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 <= GMP_NUMB_MAX / 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 62 mp_limb_t 63 mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[7]) 64 { 65 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r; 66 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb; 67 mp_size_t i; 68 int cnt; 69 70 B1modb = cps[2]; 71 B2modb = cps[3]; 72 B3modb = cps[4]; 73 B4modb = cps[5]; 74 B5modb = cps[6]; 75 76 umul_ppmm (ph, pl, ap[n - 3], B1modb); 77 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 4]); 78 79 umul_ppmm (ch, cl, ap[n - 2], B2modb); 80 add_ssaaaa (ph, pl, ph, pl, ch, cl); 81 82 umul_ppmm (ch, cl, ap[n - 1], B3modb); 83 add_ssaaaa (rh, rl, ph, pl, ch, cl); 84 85 for (i = n - 8; i >= 0; i -= 4) 86 { 87 /* rr = ap[i] < B 88 + ap[i+1] * (B mod b) <= (B-1)(b-1) 89 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1) 90 + ap[i+3] * (B^3 mod b) <= (B-1)(b-1) 91 + LO(rr) * (B^4 mod b) <= (B-1)(b-1) 92 + HI(rr) * (B^5 mod b) <= (B-1)(b-1) 93 */ 94 umul_ppmm (ph, pl, ap[i + 1], B1modb); 95 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]); 96 97 umul_ppmm (ch, cl, ap[i + 2], B2modb); 98 add_ssaaaa (ph, pl, ph, pl, ch, cl); 99 100 umul_ppmm (ch, cl, ap[i + 3], B3modb); 101 add_ssaaaa (ph, pl, ph, pl, ch, cl); 102 103 umul_ppmm (ch, cl, rl, B4modb); 104 add_ssaaaa (ph, pl, ph, pl, ch, cl); 105 106 umul_ppmm (rh, rl, rh, B5modb); 107 add_ssaaaa (rh, rl, rh, rl, ph, pl); 108 } 109 110 if (i >= -3) 111 { 112 umul_ppmm (ph, pl, rl, B1modb); 113 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 3]); 114 umul_ppmm (rh, rl, rh, B2modb); 115 add_ssaaaa (rh, rl, rh, rl, ph, pl); 116 if (i >= -2) 117 { 118 umul_ppmm (ph, pl, rl, B1modb); 119 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 2]); 120 umul_ppmm (rh, rl, rh, B2modb); 121 add_ssaaaa (rh, rl, rh, rl, ph, pl); 122 if (i >= -1) 123 { 124 umul_ppmm (ph, pl, rl, B1modb); 125 add_ssaaaa (ph, pl, ph, pl, 0, ap[0]); 126 umul_ppmm (rh, rl, rh, B2modb); 127 add_ssaaaa (rh, rl, rh, rl, ph, pl); 128 } 129 } 130 } 131 132 bi = cps[0]; 133 cnt = cps[1]; 134 135 #if 1 136 umul_ppmm (rh, cl, rh, B1modb); 137 add_ssaaaa (rh, rl, rh, rl, 0, cl); 138 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 139 #else 140 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt), 141 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi); 142 ASSERT (q <= 4); /* optimize for small quotient? */ 143 #endif 144 145 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi); 146 147 return r >> cnt; 148 } 149