1 /* mpf_div_2exp -- Divide a float by 2^n. 2 3 Copyright 1993, 1994, 1996, 2000-2002, 2004 Free Software Foundation, Inc. 4 5 This file is part of the GNU MP Library. 6 7 The GNU MP Library is free software; you can redistribute it and/or modify 8 it under the terms of either: 9 10 * the GNU Lesser General Public License as published by the Free 11 Software Foundation; either version 3 of the License, or (at your 12 option) any later version. 13 14 or 15 16 * the GNU General Public License as published by the Free Software 17 Foundation; either version 2 of the License, or (at your option) any 18 later version. 19 20 or both in parallel, as here. 21 22 The GNU MP Library is distributed in the hope that it will be useful, but 23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 25 for more details. 26 27 You should have received copies of the GNU General Public License and the 28 GNU Lesser General Public License along with the GNU MP Library. If not, 29 see https://www.gnu.org/licenses/. */ 30 31 #include "gmp-impl.h" 32 33 34 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from 35 EXP(u) to set EXP(r). The remainder exp%GMP_NUMB_BITS is then a right 36 shift for the limb data. 37 38 If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just 39 do an mpz_set with changed EXP(r). Like mpz_set we take prec+1 limbs in 40 this case. Although just prec would suffice, it's nice to have 41 mpf_div_2exp with exp==0 come out the same as mpz_set. 42 43 When shifting we take up to prec many limbs from the input. Our shift is 44 cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low 45 limbs dropped from u, and the carry out is stored to PTR(r)[0]. We don't 46 try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available) 47 into that low carry limb. Just prec limbs (with the high non-zero) from 48 the input is enough bits for the application requested precision, no need 49 to do extra work. 50 51 If r==u the shift will have overlapping operands. When k>=1 (ie. when 52 usize > prec), the overlap is in the style supported by rshift (ie. dst 53 <= src). 54 55 But when r==u and k==0 (ie. usize <= prec), we would have an invalid 56 overlap (mpn_rshift (rp+1, rp, ...)). In this case we must instead use 57 mpn_lshift (PTR(r), PTR(u), size, NUMB-shift). An lshift by NUMB-shift 58 bits gives identical data of course, it's just its overlap restrictions 59 which differ. 60 61 In both shift cases, the resulting data is abs_usize+1 limbs. "adj" is 62 used to add +1 to that size if the high is non-zero (it may of course 63 have become zero by the shifting). EXP(u) is the exponent just above 64 those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is 65 zero, or no change if the high is non-zero. 66 67 Enhancements: 68 69 The way mpn_lshift is used means successive mpf_div_2exp calls on the 70 same operand will accumulate low zero limbs, until prec+1 limbs is 71 reached. This is wasteful for subsequent operations. When abs_usize <= 72 prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0], 73 ie. those which would be shifted out by an mpn_rshift. If they're zero 74 then use that mpn_rshift. */ 75 76 void 77 mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp) 78 { 79 mp_srcptr up; 80 mp_ptr rp = r->_mp_d; 81 mp_size_t usize; 82 mp_size_t abs_usize; 83 mp_size_t prec = r->_mp_prec; 84 mp_exp_t uexp = u->_mp_exp; 85 86 usize = u->_mp_size; 87 88 if (UNLIKELY (usize == 0)) 89 { 90 r->_mp_size = 0; 91 r->_mp_exp = 0; 92 return; 93 } 94 95 abs_usize = ABS (usize); 96 up = u->_mp_d; 97 98 if (exp % GMP_NUMB_BITS == 0) 99 { 100 prec++; /* retain more precision here as we don't need 101 to account for carry-out here */ 102 if (abs_usize > prec) 103 { 104 up += abs_usize - prec; 105 abs_usize = prec; 106 } 107 if (rp != up) 108 MPN_COPY_INCR (rp, up, abs_usize); 109 r->_mp_exp = uexp - exp / GMP_NUMB_BITS; 110 } 111 else 112 { 113 mp_limb_t cy_limb; 114 mp_size_t adj; 115 if (abs_usize > prec) 116 { 117 up += abs_usize - prec; 118 abs_usize = prec; 119 /* Use mpn_rshift since mpn_lshift operates downwards, and we 120 therefore would clobber part of U before using that part, in case 121 R is the same variable as U. */ 122 cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS); 123 rp[0] = cy_limb; 124 adj = rp[abs_usize] != 0; 125 } 126 else 127 { 128 cy_limb = mpn_lshift (rp, up, abs_usize, 129 GMP_NUMB_BITS - exp % GMP_NUMB_BITS); 130 rp[abs_usize] = cy_limb; 131 adj = cy_limb != 0; 132 } 133 134 abs_usize += adj; 135 r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj; 136 } 137 r->_mp_size = usize >= 0 ? abs_usize : -abs_usize; 138 } 139