regex-engine/lib/convert.c

/*
 * Copyright (c) Camden Dixie O'Brien
 * SPDX-License-Identifier: AGPL-3.0-only
 */

#include "convert.h"

#include "min_heap.h"

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

#define BUFFER_START_CAPACITY 8

#define TABLE_START_CAPACITY 32
#define TABLE_START_SHIFT 27 // 32 - log_2(TABLE_START_CAPACITY)
#define TABLE_WRAP_COEFF 2654435769 // Closest odd number to 2^32 / φ
#define TABLE_DOUBLING_THRESHOLD 6

typedef struct {
	int count, capacity, *states;
} buffer_t;

typedef struct {
	int probe_count, nfa_state_count, dfa_state, *nfa_states;
} table_entry_t;

typedef struct {
	int capacity, shift, max_probe_count;
	table_entry_t *entries;
} table_t;

typedef struct {
	const fsa_t *nfa;
	fsa_t *dfa;
	buffer_t buffer;
	table_t table;
} conversion_context_t;

static bool add_state(buffer_t *buffer, int nfa_state)
{
	for (int i = 0; i < buffer->count; ++i) {
		if (nfa_state == buffer->states[i])
			return false;
	}
	if (buffer->capacity < buffer->count + 1) {
		buffer->capacity *= 2;
		buffer->states
		    = realloc(buffer->states, buffer->capacity * sizeof(int));
		assert(NULL != buffer->states);
	}
	buffer->states[buffer->count++] = nfa_state;
	return true;
}

static void get_epsilon_closure(conversion_context_t *ctx, int nfa_state)
{
	if (!add_state(&ctx->buffer, nfa_state))
		return;
	for (int i = 0; i < ctx->nfa->states[nfa_state].count; ++i) {
		const fsa_rule_t *rule = &ctx->nfa->states[nfa_state].rules[i];
		if (EPSILON == rule->input)
			get_epsilon_closure(ctx, rule->next);
	}
}

static int *move_buffer_sorted(buffer_t *buffer)
{
	int *states, *p;
	p = states = malloc(buffer->count * sizeof(int));
	assert(NULL != states);

	min_heap_heapify(buffer->states, buffer->count);
	do
		*p++ = min_heap_pop(buffer->states, &buffer->count);
	while (0 < buffer->count);

	return states;
}

static uint32_t hash(const int *states, int count)
{
	assert(count > 0);
	uint32_t x = states[0];
	for (int i = 1; i < count; ++i)
		x ^= (uint32_t)states[i];
	return x;
}

static uint32_t wrap(uint32_t hash, int probe_count, int shift)
{
	hash += probe_count;
	hash *= TABLE_WRAP_COEFF;
	return hash >> shift;
}

static bool lookup(
    const table_t *table, const int *nfa_states, int count,
    int *dfa_state_out)
{
	const uint32_t h = hash(nfa_states, count);
	for (int i = 0; i <= table->max_probe_count; ++i) {
		const uint32_t loc = wrap(h, i, table->shift);
		const table_entry_t *entry = &table->entries[loc];
		if (entry->nfa_state_count != count)
			continue;

		int size = count * sizeof(int);
		if (memcmp(entry->nfa_states, nfa_states, size) == 0) {
			*dfa_state_out = entry->dfa_state;
			return true;
		}
	}
	return false;
}

static void insert(table_t *table, int *nfa_states, int count, int dfa_state)
{
	uint32_t h = hash(nfa_states, count);
	for (int i = 0; i < TABLE_DOUBLING_THRESHOLD; ++i) {
		const uint32_t loc = wrap(h, i, table->shift);
		table_entry_t *entry = &table->entries[loc];
		if (0 == entry->nfa_state_count) {
			// Slot is empty: insert the entry here.
			entry->nfa_states = nfa_states;
			entry->nfa_state_count = count;
			entry->dfa_state = dfa_state;
			entry->probe_count = i;
			if (entry->probe_count > table->max_probe_count)
				table->max_probe_count = entry->probe_count;
			return;
		} else if (entry->probe_count < i) {
			// Slot contains entry with lesser probe count: steal the
			// slot for the current entry.
			table_entry_t tmp;
			memcpy(&tmp, entry, sizeof(table_entry_t));
			entry->nfa_states = nfa_states;
			entry->nfa_state_count = count;
			entry->dfa_state = dfa_state;
			entry->probe_count = i;
			if (entry->probe_count > table->max_probe_count)
				table->max_probe_count = entry->probe_count;

			// Continue with the slot's previous entry.
			nfa_states = tmp.nfa_states;
			count = tmp.nfa_state_count;
			dfa_state = tmp.dfa_state;
			i = tmp.probe_count;
			h = hash(nfa_states, count);
		}
	}

	// Double the capacity of the table.
	table_entry_t *entries = table->entries;
	const int old_capacity = table->capacity;
	--table->shift;
	table->capacity *= 2;
	table->entries = calloc(table->capacity, sizeof(table_entry_t));
	assert(NULL != table->entries);
	for (int i = 0; i < old_capacity; ++i) {
		if (0 != entries[i].nfa_state_count) {
			insert(
			    table, entries[i].nfa_states, entries[i].nfa_state_count,
			    entries[i].dfa_state);
		}
	}
	free(entries);

	// Recurse to insert the entry now that the table has been
	// expanded.
	insert(table, nfa_states, count, dfa_state);
}

static bool lookup_or_create(
    conversion_context_t *ctx, int *nfa_states, int count,
    int *dfa_state_out)
{
	// Check if the DFA state for these NFA states already exists.
	if (lookup(&ctx->table, nfa_states, count, dfa_state_out))
		return false;

	// Create the DFA state, marking it as final if any of the NFA
	// states are final.
	const int dfa_state = fsa_add_state(ctx->dfa);
	for (int i = 0; i < count; ++i) {
		if (ctx->nfa->states[nfa_states[i]].final) {
			ctx->dfa->states[dfa_state].final = true;
			break;
		}
	}

	// Insert the DFA state into the table under the NFA states.
	insert(&ctx->table, nfa_states, count, dfa_state);

	*dfa_state_out = dfa_state;
	return true;
}

int convert_step(conversion_context_t *ctx)
{
	assert(0 != ctx->buffer.count);

	int count = ctx->buffer.count;
	int *nfa_states = move_buffer_sorted(&ctx->buffer);
	int dfa_state;
	if (!lookup_or_create(ctx, nfa_states, count, &dfa_state)) {
		// Base case: state already exists.
		free(nfa_states);
		return dfa_state;
	}

	bool handled[CHAR_COUNT] = { 0 };
	for (int i = 0; i < count; ++i) {
		const fsa_state_t *nfa_state = &ctx->nfa->states[nfa_states[i]];
		for (int j = 0; j < nfa_state->count; ++j) {
			const int input = nfa_state->rules[j].input;
			if (EPSILON == input || handled[input])
				continue;

			// Get epsilon closure of the target of this rule.
			get_epsilon_closure(ctx, nfa_state->rules[j].next);

			// Get epsilon closure for targets of any other rules the
			// current state has with this input.
			for (int k = j + 1; k < nfa_state->count; ++k) {
				if (input == nfa_state->rules[k].input)
					get_epsilon_closure(ctx, nfa_state->rules[k].next);
			}

			// Do the same for all states after this one (we have
			// already done them if they came before).
			for (int k = i + 1; k < count; ++k) {
				const fsa_state_t *nfa_state
				    = &ctx->nfa->states[nfa_states[k]];
				for (int l = 0; l < nfa_state->count; ++l) {
					if (input == nfa_state->rules[l].input)
						get_epsilon_closure(ctx, nfa_state->rules[l].next);
				}
			}

			// The buffer now contains the all states reachable via
			// epsilon move or the given input -- recurse.
			int new_dfa_state = convert_step(ctx);

			fsa_add_rule(ctx->dfa, dfa_state, new_dfa_state, input);
			handled[input] = true;
		}
	}

	return dfa_state;
}

void convert_to_dfa(const fsa_t *nfa, fsa_t *dfa_out)
{
	fsa_init(dfa_out);

	conversion_context_t ctx = { .nfa = nfa, .dfa = dfa_out };

	ctx.buffer.count = 0;
	ctx.buffer.capacity = BUFFER_START_CAPACITY;
	ctx.buffer.states = malloc(ctx.buffer.capacity * sizeof(int));
	assert(NULL != ctx.buffer.states);

	ctx.table.capacity = TABLE_START_CAPACITY;
	ctx.table.shift = TABLE_START_SHIFT;
	ctx.table.max_probe_count = 0;
	ctx.table.entries = calloc(ctx.table.capacity, sizeof(table_entry_t));
	assert(NULL != ctx.table.entries);

	get_epsilon_closure(&ctx, nfa->initial);
	ctx.dfa->initial = convert_step(&ctx);

	free(ctx.buffer.states);
	for (int i = 0; i < ctx.table.capacity; ++i)
		free(ctx.table.entries[i].nfa_states);
	free(ctx.table.entries);
}