1 /* Compute {up,n}^(-1) mod B^n.
3 Contributed to the GNU project by Torbjorn Granlund.
5 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
6 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
7 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
9 Copyright (C) 2004, 2005, 2006, 2007, 2009 Free Software Foundation, Inc.
11 This file is part of the GNU MP Library.
13 The GNU MP Library is free software; you can redistribute it and/or modify
14 it under the terms of the GNU Lesser General Public License as published by
15 the Free Software Foundation; either version 3 of the License, or (at your
16 option) any later version.
18 The GNU MP Library is distributed in the hope that it will be useful, but
19 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
20 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
21 License for more details.
23 You should have received a copy of the GNU Lesser General Public License
24 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
31 r[k+1] = r[k] - r[k] * (u*r[k] - 1)
32 r[k+1] = r[k] + r[k] - r[k]*(u*r[k])
35 /* This is intended for constant THRESHOLDs only, where the compiler can
36 completely fold the result. */
38 (((n) >= 0x1) + ((n) >= 0x2) + ((n) >= 0x4) + ((n) >= 0x8) + \
39 ((n) >= 0x10) + ((n) >= 0x20) + ((n) >= 0x40) + ((n) >= 0x80) + \
40 ((n) >= 0x100) + ((n) >= 0x200) + ((n) >= 0x400) + ((n) >= 0x800) + \
41 ((n) >= 0x1000) + ((n) >= 0x2000) + ((n) >= 0x4000) + ((n) >= 0x8000))
43 #if TUNE_PROGRAM_BUILD
45 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)))
48 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)) - LOG2C (BINV_NEWTON_THRESHOLD))
52 mpn_binvert_itch (mp_size_t n)
54 mp_size_t itch_local = mpn_mulmod_bnm1_next_size (n);
55 mp_size_t itch_out = mpn_mulmod_bnm1_itch (itch_local, n, (n + 1) >> 1);
56 return itch_local + itch_out;
60 mpn_binvert (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr scratch)
64 mp_size_t sizes[NPOWS], *sizp;
67 /* Compute the computation precisions from highest to lowest, leaving the
68 base case size in 'rn'. */
70 for (rn = n; ABOVE_THRESHOLD (rn, BINV_NEWTON_THRESHOLD); rn = (rn + 1) >> 1)
75 /* Compute a base value of rn limbs. */
78 binvert_limb (di, up[0]);
79 if (BELOW_THRESHOLD (rn, DC_BDIV_Q_THRESHOLD))
80 mpn_sbpi1_bdiv_q (rp, xp, rn, up, rn, -di);
82 mpn_dcpi1_bdiv_q (rp, xp, rn, up, rn, -di);
84 /* Use Newton iterations to get the desired precision. */
85 for (; rn < n; rn = newrn)
91 m = mpn_mulmod_bnm1_next_size (newrn);
92 mpn_mulmod_bnm1 (xp, m, up, newrn, rp, rn, xp + m);
93 mpn_sub_1 (xp + m, xp, rn - (m - newrn), 1);
96 mpn_mullo_n (rp + rn, rp, xp + rn, newrn - rn);
97 mpn_neg (rp + rn, rp + rn, newrn - rn);