1 /*
2 * arbitrary precision integers
3 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
4 *
5 * This library is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Lesser General Public
7 * License as published by the Free Software Foundation; either
8 * version 2 of the License, or (at your option) any later version.
9 *
10 * This library is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * Lesser General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public
16 * License along with this library; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
18 *
19 */
21 /**
22 * @file integer.c
23 * arbitrary precision integers.
24 * @author Michael Niedermayer <michaelni@gmx.at>
25 */
27 #include "common.h"
28 #include "integer.h"
30 AVInteger av_add_i(AVInteger a, AVInteger b){
31 int i, carry=0;
33 for(i=0; i<AV_INTEGER_SIZE; i++){
34 carry= (carry>>16) + a.v[i] + b.v[i];
35 a.v[i]= carry;
36 }
37 return a;
38 }
40 AVInteger av_sub_i(AVInteger a, AVInteger b){
41 int i, carry=0;
43 for(i=0; i<AV_INTEGER_SIZE; i++){
44 carry= (carry>>16) + a.v[i] - b.v[i];
45 a.v[i]= carry;
46 }
47 return a;
48 }
50 /**
51 * returns the rounded down value of the logarithm of base 2 of the given AVInteger.
52 * this is simply the index of the most significant bit which is 1. Or 0 of all bits are 0
53 */
54 int av_log2_i(AVInteger a){
55 int i;
57 for(i=AV_INTEGER_SIZE-1; i>=0; i--){
58 if(a.v[i])
59 return av_log2_16bit(a.v[i]) + 16*i;
60 }
61 return -1;
62 }
64 AVInteger av_mul_i(AVInteger a, AVInteger b){
65 AVInteger out;
66 int i, j;
67 int na= (av_log2_i(a)+16) >> 4;
68 int nb= (av_log2_i(b)+16) >> 4;
70 memset(&out, 0, sizeof(out));
72 for(i=0; i<na; i++){
73 unsigned int carry=0;
75 if(a.v[i])
76 for(j=i; j<AV_INTEGER_SIZE && j-i<=nb; j++){
77 carry= (carry>>16) + out.v[j] + a.v[i]*b.v[j-i];
78 out.v[j]= carry;
79 }
80 }
82 return out;
83 }
85 /**
86 * returns 0 if a==b, 1 if a>b and -1 if a<b.
87 */
88 int av_cmp_i(AVInteger a, AVInteger b){
89 int i;
90 int v= (int16_t)a.v[AV_INTEGER_SIZE-1] - (int16_t)b.v[AV_INTEGER_SIZE-1];
91 if(v) return (v>>16)|1;
93 for(i=AV_INTEGER_SIZE-2; i>=0; i--){
94 int v= a.v[i] - b.v[i];
95 if(v) return (v>>16)|1;
96 }
97 return 0;
98 }
100 /**
101 * bitwise shift.
102 * @param s the number of bits by which the value should be shifted right, may be negative for shifting left
103 */
104 AVInteger av_shr_i(AVInteger a, int s){
105 AVInteger out;
106 int i;
108 for(i=0; i<AV_INTEGER_SIZE; i++){
109 int index= i + (s>>4);
110 unsigned int v=0;
111 if(index+1<AV_INTEGER_SIZE && index+1>=0) v = a.v[index+1]<<16;
112 if(index <AV_INTEGER_SIZE && index >=0) v+= a.v[index ];
113 out.v[i]= v >> (s&15);
114 }
115 return out;
116 }
118 /**
119 * returns a % b.
120 * @param quot a/b will be stored here
121 */
122 AVInteger av_mod_i(AVInteger *quot, AVInteger a, AVInteger b){
123 int i= av_log2_i(a) - av_log2_i(b);
124 AVInteger quot_temp;
125 if(!quot) quot = &quot_temp;
127 assert((int16_t)a[AV_INTEGER_SIZE-1] >= 0 && (int16_t)b[AV_INTEGER_SIZE-1] >= 0);
128 assert(av_log2(b)>=0);
130 if(i > 0)
131 b= av_shr_i(b, -i);
133 memset(quot, 0, sizeof(AVInteger));
135 while(i-- >= 0){
136 *quot= av_shr_i(*quot, -1);
137 if(av_cmp_i(a, b) >= 0){
138 a= av_sub_i(a, b);
139 quot->v[0] += 1;
140 }
141 b= av_shr_i(b, 1);
142 }
143 return a;
144 }
146 /**
147 * returns a/b.
148 */
149 AVInteger av_div_i(AVInteger a, AVInteger b){
150 AVInteger quot;
151 av_mod_i(&quot, a, b);
152 return quot;
153 }
155 /**
156 * converts the given int64_t to an AVInteger.
157 */
158 AVInteger av_int2i(int64_t a){
159 AVInteger out;
160 int i;
162 for(i=0; i<AV_INTEGER_SIZE; i++){
163 out.v[i]= a;
164 a>>=16;
165 }
166 return out;
167 }
169 /**
170 * converts the given AVInteger to an int64_t.
171 * if the AVInteger is too large to fit into an int64_t,
172 * then only the least significant 64bit will be used
173 */
174 int64_t av_i2int(AVInteger a){
175 int i;
176 int64_t out=(int8_t)a.v[AV_INTEGER_SIZE-1];
178 for(i= AV_INTEGER_SIZE-2; i>=0; i--){
179 out = (out<<16) + a.v[i];
180 }
181 return out;
182 }
184 #if 0
185 #undef NDEBUG
186 #include <assert.h>
188 const uint8_t ff_log2_tab[256]={
189 0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
190 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
191 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
192 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
193 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
194 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
195 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
196 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
197 };
199 main(){
200 int64_t a,b;
202 for(a=7; a<256*256*256; a+=13215){
203 for(b=3; b<256*256*256; b+=27118){
204 AVInteger ai= av_int2i(a);
205 AVInteger bi= av_int2i(b);
207 assert(av_i2int(ai) == a);
208 assert(av_i2int(bi) == b);
209 assert(av_i2int(av_add_i(ai,bi)) == a+b);
210 assert(av_i2int(av_sub_i(ai,bi)) == a-b);
211 assert(av_i2int(av_mul_i(ai,bi)) == a*b);
212 assert(av_i2int(av_shr_i(ai, 9)) == a>>9);
213 assert(av_i2int(av_shr_i(ai,-9)) == a<<9);
214 assert(av_i2int(av_shr_i(ai, 17)) == a>>17);
215 assert(av_i2int(av_shr_i(ai,-17)) == a<<17);
216 assert(av_log2_i(ai) == av_log2(a));
217 assert(av_i2int(av_div_i(ai,bi)) == a/b);
218 }
219 }
220 }
221 #endif