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Diffstat (limited to 'Build/source/libs/gmp/gmp-6.0.0/mpn/generic/bsqrtinv.c')
-rw-r--r-- | Build/source/libs/gmp/gmp-6.0.0/mpn/generic/bsqrtinv.c | 105 |
1 files changed, 105 insertions, 0 deletions
diff --git a/Build/source/libs/gmp/gmp-6.0.0/mpn/generic/bsqrtinv.c b/Build/source/libs/gmp/gmp-6.0.0/mpn/generic/bsqrtinv.c new file mode 100644 index 00000000000..33df6a3c158 --- /dev/null +++ b/Build/source/libs/gmp/gmp-6.0.0/mpn/generic/bsqrtinv.c @@ -0,0 +1,105 @@ +/* mpn_bsqrtinv, compute r such that r^2 * y = 1 (mod 2^{b+1}). + + Contributed to the GNU project by Martin Boij (as part of perfpow.c). + +Copyright 2009, 2010, 2012 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 either: + + * 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. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +#include "gmp.h" +#include "gmp-impl.h" + +/* Compute r such that r^2 * y = 1 (mod 2^{b+1}). + Return non-zero if such an integer r exists. + + Iterates + r' <-- (3r - r^3 y) / 2 + using Hensel lifting. Since we divide by two, the Hensel lifting is + somewhat degenerates. Therefore, we lift from 2^b to 2^{b+1}-1. + + FIXME: + (1) Simplify to do precision book-keeping in limbs rather than bits. + + (2) Rewrite iteration as + r' <-- r - r (r^2 y - 1) / 2 + and take advantage of zero low part of r^2 y - 1. + + (3) Use wrap-around trick. + + (4) Use a small table to get starting value. +*/ +int +mpn_bsqrtinv (mp_ptr rp, mp_srcptr yp, mp_bitcnt_t bnb, mp_ptr tp) +{ + mp_ptr tp2, tp3; + mp_limb_t k; + mp_size_t bn, order[GMP_LIMB_BITS + 1]; + int i, d; + + ASSERT (bnb > 0); + + bn = 1 + bnb / GMP_LIMB_BITS; + + tp2 = tp + bn; + tp3 = tp + 2 * bn; + k = 3; + + rp[0] = 1; + if (bnb == 1) + { + if ((yp[0] & 3) != 1) + return 0; + } + else + { + if ((yp[0] & 7) != 1) + return 0; + + d = 0; + for (; bnb != 2; bnb = (bnb + 2) >> 1) + order[d++] = bnb; + + for (i = d - 1; i >= 0; i--) + { + bnb = order[i]; + bn = 1 + bnb / GMP_LIMB_BITS; + + mpn_mul_1 (tp, rp, bn, k); + + mpn_powlo (tp2, rp, &k, 1, bn, tp3); + mpn_mullo_n (rp, yp, tp2, bn); + +#if HAVE_NATIVE_mpn_rsh1sub_n + mpn_rsh1sub_n (rp, tp, rp, bn); +#else + mpn_sub_n (tp2, tp, rp, bn); + mpn_rshift (rp, tp2, bn, 1); +#endif + } + } + return 1; +} |