1 /* mpn_remove -- divide out all multiples of odd mpn number from another mpn 2 number. 3 4 Contributed to the GNU project by Torbjorn Granlund. 5 6 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY 7 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 8 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE. 9 10 Copyright 2009, 2012 Free Software Foundation, Inc. 11 12 This file is part of the GNU MP Library. 13 14 The GNU MP Library is free software; you can redistribute it and/or modify 15 it under the terms of the GNU Lesser General Public License as published by 16 the Free Software Foundation; either version 3 of the License, or (at your 17 option) any later version. 18 19 The GNU MP Library is distributed in the hope that it will be useful, but 20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 21 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 22 License for more details. 23 24 You should have received a copy of the GNU Lesser General Public License 25 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 26 27 #include "gmp.h" 28 #include "gmp-impl.h" 29 30 #if GMP_LIMB_BITS > 50 31 #define LOG 50 32 #else 33 #define LOG GMP_LIMB_BITS 34 #endif 35 36 37 /* Input: U = {up,un}, V = {vp,vn} must be odd, cap 38 Ouput W = {wp,*wn} allocation need is exactly *wn 39 40 Set W = U / V^k, where k is the largest integer <= cap such that the 41 division yields an integer. 42 43 FIXME: We currently allow any operand overlap. This is quite non mpn-ish 44 and might be changed, since it cost significant temporary space. 45 * If we require W to have space for un limbs, we could save qp or qp2 (but 46 we will still need to copy things into wp 50% of the time). 47 * If we allow ourselves to clobber U, we could save the other of qp and qp2. 48 */ 49 50 /* FIXME: We need to wrap mpn_bdiv_qr due to the itch interface. This need 51 indicates a flaw in the current itch mechanism: Which operands not greater 52 than un,un will incur the worst itch? We need a parallel foo_maxitch set 53 of functions. */ 54 static void 55 mpn_bdiv_qr_wrap (mp_ptr qp, mp_ptr rp, 56 mp_srcptr np, mp_size_t nn, 57 mp_srcptr dp, mp_size_t dn) 58 { 59 mp_ptr scratch_out; 60 TMP_DECL; 61 62 TMP_MARK; 63 scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (nn, dn)); 64 mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch_out); 65 66 TMP_FREE; 67 } 68 69 mp_bitcnt_t 70 mpn_remove (mp_ptr wp, mp_size_t *wn, 71 mp_ptr up, mp_size_t un, mp_ptr vp, mp_size_t vn, 72 mp_bitcnt_t cap) 73 { 74 mp_ptr pwpsp[LOG]; 75 mp_size_t pwpsn[LOG]; 76 mp_size_t npowers; 77 mp_ptr tp, qp, np, pp, qp2; 78 mp_size_t pn, nn, qn, i; 79 mp_bitcnt_t pwr; 80 TMP_DECL; 81 82 ASSERT (un > 0); 83 ASSERT (vn > 0); 84 ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */ 85 ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */ 86 87 TMP_MARK; 88 89 tp = TMP_ALLOC_LIMBS ((un + 1 + vn) / 2); /* remainder */ 90 qp = TMP_ALLOC_LIMBS (un + 1); /* quotient, alternating */ 91 qp2 = TMP_ALLOC_LIMBS (un + 1); /* quotient, alternating */ 92 np = TMP_ALLOC_LIMBS (un + LOG); /* powers of V */ 93 pp = vp; 94 pn = vn; 95 96 MPN_COPY (qp, up, un); 97 qn = un; 98 99 npowers = 0; 100 while (qn >= pn) 101 { 102 qp[qn] = 0; 103 mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn); 104 if (!mpn_zero_p (tp, pn)) 105 break; /* could not divide by V^npowers */ 106 107 MP_PTR_SWAP (qp, qp2); 108 qn = qn - pn; 109 qn += qp[qn] != 0; 110 111 pwpsp[npowers] = pp; 112 pwpsn[npowers] = pn; 113 npowers++; 114 115 if (((mp_bitcnt_t) 2 << npowers) - 1 > cap) 116 break; 117 118 nn = 2 * pn - 1; /* next power will be at least this large */ 119 if (nn > qn) 120 break; /* next power would be overlarge */ 121 122 mpn_sqr (np, pp, pn); 123 nn += np[nn] != 0; 124 pp = np; 125 pn = nn; 126 np += nn; 127 } 128 129 pwr = ((mp_bitcnt_t) 1 << npowers) - 1; 130 131 for (i = npowers - 1; i >= 0; i--) 132 { 133 pp = pwpsp[i]; 134 pn = pwpsn[i]; 135 if (qn < pn) 136 continue; 137 138 if (pwr + ((mp_bitcnt_t) 1 << i) > cap) 139 continue; /* V^i would bring us past cap */ 140 141 qp[qn] = 0; 142 mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn); 143 if (!mpn_zero_p (tp, pn)) 144 continue; /* could not divide by V^i */ 145 146 MP_PTR_SWAP (qp, qp2); 147 qn = qn - pn; 148 qn += qp[qn] != 0; 149 150 pwr += (mp_bitcnt_t) 1 << i; 151 } 152 153 MPN_COPY (wp, qp, qn); 154 *wn = qn; 155 156 TMP_FREE; 157 158 return pwr; 159 } 160