tor/src/common/container.c

/* Copyright (c) 2003-2004, Roger Dingledine
 * Copyright (c) 2004-2006, Roger Dingledine, Nick Mathewson.
 * Copyright (c) 2007-2017, The Tor Project, Inc. */
/* See LICENSE for licensing information */

/**
 * \file container.c
 * \brief Implements a smartlist (a resizable array) along
 * with helper functions to use smartlists.  Also includes
 * hash table implementations of a string-to-void* map, and of
 * a digest-to-void* map.
 **/

#include "compat.h"
#include "util.h"
#include "torlog.h"
#include "container.h"
#include "crypto.h"

#include <stdlib.h>
#include <string.h>
#include <assert.h>

#include "ht.h"

/** All newly allocated smartlists have this capacity. */
#define SMARTLIST_DEFAULT_CAPACITY 16

/** Allocate and return an empty smartlist.
 */
MOCK_IMPL(smartlist_t *,
smartlist_new,(void))
{
  smartlist_t *sl = tor_malloc(sizeof(smartlist_t));
  sl->num_used = 0;
  sl->capacity = SMARTLIST_DEFAULT_CAPACITY;
  sl->list = tor_calloc(sizeof(void *), sl->capacity);
  return sl;
}

/** Deallocate a smartlist.  Does not release storage associated with the
 * list's elements.
 */
MOCK_IMPL(void,
smartlist_free_,(smartlist_t *sl))
{
  if (!sl)
    return;
  tor_free(sl->list);
  tor_free(sl);
}

/** Remove all elements from the list.
 */
void
smartlist_clear(smartlist_t *sl)
{
  memset(sl->list, 0, sizeof(void *) * sl->num_used);
  sl->num_used = 0;
}

#if SIZE_MAX < INT_MAX
#error "We don't support systems where size_t is smaller than int."
#endif

/** Make sure that <b>sl</b> can hold at least <b>size</b> entries. */
static inline void
smartlist_ensure_capacity(smartlist_t *sl, size_t size)
{
  /* Set MAX_CAPACITY to MIN(INT_MAX, SIZE_MAX / sizeof(void*)) */
#if (SIZE_MAX/SIZEOF_VOID_P) > INT_MAX
#define MAX_CAPACITY (INT_MAX)
#else
#define MAX_CAPACITY (int)((SIZE_MAX / (sizeof(void*))))
#endif

  tor_assert(size <= MAX_CAPACITY);

  if (size > (size_t) sl->capacity) {
    size_t higher = (size_t) sl->capacity;
    if (PREDICT_UNLIKELY(size > MAX_CAPACITY/2)) {
      higher = MAX_CAPACITY;
    } else {
      while (size > higher)
        higher *= 2;
    }
    sl->list = tor_reallocarray(sl->list, sizeof(void *),
                                ((size_t)higher));
    memset(sl->list + sl->capacity, 0,
           sizeof(void *) * (higher - sl->capacity));
    sl->capacity = (int) higher;
  }
#undef ASSERT_CAPACITY
#undef MAX_CAPACITY
}

/** Append element to the end of the list. */
void
smartlist_add(smartlist_t *sl, void *element)
{
  smartlist_ensure_capacity(sl, ((size_t) sl->num_used)+1);
  sl->list[sl->num_used++] = element;
}

/** Append each element from S2 to the end of S1. */
void
smartlist_add_all(smartlist_t *s1, const smartlist_t *s2)
{
  size_t new_size = (size_t)s1->num_used + (size_t)s2->num_used;
  tor_assert(new_size >= (size_t) s1->num_used); /* check for overflow. */
  smartlist_ensure_capacity(s1, new_size);
  memcpy(s1->list + s1->num_used, s2->list, s2->num_used*sizeof(void*));
  tor_assert(new_size <= INT_MAX); /* redundant. */
  s1->num_used = (int) new_size;
}

/** Remove all elements E from sl such that E==element.  Preserve
 * the order of any elements before E, but elements after E can be
 * rearranged.
 */
void
smartlist_remove(smartlist_t *sl, const void *element)
{
  int i;
  if (element == NULL)
    return;
  for (i=0; i < sl->num_used; i++)
    if (sl->list[i] == element) {
      sl->list[i] = sl->list[--sl->num_used]; /* swap with the end */
      i--; /* so we process the new i'th element */
      sl->list[sl->num_used] = NULL;
    }
}

/** As <b>smartlist_remove</b>, but do not change the order of
 * any elements not removed */
void
smartlist_remove_keeporder(smartlist_t *sl, const void *element)
{
  int i, j, num_used_orig = sl->num_used;
  if (element == NULL)
    return;

  for (i=j=0; j < num_used_orig; ++j) {
    if (sl->list[j] == element) {
      --sl->num_used;
    } else {
      sl->list[i++] = sl->list[j];
    }
  }
}

/** If <b>sl</b> is nonempty, remove and return the final element.  Otherwise,
 * return NULL. */
void *
smartlist_pop_last(smartlist_t *sl)
{
  tor_assert(sl);
  if (sl->num_used) {
    void *tmp = sl->list[--sl->num_used];
    sl->list[sl->num_used] = NULL;
    return tmp;
  } else
    return NULL;
}

/** Reverse the order of the items in <b>sl</b>. */
void
smartlist_reverse(smartlist_t *sl)
{
  int i, j;
  void *tmp;
  tor_assert(sl);
  for (i = 0, j = sl->num_used-1; i < j; ++i, --j) {
    tmp = sl->list[i];
    sl->list[i] = sl->list[j];
    sl->list[j] = tmp;
  }
}

/** If there are any strings in sl equal to element, remove and free them.
 * Does not preserve order. */
void
smartlist_string_remove(smartlist_t *sl, const char *element)
{
  int i;
  tor_assert(sl);
  tor_assert(element);
  for (i = 0; i < sl->num_used; ++i) {
    if (!strcmp(element, sl->list[i])) {
      tor_free(sl->list[i]);
      sl->list[i] = sl->list[--sl->num_used]; /* swap with the end */
      i--; /* so we process the new i'th element */
      sl->list[sl->num_used] = NULL;
    }
  }
}

/** Return true iff some element E of sl has E==element.
 */
int
smartlist_contains(const smartlist_t *sl, const void *element)
{
  int i;
  for (i=0; i < sl->num_used; i++)
    if (sl->list[i] == element)
      return 1;
  return 0;
}

/** Return true iff <b>sl</b> has some element E such that
 * !strcmp(E,<b>element</b>)
 */
int
smartlist_contains_string(const smartlist_t *sl, const char *element)
{
  int i;
  if (!sl) return 0;
  for (i=0; i < sl->num_used; i++)
    if (strcmp((const char*)sl->list[i],element)==0)
      return 1;
  return 0;
}

/** If <b>element</b> is equal to an element of <b>sl</b>, return that
 * element's index.  Otherwise, return -1. */
int
smartlist_string_pos(const smartlist_t *sl, const char *element)
{
  int i;
  if (!sl) return -1;
  for (i=0; i < sl->num_used; i++)
    if (strcmp((const char*)sl->list[i],element)==0)
      return i;
  return -1;
}

/** If <b>element</b> is the same pointer as an element of <b>sl</b>, return
 * that element's index.  Otherwise, return -1. */
int
smartlist_pos(const smartlist_t *sl, const void *element)
{
  int i;
  if (!sl) return -1;
  for (i=0; i < sl->num_used; i++)
    if (element == sl->list[i])
      return i;
  return -1;
}

/** Return true iff <b>sl</b> has some element E such that
 * !strcasecmp(E,<b>element</b>)
 */
int
smartlist_contains_string_case(const smartlist_t *sl, const char *element)
{
  int i;
  if (!sl) return 0;
  for (i=0; i < sl->num_used; i++)
    if (strcasecmp((const char*)sl->list[i],element)==0)
      return 1;
  return 0;
}

/** Return true iff <b>sl</b> has some element E such that E is equal
 * to the decimal encoding of <b>num</b>.
 */
int
smartlist_contains_int_as_string(const smartlist_t *sl, int num)
{
  char buf[32]; /* long enough for 64-bit int, and then some. */
  tor_snprintf(buf,sizeof(buf),"%d", num);
  return smartlist_contains_string(sl, buf);
}

/** Return true iff the two lists contain the same strings in the same
 * order, or if they are both NULL. */
int
smartlist_strings_eq(const smartlist_t *sl1, const smartlist_t *sl2)
{
  if (sl1 == NULL)
    return sl2 == NULL;
  if (sl2 == NULL)
    return 0;
  if (smartlist_len(sl1) != smartlist_len(sl2))
    return 0;
  SMARTLIST_FOREACH(sl1, const char *, cp1, {
      const char *cp2 = smartlist_get(sl2, cp1_sl_idx);
      if (strcmp(cp1, cp2))
        return 0;
    });
  return 1;
}

/** Return true iff the two lists contain the same int pointer values in
 * the same order, or if they are both NULL. */
int
smartlist_ints_eq(const smartlist_t *sl1, const smartlist_t *sl2)
{
  if (sl1 == NULL)
    return sl2 == NULL;
  if (sl2 == NULL)
    return 0;
  if (smartlist_len(sl1) != smartlist_len(sl2))
    return 0;
  SMARTLIST_FOREACH(sl1, int *, cp1, {
      int *cp2 = smartlist_get(sl2, cp1_sl_idx);
      if (*cp1 != *cp2)
        return 0;
    });
  return 1;
}

/** Return true iff <b>sl</b> has some element E such that
 * tor_memeq(E,<b>element</b>,DIGEST_LEN)
 */
int
smartlist_contains_digest(const smartlist_t *sl, const char *element)
{
  int i;
  if (!sl) return 0;
  for (i=0; i < sl->num_used; i++)
    if (tor_memeq((const char*)sl->list[i],element,DIGEST_LEN))
      return 1;
  return 0;
}

/** Return true iff some element E of sl2 has smartlist_contains(sl1,E).
 */
int
smartlist_overlap(const smartlist_t *sl1, const smartlist_t *sl2)
{
  int i;
  for (i=0; i < sl2->num_used; i++)
    if (smartlist_contains(sl1, sl2->list[i]))
      return 1;
  return 0;
}

/** Remove every element E of sl1 such that !smartlist_contains(sl2,E).
 * Does not preserve the order of sl1.
 */
void
smartlist_intersect(smartlist_t *sl1, const smartlist_t *sl2)
{
  int i;
  for (i=0; i < sl1->num_used; i++)
    if (!smartlist_contains(sl2, sl1->list[i])) {
      sl1->list[i] = sl1->list[--sl1->num_used]; /* swap with the end */
      i--; /* so we process the new i'th element */
      sl1->list[sl1->num_used] = NULL;
    }
}

/** Remove every element E of sl1 such that smartlist_contains(sl2,E).
 * Does not preserve the order of sl1.
 */
void
smartlist_subtract(smartlist_t *sl1, const smartlist_t *sl2)
{
  int i;
  for (i=0; i < sl2->num_used; i++)
    smartlist_remove(sl1, sl2->list[i]);
}

/** Remove the <b>idx</b>th element of sl; if idx is not the last
 * element, swap the last element of sl into the <b>idx</b>th space.
 */
void
smartlist_del(smartlist_t *sl, int idx)
{
  tor_assert(sl);
  tor_assert(idx>=0);
  tor_assert(idx < sl->num_used);
  sl->list[idx] = sl->list[--sl->num_used];
  sl->list[sl->num_used] = NULL;
}

/** Remove the <b>idx</b>th element of sl; if idx is not the last element,
 * moving all subsequent elements back one space. Return the old value
 * of the <b>idx</b>th element.
 */
void
smartlist_del_keeporder(smartlist_t *sl, int idx)
{
  tor_assert(sl);
  tor_assert(idx>=0);
  tor_assert(idx < sl->num_used);
  --sl->num_used;
  if (idx < sl->num_used)
    memmove(sl->list+idx, sl->list+idx+1, sizeof(void*)*(sl->num_used-idx));
  sl->list[sl->num_used] = NULL;
}

/** Insert the value <b>val</b> as the new <b>idx</b>th element of
 * <b>sl</b>, moving all items previously at <b>idx</b> or later
 * forward one space.
 */
void
smartlist_insert(smartlist_t *sl, int idx, void *val)
{
  tor_assert(sl);
  tor_assert(idx>=0);
  tor_assert(idx <= sl->num_used);
  if (idx == sl->num_used) {
    smartlist_add(sl, val);
  } else {
    smartlist_ensure_capacity(sl, ((size_t) sl->num_used)+1);
    /* Move other elements away */
    if (idx < sl->num_used)
      memmove(sl->list + idx + 1, sl->list + idx,
              sizeof(void*)*(sl->num_used-idx));
    sl->num_used++;
    sl->list[idx] = val;
  }
}

/**
 * Split a string <b>str</b> along all occurrences of <b>sep</b>,
 * appending the (newly allocated) split strings, in order, to
 * <b>sl</b>.  Return the number of strings added to <b>sl</b>.
 *
 * If <b>flags</b>&amp;SPLIT_SKIP_SPACE is true, remove initial and
 * trailing space from each entry.
 * If <b>flags</b>&amp;SPLIT_IGNORE_BLANK is true, remove any entries
 * of length 0.
 * If <b>flags</b>&amp;SPLIT_STRIP_SPACE is true, strip spaces from each
 * split string.
 *
 * If <b>max</b>\>0, divide the string into no more than <b>max</b> pieces. If
 * <b>sep</b> is NULL, split on any sequence of horizontal space.
 */
int
smartlist_split_string(smartlist_t *sl, const char *str, const char *sep,
                       int flags, int max)
{
  const char *cp, *end, *next;
  int n = 0;

  tor_assert(sl);
  tor_assert(str);

  cp = str;
  while (1) {
    if (flags&SPLIT_SKIP_SPACE) {
      while (TOR_ISSPACE(*cp)) ++cp;
    }

    if (max>0 && n == max-1) {
      end = strchr(cp,'\0');
    } else if (sep) {
      end = strstr(cp,sep);
      if (!end)
        end = strchr(cp,'\0');
    } else {
      for (end = cp; *end && *end != '\t' && *end != ' '; ++end)
        ;
    }

    tor_assert(end);

    if (!*end) {
      next = NULL;
    } else if (sep) {
      next = end+strlen(sep);
    } else {
      next = end+1;
      while (*next == '\t' || *next == ' ')
        ++next;
    }

    if (flags&SPLIT_SKIP_SPACE) {
      while (end > cp && TOR_ISSPACE(*(end-1)))
        --end;
    }
    if (end != cp || !(flags&SPLIT_IGNORE_BLANK)) {
      char *string = tor_strndup(cp, end-cp);
      if (flags&SPLIT_STRIP_SPACE)
        tor_strstrip(string, " ");
      smartlist_add(sl, string);
      ++n;
    }
    if (!next)
      break;
    cp = next;
  }

  return n;
}

/** Allocate and return a new string containing the concatenation of
 * the elements of <b>sl</b>, in order, separated by <b>join</b>.  If
 * <b>terminate</b> is true, also terminate the string with <b>join</b>.
 * If <b>len_out</b> is not NULL, set <b>len_out</b> to the length of
 * the returned string. Requires that every element of <b>sl</b> is
 * NUL-terminated string.
 */
char *
smartlist_join_strings(smartlist_t *sl, const char *join,
                       int terminate, size_t *len_out)
{
  return smartlist_join_strings2(sl,join,strlen(join),terminate,len_out);
}

/** As smartlist_join_strings, but instead of separating/terminated with a
 * NUL-terminated string <b>join</b>, uses the <b>join_len</b>-byte sequence
 * at <b>join</b>.  (Useful for generating a sequence of NUL-terminated
 * strings.)
 */
char *
smartlist_join_strings2(smartlist_t *sl, const char *join,
                        size_t join_len, int terminate, size_t *len_out)
{
  int i;
  size_t n = 0;
  char *r = NULL, *dst, *src;

  tor_assert(sl);
  tor_assert(join);

  if (terminate)
    n = join_len;

  for (i = 0; i < sl->num_used; ++i) {
    n += strlen(sl->list[i]);
    if (i+1 < sl->num_used) /* avoid double-counting the last one */
      n += join_len;
  }
  dst = r = tor_malloc(n+1);
  for (i = 0; i < sl->num_used; ) {
    for (src = sl->list[i]; *src; )
      *dst++ = *src++;
    if (++i < sl->num_used) {
      memcpy(dst, join, join_len);
      dst += join_len;
    }
  }
  if (terminate) {
    memcpy(dst, join, join_len);
    dst += join_len;
  }
  *dst = '\0';

  if (len_out)
    *len_out = dst-r;
  return r;
}

/** Sort the members of <b>sl</b> into an order defined by
 * the ordering function <b>compare</b>, which returns less then 0 if a
 * precedes b, greater than 0 if b precedes a, and 0 if a 'equals' b.
 */
void
smartlist_sort(smartlist_t *sl, int (*compare)(const void **a, const void **b))
{
  if (!sl->num_used)
    return;
  qsort(sl->list, sl->num_used, sizeof(void*),
        (int (*)(const void *,const void*))compare);
}

/** Given a smartlist <b>sl</b> sorted with the function <b>compare</b>,
 * return the most frequent member in the list.  Break ties in favor of
 * later elements.  If the list is empty, return NULL.  If count_out is
 * non-null, set it to the count of the most frequent member.
 */
void *
smartlist_get_most_frequent_(const smartlist_t *sl,
                             int (*compare)(const void **a, const void **b),
                             int *count_out)
{
  const void *most_frequent = NULL;
  int most_frequent_count = 0;

  const void *cur = NULL;
  int i, count=0;

  if (!sl->num_used) {
    if (count_out)
      *count_out = 0;
    return NULL;
  }
  for (i = 0; i < sl->num_used; ++i) {
    const void *item = sl->list[i];
    if (cur && 0 == compare(&cur, &item)) {
      ++count;
    } else {
      if (cur && count >= most_frequent_count) {
        most_frequent = cur;
        most_frequent_count = count;
      }
      cur = item;
      count = 1;
    }
  }
  if (cur && count >= most_frequent_count) {
    most_frequent = cur;
    most_frequent_count = count;
  }
  if (count_out)
    *count_out = most_frequent_count;
  return (void*)most_frequent;
}

/** Given a sorted smartlist <b>sl</b> and the comparison function used to
 * sort it, remove all duplicate members.  If free_fn is provided, calls
 * free_fn on each duplicate.  Otherwise, just removes them.  Preserves order.
 */
void
smartlist_uniq(smartlist_t *sl,
               int (*compare)(const void **a, const void **b),
               void (*free_fn)(void *a))
{
  int i;
  for (i=1; i < sl->num_used; ++i) {
    if (compare((const void **)&(sl->list[i-1]),
                (const void **)&(sl->list[i])) == 0) {
      if (free_fn)
        free_fn(sl->list[i]);
      smartlist_del_keeporder(sl, i--);
    }
  }
}

/** Assuming the members of <b>sl</b> are in order, return a pointer to the
 * member that matches <b>key</b>.  Ordering and matching are defined by a
 * <b>compare</b> function that returns 0 on a match; less than 0 if key is
 * less than member, and greater than 0 if key is greater then member.
 */
void *
smartlist_bsearch(smartlist_t *sl, const void *key,
                  int (*compare)(const void *key, const void **member))
{
  int found, idx;
  idx = smartlist_bsearch_idx(sl, key, compare, &found);
  return found ? smartlist_get(sl, idx) : NULL;
}

/** Assuming the members of <b>sl</b> are in order, return the index of the
 * member that matches <b>key</b>.  If no member matches, return the index of
 * the first member greater than <b>key</b>, or smartlist_len(sl) if no member
 * is greater than <b>key</b>.  Set <b>found_out</b> to true on a match, to
 * false otherwise.  Ordering and matching are defined by a <b>compare</b>
 * function that returns 0 on a match; less than 0 if key is less than member,
 * and greater than 0 if key is greater then member.
 */
int
smartlist_bsearch_idx(const smartlist_t *sl, const void *key,
                      int (*compare)(const void *key, const void **member),
                      int *found_out)
{
  int hi, lo, cmp, mid, len, diff;

  tor_assert(sl);
  tor_assert(compare);
  tor_assert(found_out);

  len = smartlist_len(sl);

  /* Check for the trivial case of a zero-length list */
  if (len == 0) {
    *found_out = 0;
    /* We already know smartlist_len(sl) is 0 in this case */
    return 0;
  }

  /* Okay, we have a real search to do */
  tor_assert(len > 0);
  lo = 0;
  hi = len - 1;

  /*
   * These invariants are always true:
   *
   * For all i such that 0 <= i < lo, sl[i] < key
   * For all i such that hi < i <= len, sl[i] > key
   */

  while (lo <= hi) {
    diff = hi - lo;
    /*
     * We want mid = (lo + hi) / 2, but that could lead to overflow, so
     * instead diff = hi - lo (non-negative because of loop condition), and
     * then hi = lo + diff, mid = (lo + lo + diff) / 2 = lo + (diff / 2).
     */
    mid = lo + (diff / 2);
    cmp = compare(key, (const void**) &(sl->list[mid]));
    if (cmp == 0) {
      /* sl[mid] == key; we found it */
      *found_out = 1;
      return mid;
    } else if (cmp > 0) {
      /*
       * key > sl[mid] and an index i such that sl[i] == key must
       * have i > mid if it exists.
       */

      /*
       * Since lo <= mid <= hi, hi can only decrease on each iteration (by
       * being set to mid - 1) and hi is initially len - 1, mid < len should
       * always hold, and this is not symmetric with the left end of list
       * mid > 0 test below.  A key greater than the right end of the list
       * should eventually lead to lo == hi == mid == len - 1, and then
       * we set lo to len below and fall out to the same exit we hit for
       * a key in the middle of the list but not matching.  Thus, we just
       * assert for consistency here rather than handle a mid == len case.
       */
      tor_assert(mid < len);
      /* Move lo to the element immediately after sl[mid] */
      lo = mid + 1;
    } else {
      /* This should always be true in this case */
      tor_assert(cmp < 0);

      /*
       * key < sl[mid] and an index i such that sl[i] == key must
       * have i < mid if it exists.
       */

      if (mid > 0) {
        /* Normal case, move hi to the element immediately before sl[mid] */
        hi = mid - 1;
      } else {
        /* These should always be true in this case */
        tor_assert(mid == lo);
        tor_assert(mid == 0);
        /*
         * We were at the beginning of the list and concluded that every
         * element e compares e > key.
         */
        *found_out = 0;
        return 0;
      }
    }
  }

  /*
   * lo > hi; we have no element matching key but we have elements falling
   * on both sides of it.  The lo index points to the first element > key.
   */
  tor_assert(lo == hi + 1); /* All other cases should have been handled */
  tor_assert(lo >= 0);
  tor_assert(lo <= len);
  tor_assert(hi >= 0);
  tor_assert(hi <= len);

  if (lo < len) {
    cmp = compare(key, (const void **) &(sl->list[lo]));
    tor_assert(cmp < 0);
  } else {
    cmp = compare(key, (const void **) &(sl->list[len-1]));
    tor_assert(cmp > 0);
  }

  *found_out = 0;
  return lo;
}

/** Helper: compare two const char **s. */
static int
compare_string_ptrs_(const void **_a, const void **_b)
{
  return strcmp((const char*)*_a, (const char*)*_b);
}

/** Sort a smartlist <b>sl</b> containing strings into lexically ascending
 * order. */
void
smartlist_sort_strings(smartlist_t *sl)
{
  smartlist_sort(sl, compare_string_ptrs_);
}

/** Return the most frequent string in the sorted list <b>sl</b> */
const char *
smartlist_get_most_frequent_string(smartlist_t *sl)
{
  return smartlist_get_most_frequent(sl, compare_string_ptrs_);
}

/** Return the most frequent string in the sorted list <b>sl</b>.
 * If <b>count_out</b> is provided, set <b>count_out</b> to the
 * number of times that string appears.
 */
const char *
smartlist_get_most_frequent_string_(smartlist_t *sl, int *count_out)
{
  return smartlist_get_most_frequent_(sl, compare_string_ptrs_, count_out);
}

/** Remove duplicate strings from a sorted list, and free them with tor_free().
 */
void
smartlist_uniq_strings(smartlist_t *sl)
{
  smartlist_uniq(sl, compare_string_ptrs_, tor_free_);
}

/** Helper: compare two pointers. */
static int
compare_ptrs_(const void **_a, const void **_b)
{
  const void *a = *_a, *b = *_b;
  if (a<b)
    return -1;
  else if (a==b)
    return 0;
  else
    return 1;
}

/** Sort <b>sl</b> in ascending order of the pointers it contains. */
void
smartlist_sort_pointers(smartlist_t *sl)
{
  smartlist_sort(sl, compare_ptrs_);
}

/* Heap-based priority queue implementation for O(lg N) insert and remove.
 * Recall that the heap property is that, for every index I, h[I] <
 * H[LEFT_CHILD[I]] and h[I] < H[RIGHT_CHILD[I]].
 *
 * For us to remove items other than the topmost item, each item must store
 * its own index within the heap.  When calling the pqueue functions, tell
 * them about the offset of the field that stores the index within the item.
 *
 * Example:
 *
 *   typedef struct timer_t {
 *     struct timeval tv;
 *     int heap_index;
 *   } timer_t;
 *
 *   static int compare(const void *p1, const void *p2) {
 *     const timer_t *t1 = p1, *t2 = p2;
 *     if (t1->tv.tv_sec < t2->tv.tv_sec) {
 *        return -1;
 *     } else if (t1->tv.tv_sec > t2->tv.tv_sec) {
 *        return 1;
 *     } else {
 *        return t1->tv.tv_usec - t2->tv_usec;
 *     }
 *   }
 *
 *   void timer_heap_insert(smartlist_t *heap, timer_t *timer) {
 *      smartlist_pqueue_add(heap, compare, offsetof(timer_t, heap_index),
 *         timer);
 *   }
 *
 *   void timer_heap_pop(smartlist_t *heap) {
 *      return smartlist_pqueue_pop(heap, compare,
 *         offsetof(timer_t, heap_index));
 *   }
 */

/** @{ */
/** Functions to manipulate heap indices to find a node's parent and children.
 *
 * For a 1-indexed array, we would use LEFT_CHILD[x] = 2*x and RIGHT_CHILD[x]
 *   = 2*x + 1.  But this is C, so we have to adjust a little. */

/* MAX_PARENT_IDX is the largest IDX in the smartlist which might have
 * children whose indices fit inside an int.
 * LEFT_CHILD(MAX_PARENT_IDX) == INT_MAX-2;
 * RIGHT_CHILD(MAX_PARENT_IDX) == INT_MAX-1;
 * LEFT_CHILD(MAX_PARENT_IDX + 1) == INT_MAX // impossible, see max list size.
 */
#define MAX_PARENT_IDX ((INT_MAX - 2) / 2)
/* If this is true, then i is small enough to potentially have children
 * in the smartlist, and it is save to use LEFT_CHILD/RIGHT_CHILD on it. */
#define IDX_MAY_HAVE_CHILDREN(i) ((i) <= MAX_PARENT_IDX)
#define LEFT_CHILD(i)  ( 2*(i) + 1 )
#define RIGHT_CHILD(i) ( 2*(i) + 2 )
#define PARENT(i)      ( ((i)-1) / 2 )
/** }@ */

/** @{ */
/** Helper macros for heaps: Given a local variable <b>idx_field_offset</b>
 * set to the offset of an integer index within the heap element structure,
 * IDX_OF_ITEM(p) gives you the index of p, and IDXP(p) gives you a pointer to
 * where p's index is stored.  Given additionally a local smartlist <b>sl</b>,
 * UPDATE_IDX(i) sets the index of the element at <b>i</b> to the correct
 * value (that is, to <b>i</b>).
 */
#define IDXP(p) ((int*)STRUCT_VAR_P(p, idx_field_offset))

#define UPDATE_IDX(i)  do {                            \
    void *updated = sl->list[i];                       \
    *IDXP(updated) = i;                                \
  } while (0)

#define IDX_OF_ITEM(p) (*IDXP(p))
/** @} */

/** Helper. <b>sl</b> may have at most one violation of the heap property:
 * the item at <b>idx</b> may be greater than one or both of its children.
 * Restore the heap property. */
static inline void
smartlist_heapify(smartlist_t *sl,
                  int (*compare)(const void *a, const void *b),
                  int idx_field_offset,
                  int idx)
{
  while (1) {
    if (! IDX_MAY_HAVE_CHILDREN(idx)) {
      /* idx is so large that it cannot have any children, since doing so
       * would mean the smartlist was over-capacity. Therefore it cannot
       * violate the heap property by being greater than a child (since it
       * doesn't have any). */
      return;
    }

    int left_idx = LEFT_CHILD(idx);
    int best_idx;

    if (left_idx >= sl->num_used)
      return;
    if (compare(sl->list[idx],sl->list[left_idx]) < 0)
      best_idx = idx;
    else
      best_idx = left_idx;
    if (left_idx+1 < sl->num_used &&
        compare(sl->list[left_idx+1],sl->list[best_idx]) < 0)
      best_idx = left_idx + 1;

    if (best_idx == idx) {
      return;
    } else {
      void *tmp = sl->list[idx];
      sl->list[idx] = sl->list[best_idx];
      sl->list[best_idx] = tmp;
      UPDATE_IDX(idx);
      UPDATE_IDX(best_idx);

      idx = best_idx;
    }
  }
}

/** Insert <b>item</b> into the heap stored in <b>sl</b>, where order is
 * determined by <b>compare</b> and the offset of the item in the heap is
 * stored in an int-typed field at position <b>idx_field_offset</b> within
 * item.
 */
void
smartlist_pqueue_add(smartlist_t *sl,
                     int (*compare)(const void *a, const void *b),
                     int idx_field_offset,
                     void *item)
{
  int idx;
  smartlist_add(sl,item);
  UPDATE_IDX(sl->num_used-1);

  for (idx = sl->num_used - 1; idx; ) {
    int parent = PARENT(idx);
    if (compare(sl->list[idx], sl->list[parent]) < 0) {
      void *tmp = sl->list[parent];
      sl->list[parent] = sl->list[idx];
      sl->list[idx] = tmp;
      UPDATE_IDX(parent);
      UPDATE_IDX(idx);
      idx = parent;
    } else {
      return;
    }
  }
}

/** Remove and return the top-priority item from the heap stored in <b>sl</b>,
 * where order is determined by <b>compare</b> and the item's position is
 * stored at position <b>idx_field_offset</b> within the item.  <b>sl</b> must
 * not be empty. */
void *
smartlist_pqueue_pop(smartlist_t *sl,
                     int (*compare)(const void *a, const void *b),
                     int idx_field_offset)
{
  void *top;
  tor_assert(sl->num_used);

  top = sl->list[0];
  *IDXP(top)=-1;
  if (--sl->num_used) {
    sl->list[0] = sl->list[sl->num_used];
    sl->list[sl->num_used] = NULL;
    UPDATE_IDX(0);
    smartlist_heapify(sl, compare, idx_field_offset, 0);
  }
  sl->list[sl->num_used] = NULL;
  return top;
}

/** Remove the item <b>item</b> from the heap stored in <b>sl</b>,
 * where order is determined by <b>compare</b> and the item's position is
 * stored at position <b>idx_field_offset</b> within the item.  <b>sl</b> must
 * not be empty. */
void
smartlist_pqueue_remove(smartlist_t *sl,
                        int (*compare)(const void *a, const void *b),
                        int idx_field_offset,
                        void *item)
{
  int idx = IDX_OF_ITEM(item);
  tor_assert(idx >= 0);
  tor_assert(sl->list[idx] == item);
  --sl->num_used;
  *IDXP(item) = -1;
  if (idx == sl->num_used) {
    sl->list[sl->num_used] = NULL;
    return;
  } else {
    sl->list[idx] = sl->list[sl->num_used];
    sl->list[sl->num_used] = NULL;
    UPDATE_IDX(idx);
    smartlist_heapify(sl, compare, idx_field_offset, idx);
  }
}

/** Assert that the heap property is correctly maintained by the heap stored
 * in <b>sl</b>, where order is determined by <b>compare</b>. */
void
smartlist_pqueue_assert_ok(smartlist_t *sl,
                           int (*compare)(const void *a, const void *b),
                           int idx_field_offset)
{
  int i;
  for (i = sl->num_used - 1; i >= 0; --i) {
    if (i>0)
      tor_assert(compare(sl->list[PARENT(i)], sl->list[i]) <= 0);
    tor_assert(IDX_OF_ITEM(sl->list[i]) == i);
  }
}

/** Helper: compare two DIGEST_LEN digests. */
static int
compare_digests_(const void **_a, const void **_b)
{
  return tor_memcmp((const char*)*_a, (const char*)*_b, DIGEST_LEN);
}

/** Sort the list of DIGEST_LEN-byte digests into ascending order. */
void
smartlist_sort_digests(smartlist_t *sl)
{
  smartlist_sort(sl, compare_digests_);
}

/** Remove duplicate digests from a sorted list, and free them with tor_free().
 */
void
smartlist_uniq_digests(smartlist_t *sl)
{
  smartlist_uniq(sl, compare_digests_, tor_free_);
}

/** Helper: compare two DIGEST256_LEN digests. */
static int
compare_digests256_(const void **_a, const void **_b)
{
  return tor_memcmp((const char*)*_a, (const char*)*_b, DIGEST256_LEN);
}

/** Sort the list of DIGEST256_LEN-byte digests into ascending order. */
void
smartlist_sort_digests256(smartlist_t *sl)
{
  smartlist_sort(sl, compare_digests256_);
}

/** Return the most frequent member of the sorted list of DIGEST256_LEN
 * digests in <b>sl</b> */
const uint8_t *
smartlist_get_most_frequent_digest256(smartlist_t *sl)
{
  return smartlist_get_most_frequent(sl, compare_digests256_);
}

/** Remove duplicate 256-bit digests from a sorted list, and free them with
 * tor_free().
 */
void
smartlist_uniq_digests256(smartlist_t *sl)
{
  smartlist_uniq(sl, compare_digests256_, tor_free_);
}

/** Helper: Declare an entry type and a map type to implement a mapping using
 * ht.h.  The map type will be called <b>maptype</b>.  The key part of each
 * entry is declared using the C declaration <b>keydecl</b>.  All functions
 * and types associated with the map get prefixed with <b>prefix</b> */
#define DEFINE_MAP_STRUCTS(maptype, keydecl, prefix)      \
  typedef struct prefix ## entry_t {                      \
    HT_ENTRY(prefix ## entry_t) node;                     \
    void *val;                                            \
    keydecl;                                              \
  } prefix ## entry_t;                                    \
  struct maptype {                                        \
    HT_HEAD(prefix ## impl, prefix ## entry_t) head;      \
  }

DEFINE_MAP_STRUCTS(strmap_t, char *key, strmap_);
DEFINE_MAP_STRUCTS(digestmap_t, char key[DIGEST_LEN], digestmap_);
DEFINE_MAP_STRUCTS(digest256map_t, uint8_t key[DIGEST256_LEN], digest256map_);

/** Helper: compare strmap_entry_t objects by key value. */
static inline int
strmap_entries_eq(const strmap_entry_t *a, const strmap_entry_t *b)
{
  return !strcmp(a->key, b->key);
}

/** Helper: return a hash value for a strmap_entry_t. */
static inline unsigned int
strmap_entry_hash(const strmap_entry_t *a)
{
  return (unsigned) siphash24g(a->key, strlen(a->key));
}

/** Helper: compare digestmap_entry_t objects by key value. */
static inline int
digestmap_entries_eq(const digestmap_entry_t *a, const digestmap_entry_t *b)
{
  return tor_memeq(a->key, b->key, DIGEST_LEN);
}

/** Helper: return a hash value for a digest_map_t. */
static inline unsigned int
digestmap_entry_hash(const digestmap_entry_t *a)
{
  return (unsigned) siphash24g(a->key, DIGEST_LEN);
}

/** Helper: compare digestmap_entry_t objects by key value. */
static inline int
digest256map_entries_eq(const digest256map_entry_t *a,
                        const digest256map_entry_t *b)
{
  return tor_memeq(a->key, b->key, DIGEST256_LEN);
}

/** Helper: return a hash value for a digest_map_t. */
static inline unsigned int
digest256map_entry_hash(const digest256map_entry_t *a)
{
  return (unsigned) siphash24g(a->key, DIGEST256_LEN);
}

HT_PROTOTYPE(strmap_impl, strmap_entry_t, node, strmap_entry_hash,
             strmap_entries_eq)
HT_GENERATE2(strmap_impl, strmap_entry_t, node, strmap_entry_hash,
             strmap_entries_eq, 0.6, tor_reallocarray_, tor_free_)

HT_PROTOTYPE(digestmap_impl, digestmap_entry_t, node, digestmap_entry_hash,
             digestmap_entries_eq)
HT_GENERATE2(digestmap_impl, digestmap_entry_t, node, digestmap_entry_hash,
             digestmap_entries_eq, 0.6, tor_reallocarray_, tor_free_)

HT_PROTOTYPE(digest256map_impl, digest256map_entry_t, node,
             digest256map_entry_hash,
             digest256map_entries_eq)
HT_GENERATE2(digest256map_impl, digest256map_entry_t, node,
             digest256map_entry_hash,
             digest256map_entries_eq, 0.6, tor_reallocarray_, tor_free_)

#define strmap_entry_free(ent) \
  FREE_AND_NULL(strmap_entry_t, strmap_entry_free_, (ent))
#define digestmap_entry_free(ent) \
  FREE_AND_NULL(digestmap_entry_t, digestmap_entry_free_, (ent))
#define digest256map_entry_free(ent) \
  FREE_AND_NULL(digest256map_entry_t, digest256map_entry_free_, (ent))

static inline void
strmap_entry_free_(strmap_entry_t *ent)
{
  tor_free(ent->key);
  tor_free(ent);
}
static inline void
digestmap_entry_free_(digestmap_entry_t *ent)
{
  tor_free(ent);
}
static inline void
digest256map_entry_free_(digest256map_entry_t *ent)
{
  tor_free(ent);
}

static inline void
strmap_assign_tmp_key(strmap_entry_t *ent, const char *key)
{
  ent->key = (char*)key;
}
static inline void
digestmap_assign_tmp_key(digestmap_entry_t *ent, const char *key)
{
  memcpy(ent->key, key, DIGEST_LEN);
}
static inline void
digest256map_assign_tmp_key(digest256map_entry_t *ent, const uint8_t *key)
{
  memcpy(ent->key, key, DIGEST256_LEN);
}
static inline void
strmap_assign_key(strmap_entry_t *ent, const char *key)
{
  ent->key = tor_strdup(key);
}
static inline void
digestmap_assign_key(digestmap_entry_t *ent, const char *key)
{
  memcpy(ent->key, key, DIGEST_LEN);
}
static inline void
digest256map_assign_key(digest256map_entry_t *ent, const uint8_t *key)
{
  memcpy(ent->key, key, DIGEST256_LEN);
}

/**
 * Macro: implement all the functions for a map that are declared in
 * container.h by the DECLARE_MAP_FNS() macro.  You must additionally define a
 * prefix_entry_free_() function to free entries (and their keys), a
 * prefix_assign_tmp_key() function to temporarily set a stack-allocated
 * entry to hold a key, and a prefix_assign_key() function to set a
 * heap-allocated entry to hold a key.
 */
#define IMPLEMENT_MAP_FNS(maptype, keytype, prefix)                     \
  /** Create and return a new empty map. */                             \
  MOCK_IMPL(maptype *,                                                  \
  prefix##_new,(void))                                                  \
  {                                                                     \
    maptype *result;                                                    \
    result = tor_malloc(sizeof(maptype));                               \
    HT_INIT(prefix##_impl, &result->head);                              \
    return result;                                                      \
  }                                                                     \
                                                                        \
  /** Return the item from <b>map</b> whose key matches <b>key</b>, or  \
   * NULL if no such value exists. */                                   \
  void *                                                                \
  prefix##_get(const maptype *map, const keytype key)                   \
  {                                                                     \
    prefix ##_entry_t *resolve;                                         \
    prefix ##_entry_t search;                                           \
    tor_assert(map);                                                    \
    tor_assert(key);                                                    \
    prefix ##_assign_tmp_key(&search, key);                             \
    resolve = HT_FIND(prefix ##_impl, &map->head, &search);             \
    if (resolve) {                                                      \
      return resolve->val;                                              \
    } else {                                                            \
      return NULL;                                                      \
    }                                                                   \
  }                                                                     \
                                                                        \
  /** Add an entry to <b>map</b> mapping <b>key</b> to <b>val</b>;      \
   * return the previous value, or NULL if no such value existed. */     \
  void *                                                                \
  prefix##_set(maptype *map, const keytype key, void *val)              \
  {                                                                     \
    prefix##_entry_t search;                                            \
    void *oldval;                                                       \
    tor_assert(map);                                                    \
    tor_assert(key);                                                    \
    tor_assert(val);                                                    \
    prefix##_assign_tmp_key(&search, key);                              \
    /* We a lot of our time in this function, so the code below is */   \
    /* meant to optimize the check/alloc/set cycle by avoiding the two */\
    /* trips to the hash table that we would do in the unoptimized */   \
    /* version of this code. (Each of HT_INSERT and HT_FIND calls */     \
    /* HT_SET_HASH and HT_FIND_P.) */                                   \
    HT_FIND_OR_INSERT_(prefix##_impl, node, prefix##_entry_hash,        \
                       &(map->head),                                    \
                       prefix##_entry_t, &search, ptr,                  \
                       {                                                \
                         /* we found an entry. */                       \
                         oldval = (*ptr)->val;                          \
                         (*ptr)->val = val;                             \
                         return oldval;                                 \
                       },                                               \
                       {                                                \
                         /* We didn't find the entry. */                \
                         prefix##_entry_t *newent =                     \
                           tor_malloc_zero(sizeof(prefix##_entry_t));   \
                         prefix##_assign_key(newent, key);              \
                         newent->val = val;                             \
                         HT_FOI_INSERT_(node, &(map->head),             \
                            &search, newent, ptr);                      \
                         return NULL;                                   \
    });                                                                 \
  }                                                                     \
                                                                        \
  /** Remove the value currently associated with <b>key</b> from the map. \
   * Return the value if one was set, or NULL if there was no entry for \
   * <b>key</b>.                                                        \
   *                                                                    \
   * Note: you must free any storage associated with the returned value. \
   */                                                                   \
  void *                                                                \
  prefix##_remove(maptype *map, const keytype key)                      \
  {                                                                     \
    prefix##_entry_t *resolve;                                          \
    prefix##_entry_t search;                                            \
    void *oldval;                                                       \
    tor_assert(map);                                                    \
    tor_assert(key);                                                    \
    prefix##_assign_tmp_key(&search, key);                              \
    resolve = HT_REMOVE(prefix##_impl, &map->head, &search);            \
    if (resolve) {                                                      \
      oldval = resolve->val;                                            \
      prefix##_entry_free(resolve);                                     \
      return oldval;                                                    \
    } else {                                                            \
      return NULL;                                                      \
    }                                                                   \
  }                                                                     \
                                                                        \
  /** Return the number of elements in <b>map</b>. */                   \
  int                                                                   \
  prefix##_size(const maptype *map)                                     \
  {                                                                     \
    return HT_SIZE(&map->head);                                         \
  }                                                                     \
                                                                        \
  /** Return true iff <b>map</b> has no entries. */                     \
  int                                                                   \
  prefix##_isempty(const maptype *map)                                  \
  {                                                                     \
    return HT_EMPTY(&map->head);                                        \
  }                                                                     \
                                                                        \
  /** Assert that <b>map</b> is not corrupt. */                         \
  void                                                                  \
  prefix##_assert_ok(const maptype *map)                                \
  {                                                                     \
    tor_assert(!prefix##_impl_HT_REP_IS_BAD_(&map->head));              \
  }                                                                     \
                                                                        \
  /** Remove all entries from <b>map</b>, and deallocate storage for    \
   * those entries.  If free_val is provided, invoked it every value in \
   * <b>map</b>. */                                                     \
  MOCK_IMPL(void,                                                       \
  prefix##_free_, (maptype *map, void (*free_val)(void*)))              \
  {                                                                     \
    prefix##_entry_t **ent, **next, *this;                              \
    if (!map)                                                           \
      return;                                                           \
    for (ent = HT_START(prefix##_impl, &map->head); ent != NULL;        \
         ent = next) {                                                  \
      this = *ent;                                                      \
      next = HT_NEXT_RMV(prefix##_impl, &map->head, ent);               \
      if (free_val)                                                     \
        free_val(this->val);                                            \
      prefix##_entry_free(this);                                        \
    }                                                                   \
    tor_assert(HT_EMPTY(&map->head));                                   \
    HT_CLEAR(prefix##_impl, &map->head);                                \
    tor_free(map);                                                      \
  }                                                                     \
                                                                        \
  /** return an <b>iterator</b> pointer to the front of a map.          \
   *                                                                    \
   * Iterator example:                                                  \
   *                                                                    \
   * \code                                                              \
   * // uppercase values in "map", removing empty values.               \
   *                                                                    \
   * strmap_iter_t *iter;                                               \
   * const char *key;                                                   \
   * void *val;                                                         \
   * char *cp;                                                          \
   *                                                                    \
   * for (iter = strmap_iter_init(map); !strmap_iter_done(iter); ) {    \
   *    strmap_iter_get(iter, &key, &val);                              \
   *    cp = (char*)val;                                                \
   *    if (!*cp) {                                                     \
   *       iter = strmap_iter_next_rmv(map,iter);                       \
   *       free(val);                                                   \
   *    } else {                                                        \
   *       for (;*cp;cp++) *cp = TOR_TOUPPER(*cp);                      \
   */                                                                   \
  prefix##_iter_t *                                                     \
  prefix##_iter_init(maptype *map)                                      \
  {                                                                     \
    tor_assert(map);                                                    \
    return HT_START(prefix##_impl, &map->head);                         \
  }                                                                     \
                                                                        \
  /** Advance <b>iter</b> a single step to the next entry, and return   \
   * its new value. */                                                  \
  prefix##_iter_t *                                                     \
  prefix##_iter_next(maptype *map, prefix##_iter_t *iter)               \
  {                                                                     \
    tor_assert(map);                                                    \
    tor_assert(iter);                                                   \
    return HT_NEXT(prefix##_impl, &map->head, iter);                    \
  }                                                                     \
  /** Advance <b>iter</b> a single step to the next entry, removing the \
   * current entry, and return its new value. */                        \
  prefix##_iter_t *                                                     \
  prefix##_iter_next_rmv(maptype *map, prefix##_iter_t *iter)           \
  {                                                                     \
    prefix##_entry_t *rmv;                                              \
    tor_assert(map);                                                    \
    tor_assert(iter);                                                   \
    tor_assert(*iter);                                                  \
    rmv = *iter;                                                        \
    iter = HT_NEXT_RMV(prefix##_impl, &map->head, iter);                \
    prefix##_entry_free(rmv);                                           \
    return iter;                                                        \
  }                                                                     \
  /** Set *<b>keyp</b> and *<b>valp</b> to the current entry pointed    \
   * to by iter. */                                                     \
  void                                                                  \
  prefix##_iter_get(prefix##_iter_t *iter, const keytype *keyp,         \
                    void **valp)                                        \
  {                                                                     \
    tor_assert(iter);                                                   \
    tor_assert(*iter);                                                  \
    tor_assert(keyp);                                                   \
    tor_assert(valp);                                                   \
    *keyp = (*iter)->key;                                               \
    *valp = (*iter)->val;                                               \
  }                                                                     \
  /** Return true iff <b>iter</b> has advanced past the last entry of   \
   * <b>map</b>. */                                                     \
  int                                                                   \
  prefix##_iter_done(prefix##_iter_t *iter)                             \
  {                                                                     \
    return iter == NULL;                                                \
  }

IMPLEMENT_MAP_FNS(strmap_t, char *, strmap)
IMPLEMENT_MAP_FNS(digestmap_t, char *, digestmap)
IMPLEMENT_MAP_FNS(digest256map_t, uint8_t *, digest256map)

/** Same as strmap_set, but first converts <b>key</b> to lowercase. */
void *
strmap_set_lc(strmap_t *map, const char *key, void *val)
{
  /* We could be a little faster by using strcasecmp instead, and a separate
   * type, but I don't think it matters. */
  void *v;
  char *lc_key = tor_strdup(key);
  tor_strlower(lc_key);
  v = strmap_set(map,lc_key,val);
  tor_free(lc_key);
  return v;
}

/** Same as strmap_get, but first converts <b>key</b> to lowercase. */
void *
strmap_get_lc(const strmap_t *map, const char *key)
{
  void *v;
  char *lc_key = tor_strdup(key);
  tor_strlower(lc_key);
  v = strmap_get(map,lc_key);
  tor_free(lc_key);
  return v;
}

/** Same as strmap_remove, but first converts <b>key</b> to lowercase */
void *
strmap_remove_lc(strmap_t *map, const char *key)
{
  void *v;
  char *lc_key = tor_strdup(key);
  tor_strlower(lc_key);
  v = strmap_remove(map,lc_key);
  tor_free(lc_key);
  return v;
}

/** Declare a function called <b>funcname</b> that acts as a find_nth_FOO
 * function for an array of type <b>elt_t</b>*.
 *
 * NOTE: The implementation kind of sucks: It's O(n log n), whereas finding
 * the kth element of an n-element list can be done in O(n).  Then again, this
 * implementation is not in critical path, and it is obviously correct. */
#define IMPLEMENT_ORDER_FUNC(funcname, elt_t)                   \
  static int                                                    \
  _cmp_ ## elt_t(const void *_a, const void *_b)                \
  {                                                             \
    const elt_t *a = _a, *b = _b;                               \
    if (*a<*b)                                                  \
      return -1;                                                \
    else if (*a>*b)                                             \
      return 1;                                                 \
    else                                                        \
      return 0;                                                 \
  }                                                             \
  elt_t                                                         \
  funcname(elt_t *array, int n_elements, int nth)               \
  {                                                             \
    tor_assert(nth >= 0);                                       \
    tor_assert(nth < n_elements);                               \
    qsort(array, n_elements, sizeof(elt_t), _cmp_ ##elt_t);     \
    return array[nth];                                          \
  }

IMPLEMENT_ORDER_FUNC(find_nth_int, int)
IMPLEMENT_ORDER_FUNC(find_nth_time, time_t)
IMPLEMENT_ORDER_FUNC(find_nth_double, double)
IMPLEMENT_ORDER_FUNC(find_nth_uint32, uint32_t)
IMPLEMENT_ORDER_FUNC(find_nth_int32, int32_t)
IMPLEMENT_ORDER_FUNC(find_nth_long, long)

/** Return a newly allocated digestset_t, optimized to hold a total of
 * <b>max_elements</b> digests with a reasonably low false positive weight. */
digestset_t *
digestset_new(int max_elements)
{
  /* The probability of false positives is about P=(1 - exp(-kn/m))^k, where k
   * is the number of hash functions per entry, m is the bits in the array,
   * and n is the number of elements inserted.  For us, k==4, n<=max_elements,
   * and m==n_bits= approximately max_elements*32.  This gives
   *   P<(1-exp(-4*n/(32*n)))^4 == (1-exp(1/-8))^4 == .00019
   *
   * It would be more optimal in space vs false positives to get this false
   * positive rate by going for k==13, and m==18.5n, but we also want to
   * conserve CPU, and k==13 is pretty big.
   */
  int n_bits = 1u << (tor_log2(max_elements)+5);
  digestset_t *r = tor_malloc(sizeof(digestset_t));
  r->mask = n_bits - 1;
  r->ba = bitarray_init_zero(n_bits);
  return r;
}

/** Free all storage held in <b>set</b>. */
void
digestset_free_(digestset_t *set)
{
  if (!set)
    return;
  bitarray_free(set->ba);
  tor_free(set);
}