1 /* mpf_mul_ui -- Multiply a float and an unsigned integer.
2
3 Copyright 1993, 1994, 1996, 2001, 2003, 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 #include "longlong.h"
33
34
35 /* The core operation is a multiply of PREC(r) limbs from u by v, producing
36 either PREC(r) or PREC(r)+1 result limbs. If u is shorter than PREC(r),
37 then we take only as much as it has. If u is longer we incorporate a
38 carry from the lower limbs.
39
40 If u has just 1 extra limb, then the carry to add is high(up[0]*v). That
41 is of course what mpn_mul_1 would do if it was called with PREC(r)+1
42 limbs of input.
43
44 If u has more than 1 extra limb, then there can be a further carry bit
45 out of lower uncalculated limbs (the way the low of one product adds to
46 the high of the product below it). This is of course what an mpn_mul_1
47 would do if it was called with the full u operand. But we instead work
48 downwards explicitly, until a carry occurs or until a value other than
49 GMP_NUMB_MAX occurs (that being the only value a carry bit can propagate
50 across).
51
52 The carry determination normally requires two umul_ppmm's, only rarely
53 will GMP_NUMB_MAX occur and require further products.
54
55 The carry limb is conveniently added into the mul_1 using mpn_mul_1c when
56 that function exists, otherwise a subsequent mpn_add_1 is needed.
57
58 Clearly when mpn_mul_1c is used the carry must be calculated first. But
59 this is also the case when add_1 is used, since if r==u and ABSIZ(r) >
60 PREC(r) then the mpn_mul_1 overwrites the low part of the input.
61
62 A reuse r==u with size > prec can occur from a size PREC(r)+1 in the
63 usual way, or it can occur from an mpf_set_prec_raw leaving a bigger
64 sized value. In both cases we can end up calling mpn_mul_1 with
65 overlapping src and dst regions, but this will be with dst < src and such
66 an overlap is permitted.
67
68 Not done:
69
70 No attempt is made to determine in advance whether the result will be
71 PREC(r) or PREC(r)+1 limbs. If it's going to be PREC(r)+1 then we could
72 take one less limb from u and generate just PREC(r), that of course
73 satisfying application requested precision. But any test counting bits
74 or forming the high product would almost certainly take longer than the
75 incremental cost of an extra limb in mpn_mul_1.
76
77 Enhancements:
78
79 Repeated mpf_mul_ui's with an even v will accumulate low zero bits on the
80 result, leaving low zero limbs after a while, which it might be nice to
81 strip to save work in subsequent operations. Calculating the low limb
82 explicitly would let us direct mpn_mul_1 to put the balance at rp when
83 the low is zero (instead of normally rp+1). But it's not clear whether
84 this would be worthwhile. Explicit code for the low limb will probably
85 be slower than having it done in mpn_mul_1, so we need to consider how
86 often a zero will be stripped and how much that's likely to save
87 later. */
88
89 void
90 mpf_mul_ui (mpf_ptr r, mpf_srcptr u, unsigned long int v)
91 {
92 mp_srcptr up;
93 mp_size_t usize;
94 mp_size_t size;
95 mp_size_t prec, excess;
96 mp_limb_t cy_limb, vl, cbit, cin;
97 mp_ptr rp;
98
99 usize = u->_mp_size;
100 if (UNLIKELY (v == 0) || UNLIKELY (usize == 0))
101 {
102 r->_mp_size = 0;
103 r->_mp_exp = 0;
104 return;
105 }
106
107 #if BITS_PER_ULONG > GMP_NUMB_BITS /* avoid warnings about shift amount */
108 if (v > GMP_NUMB_MAX)
109 {
110 mpf_t vf;
111 mp_limb_t vp[2];
112 vp[0] = v & GMP_NUMB_MASK;
113 vp[1] = v >> GMP_NUMB_BITS;
114 PTR(vf) = vp;
115 SIZ(vf) = 2;
116 ASSERT_CODE (PREC(vf) = 2);
117 EXP(vf) = 2;
118 mpf_mul (r, u, vf);
119 return;
120 }
121 #endif
122
123 size = ABS (usize);
124 prec = r->_mp_prec;
125 up = u->_mp_d;
126 vl = v;
127 excess = size - prec;
128 cin = 0;
129
130 if (excess > 0)
131 {
132 /* up is bigger than desired rp, shorten it to prec limbs and
133 determine a carry-in */
134
135 mp_limb_t vl_shifted = vl << GMP_NAIL_BITS;
136 mp_limb_t hi, lo, next_lo, sum;
137 mp_size_t i;
138
139 /* high limb of top product */
140 i = excess - 1;
141 umul_ppmm (cin, lo, up[i], vl_shifted);
142
143 /* and carry bit out of products below that, if any */
144 for (;;)
145 {
146 i--;
147 if (i < 0)
148 break;
149
150 umul_ppmm (hi, next_lo, up[i], vl_shifted);
151 lo >>= GMP_NAIL_BITS;
152 ADDC_LIMB (cbit, sum, hi, lo);
153 cin += cbit;
154 lo = next_lo;
155
156 /* Continue only if the sum is GMP_NUMB_MAX. GMP_NUMB_MAX is the
157 only value a carry from below can propagate across. If we've
158 just seen the carry out (ie. cbit!=0) then sum!=GMP_NUMB_MAX,
159 so this test stops us for that case too. */
160 if (LIKELY (sum != GMP_NUMB_MAX))
161 break;
162 }
163
164 up += excess;
165 size = prec;
166 }
167
168 rp = r->_mp_d;
169 #if HAVE_NATIVE_mpn_mul_1c
170 cy_limb = mpn_mul_1c (rp, up, size, vl, cin);
171 #else
172 cy_limb = mpn_mul_1 (rp, up, size, vl);
173 __GMPN_ADD_1 (cbit, rp, rp, size, cin);
174 cy_limb += cbit;
175 #endif
176 rp[size] = cy_limb;
177 cy_limb = cy_limb != 0;
178 r->_mp_exp = u->_mp_exp + cy_limb;
179 size += cy_limb;
180 r->_mp_size = usize >= 0 ? size : -size;
181 }