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 the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 3 of the License, or (at your
10 option) any later version.
11
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15 License for more details.
16
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
19
20 #include "gmp.h"
21 #include "gmp-impl.h"
22 #include "longlong.h"
23
24
25 /* The core operation is a multiply of PREC(r) limbs from u by v, producing
26 either PREC(r) or PREC(r)+1 result limbs. If u is shorter than PREC(r),
27 then we take only as much as it has. If u is longer we incorporate a
28 carry from the lower limbs.
29
30 If u has just 1 extra limb, then the carry to add is high(up[0]*v). That
31 is of course what mpn_mul_1 would do if it was called with PREC(r)+1
32 limbs of input.
33
34 If u has more than 1 extra limb, then there can be a further carry bit
35 out of lower uncalculated limbs (the way the low of one product adds to
36 the high of the product below it). This is of course what an mpn_mul_1
37 would do if it was called with the full u operand. But we instead work
38 downwards explicitly, until a carry occurs or until a value other than
39 GMP_NUMB_MAX occurs (that being the only value a carry bit can propagate
40 across).
41
42 The carry determination normally requires two umul_ppmm's, only rarely
43 will GMP_NUMB_MAX occur and require further products.
44
45 The carry limb is conveniently added into the mul_1 using mpn_mul_1c when
46 that function exists, otherwise a subsequent mpn_add_1 is needed.
47
48 Clearly when mpn_mul_1c is used the carry must be calculated first. But
49 this is also the case when add_1 is used, since if r==u and ABSIZ(r) >
50 PREC(r) then the mpn_mul_1 overwrites the low part of the input.
51
52 A reuse r==u with size > prec can occur from a size PREC(r)+1 in the
53 usual way, or it can occur from an mpf_set_prec_raw leaving a bigger
54 sized value. In both cases we can end up calling mpn_mul_1 with
55 overlapping src and dst regions, but this will be with dst < src and such
56 an overlap is permitted.
57
58 Not done:
59
60 No attempt is made to determine in advance whether the result will be
61 PREC(r) or PREC(r)+1 limbs. If it's going to be PREC(r)+1 then we could
62 take one less limb from u and generate just PREC(r), that of course
63 satisfying application requested precision. But any test counting bits
64 or forming the high product would almost certainly take longer than the
65 incremental cost of an extra limb in mpn_mul_1.
66
67 Enhancements:
68
69 Repeated mpf_mul_ui's with an even v will accumulate low zero bits on the
70 result, leaving low zero limbs after a while, which it might be nice to
71 strip to save work in subsequent operations. Calculating the low limb
72 explicitly would let us direct mpn_mul_1 to put the balance at rp when
73 the low is zero (instead of normally rp+1). But it's not clear whether
74 this would be worthwhile. Explicit code for the low limb will probably
75 be slower than having it done in mpn_mul_1, so we need to consider how
76 often a zero will be stripped and how much that's likely to save
77 later. */
78
79 void
mpf_mul_ui(mpf_ptr r,mpf_srcptr u,unsigned long int v)80 mpf_mul_ui (mpf_ptr r, mpf_srcptr u, unsigned long int v)
81 {
82 mp_srcptr up;
83 mp_size_t usize;
84 mp_size_t size;
85 mp_size_t prec, excess;
86 mp_limb_t cy_limb, vl, cbit, cin;
87 mp_ptr rp;
88
89 usize = u->_mp_size;
90 if (UNLIKELY (v == 0) || UNLIKELY (usize == 0))
91 {
92 r->_mp_size = 0;
93 r->_mp_exp = 0;
94 return;
95 }
96
97 #if BITS_PER_ULONG > GMP_NUMB_BITS /* avoid warnings about shift amount */
98 if (v > GMP_NUMB_MAX)
99 {
100 mpf_t vf;
101 mp_limb_t vp[2];
102 vp[0] = v & GMP_NUMB_MASK;
103 vp[1] = v >> GMP_NUMB_BITS;
104 PTR(vf) = vp;
105 SIZ(vf) = 2;
106 ASSERT_CODE (PREC(vf) = 2);
107 EXP(vf) = 2;
108 mpf_mul (r, u, vf);
109 return;
110 }
111 #endif
112
113 size = ABS (usize);
114 prec = r->_mp_prec;
115 up = u->_mp_d;
116 vl = v;
117 excess = size - prec;
118 cin = 0;
119
120 if (excess > 0)
121 {
122 /* up is bigger than desired rp, shorten it to prec limbs and
123 determine a carry-in */
124
125 mp_limb_t vl_shifted = vl << GMP_NAIL_BITS;
126 mp_limb_t hi, lo, next_lo, sum;
127 mp_size_t i;
128
129 /* high limb of top product */
130 i = excess - 1;
131 umul_ppmm (cin, lo, up[i], vl_shifted);
132
133 /* and carry bit out of products below that, if any */
134 for (;;)
135 {
136 i--;
137 if (i < 0)
138 break;
139
140 umul_ppmm (hi, next_lo, up[i], vl_shifted);
141 lo >>= GMP_NAIL_BITS;
142 ADDC_LIMB (cbit, sum, hi, lo);
143 cin += cbit;
144 lo = next_lo;
145
146 /* Continue only if the sum is GMP_NUMB_MAX. GMP_NUMB_MAX is the
147 only value a carry from below can propagate across. If we've
148 just seen the carry out (ie. cbit!=0) then sum!=GMP_NUMB_MAX,
149 so this test stops us for that case too. */
150 if (LIKELY (sum != GMP_NUMB_MAX))
151 break;
152 }
153
154 up += excess;
155 size = prec;
156 }
157
158 rp = r->_mp_d;
159 #if HAVE_NATIVE_mpn_mul_1c
160 cy_limb = mpn_mul_1c (rp, up, size, vl, cin);
161 #else
162 cy_limb = mpn_mul_1 (rp, up, size, vl);
163 __GMPN_ADD_1 (cbit, rp, rp, size, cin);
164 cy_limb += cbit;
165 #endif
166 rp[size] = cy_limb;
167 cy_limb = cy_limb != 0;
168 r->_mp_exp = u->_mp_exp + cy_limb;
169 size += cy_limb;
170 r->_mp_size = usize >= 0 ? size : -size;
171 }
172