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      1 /* mpf_mul_2exp -- Multiply 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 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 
     70 void
     71 mpf_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