contrib/gmp/mpf/mul_2exp.c

   1 /* mpf_mul_2exp -- Multiply 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 added to EXP(u)
  26    to set EXP(r).  The remainder exp%GMP_NUMB_BITS is then a left shift for
  27    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_mul_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_lshift (PTR(r), PTR(u)+k, size, ...), where k is the number of
  36    low limbs dropped from u, and the carry out is stored to PTR(r)[size].
  37
  38    It may be noted that the low limb PTR(r)[0] doesn't incorporate bits from
  39    PTR(u)[k-1] (when k>=1 makes that limb available).  Taking just prec
  40    limbs from the input (with the high non-zero) is enough bits for the
  41    application requested precision, there's no need for extra work.
  42
  43    If r==u the shift will have overlapping operands.  When k==0 (ie. when
  44    usize <= prec), the overlap is supported by lshift (ie. dst == src).
  45
  46    But when r==u and k>=1 (ie. usize > prec), we would have an invalid
  47    overlap (ie. mpn_lshift (rp, rp+k, ...)).  In this case we must instead
  48    use mpn_rshift (PTR(r)+1, PTR(u)+k, size, NUMB-shift) with the carry out
  49    stored to PTR(r)[0].  An rshift by NUMB-shift bits like this gives
  50    identical data, it's just its overlap restrictions which differ.
  51
  52    Enhancements:
  53
  54    The way mpn_lshift is used means successive mpf_mul_2exp calls on the
  55    same operand will accumulate low zero limbs, until prec+1 limbs is
  56    reached.  This is wasteful for subsequent operations.  When abs_usize <=
  57    prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0],
  58    ie. those which would be shifted out by an mpn_rshift.  If they're zero
  59    then use that mpn_rshift.  */
  60
  61 void
  62 mpf_mul_2exp (mpf_ptr r, mpf_srcptr u, unsigned long int exp)
  63 {
  64   mp_srcptr up;
  65   mp_ptr rp = r->_mp_d;
  66   mp_size_t usize;
  67   mp_size_t abs_usize;
  68   mp_size_t prec = r->_mp_prec;
  69   mp_exp_t uexp = u->_mp_exp;
  70
  71   usize = u->_mp_size;
  72
  73   if (UNLIKELY (usize == 0))
  74     {
  75       r->_mp_size = 0;
  76       r->_mp_exp = 0;
  77       return;
  78     }
  79
  80   abs_usize = ABS (usize);
  81   up = u->_mp_d;
  82
  83   if (exp % GMP_NUMB_BITS == 0)
  84     {
  85       prec++;                   /* retain more precision here as we don't need
  86                                    to account for carry-out here */
  87       if (abs_usize > prec)
  88         {
  89           up += abs_usize - prec;
  90           abs_usize = prec;
  91         }
  92       if (rp != up)
  93         MPN_COPY_INCR (rp, up, abs_usize);
  94       r->_mp_exp = uexp + exp / GMP_NUMB_BITS;
  95     }
  96   else
  97     {
  98       mp_limb_t cy_limb;
  99       mp_size_t adj;
 100       if (abs_usize > prec)
 101         {
 102           up += abs_usize - prec;
 103           abs_usize = prec;
 104           /* Use mpn_rshift since mpn_lshift operates downwards, and we
 105              therefore would clobber part of U before using that part, in case
 106              R is the same variable as U.  */
 107           cy_limb = mpn_rshift (rp + 1, up, abs_usize,
 108                                 GMP_NUMB_BITS - exp % GMP_NUMB_BITS);
 109           rp[0] = cy_limb;
 110           adj = rp[abs_usize] != 0;
 111         }
 112       else
 113         {
 114           cy_limb = mpn_lshift (rp, up, abs_usize, exp % GMP_NUMB_BITS);
 115           rp[abs_usize] = cy_limb;
 116           adj = cy_limb != 0;
 117         }
 118
 119       abs_usize += adj;
 120       r->_mp_exp = uexp + exp / GMP_NUMB_BITS + adj;
 121     }
 122   r->_mp_size = usize >= 0 ? abs_usize : -abs_usize;
 123 }