1 /* mpf_div_2exp -- Divide a float by 2^n. 2 3 Copyright 1993, 1994, 1996, 2000, 2001, 2002, 2004 Free Software Foundation, 4 Inc. 5 6 This file is part of the GNU MP Library. 7 8 The GNU MP Library is free software; you can redistribute it and/or modify 9 it under the terms of the GNU Lesser General Public License as published by 10 the Free Software Foundation; either version 3 of the License, or (at your 11 option) any later version. 12 13 The GNU MP Library is distributed in the hope that it will be useful, but 14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16 License for more details. 17 18 You should have received a copy of the GNU Lesser General Public License 19 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 20 21 #include "gmp.h" 22 #include "gmp-impl.h" 23 24 25 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from 26 EXP(u) to set EXP(r). The remainder exp%GMP_NUMB_BITS is then a right 27 shift for the limb data. 28 29 If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just 30 do an mpz_set with changed EXP(r). Like mpz_set we take prec+1 limbs in 31 this case. Although just prec would suffice, it's nice to have 32 mpf_div_2exp with exp==0 come out the same as mpz_set. 33 34 When shifting we take up to prec many limbs from the input. Our shift is 35 cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low 36 limbs dropped from u, and the carry out is stored to PTR(r)[0]. We don't 37 try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available) 38 into that low carry limb. Just prec limbs (with the high non-zero) from 39 the input is enough bits for the application requested precision, no need 40 to do extra work. 41 42 If r==u the shift will have overlapping operands. When k>=1 (ie. when 43 usize > prec), the overlap is in the style supported by rshift (ie. dst 44 <= src). 45 46 But when r==u and k==0 (ie. usize <= prec), we would have an invalid 47 overlap (mpn_rshift (rp+1, rp, ...)). In this case we must instead use 48 mpn_lshift (PTR(r), PTR(u), size, NUMB-shift). An lshift by NUMB-shift 49 bits gives identical data of course, it's just its overlap restrictions 50 which differ. 51 52 In both shift cases, the resulting data is abs_usize+1 limbs. "adj" is 53 used to add +1 to that size if the high is non-zero (it may of course 54 have become zero by the shifting). EXP(u) is the exponent just above 55 those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is 56 zero, or no change if the high is non-zero. 57 58 Enhancements: 59 60 The way mpn_lshift is used means successive mpf_div_2exp calls on the 61 same operand will accumulate low zero limbs, until prec+1 limbs is 62 reached. This is wasteful for subsequent operations. When abs_usize <= 63 prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0], 64 ie. those which would be shifted out by an mpn_rshift. If they're zero 65 then use that mpn_rshift. */ 66 67 void 68 mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp) 69 { 70 mp_srcptr up; 71 mp_ptr rp = r->_mp_d; 72 mp_size_t usize; 73 mp_size_t abs_usize; 74 mp_size_t prec = r->_mp_prec; 75 mp_exp_t uexp = u->_mp_exp; 76 77 usize = u->_mp_size; 78 79 if (UNLIKELY (usize == 0)) 80 { 81 r->_mp_size = 0; 82 r->_mp_exp = 0; 83 return; 84 } 85 86 abs_usize = ABS (usize); 87 up = u->_mp_d; 88 89 if (exp % GMP_NUMB_BITS == 0) 90 { 91 prec++; /* retain more precision here as we don't need 92 to account for carry-out here */ 93 if (abs_usize > prec) 94 { 95 up += abs_usize - prec; 96 abs_usize = prec; 97 } 98 if (rp != up) 99 MPN_COPY_INCR (rp, up, abs_usize); 100 r->_mp_exp = uexp - exp / GMP_NUMB_BITS; 101 } 102 else 103 { 104 mp_limb_t cy_limb; 105 mp_size_t adj; 106 if (abs_usize > prec) 107 { 108 up += abs_usize - prec; 109 abs_usize = prec; 110 /* Use mpn_rshift since mpn_lshift operates downwards, and we 111 therefore would clobber part of U before using that part, in case 112 R is the same variable as U. */ 113 cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS); 114 rp[0] = cy_limb; 115 adj = rp[abs_usize] != 0; 116 } 117 else 118 { 119 cy_limb = mpn_lshift (rp, up, abs_usize, 120 GMP_NUMB_BITS - exp % GMP_NUMB_BITS); 121 rp[abs_usize] = cy_limb; 122 adj = cy_limb != 0; 123 } 124 125 abs_usize += adj; 126 r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj; 127 } 128 r->_mp_size = usize >= 0 ? abs_usize : -abs_usize; 129 } 130