source/libs/gmp/gmp-src/mpf/mul_2exp.c

   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.h"
  32 #include "gmp-impl.h"
  33
  34
  35 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount added to EXP(u)
  36    to set EXP(r).  The remainder exp%GMP_NUMB_BITS is then a left shift for
  37    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_mul_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_lshift (PTR(r), PTR(u)+k, size, ...), where k is the number of
  46    low limbs dropped from u, and the carry out is stored to PTR(r)[size].
  47
  48    It may be noted that the low limb PTR(r)[0] doesn't incorporate bits from
  49    PTR(u)[k-1] (when k>=1 makes that limb available).  Taking just prec
  50    limbs from the input (with the high non-zero) is enough bits for the
  51    application requested precision, there's no need for extra work.
  52
  53    If r==u the shift will have overlapping operands.  When k==0 (ie. when
  54    usize <= prec), the overlap is supported by lshift (ie. dst == src).
  55
  56    But when r==u and k>=1 (ie. usize > prec), we would have an invalid
  57    overlap (ie. mpn_lshift (rp, rp+k, ...)).  In this case we must instead
  58    use mpn_rshift (PTR(r)+1, PTR(u)+k, size, NUMB-shift) with the carry out
  59    stored to PTR(r)[0].  An rshift by NUMB-shift bits like this gives
  60    identical data, it's just its overlap restrictions which differ.
  61
  62    Enhancements:
  63
  64    The way mpn_lshift is used means successive mpf_mul_2exp calls on the
  65    same operand will accumulate low zero limbs, until prec+1 limbs is
  66    reached.  This is wasteful for subsequent operations.  When abs_usize <=
  67    prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0],
  68    ie. those which would be shifted out by an mpn_rshift.  If they're zero
  69    then use that mpn_rshift.  */
  70
  71 void
  72 mpf_mul_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp)
  73 {
  74   mp_srcptr up;
  75   mp_ptr rp = r->_mp_d;
  76   mp_size_t usize;
  77   mp_size_t abs_usize;
  78   mp_size_t prec = r->_mp_prec;
  79   mp_exp_t uexp = u->_mp_exp;
  80
  81   usize = u->_mp_size;
  82
  83   if (UNLIKELY (usize == 0))
  84     {
  85       r->_mp_size = 0;
  86       r->_mp_exp = 0;
  87       return;
  88     }
  89
  90   abs_usize = ABS (usize);
  91   up = u->_mp_d;
  92
  93   if (exp % GMP_NUMB_BITS == 0)
  94     {
  95       prec++;                   /* retain more precision here as we don't need
  96                                    to account for carry-out here */
  97       if (abs_usize > prec)
  98         {
  99           up += abs_usize - prec;
 100           abs_usize = prec;
 101         }
 102       if (rp != up)
 103         MPN_COPY_INCR (rp, up, abs_usize);
 104       r->_mp_exp = uexp + exp / GMP_NUMB_BITS;
 105     }
 106   else
 107     {
 108       mp_limb_t cy_limb;
 109       mp_size_t adj;
 110       if (abs_usize > prec)
 111         {
 112           up += abs_usize - prec;
 113           abs_usize = prec;
 114           /* Use mpn_rshift since mpn_lshift operates downwards, and we
 115              therefore would clobber part of U before using that part, in case
 116              R is the same variable as U.  */
 117           cy_limb = mpn_rshift (rp + 1, up, abs_usize,
 118                                 GMP_NUMB_BITS - exp % GMP_NUMB_BITS);
 119           rp[0] = cy_limb;
 120           adj = rp[abs_usize] != 0;
 121         }
 122       else
 123         {
 124           cy_limb = mpn_lshift (rp, up, abs_usize, exp % GMP_NUMB_BITS);
 125           rp[abs_usize] = cy_limb;
 126           adj = cy_limb != 0;
 127         }
 128
 129       abs_usize += adj;
 130       r->_mp_exp = uexp + exp / GMP_NUMB_BITS + adj;
 131     }
 132   r->_mp_size = usize >= 0 ? abs_usize : -abs_usize;
 133 }