1 /* mpn_mu_div_q, mpn_preinv_mu_div_q. 2 3 Contributed to the GNU project by Torbj�rn Granlund. 4 5 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH A MUTABLE INTERFACE. IT IS 6 ONLY SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS 7 ALMOST GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP 8 RELEASE. 9 10 Copyright 2005, 2006, 2007 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 28 /* 29 Things to work on: 30 31 1. This is a rudimentary implementation of mpn_mu_div_q. The algorithm is 32 probably close to optimal, except when mpn_mu_divappr_q fails. 33 34 An alternative which could be considered for much simpler code for the 35 complex qn>=dn arm would be to allocate a temporary nn+1 limb buffer, then 36 simply call mpn_mu_divappr_q. Such a temporary allocation is 37 unfortunately very large. 38 39 2. Instead of falling back to mpn_mu_div_qr when we detect a possible 40 mpn_mu_divappr_q rounding problem, we could multiply and compare. 41 Unfortunately, since mpn_mu_divappr_q does not return the partial 42 remainder, this also doesn't become optimal. A mpn_mu_divappr_qr 43 could solve that. 44 45 3. The allocations done here should be made from the scratch area. 46 */ 47 48 #include <stdlib.h> /* for NULL */ 49 #include "gmp.h" 50 #include "gmp-impl.h" 51 52 53 mp_limb_t 54 mpn_mu_div_q (mp_ptr qp, 55 mp_ptr np, mp_size_t nn, 56 mp_srcptr dp, mp_size_t dn, 57 mp_ptr scratch) 58 { 59 mp_ptr tp, rp, ip, this_ip; 60 mp_size_t qn, in, this_in; 61 mp_limb_t cy; 62 TMP_DECL; 63 64 TMP_MARK; 65 66 qn = nn - dn; 67 68 tp = TMP_BALLOC_LIMBS (qn + 1); 69 70 if (qn >= dn) /* nn >= 2*dn + 1 */ 71 { 72 /* Find max inverse size needed by the two preinv calls. */ 73 if (dn != qn) 74 { 75 mp_size_t in1, in2; 76 77 in1 = mpn_mu_div_qr_choose_in (qn - dn, dn, 0); 78 in2 = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); 79 in = MAX (in1, in2); 80 } 81 else 82 { 83 in = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); 84 } 85 86 ip = TMP_BALLOC_LIMBS (in + 1); 87 88 if (dn == in) 89 { 90 MPN_COPY (scratch + 1, dp, in); 91 scratch[0] = 1; 92 mpn_invert (ip, scratch, in + 1, NULL); 93 MPN_COPY_INCR (ip, ip + 1, in); 94 } 95 else 96 { 97 cy = mpn_add_1 (scratch, dp + dn - (in + 1), in + 1, 1); 98 if (UNLIKELY (cy != 0)) 99 MPN_ZERO (ip, in); 100 else 101 { 102 mpn_invert (ip, scratch, in + 1, NULL); 103 MPN_COPY_INCR (ip, ip + 1, in); 104 } 105 } 106 107 /* |_______________________| dividend 108 |________| divisor */ 109 rp = TMP_BALLOC_LIMBS (2 * dn + 1); 110 if (dn != qn) /* FIXME: perhaps mpn_mu_div_qr should DTRT */ 111 { 112 this_in = mpn_mu_div_qr_choose_in (qn - dn, dn, 0); 113 this_ip = ip + in - this_in; 114 mpn_preinv_mu_div_qr (tp + dn + 1, rp + dn + 1, np + dn, qn, dp, dn, 115 this_ip, this_in, scratch); 116 } 117 else 118 MPN_COPY (rp + dn + 1, np + dn, dn); 119 120 MPN_COPY (rp + 1, np, dn); 121 rp[0] = 0; 122 this_in = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); 123 this_ip = ip + in - this_in; 124 mpn_preinv_mu_divappr_q (tp, rp, 2*dn + 1, dp, dn, this_ip, this_in, scratch); 125 126 /* The max error of mpn_mu_divappr_q is +4. If the low quotient limb is 127 greater than the max error, we cannot trust the quotient. */ 128 if (tp[0] > 4) 129 { 130 MPN_COPY (qp, tp + 1, qn); 131 } 132 else 133 { 134 /* Fall back to plain mpn_mu_div_qr. */ 135 mpn_mu_div_qr (qp, rp, np, nn, dp, dn, scratch); 136 } 137 } 138 else 139 { 140 /* |_______________________| dividend 141 |________________| divisor */ 142 mpn_mu_divappr_q (tp, np + nn - (2*qn + 2), 2*qn + 2, dp + dn - (qn + 1), qn + 1, scratch); 143 144 if (tp[0] > 4) 145 { 146 MPN_COPY (qp, tp + 1, qn); 147 } 148 else 149 { 150 rp = TMP_BALLOC_LIMBS (dn); 151 mpn_mu_div_qr (qp, rp, np, nn, dp, dn, scratch); 152 } 153 } 154 155 TMP_FREE; 156 return 0; 157 } 158