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