1 /* Compute {up,n}^(-1) mod B^n. 2 3 Contributed to the GNU project by Torbjorn Granlund. 4 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. 8 9 Copyright (C) 2004, 2005, 2006, 2007, 2009 Free Software Foundation, Inc. 10 11 This file is part of the GNU MP Library. 12 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. 17 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. 22 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/. */ 25 26 #include "gmp.h" 27 #include "gmp-impl.h" 28 29 30 /* 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]) 33 */ 34 35 /* This is intended for constant THRESHOLDs only, where the compiler can 36 completely fold the result. */ 37 #define LOG2C(n) \ 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)) 42 43 #if TUNE_PROGRAM_BUILD 44 #define NPOWS \ 45 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t))) 46 #else 47 #define NPOWS \ 48 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)) - LOG2C (BINV_NEWTON_THRESHOLD)) 49 #endif 50 51 mp_size_t 52 mpn_binvert_itch (mp_size_t n) 53 { 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; 57 } 58 59 void 60 mpn_binvert (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr scratch) 61 { 62 mp_ptr xp; 63 mp_size_t rn, newrn; 64 mp_size_t sizes[NPOWS], *sizp; 65 mp_limb_t di; 66 67 /* Compute the computation precisions from highest to lowest, leaving the 68 base case size in 'rn'. */ 69 sizp = sizes; 70 for (rn = n; ABOVE_THRESHOLD (rn, BINV_NEWTON_THRESHOLD); rn = (rn + 1) >> 1) 71 *sizp++ = rn; 72 73 xp = scratch; 74 75 /* Compute a base value of rn limbs. */ 76 MPN_ZERO (xp, rn); 77 xp[0] = 1; 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); 81 else 82 mpn_dcpi1_bdiv_q (rp, xp, rn, up, rn, -di); 83 84 /* Use Newton iterations to get the desired precision. */ 85 for (; rn < n; rn = newrn) 86 { 87 mp_size_t m; 88 newrn = *--sizp; 89 90 /* X <- UR. */ 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); 94 95 /* R = R(X/B^rn) */ 96 mpn_mullo_n (rp + rn, rp, xp + rn, newrn - rn); 97 mpn_neg (rp + rn, rp + rn, newrn - rn); 98 } 99 } 100