1 /* mpn_divisible_p -- mpn by mpn divisibility test 2 3 THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST 4 CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN 5 FUTURE GNU MP RELEASES. 6 7 Copyright 2001, 2002, 2005 Free Software Foundation, Inc. 8 9 This file is part of the GNU MP Library. 10 11 The GNU MP Library is free software; you can redistribute it and/or modify 12 it under the terms of the GNU Lesser General Public License as published by 13 the Free Software Foundation; either version 3 of the License, or (at your 14 option) any later version. 15 16 The GNU MP Library is distributed in the hope that it will be useful, but 17 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 18 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 19 License for more details. 20 21 You should have received a copy of the GNU Lesser General Public License 22 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 23 24 #include "gmp.h" 25 #include "gmp-impl.h" 26 #include "longlong.h" 27 28 29 /* Determine whether {ap,asize} is divisible by {dp,dsize}. Must have both 30 operands normalized, meaning high limbs non-zero, except that asize==0 is 31 allowed. 32 33 There usually won't be many low zero bits on d, but the checks for this 34 are fast and might pick up a few operand combinations, in particular they 35 might reduce d to fit the single-limb mod_1/modexact_1 code. 36 37 Future: 38 39 This is currently not much faster than the user doing an mpz_tdiv_r 40 and testing for a zero remainder, but hopefully it can be improved. 41 42 mpn_bdivmod is one possibility, but it only trades udiv_qrnnd's for 43 multiplies, it won't save crossproducts the way it can in mpz_divexact. 44 Definitely worthwhile on small operands for most processors, but a 45 sub-quadratic version will be wanted before it can be used on all sizes. 46 47 Getting the remainder limb by limb would make an early exit possible on 48 finding a non-zero. This would probably have to be bdivmod style so 49 there's no addback, but it would need a multi-precision inverse and so 50 might be slower than the plain method (on small sizes at least). 51 52 When d must be normalized (shifted to high bit set), it's possible to 53 just append a low zero limb to "a" rather than bit-shifting as 54 mpn_tdiv_qr does internally, so long as it's already been checked that a 55 has at least as many trailing zeros bits as d. Or equivalently, pass 56 qxn==1 to mpn_tdiv_qr, if/when it accepts that. 57 58 When called from mpz_congruent_p, {ap,asize} is a temporary which can be 59 destroyed. Maybe it'd be possible to get into mpn_tdiv_qr at a lower 60 level to save copying it, or maybe that function could accept rp==ap. 61 62 Could use __attribute__ ((regparm (2))) on i386, so the parameters 63 wouldn't need extra stack when called from mpz_divisible_p, but a 64 pre-release gcc 3 didn't generate particularly good register juggling in 65 that case, so this isn't done for now. */ 66 67 int 68 mpn_divisible_p (mp_srcptr ap, mp_size_t asize, 69 mp_srcptr dp, mp_size_t dsize) 70 { 71 mp_limb_t alow, dlow, dmask; 72 mp_ptr qp, rp; 73 mp_size_t i; 74 TMP_DECL; 75 76 ASSERT (asize >= 0); 77 ASSERT (asize == 0 || ap[asize-1] != 0); 78 ASSERT (dsize >= 1); 79 ASSERT (dp[dsize-1] != 0); 80 ASSERT_MPN (ap, asize); 81 ASSERT_MPN (dp, dsize); 82 83 /* When a<d only a==0 is divisible. 84 Notice this test covers all cases of asize==0. */ 85 if (asize < dsize) 86 return (asize == 0); 87 88 /* Strip low zero limbs from d, requiring a==0 on those. */ 89 for (;;) 90 { 91 alow = *ap; 92 dlow = *dp; 93 94 if (dlow != 0) 95 break; 96 97 if (alow != 0) 98 return 0; /* a has fewer low zero limbs than d, so not divisible */ 99 100 /* a!=0 and d!=0 so won't get to size==0 */ 101 asize--; ASSERT (asize >= 1); 102 dsize--; ASSERT (dsize >= 1); 103 ap++; 104 dp++; 105 } 106 107 /* a must have at least as many low zero bits as d */ 108 dmask = LOW_ZEROS_MASK (dlow); 109 if ((alow & dmask) != 0) 110 return 0; 111 112 if (dsize == 1) 113 { 114 if (BELOW_THRESHOLD (asize, MODEXACT_1_ODD_THRESHOLD)) 115 return mpn_mod_1 (ap, asize, dlow) == 0; 116 117 if ((dlow & 1) == 0) 118 { 119 unsigned twos; 120 count_trailing_zeros (twos, dlow); 121 dlow >>= twos; 122 } 123 return mpn_modexact_1_odd (ap, asize, dlow) == 0; 124 } 125 126 if (dsize == 2) 127 { 128 mp_limb_t dsecond = dp[1]; 129 if (dsecond <= dmask) 130 { 131 unsigned twos; 132 count_trailing_zeros (twos, dlow); 133 dlow = (dlow >> twos) | (dsecond << (GMP_NUMB_BITS-twos)); 134 ASSERT_LIMB (dlow); 135 return MPN_MOD_OR_MODEXACT_1_ODD (ap, asize, dlow) == 0; 136 } 137 } 138 139 TMP_MARK; 140 141 rp = TMP_ALLOC_LIMBS (asize+1); 142 qp = rp + dsize; 143 144 mpn_tdiv_qr (qp, rp, (mp_size_t) 0, ap, asize, dp, dsize); 145 146 /* test for {rp,dsize} zero or non-zero */ 147 i = 0; 148 do 149 { 150 if (rp[i] != 0) 151 { 152 TMP_FREE; 153 return 0; 154 } 155 } 156 while (++i < dsize); 157 158 TMP_FREE; 159 return 1; 160 } 161