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 / 3. 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_3p_cps (mp_limb_t cps[6], mp_limb_t b) 34 { 35 mp_limb_t bi; 36 mp_limb_t B1modb, B2modb, B3modb, B4modb; 37 int cnt; 38 39 ASSERT (b <= GMP_NUMB_MAX / 3); 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 52 cps[0] = bi; 53 cps[1] = cnt; 54 cps[2] = B1modb >> cnt; 55 cps[3] = B2modb >> cnt; 56 cps[4] = B3modb >> cnt; 57 cps[5] = B4modb >> cnt; 58 } 59 60 mp_limb_t 61 mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[6]) 62 { 63 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r; 64 mp_limb_t B1modb, B2modb, B3modb, B4modb; 65 mp_size_t i; 66 int cnt; 67 68 B1modb = cps[2]; 69 B2modb = cps[3]; 70 B3modb = cps[4]; 71 B4modb = cps[5]; 72 73 umul_ppmm (ph, pl, ap[n - 2], B1modb); 74 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]); 75 umul_ppmm (ch, cl, ap[n - 1], B2modb); 76 add_ssaaaa (rh, rl, ph, pl, ch, cl); 77 78 for (i = n - 6; i >= 0; i -= 3) 79 { 80 /* rr = ap[i] < B 81 + ap[i+1] * (B mod b) <= (B-1)(b-1) 82 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1) 83 + LO(rr) * (B^3 mod b) <= (B-1)(b-1) 84 + HI(rr) * (B^4 mod b) <= (B-1)(b-1) 85 */ 86 umul_ppmm (ph, pl, ap[i + 1], B1modb); 87 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]); 88 89 umul_ppmm (ch, cl, ap[i + 2], B2modb); 90 add_ssaaaa (ph, pl, ph, pl, ch, cl); 91 92 umul_ppmm (ch, cl, rl, B3modb); 93 add_ssaaaa (ph, pl, ph, pl, ch, cl); 94 95 umul_ppmm (rh, rl, rh, B4modb); 96 add_ssaaaa (rh, rl, rh, rl, ph, pl); 97 } 98 99 if (i >= -2) 100 { 101 umul_ppmm (ph, pl, rl, B1modb); 102 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 2]); 103 umul_ppmm (rh, rl, rh, B2modb); 104 add_ssaaaa (rh, rl, rh, rl, ph, pl); 105 if (i >= -1) 106 { 107 umul_ppmm (ph, pl, rl, B1modb); 108 add_ssaaaa (ph, pl, ph, pl, 0, ap[0]); 109 umul_ppmm (rh, rl, rh, B2modb); 110 add_ssaaaa (rh, rl, rh, rl, ph, pl); 111 } 112 } 113 114 bi = cps[0]; 115 cnt = cps[1]; 116 117 #if 1 118 umul_ppmm (rh, cl, rh, B1modb); 119 add_ssaaaa (rh, rl, rh, rl, 0, cl); 120 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)); 121 #else 122 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt), 123 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi); 124 ASSERT (q <= 3); /* optimize for small quotient? */ 125 #endif 126 127 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi); 128 129 return r >> cnt; 130 } 131