1 /* mpn_mod_1s_3p (ap, n, b, cps) 2 Divide (ap,,n) by b. Return the single-limb remainder. 3 Requires that d < B / 4. 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_4p_cps (mp_limb_t cps[7], mp_limb_t b) 34 { 35 mp_limb_t bi; 36 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb; 37 int cnt; 38 39 ASSERT (b <= (~(mp_limb_t) 0) / 4); 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 udiv_rnd_preinv (B4modb, B3modb, b, bi); 51 udiv_rnd_preinv (B5modb, B4modb, b, bi); 52 53 cps[0] = bi; 54 cps[1] = cnt; 55 cps[2] = B1modb >> cnt; 56 cps[3] = B2modb >> cnt; 57 cps[4] = B3modb >> cnt; 58 cps[5] = B4modb >> cnt; 59 cps[6] = B5modb >> cnt; 60 61 #if WANT_ASSERT 62 { 63 int i; 64 b = cps[2]; 65 for (i = 3; i <= 6; i++) 66 { 67 b += cps[i]; 68 ASSERT (b >= cps[i]); 69 } 70 } 71 #endif 72 } 73 74 mp_limb_t 75 mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[7]) 76 { 77 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r; 78 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb; 79 mp_size_t i; 80 int cnt; 81 82 ASSERT (n >= 1); 83 84 B1modb = cps[2]; 85 B2modb = cps[3]; 86 B3modb = cps[4]; 87 B4modb = cps[5]; 88 B5modb = cps[6]; 89 90 switch (n & 3) 91 { 92 case 0: 93 umul_ppmm (ph, pl, ap[n - 3], B1modb); 94 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 4]); 95 umul_ppmm (ch, cl, ap[n - 2], B2modb); 96 add_ssaaaa (ph, pl, ph, pl, ch, cl); 97 umul_ppmm (rh, rl, ap[n - 1], B3modb); 98 add_ssaaaa (rh, rl, rh, rl, ph, pl); 99 n -= 4; 100 break; 101 case 1: 102 rh = 0; 103 rl = ap[n - 1]; 104 n -= 1; 105 break; 106 case 2: 107 umul_ppmm (ph, pl, ap[n - 1], B1modb); 108 add_ssaaaa (rh, rl, ph, pl, 0, ap[n - 2]); 109 n -= 2; 110 break; 111 case 3: 112 umul_ppmm (ph, pl, ap[n - 2], B1modb); 113 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]); 114 umul_ppmm (rh, rl, ap[n - 1], B2modb); 115 add_ssaaaa (rh, rl, rh, rl, ph, pl); 116 n -= 3; 117 break; 118 } 119 120 for (i = n - 4; i >= 0; i -= 4) 121 { 122 /* rr = ap[i] < B 123 + ap[i+1] * (B mod b) <= (B-1)(b-1) 124 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1) 125 + ap[i+3] * (B^3 mod b) <= (B-1)(b-1) 126 + LO(rr) * (B^4 mod b) <= (B-1)(b-1) 127 + HI(rr) * (B^5 mod b) <= (B-1)(b-1) 128 */ 129 umul_ppmm (ph, pl, ap[i + 1], B1modb); 130 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]); 131 132 umul_ppmm (ch, cl, ap[i + 2], B2modb); 133 add_ssaaaa (ph, pl, ph, pl, ch, cl); 134 135 umul_ppmm (ch, cl, ap[i + 3], B3modb); 136 add_ssaaaa (ph, pl, ph, pl, ch, cl); 137 138 umul_ppmm (ch, cl, rl, B4modb); 139 add_ssaaaa (ph, pl, ph, pl, ch, cl); 140 141 umul_ppmm (rh, rl, rh, B5modb); 142 add_ssaaaa (rh, rl, rh, rl, ph, pl); 143 } 144 145 bi = cps[0]; 146 cnt = cps[1]; 147 148 #if 1 149 umul_ppmm (rh, cl, rh, B1modb); 150 add_ssaaaa (rh, rl, rh, rl, 0, cl); 151 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 152 #else 153 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt), 154 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi); 155 ASSERT (q <= 4); /* optimize for small quotient? */ 156 #endif 157 158 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi); 159 160 return r >> cnt; 161 } 162