1 /* mpn_mod_1s_2p (ap, n, b, cps) 2 Divide (ap,,n) by b. Return the single-limb remainder. 3 Requires that b < B / 2. 4 5 Contributed to the GNU project by Torbjorn Granlund. 6 Based on a suggestion by Peter L. Montgomery. 7 8 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY 9 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 10 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 11 12 Copyright 2008, 2009, 2010 Free Software Foundation, Inc. 13 14 This file is part of the GNU MP Library. 15 16 The GNU MP Library is free software; you can redistribute it and/or modify 17 it under the terms of the GNU Lesser General Public License as published by 18 the Free Software Foundation; either version 3 of the License, or (at your 19 option) any later version. 20 21 The GNU MP Library is distributed in the hope that it will be useful, but 22 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 23 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 24 License for more details. 25 26 You should have received a copy of the GNU Lesser General Public License 27 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 28 29 #include "gmp.h" 30 #include "gmp-impl.h" 31 #include "longlong.h" 32 33 void 34 mpn_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b) 35 { 36 mp_limb_t bi; 37 mp_limb_t B1modb, B2modb, B3modb; 38 int cnt; 39 40 ASSERT (b <= (~(mp_limb_t) 0) / 2); 41 42 count_leading_zeros (cnt, b); 43 44 b <<= cnt; 45 invert_limb (bi, b); 46 47 cps[0] = bi; 48 cps[1] = cnt; 49 50 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt)); 51 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */ 52 cps[2] = B1modb >> cnt; 53 54 udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi); 55 cps[3] = B2modb >> cnt; 56 57 udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi); 58 cps[4] = B3modb >> cnt; 59 60 #if WANT_ASSERT 61 { 62 int i; 63 b = cps[2]; 64 for (i = 3; i <= 4; i++) 65 { 66 b += cps[i]; 67 ASSERT (b >= cps[i]); 68 } 69 } 70 #endif 71 } 72 73 mp_limb_t 74 mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[5]) 75 { 76 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r; 77 mp_limb_t B1modb, B2modb, B3modb; 78 mp_size_t i; 79 int cnt; 80 81 ASSERT (n >= 1); 82 83 B1modb = cps[2]; 84 B2modb = cps[3]; 85 B3modb = cps[4]; 86 87 if ((n & 1) != 0) 88 { 89 if (n == 1) 90 { 91 rl = ap[n - 1]; 92 bi = cps[0]; 93 cnt = cps[1]; 94 udiv_rnnd_preinv (r, rl >> (GMP_LIMB_BITS - cnt), 95 rl << cnt, b, bi); 96 return r >> cnt; 97 } 98 99 umul_ppmm (ph, pl, ap[n - 2], B1modb); 100 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]); 101 umul_ppmm (rh, rl, ap[n - 1], B2modb); 102 add_ssaaaa (rh, rl, rh, rl, ph, pl); 103 n--; 104 } 105 else 106 { 107 rh = ap[n - 1]; 108 rl = ap[n - 2]; 109 } 110 111 for (i = n - 4; i >= 0; i -= 2) 112 { 113 /* rr = ap[i] < B 114 + ap[i+1] * (B mod b) <= (B-1)(b-1) 115 + LO(rr) * (B^2 mod b) <= (B-1)(b-1) 116 + HI(rr) * (B^3 mod b) <= (B-1)(b-1) 117 */ 118 umul_ppmm (ph, pl, ap[i + 1], B1modb); 119 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]); 120 121 umul_ppmm (ch, cl, rl, B2modb); 122 add_ssaaaa (ph, pl, ph, pl, ch, cl); 123 124 umul_ppmm (rh, rl, rh, B3modb); 125 add_ssaaaa (rh, rl, rh, rl, ph, pl); 126 } 127 128 umul_ppmm (rh, cl, rh, B1modb); 129 add_ssaaaa (rh, rl, rh, rl, 0, cl); 130 131 cnt = cps[1]; 132 bi = cps[0]; 133 134 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 135 udiv_rnnd_preinv (r, r, rl << cnt, b, bi); 136 137 return r >> cnt; 138 } 139