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 }