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.h" 32 #include "gmp-impl.h" 33 34 35 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from 36 EXP(u) to set EXP(r). The remainder exp%GMP_NUMB_BITS is then a right 37 shift for the limb data. 38 39 If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just 40 do an mpz_set with changed EXP(r). Like mpz_set we take prec+1 limbs in 41 this case. Although just prec would suffice, it's nice to have 42 mpf_div_2exp with exp==0 come out the same as mpz_set. 43 44 When shifting we take up to prec many limbs from the input. Our shift is 45 cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low 46 limbs dropped from u, and the carry out is stored to PTR(r)[0]. We don't 47 try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available) 48 into that low carry limb. Just prec limbs (with the high non-zero) from 49 the input is enough bits for the application requested precision, no need 50 to do extra work. 51 52 If r==u the shift will have overlapping operands. When k>=1 (ie. when 53 usize > prec), the overlap is in the style supported by rshift (ie. dst 54 <= src). 55 56 But when r==u and k==0 (ie. usize <= prec), we would have an invalid 57 overlap (mpn_rshift (rp+1, rp, ...)). In this case we must instead use 58 mpn_lshift (PTR(r), PTR(u), size, NUMB-shift). An lshift by NUMB-shift 59 bits gives identical data of course, it's just its overlap restrictions 60 which differ. 61 62 In both shift cases, the resulting data is abs_usize+1 limbs. "adj" is 63 used to add +1 to that size if the high is non-zero (it may of course 64 have become zero by the shifting). EXP(u) is the exponent just above 65 those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is 66 zero, or no change if the high is non-zero. 67 68 Enhancements: 69 70 The way mpn_lshift is used means successive mpf_div_2exp calls on the 71 same operand will accumulate low zero limbs, until prec+1 limbs is 72 reached. This is wasteful for subsequent operations. When abs_usize <= 73 prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0], 74 ie. those which would be shifted out by an mpn_rshift. If they're zero 75 then use that mpn_rshift. */ 76 77 void 78 mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp) 79 { 80 mp_srcptr up; 81 mp_ptr rp = r->_mp_d; 82 mp_size_t usize; 83 mp_size_t abs_usize; 84 mp_size_t prec = r->_mp_prec; 85 mp_exp_t uexp = u->_mp_exp; 86 87 usize = u->_mp_size; 88 89 if (UNLIKELY (usize == 0)) 90 { 91 r->_mp_size = 0; 92 r->_mp_exp = 0; 93 return; 94 } 95 96 abs_usize = ABS (usize); 97 up = u->_mp_d; 98 99 if (exp % GMP_NUMB_BITS == 0) 100 { 101 prec++; /* retain more precision here as we don't need 102 to account for carry-out here */ 103 if (abs_usize > prec) 104 { 105 up += abs_usize - prec; 106 abs_usize = prec; 107 } 108 if (rp != up) 109 MPN_COPY_INCR (rp, up, abs_usize); 110 r->_mp_exp = uexp - exp / GMP_NUMB_BITS; 111 } 112 else 113 { 114 mp_limb_t cy_limb; 115 mp_size_t adj; 116 if (abs_usize > prec) 117 { 118 up += abs_usize - prec; 119 abs_usize = prec; 120 /* Use mpn_rshift since mpn_lshift operates downwards, and we 121 therefore would clobber part of U before using that part, in case 122 R is the same variable as U. */ 123 cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS); 124 rp[0] = cy_limb; 125 adj = rp[abs_usize] != 0; 126 } 127 else 128 { 129 cy_limb = mpn_lshift (rp, up, abs_usize, 130 GMP_NUMB_BITS - exp % GMP_NUMB_BITS); 131 rp[abs_usize] = cy_limb; 132 adj = cy_limb != 0; 133 } 134 135 abs_usize += adj; 136 r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj; 137 } 138 r->_mp_size = usize >= 0 ? abs_usize : -abs_usize; 139 } 140