text: /*
   * Copyright (C) the libgit2 contributors. All rights reserved.
   *
   * This file is part of libgit2, distributed under the GNU GPL v2 with
   * a Linking Exception. For full terms see the included COPYING file.
   */
  
  #include <stdio.h>
  
  #include "sha1_lookup.h"
  #include "common.h"
  
  /*
   * Conventional binary search loop looks like this:
   *
   *	unsigned lo, hi;
   *		do {
   *				unsigned mi = (lo + hi) / 2;
   *				int cmp = "entry pointed at by mi" minus "target";
   *				if (!cmp)
   *						return (mi is the wanted one)
   *				if (cmp > 0)
   *						hi = mi; "mi is larger than target"
   *				else
   *						lo = mi+1; "mi is smaller than target"
   *		} while (lo < hi);
   *
   * The invariants are:
   *
   * - When entering the loop, lo points at a slot that is never
   *	above the target (it could be at the target), hi points at a
   *	slot that is guaranteed to be above the target (it can never
   *	be at the target).
   *
   * - We find a point 'mi' between lo and hi (mi could be the same
   *	as lo, but never can be as same as hi), and check if it hits
   *	the target. There are three cases:
   *
   *	- if it is a hit, we are happy.
   *
   *	- if it is strictly higher than the target, we set it to hi,
   *		and repeat the search.
   *
   *	- if it is strictly lower than the target, we update lo to
   *		one slot after it, because we allow lo to be at the target.
   *
   *	If the loop exits, there is no matching entry.
   *
   * When choosing 'mi', we do not have to take the "middle" but
   * anywhere in between lo and hi, as long as lo <= mi < hi is
   * satisfied. When we somehow know that the distance between the
   * target and lo is much shorter than the target and hi, we could
   * pick mi that is much closer to lo than the midway.
   *
   * Now, we can take advantage of the fact that SHA-1 is a good hash
   * function, and as long as there are enough entries in the table, we
   * can expect uniform distribution. An entry that begins with for
   * example "deadbeef..." is much likely to appear much later than in
   * the midway of the table. It can reasonably be expected to be near
   * 87% (222/256) from the top of the table.
   *
   * However, we do not want to pick "mi" too precisely. If the entry at
   * the 87% in the above example turns out to be higher than the target
   * we are looking for, we would end up narrowing the search space down
   * only by 13%, instead of 50% we would get if we did a simple binary
   * search. So we would want to hedge our bets by being less aggressive.
   *
   * The table at "table" holds at least "nr" entries of "elem_size"
   * bytes each. Each entry has the SHA-1 key at "key_offset". The
   * table is sorted by the SHA-1 key of the entries. The caller wants
   * to find the entry with "key", and knows that the entry at "lo" is
   * not higher than the entry it is looking for, and that the entry at
   * "hi" is higher than the entry it is looking for.
   */
  int sha1_entry_pos(const void *table,
  			size_t elem_size,
  			size_t key_offset,
  			unsigned lo, unsigned hi, unsigned nr,
  			const unsigned char *key)
  {
  	const unsigned char *base = (const unsigned char*)table;
  	const unsigned char *hi_key, *lo_key;
  	unsigned ofs_0;
  
  	if (!nr || lo >= hi)
  		return -1;
  
  	if (nr == hi)
  		hi_key = NULL;
  	else
  		hi_key = base + elem_size * hi + key_offset;
  	lo_key = base + elem_size * lo + key_offset;
  
  	ofs_0 = 0;
  	do {
  		int cmp;
  		unsigned ofs, mi, range;
  		unsigned lov, hiv, kyv;
  		const unsigned char *mi_key;
  
  		range = hi - lo;
  		if (hi_key) {
  			for (ofs = ofs_0; ofs < 20; ofs++)
  				if (lo_key[ofs] != hi_key[ofs])
  					break;
  			ofs_0 = ofs;
  			/*
  			 * byte 0 thru (ofs-1) are the same between
  			 * lo and hi; ofs is the first byte that is
  			 * different.
  			 */
  			hiv = hi_key[ofs_0];
  			if (ofs_0 < 19)
  				hiv = (hiv << 8) | hi_key[ofs_0+1];
  		} else {
  			hiv = 256;
  			if (ofs_0 < 19)
  				hiv <<= 8;
  		}
  		lov = lo_key[ofs_0];
  		kyv = key[ofs_0];
  		if (ofs_0 < 19) {
  			lov = (lov << 8) | lo_key[ofs_0+1];
  			kyv = (kyv << 8) | key[ofs_0+1];
  		}
  		assert(lov < hiv);
  
  		if (kyv < lov)
  			return -1 - lo;
  		if (hiv < kyv)
  			return -1 - hi;
  
  		/*
  		 * Even if we know the target is much closer to 'hi'
  		 * than 'lo', if we pick too precisely and overshoot
  		 * (e.g. when we know 'mi' is closer to 'hi' than to
  		 * 'lo', pick 'mi' that is higher than the target), we
  		 * end up narrowing the search space by a smaller
  		 * amount (i.e. the distance between 'mi' and 'hi')
  		 * than what we would have (i.e. about half of 'lo'
  		 * and 'hi'). Hedge our bets to pick 'mi' less
  		 * aggressively, i.e. make 'mi' a bit closer to the
  		 * middle than we would otherwise pick.
  		 */
  		kyv = (kyv * 6 + lov + hiv) / 8;
  		if (lov < hiv - 1) {
  			if (kyv == lov)
  				kyv++;
  			else if (kyv == hiv)
  				kyv--;
  		}
  		mi = (range - 1) * (kyv - lov) / (hiv - lov) + lo;
  
  #ifdef INDEX_DEBUG_LOOKUP
  		printf("lo %u hi %u rg %u mi %u ", lo, hi, range, mi);
  		printf("ofs %u lov %x, hiv %x, kyv %x\n",
  				ofs_0, lov, hiv, kyv);
  #endif
  
  		if (!(lo <= mi && mi < hi)) {
  			giterr_set(GITERR_INVALID, "Assertion failure. Binary search invariant is false");
  			return -1;
  		}
  
  		mi_key = base + elem_size * mi + key_offset;
  		cmp = memcmp(mi_key + ofs_0, key + ofs_0, 20 - ofs_0);
  		if (!cmp)
  			return mi;
  		if (cmp > 0) {
  			hi = mi;
  			hi_key = mi_key;
  		} else {
  			lo = mi + 1;
  			lo_key = mi_key + elem_size;
  		}
  	} while (lo < hi);
  	return -((int)lo)-1;
  }
  