mul_2exp.c revision 1.1.1.3
1/* mpf_mul_2exp -- Multiply a float by 2^n. 2 3Copyright 1993, 1994, 1996, 2000-2002, 2004 Free Software Foundation, Inc. 4 5This file is part of the GNU MP Library. 6 7The GNU MP Library is free software; you can redistribute it and/or modify 8it 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 14or 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 20or both in parallel, as here. 21 22The GNU MP Library is distributed in the hope that it will be useful, but 23WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 25for more details. 26 27You should have received copies of the GNU General Public License and the 28GNU Lesser General Public License along with the GNU MP Library. If not, 29see 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 added to EXP(u) 35 to set EXP(r). The remainder exp%GMP_NUMB_BITS is then a left shift for 36 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_mul_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_lshift (PTR(r), PTR(u)+k, size, ...), where k is the number of 45 low limbs dropped from u, and the carry out is stored to PTR(r)[size]. 46 47 It may be noted that the low limb PTR(r)[0] doesn't incorporate bits from 48 PTR(u)[k-1] (when k>=1 makes that limb available). Taking just prec 49 limbs from the input (with the high non-zero) is enough bits for the 50 application requested precision, there's no need for extra work. 51 52 If r==u the shift will have overlapping operands. When k==0 (ie. when 53 usize <= prec), the overlap is supported by lshift (ie. dst == src). 54 55 But when r==u and k>=1 (ie. usize > prec), we would have an invalid 56 overlap (ie. mpn_lshift (rp, rp+k, ...)). In this case we must instead 57 use mpn_rshift (PTR(r)+1, PTR(u)+k, size, NUMB-shift) with the carry out 58 stored to PTR(r)[0]. An rshift by NUMB-shift bits like this gives 59 identical data, it's just its overlap restrictions which differ. 60 61 Enhancements: 62 63 The way mpn_lshift is used means successive mpf_mul_2exp calls on the 64 same operand will accumulate low zero limbs, until prec+1 limbs is 65 reached. This is wasteful for subsequent operations. When abs_usize <= 66 prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0], 67 ie. those which would be shifted out by an mpn_rshift. If they're zero 68 then use that mpn_rshift. */ 69 70void 71mpf_mul_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp) 72{ 73 mp_srcptr up; 74 mp_ptr rp = r->_mp_d; 75 mp_size_t usize; 76 mp_size_t abs_usize; 77 mp_size_t prec = r->_mp_prec; 78 mp_exp_t uexp = u->_mp_exp; 79 80 usize = u->_mp_size; 81 82 if (UNLIKELY (usize == 0)) 83 { 84 r->_mp_size = 0; 85 r->_mp_exp = 0; 86 return; 87 } 88 89 abs_usize = ABS (usize); 90 up = u->_mp_d; 91 92 if (exp % GMP_NUMB_BITS == 0) 93 { 94 prec++; /* retain more precision here as we don't need 95 to account for carry-out here */ 96 if (abs_usize > prec) 97 { 98 up += abs_usize - prec; 99 abs_usize = prec; 100 } 101 if (rp != up) 102 MPN_COPY_INCR (rp, up, abs_usize); 103 r->_mp_exp = uexp + exp / GMP_NUMB_BITS; 104 } 105 else 106 { 107 mp_limb_t cy_limb; 108 mp_size_t adj; 109 if (abs_usize > prec) 110 { 111 up += abs_usize - prec; 112 abs_usize = prec; 113 /* Use mpn_rshift since mpn_lshift operates downwards, and we 114 therefore would clobber part of U before using that part, in case 115 R is the same variable as U. */ 116 cy_limb = mpn_rshift (rp + 1, up, abs_usize, 117 GMP_NUMB_BITS - exp % GMP_NUMB_BITS); 118 rp[0] = cy_limb; 119 adj = rp[abs_usize] != 0; 120 } 121 else 122 { 123 cy_limb = mpn_lshift (rp, up, abs_usize, exp % GMP_NUMB_BITS); 124 rp[abs_usize] = cy_limb; 125 adj = cy_limb != 0; 126 } 127 128 abs_usize += adj; 129 r->_mp_exp = uexp + exp / GMP_NUMB_BITS + adj; 130 } 131 r->_mp_size = usize >= 0 ? abs_usize : -abs_usize; 132} 133