#include "module-list.h"
#include "module-run.h"
#include "module-text.h"
#include <math.h>
#include <stddef.h>
#include <stdlib.h>
#include <string.h>

/* A list's items live in a persistent B+tree: leaves hold up to FANOUT
 * items, inner nodes up to FANOUT children, and every node knows how many
 * items lie below it and the leaf holding the first of them. An inner node
 * also keeps, beside its children, how many items lie below each and (in a
 * list keyed by a number field) each one's first key: its guide. So an item
 * is found by position, and a keyed list searched by key, reading one node a
 * level, in O(log n) whatever the list's length; a run of positions is read
 * through a finger (the last leaf a thread read) or a leaf at a time
 * (pure_list_run).
 *
 * A leaf keeps its items field by field: each field's cells side by side,
 * numbers as binary64 values and texts as spans of bytes the list owns. So
 * reading one field of items after one another reads memory in order, an
 * item takes no allocation of its own and a leaf is copied in one piece.
 *
 * Nodes carry the list's share count when they were made, and so do texts.
 * One made before the last share may be read by a shared copy (a snapshot),
 * so it never changes again: the list copies the nodes on the way to a change
 * (the path) and retires the ones it replaced, and retires a text it lets go
 * instead of freeing it. A share is then a root and a count, however long
 * the list. */
enum { FANOUT = PURE_LIST_RUN, DEPTH = 16, SPARE_NODES = 8, PREFETCHED = 1 << 17 };

typedef struct Node {
    uint64_t made;            /* the list's share count when made: shared once below it */
    uint32_t count;           /* items (a leaf) or children */
    bool leaf;
    size_t items;             /* items below */
    const struct Node *first; /* the leaf holding the first item below; NULL when there is none */
    double lead;              /* the first item's key, in a list keyed by a number field (else 0) */
    struct Node *child[];     /* an inner node's children, then its guide; a leaf's columns are here instead */
} Node;

/* An inner node's guide, after its children: the items before each child
 * and each child's lead, kept by sum; past the last child the counts and
 * keys are above any position and key. So a level is searched in one node,
 * by a binary search of fixed length whose steps are selections, not
 * branches (upper). */
typedef struct { uint32_t before[FANOUT]; double keys[FANOUT]; } Guide;

enum { INNER_SIZE = sizeof(Node) + FANOUT * sizeof(Node *) + sizeof(Guide) };

/* Where a leaf keeps each field's cells, and what an item stores. */
typedef struct {
    unsigned fields, texts;
    uint8_t kinds[16];      /* each field's (PURE_CELL_...) */
    uint8_t text_field[16]; /* the text fields, in order */
    uint32_t column[16];    /* where each field's cells start in a leaf */
    size_t leaf_size;
    size_t number_bytes;    /* an item's numbers, stored */
    int key;                /* the number field whose order the list keeps (its leads), or -1 */
} Layout;

struct PureList {
    Layout layout;
    Node *root;           /* NULL when the list has no item */
    size_t count, bytes;  /* items, and their stored bytes */
    /* A stored list's changes since they were last taken, as records
     * (pure_list_replay); none are kept while journaled is false. */
    bool journaled;
    unsigned char *journal;
    size_t journal_size, journal_capacity;
    uint64_t id, version; /* which list, and a number every change moves on */
    uint64_t shares;      /* the last copy's epoch: a node or text made before it is shared */
    PureRetired *retired; /* where shared nodes and texts go when the list lets them go */
    Node **spare[2];      /* inner nodes and leaves let go that no copy reads, kept for the next ones */
    unsigned spares[2], spare_room[2];
    unsigned needed[2];   /* inner nodes and leaves it made lately: halved each time the retired come back */
    unsigned refs;        /* a shared copy's references */
    bool copy;            /* a shared copy: it owns none of its nodes or texts */
    /* Its keys as a set, beside the tree (pure_list_hashed; NULL: none):
     * while every key is a whole number below BITMAP_KEYS, a bit per number
     * (member_capacity words); else a key's bits (-0 as +0) by open
     * addressing (member_capacity slots), VACANT where none is. */
    uint64_t *members;
    size_t member_capacity, member_count;
    bool bitmap;
    /* An event's list may keep its items in arrays rather than a tree
     * (pure_list_arrays, docs/design/021): FLAT, each field's cells side by
     * side in the list's order; DENSE (keyed by small whole numbers, its keys
     * as bits), each field's cells at its key; HASHED (keyed by numbers that
     * came out of order), each field's cells at its key's slot in its
     * members' table (as a DENSE list's at its key). What the arrays cannot answer at
     * once (a position in a DENSE or HASHED list; a change logged to be
     * undone, a record, a share) makes them FLAT, or a tree, first. */
    uint8_t form;
    bool arrays;       /* it may be FLAT or DENSE: an event's list */
    uint8_t flattened; /* DENSE made FLAT since it was cleared: twice, and it stays FLAT or a tree */
    void *columns[16]; /* each field's cells */
    uint8_t width[16]; /* the bytes of a cell in each: array_width */
    size_t room;       /* the rows the columns hold: FLAT items, DENSE keys */
    size_t moved;      /* FLAT: items moved by changes inside it since it was cleared */
    /* A stored list keyed by a number and searched by key often at one
     * version is packed when an event ends (pure_list_settle, docs/design
     * 022): FLAT, its columns a Pack's, which its copies share and nothing
     * changes (a change makes the list a tree again first). searched counts
     * its searches by key at searched_version; aligned is the fewest
     * trailing zero bits of a whole key searched then (64: none). */
    struct Pack *pack;
    uint64_t searched, searched_version;
    uint8_t aligned;
    /* Last, apart from what is read often: a DENSE list's keys as last counted (dense_keys, docs/design/023):
     * whether they are every number below its count (full: a key is its
     * position), else the keys below each word of its bits (ranks); for the
     * keys it had when keys_seen was keys_token (its key count, and removes:
     * keys taken out or the bits begun again, so a token never comes back). */
    uint64_t removes, keys_seen;
    bool full;
    uint32_t *ranks;
    size_t ranks_room;
};

/* The log of an event's changes: a removed item's cells wait in the log's
 * cells (its texts owned by the log) until the event is undone or kept. */
typedef enum { INSERTED, REMOVED, CHANGED } Change;
typedef struct {
    Change change;
    unsigned field;
    PureList *list;
    size_t at;
    union {
        PureCell old; /* CHANGED: the replaced cell */
        size_t cells; /* REMOVED: where the item's cells start in the log's cells */
    };
} Entry;
/* A node or text let go while a copy may read it, and what the copies and
 * the lists ask of it (so neither reads it again). */
typedef struct {
    void *pointer;
    uint64_t made;  /* the share count it was made at */
    uint32_t size;  /* a node's */
    bool text, leaf;
} Retired;

static uint64_t lists_made;

/* The leaf a thread read last, and where it starts: a list read position
 * by position (a view's rows, a fold, a walk) finds each next item there,
 * and an item found by key is read there. It holds for its list (its id) as
 * it was (its version) and no other. (Four, one a list, cost the bank's
 * queries more than they saved and a search no time: research 121.) */
typedef struct { uint64_t id, version; const Node *leaf; size_t start; } Finger;
static _Thread_local Finger finger;

/* The finger's leaf when it holds position at of the list as it is, or NULL. */
static const Node *fingered(const PureList *list, size_t at, size_t *within) {
    if (!finger.leaf || finger.id != list->id || finger.version != list->version || at < finger.start ||
        at >= finger.start + finger.leaf->count)
        return NULL;
    *within = at - finger.start;
    return finger.leaf;
}

static void finger_keep(const PureList *list, const Node *leaf, size_t start) {
    finger = (Finger){list->id, list->version, leaf, start};
}

/* ---- A keyed list's keys as a set
 * Node numbers, ranks and counts are small whole numbers: as bits they fit
 * the caches (100,000 keys in 12.5 KB), where a table of them does not. */

enum { BITMAP_KEYS = 1 << 22, BITMAP_KEPT = 1 << 13 /* words a cleared bitmap keeps (64 KiB) */ };
static const uint64_t VACANT = UINT64_C(0x7FF8000000000001); /* a NaN: never a key */

static uint64_t key_bits(double key) {
    if (key == 0) key = 0; /* -0 and +0 are one key */
    uint64_t bits;
    memcpy(&bits, &key, sizeof(bits));
    return bits;
}

static bool small_key(double key) { return key >= 0 && key < BITMAP_KEYS && (double)(uint32_t)key == key; }

static size_t member_slot(uint64_t bits, size_t mask) {
    bits ^= bits >> 33;
    bits *= UINT64_C(0xff51afd7ed558ccd);
    bits ^= bits >> 33;
    return (size_t)bits & mask;
}

/* The set given up (memory ran out growing it): the list is searched without it. */
static void members_drop(PureList *list) {
    ++list->removes;
    free(list->members);
    list->members = NULL;
    list->member_capacity = list->member_count = 0;
}

/* A new set, empty, as bits. */
static bool members_start(PureList *list) {
    ++list->removes;
    list->members = calloc(1, sizeof(*list->members));
    list->member_capacity = list->members ? 1 : 0;
    list->member_count = 0;
    list->bitmap = true;
    return list->members != NULL;
}

static void member_put(PureList *list, uint64_t bits) {
    size_t mask = list->member_capacity - 1, at = member_slot(bits, mask);
    while (list->members[at] != VACANT && list->members[at] != bits) at = (at + 1) & mask;
    if (list->members[at] == VACANT) list->members[at] = bits, ++list->member_count;
}

/* A table of capacity slots holding the keys the set holds. False when memory runs out. */
static bool members_table(PureList *list, size_t capacity) {
    uint64_t *old = list->members, *table = malloc(capacity * sizeof(*table));
    if (!table) return false;
    size_t was = list->member_capacity;
    bool bits = list->bitmap;
    for (size_t i = 0; i < capacity; ++i) table[i] = VACANT;
    ++list->removes;
    list->members = table, list->member_capacity = capacity, list->member_count = 0, list->bitmap = false;
    for (size_t i = 0; i < was; ++i) {
        if (!bits) { if (old[i] != VACANT) member_put(list, old[i]); continue; }
        for (uint64_t word = old[i]; word; word &= word - 1)
            member_put(list, key_bits((double)(i * 64 + (size_t)__builtin_ctzll(word))));
    }
    free(old);
    return true;
}

static void member_add(PureList *list, double key) {
    if (!list->members) return;
    if (list->bitmap && small_key(key)) {
        size_t bit = (size_t)key, word = bit / 64;
        if (word >= list->member_capacity) { /* the bits grown to hold it */
            size_t capacity = list->member_capacity;
            while (capacity <= word) capacity *= 2;
            uint64_t *grown = realloc(list->members, capacity * sizeof(*grown));
            if (!grown) { members_drop(list); return; }
            memset(grown + list->member_capacity, 0, (capacity - list->member_capacity) * sizeof(*grown));
            list->members = grown, list->member_capacity = capacity;
        }
        uint64_t mask = UINT64_C(1) << (bit % 64);
        list->member_count += !(list->members[word] & mask);
        list->members[word] |= mask;
        return;
    }
    size_t need = 2 * (list->member_count + 1), capacity = list->bitmap ? 64 : list->member_capacity;
    while (capacity < need) capacity *= 2;
    if ((list->bitmap || capacity != list->member_capacity) && !members_table(list, capacity)) { members_drop(list); return; }
    member_put(list, key_bits(key));
}

/* A key out of the set; in a table the keys after it in its run moved back (no gap left behind them). */
static void member_remove(PureList *list, double key) {
    if (!list->members) return;
    ++list->removes;
    if (list->bitmap) {
        if (!small_key(key) || (size_t)key / 64 >= list->member_capacity) return;
        uint64_t *word = &list->members[(size_t)key / 64], mask = UINT64_C(1) << ((size_t)key % 64);
        list->member_count -= (*word & mask) != 0;
        *word &= ~mask;
        return;
    }
    uint64_t bits = key_bits(key);
    size_t mask = list->member_capacity - 1, at = member_slot(bits, mask);
    while (list->members[at] != bits) {
        if (list->members[at] == VACANT) return;
        at = (at + 1) & mask;
    }
    for (size_t next = (at + 1) & mask; list->members[next] != VACANT; next = (next + 1) & mask) {
        size_t home = member_slot(list->members[next], mask);
        /* next may fill the gap at when its home is not cyclically within (at, next] */
        bool stays = at <= next ? (home > at && home <= next) : (home > at || home <= next);
        if (!stays) list->members[at] = list->members[next], at = next;
    }
    list->members[at] = VACANT;
    --list->member_count;
}

static Node *child(const Node *node, unsigned i) { return node->child[i]; }
static Guide *guide(const Node *node) { return (Guide *)((char *)node + sizeof(Node) + FANOUT * sizeof(Node *)); }

/* How many of n (at least one) ascending values are below key. */
static unsigned lower(const double *values, unsigned n, double key) {
    const double *base = values;
    for (; n > 1; n -= n / 2) base = base[n / 2] < key ? base + n / 2 : base;
    return (unsigned)(base - values) + (*base < key);
}
/* The child of an inner node holding its item at (counted from the node's
 * first): its children after the first whose items begin at or before at,
 * counted rather than halved (no load waits for another; past the last
 * child the counts are above any position). The end is in the last child. */
static unsigned child_at(const Node *node, size_t at) {
    if (at >= node->items) return node->count - 1;
    const uint32_t *before = guide(node)->before;
    uint32_t n = 0, position = (uint32_t)at; /* every child, the first's 0 at or below any: a whole number of vectors */
    for (unsigned i = 0; i < FANOUT; ++i) n += before[i] <= position;
    return n - 1;
}
/* An inner node's last child whose lead is at or below key (the first when
 * none is): its leads after the first at or below key, counted (past the
 * last child they are above any key). */
static unsigned child_by_key(const Node *node, double key) {
    const double *keys = guide(node)->keys;
    uint64_t n = 0; /* every child's (a whole number of vectors), less the first's */
    for (unsigned i = 0; i < FANOUT; ++i) n += keys[i] <= key;
    return (unsigned)n - (keys[0] <= key);
}
static double *numbers(const Layout *l, const Node *leaf, unsigned f) { return (double *)((char *)leaf + l->column[f]); }
static int64_t *integers(const Layout *l, const Node *leaf, unsigned f) { return (int64_t *)((char *)leaf + l->column[f]); }
static PureSpan *texts(const Layout *l, const Node *leaf, unsigned f) { return (PureSpan *)((char *)leaf + l->column[f]); }

/* A number's, bool's or integer's cell is its 8 bytes, read as they are
 * (whichever it holds; the reader's kind says which). */
static PureCell cell_at(const Layout *l, const Node *leaf, unsigned i, unsigned f) {
    PureCell cell = {0};
    if (!pure_cell_text(l->kinds[f])) memcpy(&cell.i64, (const char *)leaf + l->column[f] + 8 * (size_t)i, 8);
    else {
        PureSpan text = texts(l, leaf, f)[i];
        cell.text = (unsigned char *)text.data, cell.size = text.size;
    }
    return cell;
}

static void put_cells(const Layout *l, Node *leaf, unsigned i, const PureCell *cells) {
    for (unsigned f = 0; f < l->fields; ++f)
        if (pure_cell_text(l->kinds[f])) texts(l, leaf, f)[i] = (PureSpan){cells[f].text, cells[f].size};
        else if (l->kinds[f] == PURE_CELL_INTEGER) integers(l, leaf, f)[i] = cells[f].i64;
        else numbers(l, leaf, f)[i] = cells[f].num;
}

/* count items or children of from, from start on, to at in to (they may overlap). */
static void move_items(const Layout *l, Node *to, unsigned at, const Node *from, unsigned start, unsigned count) {
    if (!count) return;
    if (!from->leaf) {
        memmove(&to->child[at], &from->child[start], count * sizeof(Node *));
        return;
    }
    for (unsigned f = 0; f < l->fields; ++f) {
        size_t width = pure_cell_text(l->kinds[f]) ? sizeof(PureSpan) : 8;
        memmove((char *)to + l->column[f] + at * width, (const char *)from + l->column[f] + start * width, count * width);
    }
}

/* A text's bytes, the list's own: after the list's share count when they
 * were made. One made before the last share may be read by a shared copy. */
static unsigned char *new_text(const PureList *list, const unsigned char *bytes, size_t size) {
    uint64_t *made = malloc(sizeof(*made) + size);
    if (!made) return NULL;
    *made = list->shares;
    memcpy(made + 1, bytes, size);
    return (unsigned char *)(made + 1);
}

static bool shared_text(const PureList *list, const unsigned char *text) { return ((const uint64_t *)text)[-1] < list->shares; }
static bool shared_node(const PureList *list, const Node *node) { return node->made < list->shares; }
static void free_text(const unsigned char *text) { if (text) free((uint64_t *)text - 1); }

/* Kept until the copies that may read it are gone (pure_retired_free), or
 * then taken back (pure_retired_reuse). */
static void retire(PureList *list, void *pointer, bool text) {
    PureRetired *retired = list->retired;
    if (retired->count == retired->capacity) {
        size_t capacity = retired->capacity ? 2 * retired->capacity : 16;
        Retired *grown = realloc(retired->entries, capacity * sizeof(*grown));
        if (!grown) return; /* kept for good rather than freed while read */
        retired->entries = grown;
        retired->capacity = capacity;
    }
    const Node *node = text ? NULL : pointer;
    ((Retired *)retired->entries)[retired->count++] =
        text ? (Retired){pointer, ((const uint64_t *)pointer)[-1], 0, true, false}
             : (Retired){pointer, node->made, node->leaf ? (uint32_t)list->layout.leaf_size : INNER_SIZE, false, node->leaf};
}

/* The list no longer has text: free it, or retire it while a copy may read it. */
static void let_go_text(PureList *list, const unsigned char *text) {
    if (!text) return;
    if (!shared_text(list, text)) free_text(text);
    else retire(list, (void *)text, true);
}

/* The texts of an item the list no longer has. */
static void let_go_cells(PureList *list, const PureCell *cells) {
    for (unsigned t = 0; t < list->layout.texts; ++t) let_go_text(list, cells[list->layout.text_field[t]].text);
}

void pure_retired_free(PureRetired *retired) {
    Retired *entries = retired->entries;
    for (size_t i = 0; i < retired->count; ++i) {
        if (entries[i].text) free_text(entries[i].pointer);
        else free(entries[i].pointer);
    }
    free(entries);
    *retired = (PureRetired){0};
}

/* Room for more entries in retired; false when memory runs out. */
static bool retired_room(PureRetired *retired, size_t more) {
    if (retired->count + more <= retired->capacity) return true;
    size_t capacity = 2 * retired->capacity > retired->count + more ? 2 * retired->capacity : retired->count + more;
    Retired *grown = realloc(retired->entries, capacity * sizeof(*grown));
    if (!grown) return false;
    retired->entries = grown;
    retired->capacity = capacity;
    return true;
}

void pure_retired_pass(PureRetired *from, uint64_t epoch, PureRetired *kept, PureRetired *gone) {
    Retired *entries = from->entries;
    size_t keeping = 0;
    for (size_t i = 0; kept && i < from->count; ++i) keeping += entries[i].made < epoch;
    bool room = (!keeping || retired_room(kept, keeping)) &&
                (!gone || keeping == from->count || retired_room(gone, from->count - keeping));
    for (size_t i = 0; i < from->count; ++i) {
        PureRetired *to = kept && entries[i].made < epoch ? kept : gone;
        if (room && to) ((Retired *)to->entries)[to->count++] = entries[i];
        /* else kept for good rather than freed while read (memory ran out) */
    }
    from->count = 0; /* its room stays, for what is retired next */
}

/* Keep node for the list's next of its kind; false when it keeps enough
 * already (or has no room for more). */
static bool keep_spare(PureList *list, Node *node, bool leaf, unsigned enough) {
    if (list->spares[leaf] >= enough) return false;
    if (list->spares[leaf] == list->spare_room[leaf]) {
        unsigned room = list->spare_room[leaf] ? 2 * list->spare_room[leaf] : SPARE_NODES;
        Node **grown = realloc(list->spare[leaf], room * sizeof(*grown));
        if (!grown) return false;
        list->spare[leaf] = grown;
        list->spare_room[leaf] = room;
    }
    list->spare[leaf][list->spares[leaf]++] = node;
    return true;
}

void pure_retired_reuse(PureRetired *returned, PureList *const *lists, unsigned count) {
    Retired *entries = returned->entries;
    for (size_t i = 0; i < returned->count; ++i) {
        const Retired *r = &entries[i];
        if (r->text) {
            free_text(r->pointer);
            continue;
        }
        bool kept = false; /* by a list of its size, as many as it made lately (at least a few) */
        for (unsigned l = 0; l < count && !kept; ++l) {
            PureList *list = lists[l];
            kept = list && (!r->leaf || list->layout.leaf_size == r->size) &&
                   keep_spare(list, r->pointer, r->leaf, list->needed[r->leaf] > SPARE_NODES ? list->needed[r->leaf] : SPARE_NODES);
        }
        if (!kept) free(r->pointer);
    }
    for (unsigned l = 0; l < count; ++l)
        if (lists[l]) lists[l]->needed[0] /= 2, lists[l]->needed[1] /= 2;
    returned->count = 0;
}

static Node *new_node(PureList *list, bool leaf) {
    Node *node;
    ++list->needed[leaf];
    if (list->spares[leaf]) node = list->spare[leaf][--list->spares[leaf]];
    else if (!(node = malloc(leaf ? list->layout.leaf_size : INNER_SIZE)))
        return NULL;
    node->made = list->shares;
    node->count = 0;
    node->leaf = leaf;
    node->items = 0;
    node->first = NULL;
    node->lead = 0;
    return node;
}

/* A node the list no longer has (its items and children dealt with):
 * retired while a copy may read it, else kept for the next or freed. */
static void drop_node(PureList *list, Node *node) {
    if (shared_node(list, node)) retire(list, node, false);
    else if (!keep_spare(list, node, node->leaf, SPARE_NODES)) free(node);
}

/* ---- The stored form: each field in order, a number as its binary64 bits
 * (little-endian), a text as a u32le length and its bytes. */

static size_t cell_bytes(const Layout *l, unsigned field, PureCell cell) { return pure_cell_text(l->kinds[field]) ? 4 + cell.size : 8; }

static size_t cells_bytes(const Layout *l, const PureCell *cells) {
    size_t size = l->number_bytes;
    for (unsigned t = 0; t < l->texts; ++t) size += 4 + cells[l->text_field[t]].size;
    return size;
}

static size_t item_bytes(const Layout *l, const Node *leaf, unsigned i) {
    size_t size = l->number_bytes;
    for (unsigned t = 0; t < l->texts; ++t) size += 4 + texts(l, leaf, l->text_field[t])[i].size;
    return size;
}

/* A node's summary, from its items or all its children. */
static void sum(const PureList *list, Node *node) {
    const Layout *l = &list->layout;
    if (node->leaf) {
        node->items = node->count;
        node->first = node->count ? node : NULL;
        node->lead = l->key >= 0 && node->count ? numbers(l, node, (unsigned)l->key)[0] : 0;
        return;
    }
    Guide *g = guide(node);
    size_t items = 0;
    for (unsigned i = 0; i < node->count; ++i) {
        const Node *below = child(node, i);
        g->before[i] = (uint32_t)items;
        g->keys[i] = below->lead;
        items += below->items;
    }
    for (unsigned i = node->count; i < FANOUT; ++i) g->before[i] = UINT32_MAX, g->keys[i] = INFINITY;
    node->items = items;
    node->first = node->count ? child(node, 0)->first : NULL;
    node->lead = node->count ? g->keys[0] : 0;
}

/* ---- Finding positions */

typedef struct { Node *node; unsigned index; } Step; /* a node on the way, and the child taken */

/* The leaf holding position at (the end is in the last leaf), and at's
 * place in it. */
static const Node *leaf_of(const PureList *list, size_t at, size_t *within) {
    const Node *kept = fingered(list, at, within);
    if (kept) return kept;
    const Node *node = list->root;
    size_t start = 0;
    while (!node->leaf) {
        unsigned i = child_at(node, at - start);
        start += guide(node)->before[i];
        node = child(node, i);
    }
    finger_keep(list, node, start);
    *within = at - start;
    return node;
}

/* The node at *place, the list's own to change: a copy (the node retired)
 * while a shared copy of the list may read it. NULL without memory. A copy
 * moves the version on even when the change it is for does not happen: the
 * list no longer has the nodes its shared copies have. A leaf's copy has the
 * texts of the leaf it copies: they stay shared, and are retired, not freed,
 * when the list lets them go. */
static Node *own(PureList *list, Node **place) {
    Node *node = *place;
    if (!shared_node(list, node)) return node;
    Node *mine = new_node(list, node->leaf);
    if (!mine) return NULL;
    uint64_t made = mine->made;
    memcpy(mine, node, node->leaf ? list->layout.leaf_size : INNER_SIZE);
    mine->made = made;
    if (mine->leaf) mine->first = mine->count ? mine : NULL;
    retire(list, node, false);
    *place = mine;
    ++list->version;
    return mine;
}

/* The path to the leaf holding position at, each node the list's own, and
 * at's place in the leaf: the number of steps, 0 without memory (the list
 * is as it was: copies replace what they copy). The nodes on the path then
 * name the leaf that holds their first item, a copied one too. */
static unsigned descend(PureList *list, size_t at, Step path[DEPTH], unsigned *within) {
    Node **place = &list->root;
    for (unsigned depth = 0; depth < DEPTH; ++depth) {
        Node *node = own(list, place);
        if (!node) return 0;
        if (node->leaf) {
            path[depth] = (Step){node, 0};
            *within = (unsigned)at;
            for (unsigned d = depth; d-- > 0;) path[d].node->first = child(path[d].node, 0)->first;
            return depth + 1;
        }
        unsigned i = child_at(node, at);
        at -= guide(node)->before[i];
        path[depth] = (Step){node, i};
        place = &node->child[i];
    }
    return 0;
}

/* After a change below the path's last node: that node summed whole, and
 * each above it through the one child on the path (the others are as they
 * were). */
static void sum_path(const PureList *list, const Step *path, unsigned depth) {
    if (!depth) return;
    sum(list, path[depth - 1].node);
    for (unsigned d = depth - 1; d-- > 0;) {
        Node *node = path[d].node;
        unsigned i = path[d].index;
        const Node *below = child(node, i);
        Guide *g = guide(node);
        size_t was = (i + 1 < node->count ? g->before[i + 1] : node->items) - g->before[i];
        if (below->items != was) {
            uint32_t moved = (uint32_t)(below->items - was); /* modulo 2^32: an item fewer is all ones */
            for (unsigned j = i + 1; j < node->count; ++j) g->before[j] += moved;
            node->items += below->items - was;
        }
        g->keys[i] = below->lead;
        node->first = child(node, 0)->first;
        node->lead = g->keys[0];
    }
}

/* ---- Placing and removing */

/* A place for an item: the path to it, and the nodes a split may take (a
 * leaf, then one a level above it and a root), made before anything changes
 * so that placing cannot fail. */
typedef struct {
    Step path[DEPTH];
    unsigned depth, within, extras, used;
    bool appending; /* at the end of the list */
    Node *extra[DEPTH + 1];
} Place;

/* The nodes a split may take, made now so that placing cannot fail. */
static bool prepare_extras(PureList *list, Place *p) {
    if (p->path[p->depth - 1].node->count < FANOUT) return true;
    for (; p->extras <= p->depth; ++p->extras)
        if (!(p->extra[p->extras] = new_node(list, !p->extras))) {
            while (p->extras) drop_node(list, p->extra[--p->extras]);
            return false;
        }
    return true;
}

static bool prepare(PureList *list, size_t at, Place *p) {
    if (!list->root && !(list->root = new_node(list, true))) return false;
    p->extras = p->used = 0;
    p->appending = at == list->count;
    if (!(p->depth = descend(list, at, p->path, &p->within))) return false;
    return prepare_extras(list, p);
}

/* The path to where key goes in a list kept in order of a number field (its
 * key), the nodes on it the list's own; where in the list that is, and
 * whether an item has the key there. False when memory runs out. */
static bool descend_key(PureList *list, double key, Place *p, size_t *at, bool *found) {
    const Layout *l = &list->layout;
    Node **place = &list->root;
    size_t start = 0;
    for (unsigned depth = 0; depth < DEPTH; ++depth) {
        Node *node = own(list, place);
        if (!node) return false;
        if (node->leaf) {
            const double *keys = numbers(l, node, (unsigned)l->key);
            unsigned low = node->count ? lower(keys, node->count, key) : 0;
            *found = low < node->count && keys[low] == key;
            p->path[depth] = (Step){node, 0};
            p->depth = depth + 1;
            p->within = low;
            *at = start + low;
            for (unsigned d = depth; d-- > 0;) p->path[d].node->first = child(p->path[d].node, 0)->first;
            return true;
        }
        const Guide *g = guide(node);
        unsigned taken = child_by_key(node, key);
        start += g->before[taken];
        p->path[depth] = (Step){node, taken};
        place = &node->child[taken];
    }
    return false;
}

static void release_extras(PureList *list, Place *p) {
    while (p->extras > p->used) drop_node(list, p->extra[--p->extras]);
}

/* An item's cells (the list owns its texts from then on) into the leaf at
 * the end of the path, before its within: a full node splits and the new
 * node goes into its parent, up to a new root. A node splits in halves, but
 * at the end of the list it stays full and the new one starts with the item
 * alone: a list that grows at its end (a history, a keyed list filled in key
 * order) fills its leaves. */
static void place(PureList *list, Place *p, const PureCell *cells) {
    const Layout *l = &list->layout;
    unsigned index = p->within;
    if (list->members) member_add(list, cells[l->key].num);
    Node *pointer = NULL; /* above the leaf: the node that goes in */
    for (unsigned d = p->depth; d-- > 0;) {
        Node *node = p->path[d].node;
        if (node->count < FANOUT) {
            move_items(l, node, index + 1, node, index, node->count - index);
            if (node->leaf) put_cells(l, node, index, cells);
            else node->child[index] = pointer;
            ++node->count;
            sum_path(list, p->path, d + 1);
            break;
        }
        unsigned keep = p->appending && index == FANOUT ? FANOUT : (FANOUT + 1) / 2;
        Node *right = p->extra[p->used++];
        if (index < keep) {
            move_items(l, right, 0, node, keep - 1, FANOUT - (keep - 1));
            move_items(l, node, index + 1, node, index, keep - 1 - index);
            if (node->leaf) put_cells(l, node, index, cells);
            else node->child[index] = pointer;
        } else {
            move_items(l, right, 0, node, keep, index - keep);
            if (node->leaf) put_cells(l, right, index - keep, cells);
            else right->child[index - keep] = pointer;
            move_items(l, right, index - keep + 1, node, index, FANOUT - index);
        }
        node->count = keep;
        right->count = FANOUT + 1 - keep;
        sum(list, node);
        sum(list, right);
        if (!d) { /* the root split: a new one above both halves */
            Node *root = p->extra[p->used++];
            root->child[0] = node;
            root->child[1] = right;
            root->count = 2;
            sum(list, root);
            list->root = root;
            break;
        }
        pointer = right;
        index = p->path[d - 1].index + 1;
    }
    release_extras(list, p);
    ++list->count;
    ++list->version;
}

/* The item at the leaf's within, out of the tree (the caller has its cells):
 * an emptied node leaves its parent, a node that fits with a neighbour
 * merges into one (when the neighbour can be made the list's own), and a
 * root with one child gives way to it. */
static void take_out(PureList *list, Step *path, unsigned depth, unsigned within) {
    const Layout *l = &list->layout;
    Node *leaf = path[depth - 1].node;
    if (list->members) member_remove(list, numbers(l, leaf, (unsigned)l->key)[within]);
    move_items(l, leaf, within, leaf, within + 1, leaf->count - within - 1);
    --leaf->count;
    unsigned d = depth - 1;
    for (;; --d) {
        Node *node = path[d].node;
        sum(list, node);
        if (!d) break;
        Node *parent = path[d - 1].node;
        unsigned at = path[d - 1].index;
        if (!node->count) {
            memmove(&parent->child[at], &parent->child[at + 1], (parent->count - at - 1) * sizeof(Node *));
            --parent->count;
            drop_node(list, node);
            continue;
        }
        unsigned other = at + 1 < parent->count ? at + 1 : at ? at - 1 : at;
        Node *neighbour = other != at && node->count + child(parent, other)->count <= FANOUT
                              ? own(list, &parent->child[other]) : NULL;
        if (!neighbour) break;
        Node *left = other < at ? neighbour : node, *right = other < at ? node : neighbour;
        unsigned left_at = other < at ? other : at;
        move_items(l, left, left->count, right, 0, right->count);
        left->count += right->count;
        sum(list, left);
        memmove(&parent->child[left_at + 1], &parent->child[left_at + 2], (parent->count - left_at - 2) * sizeof(Node *));
        --parent->count;
        drop_node(list, right);
    }
    sum_path(list, path, d);
    while (!list->root->leaf && list->root->count == 1) {
        Node *old = list->root;
        list->root = child(old, 0);
        drop_node(list, old);
    }
    if (!list->root->count) { /* no item left */
        drop_node(list, list->root);
        list->root = NULL;
    }
    --list->count;
    ++list->version;
}

/* ---- An event's list in arrays (docs/design/021) */

enum { TREE, FLAT, DENSE, HASHED };
/* The arrays a clear keeps for the next event; the most they grow to (a
 * larger list is a tree: doubling arrays would hold twice its items); a
 * DENSE list's slack beyond four times its items (so it never holds far more
 * than a tree would); the items a FLAT list moves freely. */
enum { ARRAYS_KEPT = 1 << 22, ARRAYS_LARGE = 1 << 26, DENSE_SLACK = 1 << 21, FLAT_SMALL = 64 };

/* A packed list's arrays (docs/design/022): each field's cells in order and,
 * keyed by a number, a bucket index: the keys' range cut into buckets a
 * power of two wide (their starts multiples of it), each bucket's first
 * position whose key is not below its start. A search for a key at a
 * bucket's start reads that one cell; another steps through its bucket's
 * keys. Never changed; freed with its last list. */
typedef struct Pack {
    unsigned refs;            /* the list and its copies */
    void *columns[16];
    uint8_t bytes[16];        /* their cells' (each as a list's width) */
    double low, high;         /* the first key and the last */
    double origin, width, scale; /* the first bucket's start, a bucket's width, 1 / width */
    size_t buckets;           /* 0: none (searched by halves) */
    uint32_t *first;          /* by bucket, and the end past the last */
    /* Keys all whole numbers below 2^53 in size and buckets 2^shift wide
     * (shift 0 or more): the same in integers, for compiled code too. */
    bool whole;
    uint32_t shift;
    int64_t origin_whole, low_whole, high_whole;
} Pack;

/* Searched by key at least an eighth of its items' times at one version, a
 * list of PACK_ITEMS or more is packed; about PACK_BUCKET items a bucket. */
enum { PACK_ITEMS = 4096, PACK_SEARCHES = 8, PACK_BUCKET = 8 };

static void pack_release(Pack *pack) {
    if (!pack || __atomic_sub_fetch(&pack->refs, 1, __ATOMIC_ACQ_REL)) return;
    for (unsigned f = 0; f < 16; ++f) free(pack->columns[f]);
    free(pack->first);
    free(pack);
}

/* The bucket holding key (the first or the last past them), and its start:
 * computed again from the bucket, which is exact (pack_index), so a
 * rounding of the division moves it one bucket at most. */
static size_t bucket_of(const Pack *pack, double key, double *start) {
    double at = (key - pack->origin) * pack->scale;
    size_t b = !(at > 0) ? 0 : at >= (double)(pack->buckets - 1) ? pack->buckets - 1 : (size_t)at;
    double begins = pack->origin + (double)b * pack->width;
    if (begins > key && b) begins = pack->origin + (double)--b * pack->width;
    else if (b + 1 < pack->buckets && pack->origin + (double)(b + 1) * pack->width <= key)
        begins = pack->origin + (double)++b * pack->width;
    *start = begins;
    return b;
}

/* The index of keys (n, ascending, finite): buckets about PACK_BUCKET items
 * wide, or narrower to start at every key searched (aligned: their fewest
 * trailing zero bits), never finer than the keys' own precision (so every
 * start is exact) nor more of them than items. False without memory; none
 * (buckets 0) when the keys span too far. */
static bool pack_index(Pack *pack, const double *keys, size_t n, unsigned aligned) {
    double low = keys[0], high = keys[n - 1], span = high - low;
    pack->low = low, pack->high = high, pack->buckets = 0;
    if (!isfinite(span)) return true;
    int exponent = 0, top;
    if (span > 0) (void)frexp(span / (double)(n / PACK_BUCKET + 1), &exponent); /* 2^exponent above span per bucket */
    if ((int)aligned < exponent) exponent = (int)aligned;
    (void)frexp(fabs(low) > fabs(high) ? low : high, &top);
    if (exponent < top - 53) exponent = top - 53; /* the keys' last bit */
    double width, origin, buckets;
    for (;; ++exponent) {
        width = ldexp(1.0, exponent), origin = floor(low / width) * width;
        buckets = floor((high - origin) / width) + 1;
        if (buckets <= (double)n) break;
    }
    pack->origin = origin, pack->width = width, pack->scale = 1 / width, pack->buckets = (size_t)buckets;
    pack->whole = exponent >= 0 && fabs(low) < 0x1p53 && fabs(high) < 0x1p53;
    for (size_t i = 0; pack->whole && i < n; ++i) pack->whole = keys[i] == floor(keys[i]);
    if (pack->whole)
        pack->shift = (uint32_t)exponent, pack->origin_whole = (int64_t)origin, pack->low_whole = (int64_t)low,
        pack->high_whole = (int64_t)high;
    if (!(pack->first = malloc((pack->buckets + 1) * sizeof(*pack->first)))) return false;
    size_t filled = 0;
    for (size_t i = 0; i < n; ++i) {
        double start;
        size_t b = bucket_of(pack, keys[i], &start);
        while (filled <= b) pack->first[filled++] = (uint32_t)i;
    }
    while (filled <= pack->buckets) pack->first[filled++] = (uint32_t)n;
    return true;
}

/* The first position whose key is not below key, in a packed list. */
static size_t pack_seek(const PureList *list, double key) {
    const Pack *pack = list->pack;
    const double *keys = list->columns[list->layout.key];
    if (!pack->buckets) return lower(keys, (unsigned)list->count, key);
    if (pack->whole && fabs(key) < 0x1p53 && key == floor(key)) { /* in integers: the bucket a shift */
        int64_t whole = (int64_t)key;
        if (whole <= pack->low_whole) return 0;
        if (whole > pack->high_whole) return list->count;
        uint64_t from = (uint64_t)(whole - pack->origin_whole), b = from >> pack->shift;
        size_t at = pack->first[b];
        if (b << pack->shift == from) return at;
        for (size_t end = pack->first[b + 1]; at < end && keys[at] < key;) ++at;
        return at;
    }
    if (!(key > pack->low)) return 0;
    if (key > pack->high) return list->count;
    double start;
    size_t b = bucket_of(pack, key, &start), at = pack->first[b];
    if (start == key) return at;
    for (size_t end = pack->first[b + 1]; at < end && keys[at] < key;) ++at;
    return at;
}

/* A search of a stored tree by its key, counted for packing it. */
static void searched_by(const PureList *list, double key) {
    PureList *kept = (PureList *)list; /* what it counts to choose its form, not what it holds */
    if (kept->searched_version != list->version || !kept->searched)
        kept->searched_version = list->version, kept->searched = 0, kept->aligned = 64;
    ++kept->searched;
    double whole = fabs(key);
    if (whole == 0) return;
    unsigned zeros = whole < 9007199254740992.0 && whole == floor(whole) ? (unsigned)__builtin_ctzll((uint64_t)whole) : 0;
    if (zeros < kept->aligned) kept->aligned = (uint8_t)zeros;
}

static size_t width(const Layout *l, unsigned f) { return pure_cell_text(l->kinds[f]) ? sizeof(PureSpan) : 8; }

/* In arrays a field's cells are as narrow as their values let them be
 * (docs/design/022): a number's or a bool's 1 byte while every one is a
 * whole number from 0 below 2^8, 4 below 2^32 (never -0), else 8; a text's
 * span; an i64's 8; a FLAT list's key 8 (searched as numbers); a DENSE
 * list's key none (a cell's key is its slot). A value that does not fit
 * makes its column wider first, once for each width. Widths change with
 * the values, never what a cell reads. */
static bool narrows(uint8_t kind) { return kind == PURE_CELL_NUMBER || kind == PURE_CELL_BOOL; }

static uint8_t width_of(double v) {
    if (!(v >= 0 && v == floor(v)) || (v == 0 && signbit(v))) return 8;
    return v < 256 ? 1 : v < 4294967296.0 ? 4 : 8;
}

static PureCell cell_in(const void *column, uint8_t bytes, size_t i) {
    PureCell cell = {0};
    switch (bytes) {
    case 0: cell.num = (double)i; break;
    case 1: cell.num = ((const uint8_t *)column)[i]; break;
    case 4: cell.num = ((const uint32_t *)column)[i]; break;
    case 8: memcpy(&cell.i64, (const char *)column + 8 * i, 8); break;
    default: {
        PureSpan text = ((const PureSpan *)column)[i];
        cell.text = (unsigned char *)text.data, cell.size = text.size;
    }
    }
    return cell;
}

/* A cell into a column of cells of bytes each (one it fits). */
static void cell_out(void *column, uint8_t bytes, size_t i, PureCell cell) {
    switch (bytes) {
    case 0: break;
    case 1: ((uint8_t *)column)[i] = (uint8_t)cell.num; break;
    case 4: ((uint32_t *)column)[i] = (uint32_t)cell.num; break;
    case 8: memcpy((char *)column + 8 * i, &cell.i64, 8); break;
    default: ((PureSpan *)column)[i] = (PureSpan){cell.text, cell.size};
    }
}

/* The widths a list's arrays start with: narrow fields at 1. */
static void widths_start(PureList *list) {
    const Layout *l = &list->layout;
    for (unsigned f = 0; f < l->fields; ++f)
        list->width[f] = (uint8_t)((int)f == l->key || !narrows(l->kinds[f]) ? width(l, f) : 1);
}

static size_t row_width(const Layout *l) {
    size_t row = 0;
    for (unsigned f = 0; f < l->fields; ++f) row += width(l, f);
    return row ? row : 1;
}

static PureCell array_cell(const PureList *list, size_t i, unsigned f) { return cell_in(list->columns[f], list->width[f], i); }

static void array_put(PureList *list, size_t i, unsigned f, PureCell cell) { cell_out(list->columns[f], list->width[f], i, cell); }

static void array_move(PureList *list, size_t to, size_t from, size_t count) {
    const Layout *l = &list->layout;
    for (unsigned f = 0; f < l->fields; ++f)
        if (list->width[f])
            memmove((char *)list->columns[f] + to * list->width[f], (const char *)list->columns[f] + from * list->width[f],
                    count * list->width[f]);
}

/* Columns of room rows each; false without memory (each as it was or grown). */
static bool arrays_room(PureList *list, size_t room) {
    const Layout *l = &list->layout;
    for (unsigned f = 0; f < l->fields; ++f) {
        if (!list->width[f]) continue;
        void *grown = realloc(list->columns[f], (room ? room : 1) * list->width[f]);
        if (!grown) return false;
        list->columns[f] = grown;
    }
    list->room = room;
    return true;
}

/* Field f's column bytes wide (wider): false without memory (as it was). */
static bool widen(PureList *list, unsigned f, uint8_t bytes) {
    size_t rows = list->form == DENSE || list->form == HASHED ? list->room : list->count;
    void *made = malloc((list->room ? list->room : 1) * bytes);
    if (!made) return false;
    for (size_t i = 0; i < rows; ++i) cell_out(made, bytes, i, array_cell(list, i, f));
    free(list->columns[f]);
    list->columns[f] = made;
    list->width[f] = bytes;
    return true;
}

/* Every column wide enough for an item's cells; false without memory. */
static bool arrays_fit(PureList *list, const PureCell *cells) {
    for (unsigned f = 0; f < list->layout.fields; ++f) {
        uint8_t now = list->width[f];
        if ((now != 1 && now != 4) || !narrows(list->layout.kinds[f])) continue;
        uint8_t need = width_of(cells[f].num);
        if (need > now && !widen(list, f, need)) return false;
    }
    return true;
}

static void arrays_free(PureList *list) {
    if (list->pack) { /* a packed list's are its pack's */
        pack_release(list->pack);
        list->pack = NULL;
        memset(list->columns, 0, sizeof(list->columns));
    } else
        for (unsigned f = 0; f < 16; ++f) free(list->columns[f]), list->columns[f] = NULL;
    list->room = 0;
}

/* A DENSE list's i-th key's slot, counted along its bits (no memory needed). */
static uint64_t keys_token(const PureList *list) { return (uint64_t)list->member_count + (list->removes << 40) + 1; }

/* A DENSE list's keys counted again when they changed since: full, else its
 * ranks; false without memory (then they are counted along the bits). */
static bool dense_keys(PureList *list) {
    uint64_t token = keys_token(list);
    if (list->keys_seen == token) return true;
    size_t n = list->member_count, words = n / 64;
    bool full = n <= list->member_capacity * 64;
    for (size_t w = 0; full && w < words; ++w) full = list->members[w] == UINT64_MAX;
    if (full && n % 64) full = (~list->members[words] & ((UINT64_C(1) << (n % 64)) - 1)) == 0;
    if (!full) {
        if (list->ranks_room < list->member_capacity + 1) {
            uint32_t *grown = realloc(list->ranks, (list->member_capacity + 1) * sizeof(*grown));
            if (!grown) return false;
            list->ranks = grown, list->ranks_room = list->member_capacity + 1;
        }
        uint32_t below = 0;
        for (size_t w = 0; w < list->member_capacity; ++w) list->ranks[w] = below, below += (uint32_t)__builtin_popcountll(list->members[w]);
        list->ranks[list->member_capacity] = below;
    }
    list->full = full;
    list->keys_seen = token;
    return true;
}

/* The keys of a DENSE list below limit: where an item at limit would be. */
static size_t dense_rank(PureList *list, size_t limit) {
    if (dense_keys(list)) {
        if (list->full) return limit < list->count ? limit : list->count;
        size_t w = limit / 64;
        if (w >= list->member_capacity) return list->count;
        return list->ranks[w] + (size_t)__builtin_popcountll(list->members[w] & ((UINT64_C(1) << (limit % 64)) - 1));
    }
    size_t below = 0; /* without memory: counted along its bits */
    for (size_t w = 0; w < list->member_capacity && w * 64 < limit; ++w) {
        uint64_t word = list->members[w];
        if ((w + 1) * 64 > limit) word &= (UINT64_C(1) << (limit - w * 64)) - 1;
        below += (size_t)__builtin_popcountll(word);
    }
    return below;
}

/* The key (its slot) of a DENSE list's item i, or SIZE_MAX past them. */
static size_t dense_slot(const PureList *list, size_t i) {
    PureList *counted = (PureList *)list; /* its counts are kept as it is read */
    if (i >= list->count) return SIZE_MAX;
    if (dense_keys(counted)) {
        if (list->full) return i;
        size_t low = 0, high = list->member_capacity - 1; /* the first word whose keys reach past i */
        while (low < high) {
            size_t middle = low + (high - low) / 2;
            if (list->ranks[middle + 1] > i) high = middle;
            else low = middle + 1;
        }
        uint64_t word = list->members[low];
        for (size_t skip = i - list->ranks[low]; skip; --skip) word &= word - 1;
        return low * 64 + (size_t)__builtin_ctzll(word);
    }
    for (size_t w = 0; w < list->member_capacity; ++w) {
        size_t bits = (size_t)__builtin_popcountll(list->members[w]);
        if (i < bits) {
            uint64_t word = list->members[w];
            for (; i; --i) word &= word - 1;
            return w * 64 + (size_t)__builtin_ctzll(word);
        }
        i -= bits;
    }
    return SIZE_MAX;
}

/* The texts of every item of a FLAT or DENSE list let go. */
static void let_go_rows(PureList *list) {
    const Layout *l = &list->layout;
    if (!l->texts) return;
    for (size_t i = 0; list->form == FLAT && i < list->count; ++i)
        for (unsigned t = 0; t < l->texts; ++t) free_text(array_cell(list, i, l->text_field[t]).text);
    for (size_t i = 0; list->form == HASHED && i < list->member_capacity; ++i)
        for (unsigned t = 0; list->members[i] != VACANT && t < l->texts; ++t) free_text(array_cell(list, i, l->text_field[t]).text);
    for (size_t w = 0; list->form == DENSE && w < list->member_capacity; ++w)
        for (uint64_t word = list->members[w]; word; word &= word - 1)
            for (unsigned t = 0; t < l->texts; ++t)
                free_text(array_cell(list, w * 64 + (size_t)__builtin_ctzll(word), l->text_field[t]).text);
}

/* The keys a DENSE list may hold: below four times its items and a slack. */
static size_t dense_limit(const PureList *list) {
    size_t row = row_width(&list->layout), limit = 4 * (list->count + 1) + DENSE_SLACK / row;
    return limit < ARRAYS_LARGE / row ? limit : ARRAYS_LARGE / row;
}

/* Whether a full FLAT list would grow its arrays past ARRAYS_LARGE. */
static bool flat_large(const PureList *list) {
    return list->count == list->room && 2 * list->room * row_width(&list->layout) > ARRAYS_LARGE;
}

static bool dense_holds(const PureList *list, double key) {
    return small_key(key) && !(key == 0 && signbit(key)) && (size_t)key < dense_limit(list); /* -0 keeps its column */
}

/* A FLAT list keyed by small whole numbers (its keys as bits) as DENSE,
 * room for key too; false when it cannot be (it stays FLAT). */
static bool make_dense(PureList *list, double key) {
    const Layout *l = &list->layout;
    if (l->key < 0 || !list->members || !list->bitmap || list->flattened >= 2 || !dense_holds(list, key)) return false;
    const double *keys = list->columns[l->key];
    size_t top = (size_t)key;
    if (list->count) {
        double last = keys[list->count - 1]; /* the greatest: FLAT keeps key order */
        if (!dense_holds(list, last)) return false;
        if ((size_t)last > top) top = (size_t)last;
    }
    size_t room = top + 1 + (top + 1) / 2, limit = dense_limit(list);
    if (room > limit) room = limit;
    if (room <= top) return false;
    for (size_t i = 0; i < list->count; ++i)
        if (keys[i] == 0 && signbit(keys[i])) return false; /* -0 keeps its column */
    void *columns[16] = {0};
    uint8_t widths[16];
    memcpy(widths, list->width, sizeof(widths));
    widths[l->key] = 0; /* a DENSE list's keys are its slots */
    for (unsigned f = 0; f < l->fields; ++f)
        if (widths[f] && !(columns[f] = malloc(room * widths[f]))) {
            for (unsigned g = 0; g < f; ++g) free(columns[g]);
            return false;
        }
    for (size_t i = 0; i < list->count; ++i)
        for (unsigned f = 0; f < l->fields; ++f) cell_out(columns[f], widths[f], (size_t)keys[i], array_cell(list, i, f));
    arrays_free(list);
    memcpy(list->columns, columns, sizeof(columns));
    memcpy(list->width, widths, sizeof(widths));
    list->room = room;
    list->form = DENSE;
    return true;
}

/* A DENSE list as FLAT, its items in key order; false without memory. */
static bool make_flat(PureList *list) {
    const Layout *l = &list->layout;
    size_t room = list->count > 16 ? list->count : 16, row = 0;
    void *columns[16] = {0};
    uint8_t widths[16];
    memcpy(widths, list->width, sizeof(widths));
    widths[l->key] = 8; /* its keys a column again, searched as numbers */
    for (unsigned f = 0; f < l->fields; ++f)
        if (!(columns[f] = malloc(room * widths[f]))) {
            for (unsigned g = 0; g < f; ++g) free(columns[g]);
            return false;
        }
    for (size_t w = 0; w < list->member_capacity; ++w)
        for (uint64_t word = list->members[w]; word; word &= word - 1, ++row)
            for (unsigned f = 0; f < l->fields; ++f)
                cell_out(columns[f], widths[f], row, array_cell(list, w * 64 + (size_t)__builtin_ctzll(word), f));
    arrays_free(list);
    memcpy(list->columns, columns, sizeof(columns));
    memcpy(list->width, widths, sizeof(widths));
    list->room = room;
    list->form = FLAT;
    list->moved = 0;
    ++list->flattened;
    return true;
}

/* Cell from of a column of cells w bytes wide copied to cell to of another. */
static inline void cell_copy(void *to_column, size_t to, const void *from_column, size_t from, size_t w) {
    char *t = (char *)to_column + to * w;
    const char *f = (const char *)from_column + from * w;
    switch (w) {
    case 1: *t = *f; break;
    case 4: memcpy(t, f, 4); break;
    case 8: memcpy(t, f, 8); break;
    default: memcpy(t, f, sizeof(PureSpan));
    }
}

/* A HASHED list's slot of key (its cells there), or SIZE_MAX. */
static size_t hashed_slot(const PureList *list, double key) {
    uint64_t bits = key_bits(key);
    size_t mask = list->member_capacity - 1;
    for (size_t at = member_slot(bits, mask);; at = (at + 1) & mask) {
        if (list->members[at] == bits) return at;
        if (list->members[at] == VACANT) return SIZE_MAX;
    }
}

/* A HASHED list's table and columns of capacity slots (a power of two
 * above twice its items), each item's cells at its key's slot: from a FLAT
 * list's rows, or a HASHED one's slots. False without memory (the list as
 * it was). */
static bool hashed_table(PureList *list, size_t capacity) {
    const Layout *l = &list->layout;
    uint64_t *table = malloc(capacity * sizeof(*table));
    void *columns[16] = {0};
    bool ok = table != NULL;
    for (unsigned f = 0; ok && f < l->fields; ++f) ok = !list->width[f] || (columns[f] = malloc(capacity * list->width[f])) != NULL;
    if (!ok) {
        free(table);
        for (unsigned f = 0; f < 16; ++f) free(columns[f]);
        return false;
    }
    for (size_t i = 0; i < capacity; ++i) table[i] = VACANT;
    bool hashed = list->form == HASHED;
    const double *keys = list->columns[l->key];
    size_t mask = capacity - 1, rows = hashed ? list->member_capacity : list->count;
    for (size_t row = 0; row < rows; ++row) {
        if (hashed && list->members[row] == VACANT) continue;
        uint64_t bits = hashed ? list->members[row] : key_bits(keys[row]);
        size_t at = member_slot(bits, mask);
        while (table[at] != VACANT) at = (at + 1) & mask;
        table[at] = bits;
        for (unsigned f = 0; f < l->fields; ++f)
            if (list->width[f]) cell_copy(columns[f], at, list->columns[f], row, list->width[f]);
    }
    arrays_free(list);
    memcpy(list->columns, columns, sizeof(columns));
    list->room = capacity;
    free(list->members);
    ++list->removes;
    list->members = table, list->member_capacity = capacity, list->member_count = list->count;
    list->bitmap = false;
    return true;
}

/* A FLAT list whose keys come out of order as HASHED; false when it may
 * not be (made FLAT twice since it was cleared, or packed) or without
 * memory: it stays FLAT. */
static bool make_hashed(PureList *list) {
    if (list->layout.key < 0 || list->pack || list->flattened >= 2) return false;
    size_t capacity = 16;
    while (capacity < 2 * (list->count + 1)) capacity *= 2;
    if (!hashed_table(list, capacity)) return false;
    list->form = HASHED;
    list->full = false, list->keys_seen = 0; /* a DENSE list's keys: counted again when it is one again */
    ++list->version;
    return true;
}

/* Whether a HASHED list's next item would grow its arrays past ARRAYS_LARGE. */
static bool hashed_large(const PureList *list) {
    return 2 * (list->count + 1) > list->member_capacity && 2 * list->member_capacity * row_width(&list->layout) > ARRAYS_LARGE;
}

/* An item (its cells the list's own, its key not there) into a HASHED
 * list at its key's slot; false without memory (as it was). */
static bool hashed_add(PureList *list, const PureCell *item) {
    const Layout *l = &list->layout;
    if (2 * (list->count + 1) > list->member_capacity && !hashed_table(list, 2 * list->member_capacity)) return false;
    uint64_t bits = key_bits(item[l->key].num);
    size_t mask = list->member_capacity - 1, at = member_slot(bits, mask);
    while (list->members[at] != VACANT) at = (at + 1) & mask;
    list->members[at] = bits;
    for (unsigned f = 0; f < l->fields; ++f) array_put(list, at, f, item[f]);
    ++list->member_count;
    ++list->count;
    ++list->version;
    return true;
}

typedef struct { uint64_t key; uint32_t slot; } Ordered;

/* A HASHED list as FLAT, its items in key order: its slots sorted by their
 * keys' bits as unsigned numbers in the keys' order (-0 as +0), eight bits
 * a pass from the lowest (a pass whose bits every key shares skipped), each
 * column made again in that order; its members' table stays its keys' set.
 * False without memory (the list as it was). */
static bool make_ordered(PureList *list) {
    const Layout *l = &list->layout;
    size_t n = list->count, room = n > 16 ? n : 16;
    Ordered *a = malloc((n ? n : 1) * sizeof(*a)), *b = malloc((n ? n : 1) * sizeof(*b));
    void *columns[16] = {0};
    bool ok = a && b;
    for (unsigned f = 0; ok && f < l->fields; ++f) ok = !list->width[f] || (columns[f] = malloc(room * list->width[f])) != NULL;
    if (!ok) {
        free(a), free(b);
        for (unsigned f = 0; f < 16; ++f) free(columns[f]);
        return false;
    }
    for (size_t slot = 0, i = 0; slot < list->member_capacity; ++slot) {
        uint64_t bits = list->members[slot];
        if (bits != VACANT) a[i++] = (Ordered){bits >> 63 ? ~bits : bits | UINT64_C(1) << 63, (uint32_t)slot};
    }
    for (unsigned shift = 0; n && shift < 64; shift += 8) {
        size_t counts[256] = {0};
        for (size_t i = 0; i < n; ++i) ++counts[a[i].key >> shift & 255];
        if (counts[a[0].key >> shift & 255] == n) continue;
        for (size_t d = 0, sum = 0; d < 256; ++d) {
            size_t c = counts[d];
            counts[d] = sum, sum += c;
        }
        for (size_t i = 0; i < n; ++i) b[counts[a[i].key >> shift & 255]++] = a[i];
        Ordered *t = a;
        a = b, b = t;
    }
    for (unsigned f = 0; f < l->fields; ++f) {
        size_t w = list->width[f];
        for (size_t i = 0; w && i < n; ++i) cell_copy(columns[f], i, list->columns[f], a[i].slot, w);
    }
    free(a), free(b);
    arrays_free(list);
    memcpy(list->columns, columns, sizeof(columns));
    list->room = room;
    list->form = FLAT;
    list->moved = 0;
    ++list->flattened;
    ++list->version;
    return true;
}

/* A list read by position that may be HASHED made FLAT: memory for it or
 * none (the process stops rather than read items out of their order). */
static void ordered_now(const PureList *list) {
    if (list->form == HASHED && !make_ordered((PureList *)list)) abort();
}

/* Every node below node freed, its texts not (they are a FLAT list's still). */
static void free_nodes(Node *node) {
    if (!node) return;
    for (unsigned i = 0; !node->leaf && i < node->count; ++i) free_nodes(child(node, i));
    free(node);
}

/* A FLAT list's items as a tree's root, built from the leaves up with full
 * leaves and full inner nodes (as a tree filled at its end has them); false
 * without memory (none made). */
static bool build_tree(PureList *list, Node **root) {
    const Layout *l = &list->layout;
    size_t n = list->count, count = (n + FANOUT - 1) / FANOUT;
    *root = NULL;
    if (!n) return true;
    Node **level = malloc(count * sizeof(*level));
    if (!level) return false;
    for (size_t i = 0; i < count; ++i) {
        Node *leaf = new_node(list, true);
        if (!leaf) {
            while (i) free(level[--i]);
            free(level);
            return false;
        }
        unsigned items = (unsigned)(n - i * FANOUT < FANOUT ? n - i * FANOUT : FANOUT);
        for (unsigned f = 0; f < l->fields; ++f)
            if (list->width[f] == width(l, f))
                memcpy((char *)leaf + l->column[f], (const char *)list->columns[f] + i * FANOUT * width(l, f), items * width(l, f));
            else
                for (unsigned j = 0; j < items; ++j) numbers(l, leaf, f)[j] = array_cell(list, i * FANOUT + j, f).num;
        leaf->count = items;
        sum(list, leaf);
        level[i] = leaf;
    }
    while (count > 1) {
        size_t above = (count + FANOUT - 1) / FANOUT;
        for (size_t i = 0; i < above; ++i) {
            Node *node = new_node(list, false);
            if (!node) { /* the nodes made above, and those not yet under one */
                for (size_t j = 0; j < i; ++j) free_nodes(level[j]);
                for (size_t j = i * FANOUT; j < count; ++j) free_nodes(level[j]);
                free(level);
                return false;
            }
            unsigned children = (unsigned)(count - i * FANOUT < FANOUT ? count - i * FANOUT : FANOUT);
            memcpy(node->child, level + i * FANOUT, children * sizeof(*level));
            node->count = children;
            sum(list, node);
            level[i] = node; /* i is below i * FANOUT, read already */
        }
        count = above;
    }
    *root = level[0];
    free(level);
    return true;
}

/* A FLAT or DENSE list as a tree (a packed one's pack let go); false
 * without memory (it is as it was). Its version moves: what was read of its
 * arrays (a finger, a run) is not read again. */
static bool make_tree(PureList *list) {
    if (list->form == TREE) return true;
    if (list->form == DENSE && !make_flat(list)) return false;
    if (list->form == HASHED && !make_ordered(list)) return false;
    Node *root;
    if (!build_tree(list, &root)) return false;
    arrays_free(list);
    list->root = root;
    list->form = TREE;
    ++list->version;
    return true;
}

static bool visit_leaves(const Node *node, bool (*visit)(void *, const Node *), void *context);

typedef struct { const Layout *layout; Pack *pack; size_t at; } Packing;

/* The widths a pack's columns need: each narrow field's widest value. */
static bool pack_widths(void *context, const Node *leaf) {
    Packing *p = context;
    const Layout *l = p->layout;
    for (unsigned f = 0; f < l->fields; ++f)
        if ((int)f != l->key && narrows(l->kinds[f]))
            for (unsigned i = 0; i < leaf->count && p->pack->bytes[f] < 8; ++i) {
                uint8_t need = width_of(numbers(l, leaf, f)[i]);
                if (need > p->pack->bytes[f]) p->pack->bytes[f] = need;
            }
    return true;
}

static bool pack_leaf(void *context, const Node *leaf) {
    Packing *p = context;
    const Layout *l = p->layout;
    for (unsigned f = 0; f < l->fields; ++f) {
        uint8_t bytes = p->pack->bytes[f];
        if (bytes == width(l, f))
            memcpy((char *)p->pack->columns[f] + p->at * bytes, (const char *)leaf + l->column[f], leaf->count * bytes);
        else
            for (unsigned i = 0; i < leaf->count; ++i) cell_out(p->pack->columns[f], bytes, p->at + i, cell_at(l, leaf, i, f));
    }
    p->at += leaf->count;
    return true;
}

static void let_go_nodes(PureList *list, Node *node);

/* A stored tree as a packed list (its texts kept, its nodes let go); false
 * without memory (it is as it was). */
static bool pack(PureList *list) {
    const Layout *l = &list->layout;
    size_t n = list->count;
    Pack *made = calloc(1, sizeof(*made));
    bool ok = made != NULL;
    if (ok) {
        for (unsigned f = 0; f < l->fields; ++f) made->bytes[f] = (uint8_t)((int)f == l->key || !narrows(l->kinds[f]) ? width(l, f) : 1);
        Packing widths = {l, made, 0};
        visit_leaves(list->root, pack_widths, &widths);
    }
    for (unsigned f = 0; ok && f < l->fields; ++f) ok = (made->columns[f] = malloc(n * made->bytes[f])) != NULL;
    if (ok) {
        Packing packing = {l, made, 0};
        visit_leaves(list->root, pack_leaf, &packing);
        ok = l->key < 0 || pack_index(made, made->columns[l->key], n, list->aligned);
    }
    if (!ok) {
        if (made) made->refs = 1;
        pack_release(made);
        return false;
    }
    made->refs = 1;
    let_go_nodes(list, list->root);
    list->root = NULL;
    list->pack = made;
    memcpy(list->columns, made->columns, sizeof(list->columns));
    memcpy(list->width, made->bytes, sizeof(list->width));
    list->room = n;
    list->form = FLAT;
    list->moved = 0;
    ++list->version;
    return true;
}

/* An item (its cells the list's own) into a FLAT list before at. */
static bool flat_insert(PureList *list, size_t at, const PureCell *item) {
    if (list->count == list->room && !arrays_room(list, list->room ? 2 * list->room : 16)) return false;
    if (at < list->count) {
        array_move(list, at + 1, at, list->count - at);
        list->moved += list->count - at;
    }
    for (unsigned f = 0; f < list->layout.fields; ++f) array_put(list, at, f, item[f]);
    if (list->members) member_add(list, item[list->layout.key].num);
    ++list->count;
    ++list->version;
    return true;
}

/* Whether a FLAT list may move the items after at (else it becomes a tree):
 * a few always, more while the moves stay within a few times its items. */
static bool flat_moves(const PureList *list, size_t at) {
    size_t after = list->count - at;
    return list->count < FLAT_SMALL || list->moved + after <= 8 * list->count + 4096;
}

/* An item (its cells the list's own) into a DENSE list at its key (one it
 * may hold); false without memory (the list as it was). */
static bool dense_add(PureList *list, const PureCell *item, double number) {
    size_t key = (size_t)number;
    if (key >= list->room) {
        size_t room = list->room + list->room / 2, limit = dense_limit(list);
        if (room <= key) room = key + 1 + (key + 1) / 2;
        if (room > limit) room = limit;
        if (!arrays_room(list, room)) return false;
    }
    if (key / 64 >= list->member_capacity) { /* the bits grown first: adding a key must not give them up */
        size_t capacity = list->member_capacity ? list->member_capacity : 1;
        while (capacity <= key / 64) capacity *= 2;
        uint64_t *grown = realloc(list->members, capacity * sizeof(*grown));
        if (!grown) return false;
        memset(grown + list->member_capacity, 0, (capacity - list->member_capacity) * sizeof(*grown));
        list->members = grown, list->member_capacity = capacity;
    }
    for (unsigned f = 0; f < list->layout.fields; ++f) array_put(list, key, f, item[f]);
    member_add(list, number);
    ++list->count;
    ++list->version;
    return true;
}

/* The list as a form that answers by position (FLAT or a tree): a DENSE
 * one made FLAT, a tree when it was made FLAT too often; false without memory. */
static bool positioned(PureList *list) {
    if (list->form == HASHED) return make_ordered(list);
    if (list->form != DENSE) return true;
    if (list->flattened >= 2) return make_tree(list);
    return make_flat(list);
}

/* The list as a tree, for a change logged to be undone or recorded, or to a
 * packed list (whose arrays never change). */
static bool logged(PureList *list, const PureUndo *undo) {
    return list->form == TREE || (!undo && !list->journaled && !list->pack) || make_tree(list);
}

/* ---- The list */

PureList *pure_list_new(unsigned fields, const uint8_t *kinds) {
    if (fields > 16) return NULL;
    PureList *list = calloc(1, sizeof(*list));
    if (!list) return NULL;
    Layout *l = &list->layout;
    l->fields = fields;
    size_t at = sizeof(Node);
    for (unsigned f = 0; f < fields; ++f) {
        l->kinds[f] = kinds[f];
        l->column[f] = (uint32_t)at;
        at += FANOUT * (pure_cell_text(kinds[f]) ? sizeof(PureSpan) : 8);
        if (pure_cell_text(kinds[f])) l->text_field[l->texts++] = (uint8_t)f;
        else l->number_bytes += 8;
    }
    l->leaf_size = at;
    l->key = -1;
    list->id = __atomic_add_fetch(&lists_made, 1, __ATOMIC_RELAXED);
    return list;
}

/* Every node below *place the list's own, summed again. */
static bool rekey(PureList *list, Node **place) {
    Node *node = own(list, place);
    if (!node) return false;
    for (unsigned i = 0; !node->leaf && i < node->count; ++i)
        if (!rekey(list, &node->child[i])) return false;
    sum(list, node);
    return true;
}

PureResult pure_list_keyed(PureList *list, int field) {
    Layout *l = &list->layout;
    int key = field >= 0 && (unsigned)field < l->fields && l->kinds[field] == PURE_CELL_NUMBER ? field : -1;
    if (key == l->key) return PURE_OK;
    if (list->count && !make_tree(list)) return PURE_ALLOCATION;
    if (list->arrays) arrays_free(list); /* its columns as wide as the new key wants */
    l->key = key;
    if (list->arrays) widths_start(list);
    if (list->root && !rekey(list, &list->root)) {
        l->key = -1; /* searched without leads, which some nodes lack */
        return PURE_ALLOCATION;
    }
    return PURE_OK;
}

/* Every node below node let go (retired where a copy may read it), not its
 * texts: the list packed keeps them. */
static void let_go_nodes(PureList *list, Node *node) {
    if (!node) return;
    for (unsigned i = 0; !node->leaf && i < node->count; ++i) let_go_nodes(list, child(node, i));
    if (shared_node(list, node)) retire(list, node, false);
    else free(node);
}

/* Every node and text below node let go (retired where a copy may read them). */
static void let_go_tree(PureList *list, Node *node) {
    if (!node) return;
    const Layout *l = &list->layout;
    for (unsigned i = 0; i < node->count; ++i) {
        if (!node->leaf) let_go_tree(list, child(node, i));
        else for (unsigned t = 0; t < l->texts; ++t) let_go_text(list, texts(l, node, l->text_field[t])[i].data);
    }
    if (shared_node(list, node)) retire(list, node, false);
    else free(node);
}

/* A packed list's texts let go (retired where a copy may read them). */
static void let_go_packed(PureList *list) {
    const Layout *l = &list->layout;
    for (size_t i = 0; l->texts && i < list->count; ++i)
        for (unsigned t = 0; t < l->texts; ++t) let_go_text(list, array_cell(list, i, l->text_field[t]).text);
}

void pure_list_free(PureList *list) {
    if (!list) return;
    if (list->copy) {
        if (__atomic_sub_fetch(&list->refs, 1, __ATOMIC_ACQ_REL)) return;
        pack_release(list->pack);
    } else {
        if (list->pack) let_go_packed(list);
        else if (list->form != TREE) let_go_rows(list);
        arrays_free(list);
        free(list->journal);
        free(list->members);
        free(list->ranks);
        let_go_tree(list, list->root);
        for (unsigned kind = 0; kind < 2; ++kind) {
            while (list->spares[kind]) free(list->spare[kind][--list->spares[kind]]);
            free(list->spare[kind]);
        }
    }
    free(list);
}

void pure_list_clear(PureList *list) {
    bool had = list->count != 0;
    if (had) {
        if (list->pack) let_go_packed(list), arrays_free(list), list->form = TREE;
        else if (list->form != TREE) let_go_rows(list);
        let_go_tree(list, list->root);
        list->root = NULL;
        list->count = list->bytes = 0;
        ++list->version;
    }
    if (list->arrays) { /* FLAT again, its arrays kept for the next event unless large or not FLAT's (a DENSE list's has no key column) */
        if (list->form != FLAT || list->room * row_width(&list->layout) > ARRAYS_KEPT) {
            arrays_free(list);
            widths_start(list);
        }
        list->form = FLAT;
        list->flattened = 0;
        list->moved = 0;
    }
    if (!had) return;
    if (!list->members) return;
    if (list->bitmap && list->member_capacity <= BITMAP_KEPT) { /* small bits are kept for the next event */
        memset(list->members, 0, list->member_capacity * sizeof(*list->members));
        list->member_count = 0;
        ++list->removes;
        return;
    }
    members_drop(list); /* else bits again, from few */
    (void)members_start(list);
}

bool pure_list_full(PureList *list) { return list->form == DENSE && list->count && dense_keys(list) && list->full; }

bool pure_list_suits(PureList *list, unsigned needs, unsigned narrow) {
    if (list->form == DENSE && !dense_keys(list)) return false; /* its keys counted: full as it is (the tier reads it, LIST_FULL_AT) */
    if (needs & 1 && list->form != DENSE && !(list->form == HASHED && needs == 1)) return false; /* by key: at its keys, or its rows (by key alone) */
    if (needs & 2 && list->form != FLAT && !(list->form == DENSE && dense_keys(list) && list->full)) return false; /* by position */
    if (needs & 4 && !(list->form == DENSE && dense_keys(list) && list->full)) return false; /* a key its position */
    if (list->form != FLAT && list->form != DENSE && list->form != HASHED) return false;
    for (unsigned f = 0; f < list->layout.fields; ++f) { /* its cells of one byte widened to four: the tier's code reads four */
        if (!(narrow >> f & 1)) continue;
        if (list->width[f] == 1 && !widen(list, f, 4)) return false;
        if (list->width[f] != 4) return false;
    }
    return true;
}

bool pure_list_hashed(PureList *list) {
    const Layout *l = &list->layout;
    if (list->members) return true;
    if (l->key < 0 || list->copy || !members_start(list)) return false;
    for (size_t at = 0; at < list->count && list->members; ++at) /* the keys it has now, once */
        member_add(list, pure_list_get(list, at, (unsigned)l->key).num);
    return list->members != NULL;
}

bool pure_list_contains(const PureList *list, double key, bool *found) {
    if (!list->members) return false;
    if (list->bitmap) {
        *found = small_key(key) && (size_t)key / 64 < list->member_capacity &&
                 list->members[(size_t)key / 64] >> ((size_t)key % 64) & 1;
        return true;
    }
    uint64_t bits = key_bits(key);
    size_t mask = list->member_capacity - 1, at = member_slot(bits, mask);
    while (list->members[at] != VACANT && list->members[at] != bits) at = (at + 1) & mask;
    *found = list->members[at] == bits;
    return true;
}

/* An event's arrays are its items, as a tree's nodes are: neither counts
 * here (the stored bytes stand for both), so a list's room runs out at the
 * same item whatever it keeps them in (021). */
size_t pure_list_extra(const PureList *list) { return list->member_capacity * sizeof(*list->members); }

bool pure_list_arrays(PureList *list) {
    if (list->arrays) return true;
    if (list->form != TREE || list->copy || list->journaled || list->count) return false;
    list->arrays = true;
    list->form = FLAT;
    widths_start(list);
    return true;
}

unsigned pure_list_form(const PureList *list) { return list->form; }

bool pure_list_settle(PureList *list) {
    if (list->pack || list->copy || list->arrays || list->form != TREE || list->layout.key < 0 || list->count < PACK_ITEMS ||
        list->searched_version != list->version || list->searched < list->count / PACK_SEARCHES)
        return false;
    return pack(list);
}

bool pure_list_packed(const PureList *list) { return list->pack != NULL; }

const size_t pure_list_layout[] = {
    [LIST_COUNT_AT] = offsetof(PureList, count), [LIST_MEMBERS_AT] = offsetof(PureList, members),
    [LIST_MEMBER_CAPACITY_AT] = offsetof(PureList, member_capacity), [LIST_BITMAP_AT] = offsetof(PureList, bitmap),
    [LIST_FORM_AT] = offsetof(PureList, form), [LIST_COLUMNS_AT] = offsetof(PureList, columns),
    [LIST_VERSION_AT] = offsetof(PureList, version), [LIST_ROOM_AT] = offsetof(PureList, room),
    [LIST_MEMBER_COUNT_AT] = offsetof(PureList, member_count), [LIST_BYTES_AT] = offsetof(PureList, bytes),
    [LIST_PACK_AT] = offsetof(PureList, pack), [LIST_WIDTH_AT] = offsetof(PureList, width), [LIST_FULL_AT] = offsetof(PureList, full)};

const size_t pure_pack_layout[] = {
    [PACK_FIRST_AT] = offsetof(Pack, first), [PACK_WHOLE_AT] = offsetof(Pack, whole), [PACK_SHIFT_AT] = offsetof(Pack, shift),
    [PACK_ORIGIN_AT] = offsetof(Pack, origin_whole), [PACK_LOW_AT] = offsetof(Pack, low_whole),
    [PACK_HIGH_AT] = offsetof(Pack, high_whole), [PACK_BUCKETS_AT] = offsetof(Pack, buckets)};

bool pure_list_lookup(const PureList *list, unsigned key_field, PureCell key, unsigned field, PureCell *cell) {
    bool found;
    if (list->form == DENSE && (int)key_field == list->layout.key) { /* at its key, by its bits */
        if (!pure_list_contains(list, key.num, &found) || !found) return false;
        *cell = array_cell(list, (size_t)key.num, field);
        return true;
    }
    if (list->form == HASHED && (int)key_field == list->layout.key) { /* at its key's slot, by its table */
        size_t slot = hashed_slot(list, key.num);
        if (slot == SIZE_MAX) return false;
        *cell = array_cell(list, slot, field);
        return true;
    }
    size_t at = pure_list_seek(list, key_field, key, &found);
    if (found) *cell = pure_list_get(list, at, field);
    return found;
}

size_t pure_list_count(const PureList *list) { return list->count; }

PureList *pure_list_share(PureList *list, PureRetired *retired, uint64_t epoch) {
    /* A copy reads a tree or a pack; an empty list (an event's, between events) stays as it is. */
    if (list->count && !list->pack && !make_tree(list)) return NULL;
    PureList *copy = malloc(sizeof(*copy));
    if (!copy) return NULL;
    *copy = (PureList){.layout = list->layout, .root = list->root, .count = list->count, .bytes = list->bytes,
                       .id = list->id, .version = list->version, .refs = 1, .copy = true};
    if (list->pack) {
        __atomic_add_fetch(&list->pack->refs, 1, __ATOMIC_RELAXED);
        copy->pack = list->pack, copy->form = FLAT, copy->room = list->count;
        memcpy(copy->columns, list->columns, sizeof(copy->columns));
        memcpy(copy->width, list->width, sizeof(copy->width));
    }
    list->retired = retired;
    list->shares = epoch > list->shares ? epoch : list->shares + 1;
    return copy;
}

void pure_list_mark(PureList *list, uint64_t epoch) {
    if (list->retired && epoch > list->shares) list->shares = epoch;
}

void pure_list_hold(PureList *copy) { __atomic_add_fetch(&copy->refs, 1, __ATOMIC_RELAXED); }

bool pure_list_current(const PureList *copy, const PureList *list) {
    return copy->id == list->id && copy->version == list->version;
}

void pure_list_stamp(const PureList *list, uint64_t *id, uint64_t *version) {
    *id = list->id;
    *version = list->version;
}

static bool log_change(PureUndo *undo, Entry entry) {
    if (undo->count == undo->capacity) {
        size_t capacity = undo->capacity ? 2 * undo->capacity : 16;
        Entry *entries = realloc(undo->entries, capacity * sizeof(*entries));
        if (!entries) return false;
        undo->entries = entries;
        undo->capacity = capacity;
    }
    ((Entry *)undo->entries)[undo->count++] = entry;
    return true;
}

/* A cell the list can keep: a text's bytes copied (NULL when empty). */
static bool own_cell(const PureList *list, unsigned field, PureCell from, PureCell *to) {
    bool text = pure_cell_text(list->layout.kinds[field]);
    *to = (PureCell){.i64 = text ? 0 : from.i64}; /* a number's or an integer's bits */
    if (!text || !from.size) return true;
    if (!(to->text = new_text(list, from.text, from.size))) return false;
    to->size = from.size;
    return true;
}

static unsigned char *encode_cell(const Layout *l, unsigned field, PureCell cell, unsigned char *out) {
    bool text = pure_cell_text(l->kinds[field]);
    uint64_t bits = text ? cell.size : (uint64_t)cell.i64; /* a number's bits, or an integer's */
    unsigned width = text ? 4 : 8;
    for (unsigned i = 0; i < width; ++i) *out++ = (unsigned char)(bits >> (8 * i));
    if (text && cell.size) { memcpy(out, cell.text, cell.size); out += cell.size; }
    return out;
}

bool pure_cell_fits(uint8_t kind, PureCell cell) {
    return kind == PURE_CELL_INTEGER || (kind == PURE_CELL_BOOL ? cell.num == 0 || cell.num == 1 : isfinite(cell.num));
}

bool pure_cell_as(uint8_t from, uint8_t to, PureCell *cell) {
    if (from == to) return true;
    if (pure_cell_text(from) || pure_cell_text(to)) return false;
    if (to == PURE_CELL_INTEGER) { /* a whole number in range: -2^63 is, 2^63 is not */
        double v = cell->num;
        if (!(v >= -9223372036854775808.0 && v < 9223372036854775808.0) || v != floor(v)) return false;
        cell->i64 = (int64_t)v;
        return true;
    }
    if (from == PURE_CELL_INTEGER) {
        if (cell->i64 > INT64_C(9007199254740992) || cell->i64 < -INT64_C(9007199254740992)) return false;
        cell->num = (double)cell->i64;
    }
    if (to == PURE_CELL_BOOL) {
        if (cell->num != 0 && cell->num != 1) return false;
        cell->num = cell->num == 1; /* -0 is false as 0 is */
    }
    return true;
}

/* Whether a number cell holds what its kind may: a finite number, a bool 0 or 1. */
static bool fits(const Layout *l, unsigned field, double value) {
    return pure_cell_fits(l->kinds[field], (PureCell){.num = value});
}

/* A stored cell of field at *at in bytes (a text's bytes borrowed from
 * them): false when it is cut short, not finite (not 0 or 1 for a bool) or
 * not UTF-8. */
static bool decode_cell(const Layout *l, unsigned field, const unsigned char *bytes, size_t size, size_t *at,
                        PureCell *cell) {
    bool text = pure_cell_text(l->kinds[field]);
    size_t width = text ? 4 : 8;
    if (size - *at < width) return false;
    uint64_t bits = 0;
    for (size_t i = 0; i < width; ++i) bits |= (uint64_t)bytes[*at + i] << (8 * i);
    *at += width;
    *cell = (PureCell){0};
    if (!text) {
        cell->i64 = (int64_t)bits;
        return l->kinds[field] == PURE_CELL_INTEGER || fits(l, field, cell->num);
    }
    if (bits > size - *at || (l->kinds[field] == PURE_CELL_TEXT && !pure_utf8_valid((PureSpan){bytes + *at, (size_t)bits})))
        return false;
    *cell = (PureCell){.text = (unsigned char *)bytes + *at, .size = (size_t)bits};
    *at += (size_t)bits;
    return true;
}

/* ---- The journal: records of a stored list's changes, in the order they
 * were made. Each is a u8 kind and the position, then for an insert the
 * item's fields, for a set the u8 field and its cell. A record is written
 * compact (kinds 4-6): the position as a varint (LEB128), a number as the
 * varint 2 * zigzag(n) when it is an integer n below 2^53 in size (not -0),
 * else 1 and its binary64 bits (8 bytes, little-endian), an integer as the
 * varint zigzag(n), a text as a varint length and its bytes. Records stored
 * before (kinds 1-3, a list's tree value "PLS2") had a u32le position and
 * cells in stored form. */

enum { FIXED_INSERT = 1, FIXED_REMOVE = 2, FIXED_SET = 3, RECORD_INSERT = 4, RECORD_REMOVE = 5, RECORD_SET = 6,
       FIXED_HEAD = 5, RECORD_HEAD = 6, JOURNAL_KEPT = 1 << 20 };

static unsigned char *put_varint(unsigned char *out, uint64_t value) {
    for (; value >= 0x80; value >>= 7) *out++ = (unsigned char)(value | 0x80);
    *out++ = (unsigned char)value;
    return out;
}

static bool get_varint(const unsigned char *bytes, size_t size, size_t *at, uint64_t *value) {
    *value = 0;
    for (unsigned shift = 0; shift < 64 && *at < size; shift += 7) {
        unsigned char byte = bytes[(*at)++];
        *value |= (uint64_t)(byte & 0x7f) << shift;
        if (!(byte & 0x80)) return true;
    }
    return false;
}

/* A cell in compact form (the most it takes: compact_bound). */
static size_t compact_bound(const Layout *l, unsigned field, PureCell cell) {
    return pure_cell_text(l->kinds[field]) ? 5 + cell.size : 10;
}

static uint64_t zigzag(int64_t n) { return (uint64_t)n << 1 ^ (n < 0 ? UINT64_MAX : 0); }
static int64_t unzigzag(uint64_t z) { return z & 1 ? -(int64_t)(z >> 1) - 1 : (int64_t)(z >> 1); }

static unsigned char *put_compact(const Layout *l, unsigned field, PureCell cell, unsigned char *out) {
    if (l->kinds[field] == PURE_CELL_INTEGER) return put_varint(out, zigzag(cell.i64));
    if (pure_cell_text(l->kinds[field])) {
        out = put_varint(out, cell.size);
        if (cell.size) memcpy(out, cell.text, cell.size);
        return out + cell.size;
    }
    double v = cell.num;
    if (fabs(v) < 9007199254740992.0 && v == (double)(int64_t)v && !(v == 0 && signbit(v)))
        return put_varint(out, zigzag((int64_t)v) << 1);
    uint64_t bits;
    memcpy(&bits, &v, sizeof(bits));
    *out++ = 1;
    for (unsigned i = 0; i < 8; ++i) *out++ = (unsigned char)(bits >> (8 * i));
    return out;
}

static bool get_compact(const Layout *l, unsigned field, const unsigned char *bytes, size_t size, size_t *at,
                        PureCell *cell) {
    uint64_t value;
    *cell = (PureCell){0};
    if (!get_varint(bytes, size, at, &value)) return false;
    if (l->kinds[field] == PURE_CELL_INTEGER) {
        cell->i64 = unzigzag(value);
        return true;
    }
    if (pure_cell_text(l->kinds[field])) {
        if (value > size - *at || (l->kinds[field] == PURE_CELL_TEXT && !pure_utf8_valid((PureSpan){bytes + *at, (size_t)value})))
            return false;
        *cell = (PureCell){.text = (unsigned char *)bytes + *at, .size = (size_t)value};
        *at += (size_t)value;
        return true;
    }
    if (!(value & 1)) { /* an integer */
        if (value >> 1 >= UINT64_C(1) << 54) return false;
        cell->num = (double)unzigzag(value >> 1);
        return fits(l, field, cell->num);
    }
    if (value != 1 || size - *at < 8) return false;
    uint64_t bits = 0;
    for (unsigned i = 0; i < 8; ++i) bits |= (uint64_t)bytes[*at + i] << (8 * i);
    *at += 8;
    memcpy(&cell->num, &bits, sizeof(bits));
    return fits(l, field, cell->num);
}

/* Room for size more bytes at the journal's end, or NULL without memory. */
static unsigned char *journal_room(PureList *list, size_t size) {
    if (list->journal_capacity - list->journal_size < size) {
        size_t capacity = list->journal_capacity ? 2 * list->journal_capacity : 256;
        while (capacity - list->journal_size < size) capacity *= 2;
        unsigned char *grown = realloc(list->journal, capacity);
        if (!grown) return NULL;
        list->journal = grown;
        list->journal_capacity = capacity;
    }
    return list->journal + list->journal_size;
}

static unsigned char *record_head(unsigned char *out, unsigned kind, size_t at) {
    *out++ = (unsigned char)kind;
    return put_varint(out, at);
}

void pure_list_journal(PureList *list, bool journaled) {
    if (journaled && list->form != TREE && !make_tree(list)) abort(); /* an event's list is never journaled */
    if (journaled) list->arrays = false;
    list->journaled = journaled;
    if (!journaled) pure_list_forget(list, 0);
}

PureSpan pure_list_changes(const PureList *list) { return (PureSpan){list->journal, list->journal_size}; }

void pure_list_forget(PureList *list, size_t size) {
    if (size >= list->journal_size) return;
    list->journal_size = size;
    if (!size && list->journal_capacity > JOURNAL_KEPT) { /* a bulk load's room goes back */
        free(list->journal);
        list->journal = NULL;
        list->journal_capacity = 0;
    }
}

/* Every leaf in order, to visit (false stops it). */
static bool visit_leaves(const Node *node, bool (*visit)(void *, const Node *), void *context) {
    if (!node) return true;
    if (node->leaf) return visit(context, node);
    for (unsigned i = 0; i < node->count; ++i)
        if (!visit_leaves(child(node, i), visit, context)) return false;
    return true;
}

typedef struct { const Layout *layout; unsigned char *at; } Encoding;

static bool encode_leaf(void *context, const Node *leaf) {
    Encoding *e = context;
    for (unsigned i = 0; i < leaf->count; ++i)
        for (unsigned f = 0; f < e->layout->fields; ++f) e->at = encode_cell(e->layout, f, cell_at(e->layout, leaf, i, f), e->at);
    return true;
}

size_t pure_list_size(const PureList *list) { return list->bytes; }

/* An event's list is never stored, shared or sorted: one that was is made a
 * tree first (memory for it or none: the process stops rather than lose
 * items). A packed list is read as it is. */
static void tree_now(const PureList *list) {
    if (list->form != TREE && !list->pack && !make_tree((PureList *)list)) abort();
}

void pure_list_encode(const PureList *list, unsigned char *out) {
    tree_now(list);
    const Layout *l = &list->layout;
    for (size_t i = 0; list->pack && i < list->count; ++i)
        for (unsigned f = 0; f < l->fields; ++f) out = encode_cell(l, f, array_cell(list, i, f), out);
    Encoding encoding = {l, out};
    visit_leaves(list->root, encode_leaf, &encoding);
}

size_t pure_list_encode_part(const PureList *list, size_t *at, unsigned char *out, size_t capacity, size_t *needed) {
    tree_now(list);
    const Layout *l = &list->layout;
    PureRun run;
    size_t used = 0;
    *needed = 0;
    if (list->pack) {
        for (; *at < list->count; ++*at) {
            PureCell cells[16];
            size_t size = l->number_bytes;
            for (unsigned f = 0; f < l->fields; ++f) cells[f] = array_cell(list, *at, f);
            for (unsigned t = 0; t < l->texts; ++t) size += 4 + cells[l->text_field[t]].size;
            if (size > capacity - used) {
                if (!used) *needed = size;
                return used;
            }
            unsigned char *end = out + used;
            for (unsigned f = 0; f < l->fields; ++f) end = encode_cell(l, f, cells[f], end);
            used += size;
        }
        return used;
    }
    if (!pure_list_run(list, *at, &run)) return 0;
    do {
        const Node *leaf = run.path[run.depth];
        for (unsigned i = (unsigned)(*at - run.start); i < leaf->count; ++i) {
            size_t size = item_bytes(l, leaf, i);
            if (size > capacity - used) {
                if (!used) *needed = size;
                return used;
            }
            unsigned char *end = out + used;
            for (unsigned f = 0; f < l->fields; ++f) end = encode_cell(l, f, cell_at(l, leaf, i, f), end);
            used += size;
            ++*at;
        }
    } while (pure_list_next(list, &run));
    return used;
}

/* An item's cells in stored form at *at in bytes. */
static bool decode_item(const Layout *l, const unsigned char *bytes, size_t size, size_t *at, PureCell *cells) {
    for (unsigned f = 0; f < l->fields; ++f)
        if (!decode_cell(l, f, bytes, size, at, &cells[f])) return false;
    return true;
}

PURE_COLD PureResult pure_list_read(PureList *list, const unsigned char *bytes, size_t size) {
    if (!make_tree(list)) return PURE_ALLOCATION;
    PureCell cells[16];
    for (size_t at = 0; at < size;) {
        if (!decode_item(&list->layout, bytes, size, &at, cells)) return PURE_STORE_ERROR;
        PureResult result = pure_list_insert(list, list->count, cells, NULL);
        if (result != PURE_OK) return result;
    }
    return PURE_OK;
}

/* A record's cell, compact or as stored before. */
static bool record_cell(const Layout *l, bool compact, unsigned field, const unsigned char *bytes, size_t size,
                        size_t *at, PureCell *cell) {
    return compact ? get_compact(l, field, bytes, size, at, cell) : decode_cell(l, field, bytes, size, at, cell);
}

PURE_COLD PureResult pure_list_replay(PureList *list, const unsigned char *bytes, size_t size) {
    if (!make_tree(list)) return PURE_ALLOCATION;
    const Layout *l = &list->layout;
    bool journaled = list->journaled;
    PureResult result = PURE_OK;
    list->journaled = false;
    for (size_t at = 0; at < size && result == PURE_OK;) {
        unsigned kind = bytes[at++];
        bool compact = kind >= RECORD_INSERT;
        uint64_t position = 0;
        if (compact) {
            if (!get_varint(bytes, size, &at, &position)) { result = PURE_STORE_ERROR; break; }
        } else {
            if (size - at < FIXED_HEAD - 1) { result = PURE_STORE_ERROR; break; }
            for (unsigned i = 0; i < 4; ++i) position |= (uint64_t)bytes[at + i] << (8 * i);
            at += FIXED_HEAD - 1;
        }
        PureCell cells[16];
        unsigned change = compact ? kind - (RECORD_INSERT - FIXED_INSERT) : kind;
        bool ok = true;
        if (change == FIXED_INSERT) {
            for (unsigned f = 0; ok && f < l->fields; ++f) ok = record_cell(l, compact, f, bytes, size, &at, &cells[f]);
            result = ok && position <= list->count ? pure_list_insert(list, (size_t)position, cells, NULL) : PURE_STORE_ERROR;
        } else if (change == FIXED_REMOVE)
            result = position < list->count ? pure_list_remove(list, (size_t)position, NULL) : PURE_STORE_ERROR;
        else if (change == FIXED_SET) {
            unsigned field = at < size ? bytes[at++] : l->fields;
            result = field < l->fields && position < list->count && record_cell(l, compact, field, bytes, size, &at, &cells[0]) ?
                     pure_list_set(list, (size_t)position, field, cells[0], NULL) : PURE_STORE_ERROR;
        } else
            result = PURE_STORE_ERROR;
    }
    list->journaled = journaled;
    return result;
}

PureResult pure_list_insert(PureList *list, size_t at, const PureCell *cells, PureUndo *undo) {
    const Layout *l = &list->layout;
    if (at > list->count || list->count == PURE_LIST_ITEMS) return PURE_LIMIT;
    if (!logged(list, undo) || !positioned(list) ||
        (list->form == FLAT && ((at < list->count && !flat_moves(list, at)) || flat_large(list)) && !make_tree(list)))
        return PURE_ALLOCATION;
    PureCell item[16];
    unsigned owned = 0;
    for (; owned < l->fields; ++owned)
        if (!own_cell(list, owned, cells[owned], &item[owned])) break;
    if (list->form == FLAT) {
        if (owned < l->fields || !arrays_fit(list, cells) || !flat_insert(list, at, item)) {
            for (unsigned f = 0; f < owned; ++f) free_text(item[f].text);
            return PURE_ALLOCATION;
        }
        list->bytes += cells_bytes(l, item);
        return PURE_OK;
    }
    size_t size = RECORD_HEAD;
    for (unsigned f = 0; list->journaled && f < l->fields; ++f) size += compact_bound(l, f, cells[f]);
    unsigned char *record = list->journaled ? journal_room(list, size) : NULL;
    Place p;
    if (owned < l->fields || (list->journaled && !record) || !prepare(list, at, &p)) {
        for (unsigned f = 0; f < owned; ++f) free_text(item[f].text);
        return PURE_ALLOCATION;
    }
    if (undo && !log_change(undo, (Entry){.change = INSERTED, .list = list, .at = at})) {
        release_extras(list, &p);
        for (unsigned f = 0; f < l->fields; ++f) free_text(item[f].text);
        return PURE_ALLOCATION;
    }
    if (record) {
        unsigned char *end = record_head(record, RECORD_INSERT, at);
        for (unsigned f = 0; f < l->fields; ++f) end = put_compact(l, f, item[f], end);
        list->journal_size += (size_t)(end - record);
    }
    list->bytes += cells_bytes(l, item);
    place(list, &p, item);
    return PURE_OK;
}

PureResult pure_list_add(PureList *list, const PureCell *cells, PureUndo *undo, size_t *at, bool *exists) {
    const Layout *l = &list->layout;
    *exists = false;
    if (l->key < 0) return PURE_INVALID; /* searched and inserted apart, then */
    if (!logged(list, undo)) return PURE_ALLOCATION;
    if (list->form != TREE) {
        double key = cells[l->key].num;
        bool found = false;
        if (list->form == HASHED) { /* by its table, at its end: no position, unless asked */
            if (hashed_slot(list, key) != SIZE_MAX && !at) return *exists = true, PURE_OK;
            if (!at && !hashed_large(list)) {
                if (list->count == PURE_LIST_ITEMS) return PURE_LIMIT;
                PureCell item[16];
                unsigned owned = 0;
                for (; owned < l->fields; ++owned)
                    if (!own_cell(list, owned, cells[owned], &item[owned])) break;
                if (owned < l->fields || !arrays_fit(list, cells) || !hashed_add(list, item)) {
                    for (unsigned f = 0; f < owned; ++f) free_text(item[f].text);
                    return PURE_ALLOCATION;
                }
                list->bytes += cells_bytes(l, item);
                return PURE_OK;
            }
            if (!positioned(list)) return PURE_ALLOCATION;
        }
        if (list->form == DENSE) { /* by its bits, at its key: no position, unless asked */
            if (pure_list_contains(list, key, &found) && found && !at) return *exists = true, PURE_OK;
            if (!at && !found && dense_holds(list, key)) {
                PureCell item[16];
                unsigned owned = 0;
                for (; owned < l->fields; ++owned)
                    if (!own_cell(list, owned, cells[owned], &item[owned])) break;
                if (owned < l->fields || !arrays_fit(list, cells) || !dense_add(list, item, key)) {
                    for (unsigned f = 0; f < owned; ++f) free_text(item[f].text);
                    return PURE_ALLOCATION;
                }
                list->bytes += cells_bytes(l, item);
                return PURE_OK;
            }
            if (!positioned(list)) return PURE_ALLOCATION;
        }
        if (list->form == FLAT) {
            const double *keys = list->columns[l->key];
            size_t n = list->count, low = n ? lower(keys, (unsigned)n, key) : 0;
            if (low < n && keys[low] == key) {
                if (at) *at = low;
                return *exists = true, PURE_OK;
            }
            if (!at && (n >= FLAT_SMALL || (low == n && key == (double)n)) && (low < n || !list->flattened) && make_dense(list, key))
                /* small keys: DENSE (in order too, and from the first when each is the count, 023) */
                return pure_list_add(list, cells, undo, at, exists);
            if (!at && n >= FLAT_SMALL && low < n && make_hashed(list)) /* other keys out of order: HASHED (023) */
                return pure_list_add(list, cells, undo, at, exists);
            if (low < n && !flat_moves(list, low) && !make_tree(list)) return PURE_ALLOCATION;
            if (list->form == FLAT) {
                if (at) *at = low;
                return pure_list_insert(list, low, cells, undo);
            }
        }
    }
    if (list->members) { /* the set says at once when the key is there */
        bool found;
        if (pure_list_contains(list, cells[l->key].num, &found) && found) {
            size_t where = pure_list_seek(list, (unsigned)l->key, cells[l->key], exists);
            if (at) *at = where;
            return PURE_OK;
        }
    }
    if (list->count == PURE_LIST_ITEMS) return PURE_LIMIT;
    if (!list->root && !(list->root = new_node(list, true))) return PURE_ALLOCATION;
    Place p = {.extras = 0, .used = 0};
    size_t where;
    if (!at) at = &where;
    if (!descend_key(list, cells[l->key].num, &p, at, exists)) return PURE_ALLOCATION;
    if (*exists) return PURE_OK;
    p.appending = *at == list->count;
    PureCell item[16];
    unsigned owned = 0;
    for (; owned < l->fields; ++owned)
        if (!own_cell(list, owned, cells[owned], &item[owned])) break;
    size_t size = RECORD_HEAD;
    for (unsigned f = 0; list->journaled && f < l->fields; ++f) size += compact_bound(l, f, cells[f]);
    unsigned char *record = list->journaled ? journal_room(list, size) : NULL;
    if (owned < l->fields || (list->journaled && !record) || !prepare_extras(list, &p)) {
        for (unsigned f = 0; f < owned; ++f) free_text(item[f].text);
        return PURE_ALLOCATION;
    }
    if (undo && !log_change(undo, (Entry){.change = INSERTED, .list = list, .at = *at})) {
        release_extras(list, &p);
        for (unsigned f = 0; f < l->fields; ++f) free_text(item[f].text);
        return PURE_ALLOCATION;
    }
    if (record) {
        unsigned char *end = record_head(record, RECORD_INSERT, *at);
        for (unsigned f = 0; f < l->fields; ++f) end = put_compact(l, f, item[f], end);
        list->journal_size += (size_t)(end - record);
    }
    list->bytes += cells_bytes(l, item);
    place(list, &p, item);
    return PURE_OK;
}

/* Room for one more item's cells in the log. */
static PureCell *log_cells(PureUndo *undo, unsigned fields) {
    if (undo->cell_count + fields > undo->cell_capacity) {
        size_t capacity = undo->cell_capacity ? 2 * undo->cell_capacity : 64;
        while (capacity < undo->cell_count + fields) capacity *= 2;
        PureCell *cells = realloc(undo->cells, capacity * sizeof(*cells));
        if (!cells) return NULL;
        undo->cells = cells;
        undo->cell_capacity = capacity;
    }
    return undo->cells + undo->cell_count;
}

PureResult pure_list_remove(PureList *list, size_t at, PureUndo *undo) {
    const Layout *l = &list->layout;
    if (at >= list->count) return PURE_NOT_FOUND;
    if (!logged(list, undo) || !positioned(list) ||
        (list->form == FLAT && at + 1 < list->count && !flat_moves(list, at + 1) && !make_tree(list)))
        return PURE_ALLOCATION;
    if (list->form == FLAT) {
        PureCell cells[16];
        for (unsigned f = 0; f < l->fields; ++f) cells[f] = array_cell(list, at, f);
        if (list->members) member_remove(list, cells[l->key].num);
        list->bytes -= cells_bytes(l, cells);
        let_go_cells(list, cells);
        array_move(list, at, at + 1, list->count - at - 1);
        list->moved += list->count - at - 1;
        --list->count;
        ++list->version;
        return PURE_OK;
    }
    Step path[DEPTH];
    unsigned within, depth = descend(list, at, path, &within);
    if (!depth) return PURE_ALLOCATION;
    Node *leaf = path[depth - 1].node;
    unsigned char *record = list->journaled ? journal_room(list, RECORD_HEAD) : NULL;
    PureCell *cells = undo ? log_cells(undo, l->fields) : NULL, kept[16];
    if ((list->journaled && !record) ||
        (undo && (!cells || !log_change(undo, (Entry){.change = REMOVED, .list = list, .at = at, .cells = undo->cell_count}))))
        return PURE_ALLOCATION;
    if (!cells) cells = kept;
    for (unsigned f = 0; f < l->fields; ++f) cells[f] = cell_at(l, leaf, within, f);
    if (record) list->journal_size += (size_t)(record_head(record, RECORD_REMOVE, at) - record);
    if (undo) undo->cell_count += l->fields;
    list->bytes -= cells_bytes(l, cells);
    if (!undo) let_go_cells(list, cells);
    take_out(list, path, depth, within);
    return PURE_OK;
}

/* A field no summary follows (any but the key) changes in its leaf alone:
 * the leaf the thread read last, when the list alone has it, else the leaf
 * at the end of the list's own path to the item. The thread's finger keeps
 * the leaf, so the item's other fields are read and changed there too. */
PureResult pure_list_set(PureList *list, size_t at, unsigned field, PureCell value, PureUndo *undo) {
    const Layout *l = &list->layout;
    if (at >= list->count) return PURE_NOT_FOUND;
    if (!logged(list, undo)) return PURE_ALLOCATION;
    size_t row = at; /* a DENSE list's item at its slot, unless its key changes (then FLAT, in order) */
    if (list->form == DENSE && (int)field != l->key) row = dense_slot(list, at);
    else if (!positioned(list)) return PURE_ALLOCATION;
    if (list->form != TREE) {
        PureCell copy, old = array_cell(list, row, field);
        uint8_t need = narrows(l->kinds[field]) && (list->width[field] == 1 || list->width[field] == 4) ? width_of(value.num) : 0;
        if (need > list->width[field] && !widen(list, field, need)) return PURE_ALLOCATION;
        if (!own_cell(list, field, value, &copy)) return PURE_ALLOCATION;
        list->bytes += cell_bytes(l, field, copy) - cell_bytes(l, field, old);
        array_put(list, row, field, copy);
        let_go_text(list, old.text);
        if ((int)field == l->key && list->members) member_remove(list, old.num), member_add(list, copy.num);
        ++list->version;
        return PURE_OK;
    }
    Step path[DEPTH];
    unsigned within, depth = 0;
    bool keyed = (int)field == l->key;
    Node *leaf;
    size_t found_within;
    const Node *kept = keyed ? NULL : fingered(list, at, &found_within);
    if (kept && !shared_node(list, kept)) {
        leaf = (Node *)kept;
        within = (unsigned)found_within;
    } else {
        if (!(depth = descend(list, at, path, &within))) return PURE_ALLOCATION;
        leaf = path[depth - 1].node;
    }
    PureCell copy;
    if (!own_cell(list, field, value, &copy)) return PURE_ALLOCATION;
    PureCell old = cell_at(l, leaf, within, field);
    size_t size = RECORD_HEAD + 1 + compact_bound(l, field, copy);
    unsigned char *record = list->journaled ? journal_room(list, size) : NULL;
    if ((list->journaled && !record) ||
        (undo && !log_change(undo, (Entry){.change = CHANGED, .list = list, .at = at, .field = field, .old = old}))) {
        free_text(copy.text);
        return PURE_ALLOCATION;
    }
    if (record) {
        unsigned char *end = record_head(record, RECORD_SET, at);
        *end++ = (unsigned char)field;
        list->journal_size += (size_t)(put_compact(l, field, copy, end) - record);
    }
    list->bytes += cell_bytes(l, field, copy) - cell_bytes(l, field, old);
    if (pure_cell_text(l->kinds[field])) texts(l, leaf, field)[within] = (PureSpan){copy.text, copy.size};
    else if (l->kinds[field] == PURE_CELL_INTEGER) integers(l, leaf, field)[within] = copy.i64;
    else numbers(l, leaf, field)[within] = copy.num;
    if (!undo) let_go_text(list, old.text);
    if (keyed) {
        sum_path(list, path, depth);
        if (list->members) member_remove(list, old.num), member_add(list, copy.num);
    }
    ++list->version;
    finger_keep(list, leaf, at - within);
    return PURE_OK;
}

PureCell pure_list_get(const PureList *list, size_t at, unsigned field) {
    ordered_now(list);
    if (list->form != TREE) { /* a DENSE list by position: FLAT from now, or counted along its bits without memory */
        if (list->form == DENSE) return array_cell(list, dense_slot(list, at), field); /* at its slot (dense_slot) */
        if (list->form == FLAT) return array_cell(list, at, field);
    }
    size_t within;
    const Node *leaf = leaf_of(list, at, &within); /* first: an argument beside it would be read in either order */
    return cell_at(&list->layout, leaf, (unsigned)within, field);
}

static void open_run(const Layout *l, const Node *leaf, PureRun *run) {
    run->count = leaf->count;
    for (unsigned f = 0; f < l->fields; ++f)
        if (pure_cell_text(l->kinds[f])) run->column[f].texts = texts(l, leaf, f);
        else if (l->kinds[f] == PURE_CELL_INTEGER) run->column[f].integers = integers(l, leaf, f);
        else run->column[f].numbers = numbers(l, leaf, f);
}

/* A FLAT list's run from at: up to PURE_LIST_RUN items of its arrays; a
 * DENSE one's (made FLAT without memory) its item at alone. */
static void open_array_run(const PureList *list, size_t at, PureRun *run) {
    const Layout *l = &list->layout;
    size_t row = list->form == DENSE ? dense_slot(list, at) : at, most = list->count - at < PURE_LIST_RUN ? list->count - at : PURE_LIST_RUN;
    run->start = at;
    if (list->form == DENSE && !(list->keys_seen == keys_token(list) && list->full)) { /* the items whose keys follow each other from its slot */
        size_t n = 1;
        while (n < most && list->members[(row + n) / 64] >> ((row + n) % 64) & 1) ++n;
        most = n;
    }
    run->count = (unsigned)most;
    run->depth = 0;
    run->pathless = false;
    for (unsigned f = 0; f < l->fields; ++f)
        if (pure_cell_text(l->kinds[f])) run->column[f].texts = (const PureSpan *)list->columns[f] + row;
        else if (l->kinds[f] == PURE_CELL_INTEGER) run->column[f].integers = (const int64_t *)list->columns[f] + row;
        else if (list->width[f] == 8) run->column[f].numbers = (const double *)list->columns[f] + row;
        else { /* narrow cells as numbers */
            for (unsigned i = 0; i < run->count; ++i) run->cells[f][i] = array_cell(list, row + i, f).num;
            run->column[f].numbers = run->cells[f];
        }
}

bool pure_list_run(const PureList *list, size_t at, PureRun *run) {
    if (at >= list->count) return false;
    ordered_now(list);
    if (list->form != TREE) {
        {
            open_array_run(list, at, run);
            return true;
        }
    }
    size_t within;
    const Node *kept = fingered(list, at, &within); /* a slice's first item, found by key just before */
    if (kept) {
        run->path[0] = kept;
        run->depth = 0;
        run->pathless = true; /* the run after it found from the root */
        run->start = at - within;
        open_run(&list->layout, kept, run);
        return true;
    }
    const Node *node = list->root;
    size_t start = 0;
    unsigned depth = 0;
    while (!node->leaf) {
        unsigned i = child_at(node, at - start);
        start += guide(node)->before[i];
        run->path[depth] = node;
        run->taken[depth++] = (uint8_t)i;
        node = child(node, i);
    }
    run->path[depth] = node;
    run->depth = depth;
    run->start = start;
    run->pathless = false;
    open_run(&list->layout, node, run);
    return true;
}

/* Up to the nearest node with a child after the one taken, then down its
 * first children to a leaf. The leaf after it (a sibling) is fetched ahead:
 * leaves copied at different times lie far apart in memory. */
bool pure_list_next(const PureList *list, PureRun *run) {
    ordered_now(list);
    if (list->form != TREE) {
        if (run->start + run->count >= list->count) return false;
        open_array_run(list, run->start + run->count, run);
        return true;
    }
    if (run->pathless) { /* the next from the root, with its path */
        size_t at = run->start + run->count;
        if (at >= list->count) return false;
        const Node *node = list->root;
        size_t start = 0;
        unsigned depth = 0;
        while (!node->leaf) {
            unsigned i = child_at(node, at - start);
            start += guide(node)->before[i];
            run->path[depth] = node;
            run->taken[depth++] = (uint8_t)i;
            node = child(node, i);
        }
        run->path[depth] = node, run->depth = depth, run->start = start, run->pathless = false;
        open_run(&list->layout, node, run);
        return true;
    }
    size_t start = run->start + run->count;
    unsigned depth = run->depth;
    while (depth && run->taken[depth - 1] + 1u >= ((const Node *)run->path[depth - 1])->count) --depth;
    if (!depth) return false;
    const Node *parent = run->path[depth - 1], *node = child(parent, ++run->taken[depth - 1]);
    while (!node->leaf) {
        run->path[depth] = parent = node;
        run->taken[depth++] = 0;
        node = child(node, 0);
    }
    unsigned after = run->taken[depth - 1] + 1u;
    if (after < parent->count) {
        const char *leaf = (const char *)child(parent, after);
        for (size_t at = 0; at < list->layout.leaf_size; at += 64) __builtin_prefetch(leaf + at);
    }
    run->path[depth] = node;
    run->depth = depth;
    run->start = start;
    open_run(&list->layout, node, run);
    return true;
}

/* How two cells of a field order: numbers and integers by value (-0 and +0
 * are one key), texts by their bytes. */
static int order(const Layout *l, unsigned field, PureCell a, PureCell b) {
    if (l->kinds[field] == PURE_CELL_INTEGER) return (a.i64 > b.i64) - (a.i64 < b.i64);
    if (!pure_cell_text(l->kinds[field])) return (a.num > b.num) - (a.num < b.num);
    size_t shorter = a.size < b.size ? a.size : b.size;
    int bytes = shorter ? memcmp(a.text, b.text, shorter) : 0;
    return bytes ? (bytes > 0) - (bytes < 0) : (a.size > b.size) - (a.size < b.size);
}

/* Down the child whose first item's key is the last at or below key (the
 * first child when none is), then the leaf's first item not below it. The
 * list's own key field is read from each node's guide; another field from
 * the children's first leaves. */
size_t pure_list_seek(const PureList *list, unsigned field, PureCell key, bool *found) {
    const Layout *l = &list->layout;
    *found = false;
    if (!list->count) return 0;
    ordered_now(list);
    if (list->form == DENSE && (int)field != l->key) (void)positioned((PureList *)list); /* another field: in order */
    if (list->form == DENSE) { /* the keys below key (whole numbers below its ceiling), counted (dense_rank) */
        size_t all = list->member_capacity * 64;
        size_t limit = key.num <= 0 ? 0 : key.num >= (double)all ? all : (size_t)ceil(key.num);
        pure_list_contains(list, key.num, found);
        return dense_rank((PureList *)list, limit);
    }
    if (list->form == FLAT) {
        size_t low = 0, high = list->count;
        if ((int)field == l->key) low = list->pack ? pack_seek(list, key.num) : lower(list->columns[field], (unsigned)list->count, key.num);
        else
            while (low < high) {
                size_t middle = low + (high - low) / 2;
                if (order(l, field, array_cell(list, middle, field), key) < 0) low = middle + 1;
                else high = middle;
            }
        *found = low < list->count && !order(l, field, array_cell(list, low, field), key);
        return low;
    }
    const Node *node = list->root;
    size_t start = 0;
    if (!node) return 0;
    if ((int)field == l->key) {
        if (!list->copy && !list->arrays) searched_by(list, key.num);
        /* The finger's leaf, when its keys reach round key, holds its place
         * (a slice's high bound is near its low one, found just before). */
        if (finger.leaf && finger.id == list->id && finger.version == list->version && finger.leaf->count) {
            const double *keys = numbers(l, finger.leaf, field);
            if (keys[0] <= key.num && key.num <= keys[finger.leaf->count - 1]) {
                unsigned low = lower(keys, finger.leaf->count, key.num);
                *found = low < finger.leaf->count && keys[low] == key.num;
                return finger.start + low;
            }
        }
        /* Each level: the last child whose lead is at or below key (the
         * first when none is); then the leaf's items below key. */
        while (!node->leaf) {
            const Guide *g = guide(node);
            unsigned taken = child_by_key(node, key.num);
            start += g->before[taken];
            node = child(node, taken);
        }
        const double *keys = numbers(l, node, field);
        if (list->count > PREFETCHED) /* leaves past the caches: the leaf's keys fetched at once, not probe by probe */
            for (unsigned i = 0; i < node->count; i += 8) __builtin_prefetch(keys + i);
        unsigned low = lower(keys, node->count, key.num);
        *found = low < node->count && keys[low] == key.num;
        finger_keep(list, node, start); /* the item found is read there next */
        return start + low;
    }
    while (!node->leaf) {
        const Guide *g = guide(node);
        unsigned low = 1, high = node->count;
        while (low < high) {
            unsigned middle = low + (high - low) / 2;
            if (order(l, field, cell_at(l, child(node, middle)->first, 0, field), key) <= 0) low = middle + 1;
            else high = middle;
        }
        start += g->before[low - 1];
        node = child(node, low - 1);
    }
    unsigned low = 0, high = node->count;
    while (low < high) {
        unsigned middle = low + (high - low) / 2;
        if (order(l, field, cell_at(l, node, middle, field), key) < 0) low = middle + 1;
        else high = middle;
    }
    *found = low < node->count && !order(l, field, cell_at(l, node, low, field), key);
    return start + low;
}

size_t pure_list_bound(const PureList *list, unsigned field, PureCell key) {
    if (list->pack && (int)field == list->layout.key && list->count) return pack_seek(list, key.num);
    bool found;
    return pure_list_seek(list, field, key, &found);
}

/* An item where it is: its leaf and its place there. */
typedef struct { const Node *leaf; unsigned index; } Ref;

static PureCell ref_cell(const Layout *l, Ref r, unsigned field) { return cell_at(l, r.leaf, r.index, field); }

/* Positions sorted by their items' field, stably (spare holds count). */
PURE_COLD static void merge_sort(const Layout *l, unsigned field, const Ref *items, size_t *at, size_t *spare,
                                 size_t count) {
    if (count < 2) return;
    size_t half = count / 2, i = 0, j = half, k = 0;
    merge_sort(l, field, items, at, spare, half);
    merge_sort(l, field, items, at + half, spare, count - half);
    while (i < half && j < count)
        spare[k++] = order(l, field, ref_cell(l, items[at[j]], field), ref_cell(l, items[at[i]], field)) < 0 ? at[j++] : at[i++];
    while (i < half) spare[k++] = at[i++];
    while (j < count) spare[k++] = at[j++];
    memcpy(at, spare, count * sizeof(*at));
}

typedef struct { Ref *items; size_t count; } Gathered;

static bool gather_leaf(void *context, const Node *leaf) {
    Gathered *g = context;
    for (unsigned i = 0; i < leaf->count; ++i) g->items[g->count++] = (Ref){leaf, i};
    return true;
}

PURE_COLD PureResult pure_list_sorted(const PureList *list, unsigned field, PureList **out, size_t *moved) {
    if (list->form != TREE && !make_tree((PureList *)list)) abort(); /* the app's own, its module changing */
    const Layout *l = &list->layout;
    *out = NULL;
    Gathered gathered = {list->count ? malloc(list->count * sizeof(Ref)) : NULL, 0};
    if (list->count && !gathered.items) return PURE_ALLOCATION;
    visit_leaves(list->root, gather_leaf, &gathered);
    const Ref *items = gathered.items;
    bool ordered = true;
    for (size_t i = 1; i < list->count && ordered; ++i)
        ordered = order(l, field, ref_cell(l, items[i - 1], field), ref_cell(l, items[i], field)) < 0;
    if (ordered) {
        free(gathered.items);
        return PURE_OK;
    }
    size_t *at = malloc(2 * list->count * sizeof(*at));
    if (!at) {
        free(gathered.items);
        return PURE_ALLOCATION;
    }
    for (size_t i = 0; i < list->count; ++i) at[i] = i;
    merge_sort(l, field, items, at, at + list->count, list->count);
    PureResult result = PURE_OK;
    for (size_t i = 1; i < list->count && result == PURE_OK; ++i)
        if (!order(l, field, ref_cell(l, items[at[i - 1]], field), ref_cell(l, items[at[i]], field))) result = PURE_CONFLICT;
    PureList *sorted = result == PURE_OK ? pure_list_new(l->fields, l->kinds) : NULL;
    if (result == PURE_OK && !sorted) result = PURE_ALLOCATION;
    for (size_t i = 0; result == PURE_OK && i < list->count; ++i) {
        PureCell cells[16];
        for (unsigned f = 0; f < l->fields; ++f) cells[f] = ref_cell(l, items[at[i]], f);
        result = pure_list_insert(sorted, i, cells, NULL);
        moved[at[i]] = i;
    }
    free(at);
    free(gathered.items);
    if (result != PURE_OK) {
        pure_list_free(sorted);
        return result;
    }
    *out = sorted;
    return PURE_OK;
}

/* Undoing needs no memory but for a node an item goes back into (the event
 * took one out and the tree was since reshaped): without it, the process
 * stops rather than keep half an event (the store keeps the last save). The
 * texts undone were made during the event: no copy reads them. */
void pure_undo_rollback(PureUndo *undo, size_t mark) {
    Entry *entries = undo->entries;
    for (size_t i = undo->count; i-- > mark;) {
        Entry *e = &entries[i];
        PureList *list = e->list;
        const Layout *l = &list->layout;
        Step path[DEPTH];
        unsigned within, depth;
        if (list->form != TREE && !make_tree(list)) abort(); /* packed since: the changes were a tree's */
        if (e->change == REMOVED) {
            Place p;
            if (!prepare(list, e->at, &p)) abort();
            list->bytes += cells_bytes(l, undo->cells + e->cells);
            place(list, &p, undo->cells + e->cells);
            undo->cell_count = e->cells;
            continue;
        }
        if (!(depth = descend(list, e->at, path, &within))) abort();
        Node *leaf = path[depth - 1].node;
        if (e->change == INSERTED) {
            list->bytes -= item_bytes(l, leaf, within);
            for (unsigned t = 0; t < l->texts; ++t) free_text(texts(l, leaf, l->text_field[t])[within].data);
            take_out(list, path, depth, within);
            continue;
        }
        list->bytes += cell_bytes(l, e->field, e->old) - cell_bytes(l, e->field, cell_at(l, leaf, within, e->field));
        if (pure_cell_text(l->kinds[e->field])) {
            PureSpan *text = &texts(l, leaf, e->field)[within];
            free_text(text->data);
            *text = (PureSpan){e->old.text, e->old.size};
        } else if (l->kinds[e->field] == PURE_CELL_INTEGER)
            integers(l, leaf, e->field)[within] = e->old.i64;
        else {
            double now = numbers(l, leaf, e->field)[within];
            numbers(l, leaf, e->field)[within] = e->old.num;
            if (list->members && (int)e->field == l->key) member_remove(list, now), member_add(list, e->old.num);
        }
        sum_path(list, path, depth);
        ++list->version;
    }
    undo->count = mark;
}

void pure_undo_commit(PureUndo *undo) {
    Entry *entries = undo->entries;
    for (size_t i = 0; i < undo->count; ++i) {
        Entry *e = &entries[i];
        if (e->change == REMOVED) let_go_cells(e->list, undo->cells + e->cells);
        else if (e->change == CHANGED) let_go_text(e->list, e->old.text);
    }
    undo->count = undo->cell_count = 0;
}

size_t pure_undo_size(const PureUndo *undo) { return undo->count * sizeof(Entry) + undo->cell_count * sizeof(PureCell); }

void pure_undo_free(PureUndo *undo) {
    free(undo->entries);
    free(undo->cells);
    *undo = (PureUndo){0};
}