blob | 5f069214d9060da8ceb001e6c037607c1d0096bf |

5 {

7 }

9 /*

10 * Conventional binary search loop looks like this:

11 *

12 * do {

13 * int mi = (lo + hi) / 2;

14 * int cmp = "entry pointed at by mi" minus "target";

15 * if (!cmp)

16 * return (mi is the wanted one)

17 * if (cmp > 0)

18 * hi = mi; "mi is larger than target"

19 * else

20 * lo = mi+1; "mi is smaller than target"

21 * } while (lo < hi);

22 *

23 * The invariants are:

24 *

25 * - When entering the loop, lo points at a slot that is never

26 * above the target (it could be at the target), hi points at a

27 * slot that is guaranteed to be above the target (it can never

28 * be at the target).

29 *

30 * - We find a point 'mi' between lo and hi (mi could be the same

31 * as lo, but never can be the same as hi), and check if it hits

32 * the target. There are three cases:

33 *

34 * - if it is a hit, we are happy.

35 *

36 * - if it is strictly higher than the target, we update hi with

37 * it.

38 *

39 * - if it is strictly lower than the target, we update lo to be

40 * one slot after it, because we allow lo to be at the target.

41 *

42 * When choosing 'mi', we do not have to take the "middle" but

43 * anywhere in between lo and hi, as long as lo <= mi < hi is

44 * satisfied. When we somehow know that the distance between the

45 * target and lo is much shorter than the target and hi, we could

46 * pick mi that is much closer to lo than the midway.

47 */

48 /*

49 * The table should contain "nr" elements.

50 * The sha1 of element i (between 0 and nr - 1) should be returned

51 * by "fn(i, table)".

52 */

54 sha1_access_fn fn)

55 {

75 /*

76 * At this point miv could be equal

77 * to hiv (but sha1 could still be higher);

78 * the invariant of (mi < hi) should be

79 * kept.

80 */

85 }

86 }

87 }

96 else

101 }

103 /*

104 * Conventional binary search loop looks like this:

105 *

106 * unsigned lo, hi;

107 * do {

108 * unsigned mi = (lo + hi) / 2;

109 * int cmp = "entry pointed at by mi" minus "target";

110 * if (!cmp)

111 * return (mi is the wanted one)

112 * if (cmp > 0)

113 * hi = mi; "mi is larger than target"

114 * else

115 * lo = mi+1; "mi is smaller than target"

116 * } while (lo < hi);

117 *

118 * The invariants are:

119 *

120 * - When entering the loop, lo points at a slot that is never

121 * above the target (it could be at the target), hi points at a

122 * slot that is guaranteed to be above the target (it can never

123 * be at the target).

124 *

125 * - We find a point 'mi' between lo and hi (mi could be the same

126 * as lo, but never can be as same as hi), and check if it hits

127 * the target. There are three cases:

128 *

129 * - if it is a hit, we are happy.

130 *

131 * - if it is strictly higher than the target, we set it to hi,

132 * and repeat the search.

133 *

134 * - if it is strictly lower than the target, we update lo to

135 * one slot after it, because we allow lo to be at the target.

136 *

137 * If the loop exits, there is no matching entry.

138 *

139 * When choosing 'mi', we do not have to take the "middle" but

140 * anywhere in between lo and hi, as long as lo <= mi < hi is

141 * satisfied. When we somehow know that the distance between the

142 * target and lo is much shorter than the target and hi, we could

143 * pick mi that is much closer to lo than the midway.

144 *

145 * Now, we can take advantage of the fact that SHA-1 is a good hash

146 * function, and as long as there are enough entries in the table, we

147 * can expect uniform distribution. An entry that begins with for

148 * example "deadbeef..." is much likely to appear much later than in

149 * the midway of the table. It can reasonably be expected to be near

150 * 87% (222/256) from the top of the table.

151 *

152 * However, we do not want to pick "mi" too precisely. If the entry at

153 * the 87% in the above example turns out to be higher than the target

154 * we are looking for, we would end up narrowing the search space down

155 * only by 13%, instead of 50% we would get if we did a simple binary

156 * search. So we would want to hedge our bets by being less aggressive.

157 *

158 * The table at "table" holds at least "nr" entries of "elem_size"

159 * bytes each. Each entry has the SHA-1 key at "key_offset". The

160 * table is sorted by the SHA-1 key of the entries. The caller wants

161 * to find the entry with "key", and knows that the entry at "lo" is

162 * not higher than the entry it is looking for, and that the entry at

163 * "hi" is higher than the entry it is looking for.

164 */

170 {

184 else

201 /*

202 * byte 0 thru (ofs-1) are the same between

203 * lo and hi; ofs is the first byte that is

204 * different.

205 *

206 * If ofs==20, then no bytes are different,

207 * meaning we have entries with duplicate

208 * keys. We know that we are in a solid run

209 * of this entry (because the entries are

210 * sorted, and our lo and hi are the same,

211 * there can be nothing but this single key

212 * in between). So we can stop the search.

213 * Either one of these entries is it (and

214 * we do not care which), or we do not have

215 * it.

216 *

217 * Furthermore, we know that one of our

218 * endpoints must be the edge of the run of

219 * duplicates. For example, given this

220 * sequence:

221 *

222 * idx 0 1 2 3 4 5

223 * key A C C C C D

224 *

225 * If we are searching for "B", we might

226 * hit the duplicate run at lo=1, hi=3

227 * (e.g., by first mi=3, then mi=0). But we

228 * can never have lo > 1, because B < C.

229 * That is, if our key is less than the

230 * run, we know that "lo" is the edge, but

231 * we can say nothing of "hi". Similarly,

232 * if our key is greater than the run, we

233 * know that "hi" is the edge, but we can

234 * say nothing of "lo".

235 *

236 * Therefore if we do not find it, we also

237 * know where it would go if it did exist:

238 * just on the far side of the edge that we

239 * know about.

240 */

249 else

251 }

260 }

266 }

274 /*

275 * Even if we know the target is much closer to 'hi'

276 * than 'lo', if we pick too precisely and overshoot

277 * (e.g. when we know 'mi' is closer to 'hi' than to

278 * 'lo', pick 'mi' that is higher than the target), we

279 * end up narrowing the search space by a smaller

280 * amount (i.e. the distance between 'mi' and 'hi')

281 * than what we would have (i.e. about half of 'lo'

282 * and 'hi'). Hedge our bets to pick 'mi' less

283 * aggressively, i.e. make 'mi' a bit closer to the

284 * middle than we would otherwise pick.

285 */

289 kyv++;

291 kyv--;

292 }

299 }

314 }

317 }