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 7 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY 8 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 9 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 10 11 Copyright 2008, 2009 Free Software Foundation, Inc. 12 13 This file is part of the GNU MP Library. 14 15 The GNU MP Library is free software; you can redistribute it and/or modify 16 it under the terms of the GNU Lesser General Public License as published by 17 the Free Software Foundation; either version 3 of the License, or (at your 18 option) any later version. 19 20 The GNU MP Library is distributed in the hope that it will be useful, but 21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 22 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 23 License for more details. 24 25 You should have received a copy of the GNU Lesser General Public License 26 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 27 28 #include "gmp.h" 29 #include "gmp-impl.h" 30 #include "longlong.h" 31 32 void 33 mpn_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b) 34 { 35 mp_limb_t bi; 36 mp_limb_t B1modb, B2modb, B3modb; 37 int cnt; 38 39 ASSERT (b <= (~(mp_limb_t) 0) / 2); 40 41 count_leading_zeros (cnt, b); 42 43 b <<= cnt; 44 invert_limb (bi, b); 45 46 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt)); 47 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */ 48 udiv_rnd_preinv (B2modb, B1modb, b, bi); 49 udiv_rnd_preinv (B3modb, B2modb, b, bi); 50 51 cps[0] = bi; 52 cps[1] = cnt; 53 cps[2] = B1modb >> cnt; 54 cps[3] = B2modb >> cnt; 55 cps[4] = B3modb >> cnt; 56 57 #if WANT_ASSERT 58 { 59 int i; 60 b = cps[2]; 61 for (i = 3; i <= 4; i++) 62 { 63 b += cps[i]; 64 ASSERT (b >= cps[i]); 65 } 66 } 67 #endif 68 } 69 70 mp_limb_t 71 mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[5]) 72 { 73 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r; 74 mp_limb_t B1modb, B2modb, B3modb; 75 mp_size_t i; 76 int cnt; 77 78 ASSERT (n >= 1); 79 80 B1modb = cps[2]; 81 B2modb = cps[3]; 82 B3modb = cps[4]; 83 84 if ((n & 1) != 0) 85 { 86 if (n == 1) 87 { 88 rl = ap[n - 1]; 89 bi = cps[0]; 90 cnt = cps[1]; 91 udiv_qrnnd_preinv (q, r, rl >> (GMP_LIMB_BITS - cnt), 92 rl << cnt, b, bi); 93 return r >> cnt; 94 } 95 96 umul_ppmm (ph, pl, ap[n - 2], B1modb); 97 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]); 98 umul_ppmm (rh, rl, ap[n - 1], B2modb); 99 add_ssaaaa (rh, rl, rh, rl, ph, pl); 100 n--; 101 } 102 else 103 { 104 umul_ppmm (rh, rl, ap[n - 1], B1modb); 105 add_ssaaaa (rh, rl, rh, rl, 0, ap[n - 2]); 106 } 107 108 for (i = n - 4; i >= 0; i -= 2) 109 { 110 /* rr = ap[i] < B 111 + ap[i+1] * (B mod b) <= (B-1)(b-1) 112 + LO(rr) * (B^2 mod b) <= (B-1)(b-1) 113 + HI(rr) * (B^3 mod b) <= (B-1)(b-1) 114 */ 115 umul_ppmm (ph, pl, ap[i + 1], B1modb); 116 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]); 117 118 umul_ppmm (ch, cl, rl, B2modb); 119 add_ssaaaa (ph, pl, ph, pl, ch, cl); 120 121 umul_ppmm (rh, rl, rh, B3modb); 122 add_ssaaaa (rh, rl, rh, rl, ph, pl); 123 } 124 125 bi = cps[0]; 126 cnt = cps[1]; 127 128 #if 1 129 umul_ppmm (rh, cl, rh, B1modb); 130 add_ssaaaa (rh, rl, rh, rl, 0, cl); 131 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 132 #else 133 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt), 134 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi); 135 ASSERT (q <= 2); /* optimize for small quotient? */ 136 #endif 137 138 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi); 139 140 return r >> cnt; 141 } 142