of b and put them in the temporary area at pp. */
+ for (i = (1 << (windowsize - 1)) - 1; i > 0; i--)
+ {
+ last_pp = this_pp;
+ this_pp += n;
+ mpn_mul_n (tp, last_pp, b2p, n);
+ MPN_REDC_X (this_pp, tp, mp, n, mip);
+ }
+
+ expbits = getbits (ep, ebi, windowsize);
+ ebi -= windowsize;
+ if (ebi < 0)
+ ebi = 0;
+
+ count_trailing_zeros (cnt, expbits);
+ ebi += cnt;
+ expbits >>= cnt;
+
+ MPN_COPY (rp, pp + n * (expbits >> 1), n);
+
+ while (ebi != 0)
+ {
+ while (getbit (ep, ebi) == 0)
+ {
+ mpn_sqr_n (tp, rp, n);
+ MPN_REDC_X (rp, tp, mp, n, mip);
+ ebi--;
+ if (ebi == 0)
+ goto done;
+ }
+
+ /* The next bit of the exponent is 1. Now extract the largest block of
+ bits <= windowsize, and such that the least significant bit is 1. */
+
+ expbits = getbits (ep, ebi, windowsize);
+ ebi -= windowsize;
+ this_windowsize = windowsize;
+ if (ebi < 0)
+ {
+ this_windowsize += ebi;
+ ebi = 0;
+ }
+
+ count_trailing_zeros (cnt, expbits);
+ this_windowsize -= cnt;
+ ebi += cnt;
+ expbits >>= cnt;
+
+ do
+ {
+ mpn_sqr_n (tp, rp, n);
+ MPN_REDC_X (rp, tp, mp, n, mip);
+ this_windowsize--;
+ }
+ while (this_windowsize != 0);
+
+ mpn_mul_n (tp, rp, pp + n * (expbits >> 1), n);
+ MPN_REDC_X (rp, tp, mp, n, mip);
+ }
+
+ done:
+ MPN_COPY (tp, rp, n);
+ MPN_ZERO (tp + n, n);
+ MPN_REDC_X (rp, tp, mp, n, mip);
+ if (mpn_cmp (rp, mp, n) >= 0)
+ mpn_sub_n (rp, rp, mp, n);
+ TMP_FREE;
+}
projects / msp430-gcc.git / blobdiff