ALSA: seq: Fix snd_seq_call_port_info_ioctl in compat mode
[linux/fpc-iii.git] / kernel / time.c
blob31ec845d0e80f615ba01a1dfead04d4a6c0dc8fc
1 /*
2 * linux/kernel/time.c
4 * Copyright (C) 1991, 1992 Linus Torvalds
6 * This file contains the interface functions for the various
7 * time related system calls: time, stime, gettimeofday, settimeofday,
8 * adjtime
9 */
11 * Modification history kernel/time.c
13 * 1993-09-02 Philip Gladstone
14 * Created file with time related functions from sched.c and adjtimex()
15 * 1993-10-08 Torsten Duwe
16 * adjtime interface update and CMOS clock write code
17 * 1995-08-13 Torsten Duwe
18 * kernel PLL updated to 1994-12-13 specs (rfc-1589)
19 * 1999-01-16 Ulrich Windl
20 * Introduced error checking for many cases in adjtimex().
21 * Updated NTP code according to technical memorandum Jan '96
22 * "A Kernel Model for Precision Timekeeping" by Dave Mills
23 * Allow time_constant larger than MAXTC(6) for NTP v4 (MAXTC == 10)
24 * (Even though the technical memorandum forbids it)
25 * 2004-07-14 Christoph Lameter
26 * Added getnstimeofday to allow the posix timer functions to return
27 * with nanosecond accuracy
30 #include <linux/export.h>
31 #include <linux/timex.h>
32 #include <linux/capability.h>
33 #include <linux/timekeeper_internal.h>
34 #include <linux/errno.h>
35 #include <linux/syscalls.h>
36 #include <linux/security.h>
37 #include <linux/fs.h>
38 #include <linux/math64.h>
39 #include <linux/ptrace.h>
41 #include <asm/uaccess.h>
42 #include <asm/unistd.h>
44 #include "timeconst.h"
47 * The timezone where the local system is located. Used as a default by some
48 * programs who obtain this value by using gettimeofday.
50 struct timezone sys_tz;
52 EXPORT_SYMBOL(sys_tz);
54 #ifdef __ARCH_WANT_SYS_TIME
57 * sys_time() can be implemented in user-level using
58 * sys_gettimeofday(). Is this for backwards compatibility? If so,
59 * why not move it into the appropriate arch directory (for those
60 * architectures that need it).
62 SYSCALL_DEFINE1(time, time_t __user *, tloc)
64 time_t i = get_seconds();
66 if (tloc) {
67 if (put_user(i,tloc))
68 return -EFAULT;
70 force_successful_syscall_return();
71 return i;
75 * sys_stime() can be implemented in user-level using
76 * sys_settimeofday(). Is this for backwards compatibility? If so,
77 * why not move it into the appropriate arch directory (for those
78 * architectures that need it).
81 SYSCALL_DEFINE1(stime, time_t __user *, tptr)
83 struct timespec tv;
84 int err;
86 if (get_user(tv.tv_sec, tptr))
87 return -EFAULT;
89 tv.tv_nsec = 0;
91 err = security_settime(&tv, NULL);
92 if (err)
93 return err;
95 do_settimeofday(&tv);
96 return 0;
99 #endif /* __ARCH_WANT_SYS_TIME */
101 SYSCALL_DEFINE2(gettimeofday, struct timeval __user *, tv,
102 struct timezone __user *, tz)
104 if (likely(tv != NULL)) {
105 struct timeval ktv;
106 do_gettimeofday(&ktv);
107 if (copy_to_user(tv, &ktv, sizeof(ktv)))
108 return -EFAULT;
110 if (unlikely(tz != NULL)) {
111 if (copy_to_user(tz, &sys_tz, sizeof(sys_tz)))
112 return -EFAULT;
114 return 0;
118 * Indicates if there is an offset between the system clock and the hardware
119 * clock/persistent clock/rtc.
121 int persistent_clock_is_local;
124 * Adjust the time obtained from the CMOS to be UTC time instead of
125 * local time.
127 * This is ugly, but preferable to the alternatives. Otherwise we
128 * would either need to write a program to do it in /etc/rc (and risk
129 * confusion if the program gets run more than once; it would also be
130 * hard to make the program warp the clock precisely n hours) or
131 * compile in the timezone information into the kernel. Bad, bad....
133 * - TYT, 1992-01-01
135 * The best thing to do is to keep the CMOS clock in universal time (UTC)
136 * as real UNIX machines always do it. This avoids all headaches about
137 * daylight saving times and warping kernel clocks.
139 static inline void warp_clock(void)
141 if (sys_tz.tz_minuteswest != 0) {
142 struct timespec adjust;
144 persistent_clock_is_local = 1;
145 adjust.tv_sec = sys_tz.tz_minuteswest * 60;
146 adjust.tv_nsec = 0;
147 timekeeping_inject_offset(&adjust);
152 * In case for some reason the CMOS clock has not already been running
153 * in UTC, but in some local time: The first time we set the timezone,
154 * we will warp the clock so that it is ticking UTC time instead of
155 * local time. Presumably, if someone is setting the timezone then we
156 * are running in an environment where the programs understand about
157 * timezones. This should be done at boot time in the /etc/rc script,
158 * as soon as possible, so that the clock can be set right. Otherwise,
159 * various programs will get confused when the clock gets warped.
162 int do_sys_settimeofday(const struct timespec *tv, const struct timezone *tz)
164 static int firsttime = 1;
165 int error = 0;
167 if (tv && !timespec_valid(tv))
168 return -EINVAL;
170 error = security_settime(tv, tz);
171 if (error)
172 return error;
174 if (tz) {
175 sys_tz = *tz;
176 update_vsyscall_tz();
177 if (firsttime) {
178 firsttime = 0;
179 if (!tv)
180 warp_clock();
183 if (tv)
184 return do_settimeofday(tv);
185 return 0;
188 SYSCALL_DEFINE2(settimeofday, struct timeval __user *, tv,
189 struct timezone __user *, tz)
191 struct timeval user_tv;
192 struct timespec new_ts;
193 struct timezone new_tz;
195 if (tv) {
196 if (copy_from_user(&user_tv, tv, sizeof(*tv)))
197 return -EFAULT;
199 if (!timeval_valid(&user_tv))
200 return -EINVAL;
202 new_ts.tv_sec = user_tv.tv_sec;
203 new_ts.tv_nsec = user_tv.tv_usec * NSEC_PER_USEC;
205 if (tz) {
206 if (copy_from_user(&new_tz, tz, sizeof(*tz)))
207 return -EFAULT;
210 return do_sys_settimeofday(tv ? &new_ts : NULL, tz ? &new_tz : NULL);
213 SYSCALL_DEFINE1(adjtimex, struct timex __user *, txc_p)
215 struct timex txc; /* Local copy of parameter */
216 int ret;
218 /* Copy the user data space into the kernel copy
219 * structure. But bear in mind that the structures
220 * may change
222 if(copy_from_user(&txc, txc_p, sizeof(struct timex)))
223 return -EFAULT;
224 ret = do_adjtimex(&txc);
225 return copy_to_user(txc_p, &txc, sizeof(struct timex)) ? -EFAULT : ret;
229 * current_fs_time - Return FS time
230 * @sb: Superblock.
232 * Return the current time truncated to the time granularity supported by
233 * the fs.
235 struct timespec current_fs_time(struct super_block *sb)
237 struct timespec now = current_kernel_time();
238 return timespec_trunc(now, sb->s_time_gran);
240 EXPORT_SYMBOL(current_fs_time);
243 * Convert jiffies to milliseconds and back.
245 * Avoid unnecessary multiplications/divisions in the
246 * two most common HZ cases:
248 unsigned int jiffies_to_msecs(const unsigned long j)
250 #if HZ <= MSEC_PER_SEC && !(MSEC_PER_SEC % HZ)
251 return (MSEC_PER_SEC / HZ) * j;
252 #elif HZ > MSEC_PER_SEC && !(HZ % MSEC_PER_SEC)
253 return (j + (HZ / MSEC_PER_SEC) - 1)/(HZ / MSEC_PER_SEC);
254 #else
255 # if BITS_PER_LONG == 32
256 return (HZ_TO_MSEC_MUL32 * j) >> HZ_TO_MSEC_SHR32;
257 # else
258 return (j * HZ_TO_MSEC_NUM) / HZ_TO_MSEC_DEN;
259 # endif
260 #endif
262 EXPORT_SYMBOL(jiffies_to_msecs);
264 unsigned int jiffies_to_usecs(const unsigned long j)
266 #if HZ <= USEC_PER_SEC && !(USEC_PER_SEC % HZ)
267 return (USEC_PER_SEC / HZ) * j;
268 #elif HZ > USEC_PER_SEC && !(HZ % USEC_PER_SEC)
269 return (j + (HZ / USEC_PER_SEC) - 1)/(HZ / USEC_PER_SEC);
270 #else
271 # if BITS_PER_LONG == 32
272 return (HZ_TO_USEC_MUL32 * j) >> HZ_TO_USEC_SHR32;
273 # else
274 return (j * HZ_TO_USEC_NUM) / HZ_TO_USEC_DEN;
275 # endif
276 #endif
278 EXPORT_SYMBOL(jiffies_to_usecs);
281 * timespec_trunc - Truncate timespec to a granularity
282 * @t: Timespec
283 * @gran: Granularity in ns.
285 * Truncate a timespec to a granularity. gran must be smaller than a second.
286 * Always rounds down.
288 * This function should be only used for timestamps returned by
289 * current_kernel_time() or CURRENT_TIME, not with do_gettimeofday() because
290 * it doesn't handle the better resolution of the latter.
292 struct timespec timespec_trunc(struct timespec t, unsigned gran)
295 * Division is pretty slow so avoid it for common cases.
296 * Currently current_kernel_time() never returns better than
297 * jiffies resolution. Exploit that.
299 if (gran <= jiffies_to_usecs(1) * 1000) {
300 /* nothing */
301 } else if (gran == 1000000000) {
302 t.tv_nsec = 0;
303 } else {
304 t.tv_nsec -= t.tv_nsec % gran;
306 return t;
308 EXPORT_SYMBOL(timespec_trunc);
310 /* Converts Gregorian date to seconds since 1970-01-01 00:00:00.
311 * Assumes input in normal date format, i.e. 1980-12-31 23:59:59
312 * => year=1980, mon=12, day=31, hour=23, min=59, sec=59.
314 * [For the Julian calendar (which was used in Russia before 1917,
315 * Britain & colonies before 1752, anywhere else before 1582,
316 * and is still in use by some communities) leave out the
317 * -year/100+year/400 terms, and add 10.]
319 * This algorithm was first published by Gauss (I think).
321 * WARNING: this function will overflow on 2106-02-07 06:28:16 on
322 * machines where long is 32-bit! (However, as time_t is signed, we
323 * will already get problems at other places on 2038-01-19 03:14:08)
325 unsigned long
326 mktime(const unsigned int year0, const unsigned int mon0,
327 const unsigned int day, const unsigned int hour,
328 const unsigned int min, const unsigned int sec)
330 unsigned int mon = mon0, year = year0;
332 /* 1..12 -> 11,12,1..10 */
333 if (0 >= (int) (mon -= 2)) {
334 mon += 12; /* Puts Feb last since it has leap day */
335 year -= 1;
338 return ((((unsigned long)
339 (year/4 - year/100 + year/400 + 367*mon/12 + day) +
340 year*365 - 719499
341 )*24 + hour /* now have hours */
342 )*60 + min /* now have minutes */
343 )*60 + sec; /* finally seconds */
346 EXPORT_SYMBOL(mktime);
349 * set_normalized_timespec - set timespec sec and nsec parts and normalize
351 * @ts: pointer to timespec variable to be set
352 * @sec: seconds to set
353 * @nsec: nanoseconds to set
355 * Set seconds and nanoseconds field of a timespec variable and
356 * normalize to the timespec storage format
358 * Note: The tv_nsec part is always in the range of
359 * 0 <= tv_nsec < NSEC_PER_SEC
360 * For negative values only the tv_sec field is negative !
362 void set_normalized_timespec(struct timespec *ts, time_t sec, s64 nsec)
364 while (nsec >= NSEC_PER_SEC) {
366 * The following asm() prevents the compiler from
367 * optimising this loop into a modulo operation. See
368 * also __iter_div_u64_rem() in include/linux/time.h
370 asm("" : "+rm"(nsec));
371 nsec -= NSEC_PER_SEC;
372 ++sec;
374 while (nsec < 0) {
375 asm("" : "+rm"(nsec));
376 nsec += NSEC_PER_SEC;
377 --sec;
379 ts->tv_sec = sec;
380 ts->tv_nsec = nsec;
382 EXPORT_SYMBOL(set_normalized_timespec);
385 * ns_to_timespec - Convert nanoseconds to timespec
386 * @nsec: the nanoseconds value to be converted
388 * Returns the timespec representation of the nsec parameter.
390 struct timespec ns_to_timespec(const s64 nsec)
392 struct timespec ts;
393 s32 rem;
395 if (!nsec)
396 return (struct timespec) {0, 0};
398 ts.tv_sec = div_s64_rem(nsec, NSEC_PER_SEC, &rem);
399 if (unlikely(rem < 0)) {
400 ts.tv_sec--;
401 rem += NSEC_PER_SEC;
403 ts.tv_nsec = rem;
405 return ts;
407 EXPORT_SYMBOL(ns_to_timespec);
410 * ns_to_timeval - Convert nanoseconds to timeval
411 * @nsec: the nanoseconds value to be converted
413 * Returns the timeval representation of the nsec parameter.
415 struct timeval ns_to_timeval(const s64 nsec)
417 struct timespec ts = ns_to_timespec(nsec);
418 struct timeval tv;
420 tv.tv_sec = ts.tv_sec;
421 tv.tv_usec = (suseconds_t) ts.tv_nsec / 1000;
423 return tv;
425 EXPORT_SYMBOL(ns_to_timeval);
428 * When we convert to jiffies then we interpret incoming values
429 * the following way:
431 * - negative values mean 'infinite timeout' (MAX_JIFFY_OFFSET)
433 * - 'too large' values [that would result in larger than
434 * MAX_JIFFY_OFFSET values] mean 'infinite timeout' too.
436 * - all other values are converted to jiffies by either multiplying
437 * the input value by a factor or dividing it with a factor
439 * We must also be careful about 32-bit overflows.
441 unsigned long msecs_to_jiffies(const unsigned int m)
444 * Negative value, means infinite timeout:
446 if ((int)m < 0)
447 return MAX_JIFFY_OFFSET;
449 #if HZ <= MSEC_PER_SEC && !(MSEC_PER_SEC % HZ)
451 * HZ is equal to or smaller than 1000, and 1000 is a nice
452 * round multiple of HZ, divide with the factor between them,
453 * but round upwards:
455 return (m + (MSEC_PER_SEC / HZ) - 1) / (MSEC_PER_SEC / HZ);
456 #elif HZ > MSEC_PER_SEC && !(HZ % MSEC_PER_SEC)
458 * HZ is larger than 1000, and HZ is a nice round multiple of
459 * 1000 - simply multiply with the factor between them.
461 * But first make sure the multiplication result cannot
462 * overflow:
464 if (m > jiffies_to_msecs(MAX_JIFFY_OFFSET))
465 return MAX_JIFFY_OFFSET;
467 return m * (HZ / MSEC_PER_SEC);
468 #else
470 * Generic case - multiply, round and divide. But first
471 * check that if we are doing a net multiplication, that
472 * we wouldn't overflow:
474 if (HZ > MSEC_PER_SEC && m > jiffies_to_msecs(MAX_JIFFY_OFFSET))
475 return MAX_JIFFY_OFFSET;
477 return (MSEC_TO_HZ_MUL32 * m + MSEC_TO_HZ_ADJ32)
478 >> MSEC_TO_HZ_SHR32;
479 #endif
481 EXPORT_SYMBOL(msecs_to_jiffies);
483 unsigned long usecs_to_jiffies(const unsigned int u)
485 if (u > jiffies_to_usecs(MAX_JIFFY_OFFSET))
486 return MAX_JIFFY_OFFSET;
487 #if HZ <= USEC_PER_SEC && !(USEC_PER_SEC % HZ)
488 return (u + (USEC_PER_SEC / HZ) - 1) / (USEC_PER_SEC / HZ);
489 #elif HZ > USEC_PER_SEC && !(HZ % USEC_PER_SEC)
490 return u * (HZ / USEC_PER_SEC);
491 #else
492 return (USEC_TO_HZ_MUL32 * u + USEC_TO_HZ_ADJ32)
493 >> USEC_TO_HZ_SHR32;
494 #endif
496 EXPORT_SYMBOL(usecs_to_jiffies);
499 * The TICK_NSEC - 1 rounds up the value to the next resolution. Note
500 * that a remainder subtract here would not do the right thing as the
501 * resolution values don't fall on second boundries. I.e. the line:
502 * nsec -= nsec % TICK_NSEC; is NOT a correct resolution rounding.
503 * Note that due to the small error in the multiplier here, this
504 * rounding is incorrect for sufficiently large values of tv_nsec, but
505 * well formed timespecs should have tv_nsec < NSEC_PER_SEC, so we're
506 * OK.
508 * Rather, we just shift the bits off the right.
510 * The >> (NSEC_JIFFIE_SC - SEC_JIFFIE_SC) converts the scaled nsec
511 * value to a scaled second value.
513 static unsigned long
514 __timespec_to_jiffies(unsigned long sec, long nsec)
516 nsec = nsec + TICK_NSEC - 1;
518 if (sec >= MAX_SEC_IN_JIFFIES){
519 sec = MAX_SEC_IN_JIFFIES;
520 nsec = 0;
522 return (((u64)sec * SEC_CONVERSION) +
523 (((u64)nsec * NSEC_CONVERSION) >>
524 (NSEC_JIFFIE_SC - SEC_JIFFIE_SC))) >> SEC_JIFFIE_SC;
528 unsigned long
529 timespec_to_jiffies(const struct timespec *value)
531 return __timespec_to_jiffies(value->tv_sec, value->tv_nsec);
534 EXPORT_SYMBOL(timespec_to_jiffies);
536 void
537 jiffies_to_timespec(const unsigned long jiffies, struct timespec *value)
540 * Convert jiffies to nanoseconds and separate with
541 * one divide.
543 u32 rem;
544 value->tv_sec = div_u64_rem((u64)jiffies * TICK_NSEC,
545 NSEC_PER_SEC, &rem);
546 value->tv_nsec = rem;
548 EXPORT_SYMBOL(jiffies_to_timespec);
551 * We could use a similar algorithm to timespec_to_jiffies (with a
552 * different multiplier for usec instead of nsec). But this has a
553 * problem with rounding: we can't exactly add TICK_NSEC - 1 to the
554 * usec value, since it's not necessarily integral.
556 * We could instead round in the intermediate scaled representation
557 * (i.e. in units of 1/2^(large scale) jiffies) but that's also
558 * perilous: the scaling introduces a small positive error, which
559 * combined with a division-rounding-upward (i.e. adding 2^(scale) - 1
560 * units to the intermediate before shifting) leads to accidental
561 * overflow and overestimates.
563 * At the cost of one additional multiplication by a constant, just
564 * use the timespec implementation.
566 unsigned long
567 timeval_to_jiffies(const struct timeval *value)
569 return __timespec_to_jiffies(value->tv_sec,
570 value->tv_usec * NSEC_PER_USEC);
572 EXPORT_SYMBOL(timeval_to_jiffies);
574 void jiffies_to_timeval(const unsigned long jiffies, struct timeval *value)
577 * Convert jiffies to nanoseconds and separate with
578 * one divide.
580 u32 rem;
582 value->tv_sec = div_u64_rem((u64)jiffies * TICK_NSEC,
583 NSEC_PER_SEC, &rem);
584 value->tv_usec = rem / NSEC_PER_USEC;
586 EXPORT_SYMBOL(jiffies_to_timeval);
589 * Convert jiffies/jiffies_64 to clock_t and back.
591 clock_t jiffies_to_clock_t(unsigned long x)
593 #if (TICK_NSEC % (NSEC_PER_SEC / USER_HZ)) == 0
594 # if HZ < USER_HZ
595 return x * (USER_HZ / HZ);
596 # else
597 return x / (HZ / USER_HZ);
598 # endif
599 #else
600 return div_u64((u64)x * TICK_NSEC, NSEC_PER_SEC / USER_HZ);
601 #endif
603 EXPORT_SYMBOL(jiffies_to_clock_t);
605 unsigned long clock_t_to_jiffies(unsigned long x)
607 #if (HZ % USER_HZ)==0
608 if (x >= ~0UL / (HZ / USER_HZ))
609 return ~0UL;
610 return x * (HZ / USER_HZ);
611 #else
612 /* Don't worry about loss of precision here .. */
613 if (x >= ~0UL / HZ * USER_HZ)
614 return ~0UL;
616 /* .. but do try to contain it here */
617 return div_u64((u64)x * HZ, USER_HZ);
618 #endif
620 EXPORT_SYMBOL(clock_t_to_jiffies);
622 u64 jiffies_64_to_clock_t(u64 x)
624 #if (TICK_NSEC % (NSEC_PER_SEC / USER_HZ)) == 0
625 # if HZ < USER_HZ
626 x = div_u64(x * USER_HZ, HZ);
627 # elif HZ > USER_HZ
628 x = div_u64(x, HZ / USER_HZ);
629 # else
630 /* Nothing to do */
631 # endif
632 #else
634 * There are better ways that don't overflow early,
635 * but even this doesn't overflow in hundreds of years
636 * in 64 bits, so..
638 x = div_u64(x * TICK_NSEC, (NSEC_PER_SEC / USER_HZ));
639 #endif
640 return x;
642 EXPORT_SYMBOL(jiffies_64_to_clock_t);
644 u64 nsec_to_clock_t(u64 x)
646 #if (NSEC_PER_SEC % USER_HZ) == 0
647 return div_u64(x, NSEC_PER_SEC / USER_HZ);
648 #elif (USER_HZ % 512) == 0
649 return div_u64(x * USER_HZ / 512, NSEC_PER_SEC / 512);
650 #else
652 * max relative error 5.7e-8 (1.8s per year) for USER_HZ <= 1024,
653 * overflow after 64.99 years.
654 * exact for HZ=60, 72, 90, 120, 144, 180, 300, 600, 900, ...
656 return div_u64(x * 9, (9ull * NSEC_PER_SEC + (USER_HZ / 2)) / USER_HZ);
657 #endif
661 * nsecs_to_jiffies64 - Convert nsecs in u64 to jiffies64
663 * @n: nsecs in u64
665 * Unlike {m,u}secs_to_jiffies, type of input is not unsigned int but u64.
666 * And this doesn't return MAX_JIFFY_OFFSET since this function is designed
667 * for scheduler, not for use in device drivers to calculate timeout value.
669 * note:
670 * NSEC_PER_SEC = 10^9 = (5^9 * 2^9) = (1953125 * 512)
671 * ULLONG_MAX ns = 18446744073.709551615 secs = about 584 years
673 u64 nsecs_to_jiffies64(u64 n)
675 #if (NSEC_PER_SEC % HZ) == 0
676 /* Common case, HZ = 100, 128, 200, 250, 256, 500, 512, 1000 etc. */
677 return div_u64(n, NSEC_PER_SEC / HZ);
678 #elif (HZ % 512) == 0
679 /* overflow after 292 years if HZ = 1024 */
680 return div_u64(n * HZ / 512, NSEC_PER_SEC / 512);
681 #else
683 * Generic case - optimized for cases where HZ is a multiple of 3.
684 * overflow after 64.99 years, exact for HZ = 60, 72, 90, 120 etc.
686 return div_u64(n * 9, (9ull * NSEC_PER_SEC + HZ / 2) / HZ);
687 #endif
691 * nsecs_to_jiffies - Convert nsecs in u64 to jiffies
693 * @n: nsecs in u64
695 * Unlike {m,u}secs_to_jiffies, type of input is not unsigned int but u64.
696 * And this doesn't return MAX_JIFFY_OFFSET since this function is designed
697 * for scheduler, not for use in device drivers to calculate timeout value.
699 * note:
700 * NSEC_PER_SEC = 10^9 = (5^9 * 2^9) = (1953125 * 512)
701 * ULLONG_MAX ns = 18446744073.709551615 secs = about 584 years
703 unsigned long nsecs_to_jiffies(u64 n)
705 return (unsigned long)nsecs_to_jiffies64(n);
709 * Add two timespec values and do a safety check for overflow.
710 * It's assumed that both values are valid (>= 0)
712 struct timespec timespec_add_safe(const struct timespec lhs,
713 const struct timespec rhs)
715 struct timespec res;
717 set_normalized_timespec(&res, lhs.tv_sec + rhs.tv_sec,
718 lhs.tv_nsec + rhs.tv_nsec);
720 if (res.tv_sec < lhs.tv_sec || res.tv_sec < rhs.tv_sec)
721 res.tv_sec = TIME_T_MAX;
723 return res;