1/* mpn_dcpi1_bdiv_qr -- divide-and-conquer Hensel division with precomputed 2 inverse, returning quotient and remainder. 3 4 Contributed to the GNU project by Niels M��ller and Torbjorn Granlund. 5 6 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY 7 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 8 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE. 9 10Copyright 2006, 2007, 2009, 2010, 2017 Free Software Foundation, Inc. 11 12This file is part of the GNU MP Library. 13 14The GNU MP Library is free software; you can redistribute it and/or modify 15it under the terms of either: 16 17 * the GNU Lesser General Public License as published by the Free 18 Software Foundation; either version 3 of the License, or (at your 19 option) any later version. 20 21or 22 23 * the GNU General Public License as published by the Free Software 24 Foundation; either version 2 of the License, or (at your option) any 25 later version. 26 27or both in parallel, as here. 28 29The GNU MP Library is distributed in the hope that it will be useful, but 30WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 31or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 32for more details. 33 34You should have received copies of the GNU General Public License and the 35GNU Lesser General Public License along with the GNU MP Library. If not, 36see https://www.gnu.org/licenses/. */ 37 38#include "gmp-impl.h" 39 40 41/* Computes Hensel binary division of {np, 2*n} by {dp, n}. 42 43 Output: 44 45 q = -n * d^{-1} mod 2^{qn * GMP_NUMB_BITS}, 46 47 r = (n + q * d) * 2^{-qn * GMP_NUMB_BITS} 48 49 Stores q at qp. Stores the n least significant limbs of r at the high half 50 of np, and returns the carry from the addition n + q*d. 51 52 d must be odd. dinv is (-d)^-1 mod 2^GMP_NUMB_BITS. */ 53 54mp_size_t 55mpn_dcpi1_bdiv_qr_n_itch (mp_size_t n) 56{ 57 return n; 58} 59 60mp_limb_t 61mpn_dcpi1_bdiv_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n, 62 mp_limb_t dinv, mp_ptr tp) 63{ 64 mp_size_t lo, hi; 65 mp_limb_t cy; 66 mp_limb_t rh; 67 68 lo = n >> 1; /* floor(n/2) */ 69 hi = n - lo; /* ceil(n/2) */ 70 71 if (BELOW_THRESHOLD (lo, DC_BDIV_QR_THRESHOLD)) 72 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * lo, dp, lo, dinv); 73 else 74 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, lo, dinv, tp); 75 76 mpn_mul (tp, dp + lo, hi, qp, lo); 77 78 mpn_incr_u (tp + lo, cy); 79 rh = mpn_add (np + lo, np + lo, n + hi, tp, n); 80 81 if (BELOW_THRESHOLD (hi, DC_BDIV_QR_THRESHOLD)) 82 cy = mpn_sbpi1_bdiv_qr (qp + lo, np + lo, 2 * hi, dp, hi, dinv); 83 else 84 cy = mpn_dcpi1_bdiv_qr_n (qp + lo, np + lo, dp, hi, dinv, tp); 85 86 mpn_mul (tp, qp + lo, hi, dp + hi, lo); 87 88 mpn_incr_u (tp + hi, cy); 89 rh += mpn_add_n (np + n, np + n, tp, n); 90 91 return rh; 92} 93 94mp_limb_t 95mpn_dcpi1_bdiv_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, 96 mp_srcptr dp, mp_size_t dn, mp_limb_t dinv) 97{ 98 mp_size_t qn; 99 mp_limb_t rr, cy; 100 mp_ptr tp; 101 TMP_DECL; 102 103 TMP_MARK; 104 105 ASSERT (dn >= 2); /* to adhere to mpn_sbpi1_div_qr's limits */ 106 ASSERT (nn - dn >= 1); /* to adhere to mpn_sbpi1_div_qr's limits */ 107 ASSERT (dp[0] & 1); 108 109 tp = TMP_SALLOC_LIMBS (dn); 110 111 qn = nn - dn; 112 113 if (qn > dn) 114 { 115 /* Reduce qn mod dn without division, optimizing small operations. */ 116 do 117 qn -= dn; 118 while (qn > dn); 119 120 /* Perform the typically smaller block first. */ 121 if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD)) 122 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv); 123 else 124 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp); 125 126 rr = 0; 127 if (qn != dn) 128 { 129 if (qn > dn - qn) 130 mpn_mul (tp, qp, qn, dp + qn, dn - qn); 131 else 132 mpn_mul (tp, dp + qn, dn - qn, qp, qn); 133 mpn_incr_u (tp + qn, cy); 134 135 rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn); 136 cy = 0; 137 } 138 139 np += qn; 140 qp += qn; 141 142 qn = nn - dn - qn; 143 do 144 { 145 rr += mpn_add_1 (np + dn, np + dn, qn, cy); 146 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, dn, dinv, tp); 147 qp += dn; 148 np += dn; 149 qn -= dn; 150 } 151 while (qn > 0); 152 TMP_FREE; 153 return rr + cy; 154 } 155 156 if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD)) 157 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv); 158 else 159 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp); 160 161 rr = 0; 162 if (qn != dn) 163 { 164 if (qn > dn - qn) 165 mpn_mul (tp, qp, qn, dp + qn, dn - qn); 166 else 167 mpn_mul (tp, dp + qn, dn - qn, qp, qn); 168 mpn_incr_u (tp + qn, cy); 169 170 rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn); 171 cy = 0; 172 } 173 174 TMP_FREE; 175 return rr + cy; 176} 177