1 /* mpn_mod_1s_3p (ap, n, b, cps) 2 Divide (ap,,n) by b. Return the single-limb remainder. 3 Requires that b < B / 3. 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 2008-2010, 2013 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 either: 18 19 * the GNU Lesser General Public License as published by the Free 20 Software Foundation; either version 3 of the License, or (at your 21 option) any later version. 22 23 or 24 25 * the GNU General Public License as published by the Free Software 26 Foundation; either version 2 of the License, or (at your option) any 27 later version. 28 29 or both in parallel, as here. 30 31 The GNU MP Library is distributed in the hope that it will be useful, but 32 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 33 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 34 for more details. 35 36 You should have received copies of the GNU General Public License and the 37 GNU Lesser General Public License along with the GNU MP Library. If not, 38 see https://www.gnu.org/licenses/. */ 39 40 #include "gmp-impl.h" 41 #include "longlong.h" 42 43 void 44 mpn_mod_1s_3p_cps (mp_limb_t cps[6], mp_limb_t b) 45 { 46 mp_limb_t bi; 47 mp_limb_t B1modb, B2modb, B3modb, B4modb; 48 int cnt; 49 50 ASSERT (b <= (~(mp_limb_t) 0) / 3); 51 52 count_leading_zeros (cnt, b); 53 54 b <<= cnt; 55 invert_limb (bi, b); 56 57 cps[0] = bi; 58 cps[1] = cnt; 59 60 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt)); 61 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */ 62 cps[2] = B1modb >> cnt; 63 64 udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi); 65 cps[3] = B2modb >> cnt; 66 67 udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi); 68 cps[4] = B3modb >> cnt; 69 70 udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi); 71 cps[5] = B4modb >> cnt; 72 73 #if WANT_ASSERT 74 { 75 int i; 76 b = cps[2]; 77 for (i = 3; i <= 5; i++) 78 { 79 b += cps[i]; 80 ASSERT (b >= cps[i]); 81 } 82 } 83 #endif 84 } 85 86 mp_limb_t 87 mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[6]) 88 { 89 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r; 90 mp_limb_t B1modb, B2modb, B3modb, B4modb; 91 mp_size_t i; 92 int cnt; 93 94 ASSERT (n >= 1); 95 96 B1modb = cps[2]; 97 B2modb = cps[3]; 98 B3modb = cps[4]; 99 B4modb = cps[5]; 100 101 /* We compute n mod 3 in a tricky way, which works except for when n is so 102 close to the maximum size that we don't need to support it. The final 103 cast to int is a workaround for HP cc. */ 104 switch ((int) ((mp_limb_t) n * MODLIMB_INVERSE_3 >> (GMP_NUMB_BITS - 2))) 105 { 106 case 0: 107 umul_ppmm (ph, pl, ap[n - 2], B1modb); 108 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]); 109 umul_ppmm (rh, rl, ap[n - 1], B2modb); 110 add_ssaaaa (rh, rl, rh, rl, ph, pl); 111 n -= 3; 112 break; 113 case 2: /* n mod 3 = 1 */ 114 rh = 0; 115 rl = ap[n - 1]; 116 n -= 1; 117 break; 118 case 1: /* n mod 3 = 2 */ 119 rh = ap[n - 1]; 120 rl = ap[n - 2]; 121 n -= 2; 122 break; 123 } 124 125 for (i = n - 3; i >= 0; i -= 3) 126 { 127 /* rr = ap[i] < B 128 + ap[i+1] * (B mod b) <= (B-1)(b-1) 129 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1) 130 + LO(rr) * (B^3 mod b) <= (B-1)(b-1) 131 + HI(rr) * (B^4 mod b) <= (B-1)(b-1) 132 */ 133 umul_ppmm (ph, pl, ap[i + 1], B1modb); 134 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]); 135 136 umul_ppmm (ch, cl, ap[i + 2], B2modb); 137 add_ssaaaa (ph, pl, ph, pl, ch, cl); 138 139 umul_ppmm (ch, cl, rl, B3modb); 140 add_ssaaaa (ph, pl, ph, pl, ch, cl); 141 142 umul_ppmm (rh, rl, rh, B4modb); 143 add_ssaaaa (rh, rl, rh, rl, ph, pl); 144 } 145 146 umul_ppmm (rh, cl, rh, B1modb); 147 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl); 148 149 cnt = cps[1]; 150 bi = cps[0]; 151 152 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 153 udiv_rnnd_preinv (r, r, rl << cnt, b, bi); 154 155 return r >> cnt; 156 } 157