Add Chromium-only Blender WebEngine parity work
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blender-5.2.0/extern/gmp-source/mpz/stronglucas.c
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blender-5.2.0/extern/gmp-source/mpz/stronglucas.c
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/* mpz_stronglucas(n, t1, t2) -- An implementation of the strong Lucas
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primality test on n, using parameters as suggested by the BPSW test.
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THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
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CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
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FUTURE GNU MP RELEASES.
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Copyright 2018, 2020 Free Software Foundation, Inc.
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Contributed by Marco Bodrato.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#include "longlong.h"
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/* Returns an approximation of the sqare root of x.
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* It gives:
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* limb_apprsqrt (x) ^ 2 <= x < (limb_apprsqrt (x)+1) ^ 2
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* or
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* x <= limb_apprsqrt (x) ^ 2 <= x * 9/8
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*/
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static mp_limb_t
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limb_apprsqrt (mp_limb_t x)
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{
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int s;
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ASSERT (x > 2);
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count_leading_zeros (s, x);
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s = (GMP_LIMB_BITS - s) >> 1;
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return ((CNST_LIMB(1) << (s - 1)) + (x >> 1 >> s));
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}
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static int
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mpz_oddjacobi_ui (mpz_t b, mp_limb_t a)
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{
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mp_limb_t b_rem;
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int result_bit1;
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ASSERT (a & 1);
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ASSERT (a > 1);
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ASSERT (SIZ (b) > 0);
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ASSERT ((*PTR (b) & 1) == 1);
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result_bit1 = 0;
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JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, PTR (b), SIZ (b), a);
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if (UNLIKELY (b_rem == 0))
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return 0;
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else
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return mpn_jacobi_base (b_rem, a, result_bit1);
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}
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/* Performs strong Lucas' test on x, with parameters suggested */
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/* for the BPSW test. Qk and V are passed to recycle variables. */
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/* Requires GCD (x,6) = 1.*/
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int
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mpz_stronglucas (mpz_srcptr x, mpz_ptr V, mpz_ptr Qk)
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{
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mp_bitcnt_t b0;
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mpz_t n;
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mp_limb_t D; /* The absolute value is stored. */
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mp_limb_t g;
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long Q;
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mpz_t T1, T2;
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/* Test on the absolute value. */
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mpz_roinit_n (n, PTR (x), ABSIZ (x));
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ASSERT (mpz_odd_p (n));
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/* ASSERT (mpz_gcd_ui (NULL, n, 6) == 1); */
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#if GMP_NUMB_BITS % 16 == 0
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/* (2^12 - 1) | (2^{GMP_NUMB_BITS*3/4} - 1) */
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g = mpn_mod_34lsub1 (PTR (n), SIZ (n));
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/* (2^12 - 1) = 3^2 * 5 * 7 * 13 */
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ASSERT (g % 3 != 0 && g % 5 != 0 && g % 7 != 0);
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if ((g % 5 & 2) != 0)
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/* (5/n) = -1, iff n = 2 or 3 (mod 5) */
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/* D = 5; Q = -1 */
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return mpn_strongfibo (PTR (n), SIZ (n), PTR (V));
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else if (! POW2_P (g % 7))
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/* (-7/n) = -1, iff n = 3,5 or 6 (mod 7) */
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D = 7; /* Q = 2 */
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/* (9/n) = -1, never: 9 = 3^2 */
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else if (mpz_oddjacobi_ui (n, 11) == -1)
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/* (-11/n) = (n/11) */
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D = 11; /* Q = 3 */
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else if ((((g % 13 - (g % 13 >> 3)) & 7) > 4) ||
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(((g % 13 - (g % 13 >> 3)) & 7) == 2))
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/* (13/n) = -1, iff n = 2,5,6,7,8 or 11 (mod 13) */
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D = 13; /* Q = -3 */
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else if (g % 3 == 2)
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/* (-15/n) = (n/15) = (n/5)*(n/3) */
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/* Here, (n/5) = 1, and */
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/* (n/3) = -1, iff n = 2 (mod 3) */
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D = 15; /* Q = 4 */
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#if GMP_NUMB_BITS % 32 == 0
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/* (2^24 - 1) | (2^{GMP_NUMB_BITS*3/4} - 1) */
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/* (2^24 - 1) = (2^12 - 1) * 17 * 241 */
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else if (! POW2_P (g % 17) && ! POW2_P (17 - g % 17))
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/* (17/n) = -1, iff n != +-1,+-2,+-4,+-8 (mod 17) */
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D = 17; /* Q = -4 */
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#endif
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#else
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if (mpz_oddjacobi_ui (n, 5) == -1)
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return mpn_strongfibo (PTR (n), SIZ (n), PTR (V));
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#endif
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else
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{
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mp_limb_t maxD;
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int jac;
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/* n is odd, to possibly be a square, n % 8 = 1 is needed. */
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if (((*PTR (n) & 6) == 0) && UNLIKELY (mpz_perfect_square_p (n)))
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return 0; /* A square is composite. */
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/* Check Ds up to square root (in case, n is prime)
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or avoid overflows */
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if (SIZ (n) == 1)
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maxD = limb_apprsqrt (* PTR (n));
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else if (BITS_PER_ULONG >= GMP_NUMB_BITS && SIZ (n) == 2)
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mpn_sqrtrem (&maxD, (mp_ptr) NULL, PTR (n), 2);
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else
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maxD = GMP_NUMB_MAX;
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maxD = MIN (maxD, ULONG_MAX);
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unsigned Ddiff = 2;
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#if GMP_NUMB_BITS % 16 == 0
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const unsigned D2 = 6;
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#if GMP_NUMB_BITS % 32 == 0
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D = 19;
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Ddiff = 4;
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#else
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D = 17;
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#endif
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#else
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const unsigned D2 = 4;
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D = 7;
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#endif
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/* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
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/* For those Ds we have (D/n) = (n/|D|) */
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/* FIXME: Should we loop only on prime Ds? */
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/* The only interesting composite D is 15, because 3 is not tested. */
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for (;;)
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{
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jac = mpz_oddjacobi_ui (n, D);
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if (jac != 1)
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break;
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if (UNLIKELY (D >= maxD))
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return 1;
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D += Ddiff;
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Ddiff = D2 - Ddiff;
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}
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if (UNLIKELY (jac == 0))
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return 0;
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}
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/* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
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Q = (D & 2) ? (D >> 2) + 1 : -(long) (D >> 2);
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/* ASSERT (mpz_si_kronecker ((D & 2) ? NEG_CAST (long, D) : D, n) == -1); */
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/* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
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b0 = mpz_scan0 (n, 0);
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mpz_init (T1);
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mpz_init (T2);
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/* If Ud != 0 && Vd != 0 */
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if (mpz_lucas_mod (V, Qk, Q, b0, n, T1, T2) == 0)
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if (LIKELY (--b0 != 0))
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for (;;)
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{
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/* V_{2k} <- V_k ^ 2 - 2Q^k */
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mpz_mul (T2, V, V);
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mpz_submul_ui (T2, Qk, 2);
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mpz_tdiv_r (V, T2, n);
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if (SIZ (V) == 0 || UNLIKELY (--b0 == 0))
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break;
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/* Q^{2k} = (Q^k)^2 */
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mpz_mul (T2, Qk, Qk);
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mpz_tdiv_r (Qk, T2, n);
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}
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mpz_clear (T1);
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mpz_clear (T2);
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return (b0 != 0);
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}
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