void mpz_powm (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m) { mp_ptr xp, tp, qp, gp, this_gp; mp_srcptr bp, ep, mp; mp_size_t bn, es, en, mn, xn; mp_limb_t invm, c; unsigned long int enb; mp_size_t i, K, j, l, k; int m_zero_cnt, e_zero_cnt; int sh; int use_redc; #if HANDLE_NEGATIVE_EXPONENT mpz_t new_b; #endif #if REDUCE_EXPONENT mpz_t new_e; #endif TMP_DECL; mp = PTR(m); mn = ABSIZ (m); if (mn == 0) DIVIDE_BY_ZERO; TMP_MARK; es = SIZ (e); if (es <= 0) { if (es == 0) { /* Exponent is zero, result is 1 mod m, i.e., 1 or 0 depending on if m equals 1. */ SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1; PTR(r)[0] = 1; TMP_FREE; /* we haven't really allocated anything here */ return; } #if HANDLE_NEGATIVE_EXPONENT MPZ_TMP_INIT (new_b, mn + 1); if (! mpz_invert (new_b, b, m)) DIVIDE_BY_ZERO; b = new_b; es = -es; #else DIVIDE_BY_ZERO; #endif } en = es; #if REDUCE_EXPONENT /* Reduce exponent by dividing it by phi(m) when m small. */ if (mn == 1 && mp[0] < 0x7fffffffL && en * GMP_NUMB_BITS > 150) { MPZ_TMP_INIT (new_e, 2); mpz_mod_ui (new_e, e, phi (mp[0])); e = new_e; } #endif use_redc = mn < POWM_THRESHOLD && mp[0] % 2 != 0; if (use_redc) { /* invm = -1/m mod 2^BITS_PER_MP_LIMB, must have m odd */ modlimb_invert (invm, mp[0]); invm = -invm; } else { /* Normalize m (i.e. make its most significant bit set) as required by division functions below. */ count_leading_zeros (m_zero_cnt, mp[mn - 1]); m_zero_cnt -= GMP_NAIL_BITS; if (m_zero_cnt != 0) { mp_ptr new_mp; new_mp = TMP_ALLOC_LIMBS (mn); mpn_lshift (new_mp, mp, mn, m_zero_cnt); mp = new_mp; } } /* Determine optimal value of k, the number of exponent bits we look at at a time. */ count_leading_zeros (e_zero_cnt, PTR(e)[en - 1]); e_zero_cnt -= GMP_NAIL_BITS; enb = en * GMP_NUMB_BITS - e_zero_cnt; /* number of bits of exponent */ k = 1; K = 2; while (2 * enb > K * (2 + k * (3 + k))) { k++; K *= 2; if (k == 10) /* cap allocation */ break; } tp = TMP_ALLOC_LIMBS (2 * mn); qp = TMP_ALLOC_LIMBS (mn + 1); gp = __GMP_ALLOCATE_FUNC_LIMBS (K / 2 * mn); /* Compute x*R^n where R=2^BITS_PER_MP_LIMB. */ bn = ABSIZ (b); bp = PTR(b); /* Handle |b| >= m by computing b mod m. FIXME: It is not strictly necessary for speed or correctness to do this when b and m have the same number of limbs, perhaps remove mpn_cmp call. */ if (bn > mn || (bn == mn && mpn_cmp (bp, mp, mn) >= 0)) { /* Reduce possibly huge base while moving it to gp[0]. Use a function call to reduce, since we don't want the quotient allocation to live until function return. */ if (use_redc) { reduce (tp + mn, bp, bn, mp, mn); /* b mod m */ MPN_ZERO (tp, mn); mpn_tdiv_qr (qp, gp, 0L, tp, 2 * mn, mp, mn); /* unnormnalized! */ } else { reduce (gp, bp, bn, mp, mn); } } else { /* |b| < m. We pad out operands to become mn limbs, which simplifies the rest of the function, but slows things down when the |b| << m. */ if (use_redc) { MPN_ZERO (tp, mn); MPN_COPY (tp + mn, bp, bn); MPN_ZERO (tp + mn + bn, mn - bn); mpn_tdiv_qr (qp, gp, 0L, tp, 2 * mn, mp, mn); } else { MPN_COPY (gp, bp, bn); MPN_ZERO (gp + bn, mn - bn); } } /* Compute xx^i for odd g < 2^i. */ xp = TMP_ALLOC_LIMBS (mn); mpn_sqr (tp, gp, mn); if (use_redc) mpn_redc_1 (xp, tp, mp, mn, invm); /* xx = x^2*R^n */ else mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn); this_gp = gp; for (i = 1; i < K / 2; i++) { mpn_mul_n (tp, this_gp, xp, mn); this_gp += mn; if (use_redc) mpn_redc_1 (this_gp,tp, mp, mn, invm); /* g[i] = x^(2i+1)*R^n */ else mpn_tdiv_qr (qp, this_gp, 0L, tp, 2 * mn, mp, mn); } /* Start the real stuff. */ ep = PTR (e); i = en - 1; /* current index */ c = ep[i]; /* current limb */ sh = GMP_NUMB_BITS - e_zero_cnt; /* significant bits in ep[i] */ sh -= k; /* index of lower bit of ep[i] to take into account */ if (sh < 0) { /* k-sh extra bits are needed */ if (i > 0) { i--; c <<= (-sh); sh += GMP_NUMB_BITS; c |= ep[i] >> sh; } }
void check_functions (void) { mp_limb_t wp[2], wp2[2], xp[2], yp[2], r; int i; memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 123; yp[0] = 456; mpn_add_n (wp, xp, yp, (mp_size_t) 1); ASSERT_ALWAYS (wp[0] == 579); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 123; wp[0] = 456; r = mpn_addmul_1 (wp, xp, (mp_size_t) 1, CNST_LIMB(2)); ASSERT_ALWAYS (wp[0] == 702); ASSERT_ALWAYS (r == 0); } #if HAVE_NATIVE_mpn_copyd memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 123; xp[1] = 456; mpn_copyd (xp+1, xp, (mp_size_t) 1); ASSERT_ALWAYS (xp[1] == 123); } #endif #if HAVE_NATIVE_mpn_copyi memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 123; xp[1] = 456; mpn_copyi (xp, xp+1, (mp_size_t) 1); ASSERT_ALWAYS (xp[0] == 456); } #endif memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 1605; mpn_divexact_1 (wp, xp, (mp_size_t) 1, CNST_LIMB(5)); ASSERT_ALWAYS (wp[0] == 321); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 1296; r = mpn_divexact_by3c (wp, xp, (mp_size_t) 1, CNST_LIMB(0)); ASSERT_ALWAYS (wp[0] == 432); ASSERT_ALWAYS (r == 0); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 578; r = mpn_divexact_byfobm1 (wp, xp, (mp_size_t) 1, CNST_LIMB(17),CNST_LIMB(-1)/CNST_LIMB(17)); ASSERT_ALWAYS (wp[0] == 34); ASSERT_ALWAYS (r == 0); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 287; r = mpn_divrem_1 (wp, (mp_size_t) 1, xp, (mp_size_t) 1, CNST_LIMB(7)); ASSERT_ALWAYS (wp[1] == 41); ASSERT_ALWAYS (wp[0] == 0); ASSERT_ALWAYS (r == 0); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 290; r = mpn_divrem_euclidean_qr_1 (wp, 0, xp, (mp_size_t) 1, CNST_LIMB(7)); ASSERT_ALWAYS (wp[0] == 41); ASSERT_ALWAYS (r == 3); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 12; r = mpn_gcd_1 (xp, (mp_size_t) 1, CNST_LIMB(9)); ASSERT_ALWAYS (r == 3); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 0x1001; mpn_lshift (wp, xp, (mp_size_t) 1, 1); ASSERT_ALWAYS (wp[0] == 0x2002); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 14; r = mpn_mod_1 (xp, (mp_size_t) 1, CNST_LIMB(4)); ASSERT_ALWAYS (r == 2); } #if (GMP_NUMB_BITS % 4) == 0 memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { int bits = (GMP_NUMB_BITS / 4) * 3; mp_limb_t mod = (CNST_LIMB(1) << bits) - 1; mp_limb_t want = GMP_NUMB_MAX % mod; xp[0] = GMP_NUMB_MAX; r = mpn_mod_34lsub1 (xp, (mp_size_t) 1); ASSERT_ALWAYS (r % mod == want); } #endif // DECL_modexact_1c_odd ((*modexact_1c_odd)); memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 14; r = mpn_mul_1 (wp, xp, (mp_size_t) 1, CNST_LIMB(4)); ASSERT_ALWAYS (wp[0] == 56); ASSERT_ALWAYS (r == 0); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 5; yp[0] = 7; mpn_mul_basecase (wp, xp, (mp_size_t) 1, yp, (mp_size_t) 1); ASSERT_ALWAYS (wp[0] == 35); ASSERT_ALWAYS (wp[1] == 0); } #if HAVE_NATIVE_mpn_preinv_divrem_1 && GMP_NAIL_BITS == 0 memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 0x101; r = mpn_preinv_divrem_1 (wp, (mp_size_t) 1, xp, (mp_size_t) 1, GMP_LIMB_HIGHBIT, refmpn_invert_limb (GMP_LIMB_HIGHBIT), 0); ASSERT_ALWAYS (wp[0] == 0x202); ASSERT_ALWAYS (wp[1] == 0); ASSERT_ALWAYS (r == 0); } #endif #if GMP_NAIL_BITS == 0 memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = GMP_LIMB_HIGHBIT+123; r = mpn_preinv_mod_1 (xp, (mp_size_t) 1, GMP_LIMB_HIGHBIT, refmpn_invert_limb (GMP_LIMB_HIGHBIT)); ASSERT_ALWAYS (r == 123); } #endif memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 5; modlimb_invert(r,xp[0]); r=-r; yp[0]=43; yp[1]=75; mpn_redc_1 (wp, yp, xp, (mp_size_t) 1,r); ASSERT_ALWAYS (wp[0] == 78); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0]=5; yp[0]=3; mpn_sumdiff_n (wp, wp2,xp, yp,1); ASSERT_ALWAYS (wp[0] == 8); ASSERT_ALWAYS (wp2[0] == 2); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 0x8008; mpn_rshift (wp, xp, (mp_size_t) 1, 1); ASSERT_ALWAYS (wp[0] == 0x4004); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 5; mpn_sqr_basecase (wp, xp, (mp_size_t) 1); ASSERT_ALWAYS (wp[0] == 25); ASSERT_ALWAYS (wp[1] == 0); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 999; yp[0] = 666; mpn_sub_n (wp, xp, yp, (mp_size_t) 1); ASSERT_ALWAYS (wp[0] == 333); } memcpy (&__gmpn_cpuvec, &initial_cpuvec, sizeof (__gmpn_cpuvec)); for (i = 0; i < 2; i++) { xp[0] = 123; wp[0] = 456; r = mpn_submul_1 (wp, xp, (mp_size_t) 1, CNST_LIMB(2)); ASSERT_ALWAYS (wp[0] == 210); ASSERT_ALWAYS (r == 0); } }
int main (void) { gmp_randstate_t rands; int j, n; mp_limb_t cp1[1000], cp2[1000], mp[1000], tp1[1000], tp2[1000], inv; tests_start (); gmp_randinit_default (rands); for (n = 1; n < 100; n++) { for (j = 1; j < 100; j++) { mpn_randomb (mp, rands, n); mp[0] |= 1; modlimb_invert (inv, mp[0]); inv = -inv; mpn_randomb (tp1, rands, 2 * n); MPN_COPY (tp2, tp1, 2 * n); ref_redc_1 (cp1, tp1, mp, n, inv); mpn_redc_1 (cp2, tp2, mp, n, inv); if (mpn_cmp (cp1, cp2, n) != 0) { printf ("mpn_redc_1 error %d\n", n); abort (); } if (n != 1 && mpn_cmp (tp1, tp2, 2 * n) != 0) { printf ("mpn_redc_1 possible error\n"); abort (); } /* we dont require the above to be the same but it could be a useful test */ } } for (n = 1; n < 100; n++) { for (j = 1; j < 100; j++) { mpn_rrandom (mp, rands, n); mp[0] |= 1; modlimb_invert (inv, mp[0]); inv = -inv; mpn_rrandom (tp1, rands, 2 * n); MPN_COPY (tp2, tp1, 2 * n); ref_redc_1 (cp1, tp1, mp, n, inv); mpn_redc_1 (cp2, tp2, mp, n, inv); if (mpn_cmp (cp1, cp2, n) != 0) { printf ("mpn_redc_1 error %d\n", n); abort (); } if (n != 1 && mpn_cmp (tp1, tp2, 2 * n) != 0) { printf ("mpn_redc_1 possible error\n"); abort (); } /* we dont require the above to be the same but it could be a useful test */ } } gmp_randclear (rands); tests_end (); exit (0); }