diff options
Diffstat (limited to 'src/timesync')
| -rw-r--r-- | src/timesync/timesyncd.c | 792 |
1 files changed, 792 insertions, 0 deletions
diff --git a/src/timesync/timesyncd.c b/src/timesync/timesyncd.c new file mode 100644 index 0000000000..5bd61dd07c --- /dev/null +++ b/src/timesync/timesyncd.c @@ -0,0 +1,792 @@ +/*-*- Mode: C; c-basic-offset: 8; indent-tabs-mode: nil -*-*/ + +/*** + This file is part of systemd. + + Copyright 2014 Kay Sievers + + systemd is free software; you can redistribute it and/or modify it + under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation; either version 2.1 of the License, or + (at your option) any later version. + + systemd is distributed in the hope that it will be useful, but + WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with systemd; If not, see <http://www.gnu.org/licenses/>. +***/ + +#include <stdlib.h> +#include <errno.h> +#include <fcntl.h> +#include <unistd.h> +#include <string.h> +#include <time.h> +#include <math.h> +#include <arpa/inet.h> +#include <netinet/in.h> +#include <netinet/ip.h> +#include <sys/timerfd.h> +#include <sys/timex.h> +#include <sys/socket.h> + +#include "missing.h" +#include "util.h" +#include "sparse-endian.h" +#include "log.h" +#include "sd-event.h" +#include "sd-daemon.h" + +#define TIME_T_MAX (time_t)((1UL << ((sizeof(time_t) << 3) - 1)) - 1) + +#ifndef ADJ_SETOFFSET +#define ADJ_SETOFFSET 0x0100 /* add 'time' to current time */ +#endif + +/* expected accuracy of time synchronization; used to adjust the poll interval */ +#define NTP_ACCURACY_SEC 0.2 + +/* + * "A client MUST NOT under any conditions use a poll interval less + * than 15 seconds." + */ +#define NTP_POLL_INTERVAL_MIN_SEC 32 +#define NTP_POLL_INTERVAL_MAX_SEC 2048 + +/* + * Maximum delta in seconds which the system clock is gradually adjusted + * (slew) to approach the network time. Deltas larger that this are set by + * letting the system time jump. The kernel's limit for adjtime is 0.5s. + */ +#define NTP_MAX_ADJUST 0.4 + +/* NTP protocol, packet header */ +#define NTP_LEAP_PLUSSEC 1 +#define NTP_LEAP_MINUSSEC 2 +#define NTP_LEAP_NOTINSYNC 3 +#define NTP_MODE_CLIENT 3 +#define NTP_MODE_SERVER 4 +#define NTP_FIELD_LEAP(f) (((f) >> 6) & 3) +#define NTP_FIELD_VERSION(f) (((f) >> 3) & 7) +#define NTP_FIELD_MODE(f) ((f) & 7) +#define NTP_FIELD(l, v, m) (((l) << 6) | ((v) << 3) | (m)) + +/* + * "NTP timestamps are represented as a 64-bit unsigned fixed-point number, + * in seconds relative to 0h on 1 January 1900." + */ +#define OFFSET_1900_1970 2208988800UL + +struct ntp_ts { + be32_t sec; + be32_t frac; +} _packed_; + +struct ntp_ts_short { + be16_t sec; + be16_t frac; +} _packed_; + +struct ntp_msg { + uint8_t field; + uint8_t stratum; + int8_t poll; + int8_t precision; + struct ntp_ts_short root_delay; + struct ntp_ts_short root_dispersion; + char refid[4]; + struct ntp_ts reference_time; + struct ntp_ts origin_time; + struct ntp_ts recv_time; + struct ntp_ts trans_time; +} _packed_; + +typedef struct Manager Manager; +struct Manager { + sd_event *event; + + /* peer */ + sd_event_source *event_receive; + char *server; + struct sockaddr_in server_addr; + int server_socket; + uint64_t packet_count; + + /* last sent packet */ + struct timespec trans_time_mon; + struct timespec trans_time; + usec_t retry_interval; + bool pending; + + /* poll timer */ + sd_event_source *event_timer; + usec_t poll_interval_usec; + bool poll_resync; + + /* history data */ + struct { + double offset; + double delay; + } samples[8]; + unsigned int samples_idx; + double samples_jitter; + + /* last change */ + bool jumped; + + /* watch for time changes */ + sd_event_source *event_clock_watch; + int clock_watch_fd; +}; + +static void manager_free(Manager *m); +DEFINE_TRIVIAL_CLEANUP_FUNC(Manager*, manager_free); +#define _cleanup_manager_free_ _cleanup_(manager_freep) + +static int sntp_arm_timer(Manager *m, usec_t next); +static int sntp_clock_watch_setup(Manager *m); +static void sntp_server_disconnect(Manager *m); + +static double ntp_ts_to_d(const struct ntp_ts *ts) { + return be32toh(ts->sec) + ((double)be32toh(ts->frac) / UINT_MAX); +} + +static double tv_to_d(const struct timeval *tv) { + return tv->tv_sec + (1.0e-6 * tv->tv_usec); +} + +static double ts_to_d(const struct timespec *ts) { + return ts->tv_sec + (1.0e-9 * ts->tv_nsec); +} + +static void d_to_tv(double d, struct timeval *tv) { + tv->tv_sec = (long)d; + tv->tv_usec = (d - tv->tv_sec) * 1000 * 1000; + + /* the kernel expects -0.3s as {-1, 7000.000} */ + if (tv->tv_usec < 0) { + tv->tv_sec -= 1; + tv->tv_usec += 1000 * 1000; + } +} + +static double square(double d) { + return d * d; +} + +static int sntp_send_request(Manager *m) { + struct ntp_msg ntpmsg = {}; + struct sockaddr_in addr = {}; + ssize_t len; + int r; + + /* + * "The client initializes the NTP message header, sends the request + * to the server, and strips the time of day from the Transmit + * Timestamp field of the reply. For this purpose, all the NTP + * header fields are set to 0, except the Mode, VN, and optional + * Transmit Timestamp fields." + */ + ntpmsg.field = NTP_FIELD(0, 4, NTP_MODE_CLIENT); + + /* + * Set transmit timestamp, remember it; the server will send that back + * as the origin timestamp and we have an indication that this is the + * matching answer to our request. + * + * The actual value does not matter, We do not care about the correct + * NTP UINT_MAX fraction; we just pass the plain nanosecond value. + */ + clock_gettime(CLOCK_MONOTONIC, &m->trans_time_mon); + clock_gettime(CLOCK_REALTIME, &m->trans_time); + ntpmsg.trans_time.sec = htobe32(m->trans_time.tv_sec + OFFSET_1900_1970); + ntpmsg.trans_time.frac = htobe32(m->trans_time.tv_nsec); + + addr.sin_family = AF_INET; + addr.sin_port = htobe16(123); + addr.sin_addr.s_addr = inet_addr(m->server); + len = sendto(m->server_socket, &ntpmsg, sizeof(ntpmsg), MSG_DONTWAIT, &addr, sizeof(addr)); + if (len == sizeof(ntpmsg)) { + m->pending = true; + log_debug("Sent NTP request to: %s", m->server); + } else + log_debug("Sending NTP request to %s failed: %m", m->server); + + /* re-arm timer with incresing timeout, in case the packets never arrive back */ + if (m->retry_interval > 0) { + if (m->retry_interval < NTP_POLL_INTERVAL_MAX_SEC * USEC_PER_SEC) + m->retry_interval *= 2; + } else + m->retry_interval = NTP_POLL_INTERVAL_MIN_SEC * USEC_PER_SEC; + r = sntp_arm_timer(m, m->retry_interval); + if (r < 0) + return r; + + return 0; +} + +static int sntp_timer(sd_event_source *source, usec_t usec, void *userdata) { + Manager *m = userdata; + + assert(m); + + sntp_send_request(m); + return 0; +} + +static int sntp_arm_timer(Manager *m, usec_t next) { + int r; + + assert(m); + assert(m->event_receive); + + if (next == 0) { + m->event_timer = sd_event_source_unref(m->event_timer); + return 0; + } + + if (m->event_timer) { + r = sd_event_source_set_time(m->event_timer, now(CLOCK_MONOTONIC) + next); + if (r < 0) + return r; + + return sd_event_source_set_enabled(m->event_timer, SD_EVENT_ONESHOT); + } + + r = sd_event_add_time( + m->event, + &m->event_timer, + CLOCK_MONOTONIC, + now(CLOCK_MONOTONIC) + next, 0, + sntp_timer, m); + if (r < 0) + return r; + + return 0; +} + +static int sntp_clock_watch(sd_event_source *source, int fd, uint32_t revents, void *userdata) { + Manager *m = userdata; + + assert(m); + assert(m->event_receive); + + /* rearm timer */ + sntp_clock_watch_setup(m); + + /* skip our own jumps */ + if (m->jumped) { + m->jumped = false; + return 0; + } + + /* resync */ + log_info("System time changed. Resyncing."); + m->poll_resync = true; + sntp_send_request(m); + + return 0; +} + +/* wake up when the system time changes underneath us */ +static int sntp_clock_watch_setup(Manager *m) { + struct itimerspec its = { .it_value.tv_sec = TIME_T_MAX }; + _cleanup_close_ int fd = -1; + sd_event *e; + sd_event_source *source; + int r; + + assert(m); + assert(m->event_receive); + + fd = timerfd_create(CLOCK_REALTIME, TFD_NONBLOCK|TFD_CLOEXEC); + if (fd < 0) { + log_error("Failed to create timerfd: %m"); + return -errno; + } + + if (timerfd_settime(fd, TFD_TIMER_ABSTIME|TFD_TIMER_CANCEL_ON_SET, &its, NULL) < 0) { + log_error("Failed to set up timerfd: %m"); + return -errno; + } + + e = sd_event_source_get_event(m->event_receive); + r = sd_event_add_io(e, &source, fd, EPOLLIN, sntp_clock_watch, m); + if (r < 0) { + log_error("Failed to create clock watch event source: %s", strerror(-r)); + return r; + } + + sd_event_source_unref(m->event_clock_watch); + m->event_clock_watch = source; + + if (m->clock_watch_fd >= 0) + close(m->clock_watch_fd); + m->clock_watch_fd = fd; + fd = -1; + + return 0; +} + +static int sntp_adjust_clock(Manager *m, double offset, int leap_sec) { + struct timex tmx = {}; + int r; + + /* + * For small deltas, tell the kernel to gradually adjust the system + * clock to the NTP time, larger deltas are just directly set. + * + * Clear STA_UNSYNC, it will enable the kernel's 11-minute mode, which + * syncs the system time periodically to the hardware clock. + */ + if (fabs(offset) < NTP_MAX_ADJUST) { + tmx.modes = ADJ_STATUS | ADJ_OFFSET | ADJ_TIMECONST | ADJ_MAXERROR | ADJ_ESTERROR; + tmx.status = STA_PLL; + tmx.offset = offset * USEC_PER_SEC; + tmx.constant = log2i(m->poll_interval_usec / USEC_PER_SEC) - 6; + tmx.maxerror = 0; + tmx.esterror = 0; + log_debug(" adjust (slew): %+f sec\n", (double)tmx.offset / USEC_PER_SEC); + } else { + tmx.modes = ADJ_SETOFFSET; + d_to_tv(offset, &tmx.time); + + m->jumped = true; + log_debug(" adjust (jump): %+f sec\n", tv_to_d(&tmx.time)); + } + + switch (leap_sec) { + case 1: + tmx.status |= STA_INS; + break; + case -1: + tmx.status |= STA_DEL; + break; + } + + //r = clock_adjtime(CLOCK_REALTIME, &tmx); + r = adjtimex(&tmx); + if (r < 0) + return r; + + log_debug(" status : %04i %s\n" + " time now : %li.%06li\n" + " constant : %li\n" + " offset : %+f sec\n" + " freq offset : %+li (%+.3f ppm)\n", + tmx.status, tmx.status & STA_UNSYNC ? "" : "sync", + tmx.time.tv_sec, tmx.time.tv_usec, + tmx.constant, + (double)tmx.offset / USEC_PER_SEC, + tmx.freq, (double)tmx.freq / 65536); + + return 0; +} + +static bool sntp_sample_spike_detection(Manager *m, double offset, double delay) { + unsigned int i, idx_cur, idx_new, idx_min; + double jitter; + double j; + + m->packet_count++; + + /* ignore initial sample */ + if (m->packet_count == 1) + return false; + + /* store the current data in our samples array */ + idx_cur = m->samples_idx; + idx_new = (idx_cur + 1) % ELEMENTSOF(m->samples); + m->samples_idx = idx_new; + m->samples[idx_new].offset = offset; + m->samples[idx_new].delay = delay; + + /* calculate new jitter value from the RMS differences relative to the lowest delay sample */ + jitter = m->samples_jitter; + for (idx_min = idx_cur, i = 0; i < ELEMENTSOF(m->samples); i++) + if (m->samples[i].delay > 0 && m->samples[i].delay < m->samples[idx_min].delay) + idx_min = i; + + j = 0; + for (i = 0; i < ELEMENTSOF(m->samples); i++) + j += square(m->samples[i].offset - m->samples[idx_min].offset); + m->samples_jitter = sqrt(j / (ELEMENTSOF(m->samples) - 1)); + + /* ignore samples when resyncing */ + if (m->poll_resync) + return false; + + /* always accept offset if we are farther off than the round-trip delay */ + if (fabs(offset) > delay) + return false; + + /* we need a few samples before looking at them */ + if (m->packet_count < 4) + return false; + + /* do not accept anything worse than the maximum possible error of the best sample */ + if (fabs(offset) > m->samples[idx_min].delay) + return true; + + /* compare the difference between the current offset to the previous offset and jitter */ + return fabs(offset - m->samples[idx_cur].offset) > 3 * jitter; +} + +static void sntp_adjust_poll(Manager *m, double offset, bool spike) { + if (m->poll_resync) { + m->poll_interval_usec = NTP_POLL_INTERVAL_MIN_SEC * USEC_PER_SEC; + m->poll_resync = false; + return; + } + + /* set to minimal poll interval */ + if (!spike && fabs(offset) > NTP_ACCURACY_SEC) { + m->poll_interval_usec = NTP_POLL_INTERVAL_MIN_SEC * USEC_PER_SEC; + return; + } + + /* increase polling interval */ + if (fabs(offset) < NTP_ACCURACY_SEC * 0.25) { + if (m->poll_interval_usec < NTP_POLL_INTERVAL_MAX_SEC * USEC_PER_SEC) + m->poll_interval_usec *= 2; + return; + } + + /* decrease polling interval */ + if (spike || fabs(offset) > NTP_ACCURACY_SEC * 0.75) { + if (m->poll_interval_usec > NTP_POLL_INTERVAL_MIN_SEC * USEC_PER_SEC) + m->poll_interval_usec /= 2; + return; + } +} + +static int sntp_receive_response(sd_event_source *source, int fd, uint32_t revents, void *userdata) { + Manager *m = userdata; + unsigned char buf[sizeof(struct ntp_msg)]; + struct iovec iov = { + .iov_base = buf, + .iov_len = sizeof(buf), + }; + union { + struct cmsghdr cmsghdr; + uint8_t buf[CMSG_SPACE(sizeof(struct timeval))]; + } control; + struct sockaddr_in server_addr; + struct msghdr msghdr = { + .msg_iov = &iov, + .msg_iovlen = 1, + .msg_control = &control, + .msg_controllen = sizeof(control), + .msg_name = &server_addr, + .msg_namelen = sizeof(server_addr), + }; + struct cmsghdr *cmsg; + struct timespec now_ts; + struct timeval *recv_time; + ssize_t len; + struct ntp_msg *ntpmsg; + double origin, receive, trans, dest; + double delay, offset; + bool spike; + int leap_sec; + int r; + + if (revents & (EPOLLHUP|EPOLLERR)) { + log_debug("Server connection returned error. Closing."); + sntp_server_disconnect(m); + return -ENOTCONN; + } + + len = recvmsg(fd, &msghdr, MSG_DONTWAIT); + if (len < 0) { + log_debug("Error receiving message. Disconnecting."); + return -EINVAL; + } + + if (iov.iov_len < sizeof(struct ntp_msg)) { + log_debug("Invalid response from server. Disconnecting."); + return -EINVAL; + } + + if (m->server_addr.sin_addr.s_addr != server_addr.sin_addr.s_addr) { + log_debug("Response from unknown server. Disconnecting."); + return -EINVAL; + } + + recv_time = NULL; + for (cmsg = CMSG_FIRSTHDR(&msghdr); cmsg; cmsg = CMSG_NXTHDR(&msghdr, cmsg)) { + if (cmsg->cmsg_level != SOL_SOCKET) + continue; + + switch (cmsg->cmsg_type) { + case SCM_TIMESTAMP: + recv_time = (struct timeval *) CMSG_DATA(cmsg); + break; + } + } + if (!recv_time) { + log_debug("Invalid packet timestamp. Disconnecting."); + return -EINVAL; + } + + ntpmsg = iov.iov_base; + if (!m->pending) { + log_debug("Unexpected reply. Ignoring."); + return 0; + } + + /* check our "time cookie" (we just stored nanoseconds in the fraction field) */ + if (be32toh(ntpmsg->origin_time.sec) != m->trans_time.tv_sec + OFFSET_1900_1970 || + be32toh(ntpmsg->origin_time.frac) != m->trans_time.tv_nsec) { + log_debug("Invalid reply; not our transmit time. Ignoring."); + return 0; + } + + if (NTP_FIELD_LEAP(ntpmsg->field) == NTP_LEAP_NOTINSYNC) { + log_debug("Server is not synchronized. Disconnecting."); + return -EINVAL; + } + + if (NTP_FIELD_VERSION(ntpmsg->field) != 4) { + log_debug("Response NTPv%d. Disconnecting.", NTP_FIELD_VERSION(ntpmsg->field)); + return -EINVAL; + } + + if (NTP_FIELD_MODE(ntpmsg->field) != NTP_MODE_SERVER) { + log_debug("Unsupported mode %d. Disconnecting.", NTP_FIELD_MODE(ntpmsg->field)); + return -EINVAL; + } + + /* valid packet */ + m->pending = false; + m->retry_interval = 0; + + /* announce leap seconds */ + if (NTP_FIELD_LEAP(ntpmsg->field) & NTP_LEAP_PLUSSEC) + leap_sec = 1; + else if (NTP_FIELD_LEAP(ntpmsg->field) & NTP_LEAP_MINUSSEC) + leap_sec = -1; + else + leap_sec = 0; + + /* + * "Timestamp Name ID When Generated + * ------------------------------------------------------------ + * Originate Timestamp T1 time request sent by client + * Receive Timestamp T2 time request received by server + * Transmit Timestamp T3 time reply sent by server + * Destination Timestamp T4 time reply received by client + * + * The round-trip delay, d, and system clock offset, t, are defined as: + * d = (T4 - T1) - (T3 - T2) t = ((T2 - T1) + (T3 - T4)) / 2" + */ + clock_gettime(CLOCK_MONOTONIC, &now_ts); + origin = tv_to_d(recv_time) - (ts_to_d(&now_ts) - ts_to_d(&m->trans_time_mon)) + OFFSET_1900_1970; + receive = ntp_ts_to_d(&ntpmsg->recv_time); + trans = ntp_ts_to_d(&ntpmsg->trans_time); + dest = tv_to_d(recv_time) + OFFSET_1900_1970; + + offset = ((receive - origin) + (trans - dest)) / 2; + delay = (dest - origin) - (trans - receive); + + spike = sntp_sample_spike_detection(m, offset, delay); + + sntp_adjust_poll(m, offset, spike); + + log_debug("NTP response:\n" + " leap : %u\n" + " version : %u\n" + " mode : %u\n" + " stratum : %u\n" + " precision : %f sec (%d)\n" + " reference : %.4s\n" + " origin : %f\n" + " receive : %f\n" + " transmit : %f\n" + " dest : %f\n" + " offset : %+f sec\n" + " delay : %+f sec\n" + " packet count : %"PRIu64"\n" + " jitter : %f%s\n" + " poll interval: %llu\n", + NTP_FIELD_LEAP(ntpmsg->field), + NTP_FIELD_VERSION(ntpmsg->field), + NTP_FIELD_MODE(ntpmsg->field), + ntpmsg->stratum, + exp2(ntpmsg->precision), ntpmsg->precision, + ntpmsg->stratum == 1 ? ntpmsg->refid : "n/a", + origin - OFFSET_1900_1970, + receive - OFFSET_1900_1970, + trans - OFFSET_1900_1970, + dest - OFFSET_1900_1970, + offset, delay, + m->packet_count, + m->samples_jitter, spike ? " spike" : "", + m->poll_interval_usec / USEC_PER_SEC); + + log_info("%4llu %+10f %10f %10f%s", + m->poll_interval_usec / USEC_PER_SEC, offset, delay, m->samples_jitter, spike ? " spike" : ""); + + if (!spike) { + r = sntp_adjust_clock(m, offset, leap_sec); + if (r < 0) + log_error("Failed to call clock_adjtime(): %m"); + } + + r = sntp_arm_timer(m, m->poll_interval_usec); + if (r < 0) + return r; + + return 0; +} + +static int sntp_server_connect(Manager *m, const char *server) { + _cleanup_free_ char *s = NULL; + + assert(m); + assert(server); + assert(m->server_socket >= 0); + + s = strdup(server); + if (!s) + return -ENOMEM; + + free(m->server); + m->server = s; + s = NULL; + + zero(m->server_addr); + m->server_addr.sin_family = AF_INET; + m->server_addr.sin_addr.s_addr = inet_addr(server); + + m->poll_interval_usec = NTP_POLL_INTERVAL_MIN_SEC * USEC_PER_SEC; + + return sntp_send_request(m); +} + +static void sntp_server_disconnect(Manager *m) { + if (!m->server) + return; + + m->event_timer = sd_event_source_unref(m->event_timer); + + m->event_clock_watch = sd_event_source_unref(m->event_clock_watch); + if (m->clock_watch_fd > 0) + close(m->clock_watch_fd); + m->clock_watch_fd = -1; + + m->event_receive = sd_event_source_unref(m->event_receive); + if (m->server_socket > 0) + close(m->server_socket); + m->server_socket = -1; + + zero(m->server_addr); + free(m->server); + m->server = NULL; +} + +static int sntp_listen_setup(Manager *m) { + _cleanup_close_ int fd = -1; + struct sockaddr_in addr; + const int on = 1; + const int tos = IPTOS_LOWDELAY; + int r; + + fd = socket(PF_INET, SOCK_DGRAM | SOCK_CLOEXEC, 0); + if (fd < 0) + return -errno; + + zero(addr); + addr.sin_family = AF_INET; + r = bind(fd, (struct sockaddr *)&addr, sizeof(addr)); + if (r < 0) + return -errno; + + r = setsockopt(fd, SOL_SOCKET, SO_TIMESTAMP, &on, sizeof(on)); + if (r < 0) + return -errno; + + r = setsockopt(fd, IPPROTO_IP, IP_TOS, &tos, sizeof(tos)); + if (r < 0) + return -errno; + + r = sd_event_add_io(m->event, &m->event_receive, fd, EPOLLIN, sntp_receive_response, m); + if (r < 0) + return r; + + m->server_socket = fd; + fd = -1; + + return 0; +} + +static int manager_new(Manager **ret) { + _cleanup_manager_free_ Manager *m = NULL; + int r; + + m = new0(Manager, 1); + if (!m) + return -ENOMEM; + + r = sd_event_default(&m->event); + if (r < 0) + return r; + + r = sntp_listen_setup(m); + if (r < 0) + return r; + + r = sntp_clock_watch_setup(m); + if (r < 0) + return r; + + *ret = m; + m = NULL; + + return 0; +} + +static void manager_free(Manager *m) { + + if (!m) + return; + + sd_event_unref(m->event); + free(m); +} + +int main(int argc, char *argv[]) { + _cleanup_manager_free_ Manager *m = NULL; + const char *server; + int r; + + log_set_target(LOG_TARGET_AUTO); + log_parse_environment(); + log_open(); + + r = manager_new(&m); + if (r < 0) + goto out; + + //server = "216.239.32.15"; /* time1.google.com */ + //server = "192.53.103.108"; /* ntp1.ptb.de */ + server = "27.54.95.11"; /* au.pool.ntp.org */ + + sd_notifyf(false, + "READY=1\n" + "STATUS=Connecting to %s", server); + + r = sntp_server_connect(m, server); + if (r < 0) + goto out; + + r = sd_event_loop(m->event); + if (r < 0) + goto out; + +out: + return r < 0 ? EXIT_FAILURE : EXIT_SUCCESS; +} |