/* $NetBSD: subr_time_arith.c,v 1.3 2025/04/01 23:14:23 riastradh Exp $ */
/*-
* Copyright (c) 2000, 2004, 2005, 2007, 2008, 2009, 2020
* The NetBSD Foundation, Inc.
* All rights reserved.
*
* This code is derived from software contributed to The NetBSD Foundation
* by Christopher G. Demetriou, by Andrew Doran, and by Jason R. Thorpe.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Copyright (c) 1982, 1986, 1989, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* @(#)kern_clock.c 8.5 (Berkeley) 1/21/94
* @(#)kern_time.c 8.4 (Berkeley) 5/26/95
*/
#include <sys/cdefs.h>
__KERNEL_RCSID(0, "$NetBSD: subr_time_arith.c,v 1.3 2025/04/01 23:14:23 riastradh Exp $");
#include <sys/types.h>
#include <sys/errno.h>
#include <sys/time.h>
#include <sys/timearith.h>
#if defined(_KERNEL)
#include <sys/kernel.h>
#include <sys/systm.h>
#include <machine/limits.h>
#elif defined(_TIME_TESTING)
#include <assert.h>
#include <limits.h>
#include <stdbool.h>
extern int hz;
extern int tick;
#define KASSERT assert
#define MIN(X, Y) ((X) < (Y) ? (X) : (Y))
#endif
/*
* Compute number of ticks in the specified amount of time.
*/
int
tvtohz(const struct timeval *tv)
{
unsigned long ticks;
long sec, usec;
/*
* If the number of usecs in the whole seconds part of the time
* difference fits in a long, then the total number of usecs will
* fit in an unsigned long. Compute the total and convert it to
* ticks, rounding up and adding 1 to allow for the current tick
* to expire. Rounding also depends on unsigned long arithmetic
* to avoid overflow.
*
* Otherwise, if the number of ticks in the whole seconds part of
* the time difference fits in a long, then convert the parts to
* ticks separately and add, using similar rounding methods and
* overflow avoidance. This method would work in the previous
* case, but it is slightly slower and assumes that hz is integral.
*
* Otherwise, round the time difference down to the maximum
* representable value.
*
* If ints are 32-bit, then the maximum value for any timeout in
* 10ms ticks is 248 days.
*/
sec = tv->tv_sec;
usec = tv->tv_usec;
KASSERT(usec >= 0);
KASSERT(usec < 1000000);
/* catch overflows in conversion time_t->int */
if (tv->tv_sec > INT_MAX)
return INT_MAX;
if (tv->tv_sec < 0)
return 0;
if (sec < 0 || (sec == 0 && usec == 0)) {
/*
* Would expire now or in the past. Return 0 ticks.
* This is different from the legacy tvhzto() interface,
* and callers need to check for it.
*/
ticks = 0;
} else if (sec <= (LONG_MAX / 1000000))
ticks = (((sec * 1000000) + (unsigned long)usec + (tick - 1))
/ tick) + 1;
else if (sec <= (LONG_MAX / hz))
ticks = (sec * hz) +
(((unsigned long)usec + (tick - 1)) / tick) + 1;
else
ticks = LONG_MAX;
if (ticks > INT_MAX)
ticks = INT_MAX;
return ((int)ticks);
}
/*
* Check that a proposed value to load into the .it_value or
* .it_interval part of an interval timer is acceptable, and
* fix it to have at least minimal value (i.e. if it is less
* than the resolution of the clock, round it up.). We don't
* timeout the 0,0 value because this means to disable the
* timer or the interval.
*/
int
itimerfix(struct timeval *tv)
{
if (tv->tv_usec < 0 || tv->tv_usec >= 1000000)
return EINVAL;
if (tv->tv_sec < 0)
return ETIMEDOUT;
if (tv->tv_sec == 0 && tv->tv_usec != 0 && tv->tv_usec < tick)
tv->tv_usec = tick;
return 0;
}
int
itimespecfix(struct timespec *ts)
{
if (ts->tv_nsec < 0 || ts->tv_nsec >= 1000000000)
return EINVAL;
if (ts->tv_sec < 0)
return ETIMEDOUT;
if (ts->tv_sec == 0 && ts->tv_nsec != 0 && ts->tv_nsec < tick * 1000)
ts->tv_nsec = tick * 1000;
return 0;
}
/*
* timespecaddok(tsp, usp)
*
* True if tsp + usp can be computed without overflow, i.e., if it
* is OK to do timespecadd(tsp, usp, ...).
*/
bool
timespecaddok(const struct timespec *tsp, const struct timespec *usp)
{
enum { TIME_MIN = __type_min(time_t), TIME_MAX = __type_max(time_t) };
time_t a = tsp->tv_sec;
time_t b = usp->tv_sec;
bool carry;
/*
* Caller is responsible for guaranteeing valid timespec
* inputs. Any user-controlled inputs must be validated or
* adjusted.
*/
KASSERT(tsp->tv_nsec >= 0);
KASSERT(usp->tv_nsec >= 0);
KASSERT(tsp->tv_nsec < 1000000000L);
KASSERT(usp->tv_nsec < 1000000000L);
__CTASSERT(1000000000L <= __type_max(long) - 1000000000L);
/*
* Fail if a + b + carry overflows TIME_MAX, or if a + b
* overflows TIME_MIN because timespecadd adds the carry after
* computing a + b.
*
* Break it into two mutually exclusive and exhaustive cases:
* I. a >= 0
* II. a < 0
*/
carry = (tsp->tv_nsec + usp->tv_nsec >= 1000000000L);
if (a >= 0) {
/*
* Case I: a >= 0. If b < 0, then b + 1 <= 0, so
*
* a + b + 1 <= a + 0 <= TIME_MAX,
*
* and
*
* a + b >= 0 + b = b >= TIME_MIN,
*
* so this can't overflow.
*
* If b >= 0, then a + b + carry >= a + b >= 0, so
* negative results and thus results below TIME_MIN are
* impossible; we need only avoid
*
* a + b + carry > TIME_MAX,
*
* which we will do by rejecting if
*
* b > TIME_MAX - a - carry,
*
* which in turn is incidentally always false if b < 0
* so we don't need extra logic to discriminate on the
* b >= 0 and b < 0 cases.
*
* Since 0 <= a <= TIME_MAX, we know
*
* 0 <= TIME_MAX - a <= TIME_MAX,
*
* and hence
*
* -1 <= TIME_MAX - a - 1 < TIME_MAX.
*
* So we can compute TIME_MAX - a - carry (i.e., either
* TIME_MAX - a or TIME_MAX - a - 1) safely without
* overflow.
*/
if (b > TIME_MAX - a - carry)
return false;
} else {
/*
* Case II: a < 0. If b >= 0, then since a + 1 <= 0,
* we have
*
* a + b + 1 <= b <= TIME_MAX,
*
* and
*
* a + b >= a >= TIME_MIN,
*
* so this can't overflow.
*
* If b < 0, then the intermediate a + b is negative
* and the outcome a + b + 1 is nonpositive, so we need
* only avoid
*
* a + b < TIME_MIN,
*
* which we will do by rejecting if
*
* a < TIME_MIN - b.
*
* (Reminder: The carry is added afterward in
* timespecadd, so to avoid overflow it is not enough
* to merely reject a + b + carry < TIME_MIN.)
*
* It is safe to compute the difference TIME_MIN - b
* because b is negative, so the result lies in
* (TIME_MIN, 0].
*/
if (b < 0 && a < TIME_MIN - b)
return false;
}
return true;
}
/*
* timespecsubok(tsp, usp)
*
* True if tsp - usp can be computed without overflow, i.e., if it
* is OK to do timespecsub(tsp, usp, ...).
*/
bool
timespecsubok(const struct timespec *tsp, const struct timespec *usp)
{
enum { TIME_MIN = __type_min(time_t), TIME_MAX = __type_max(time_t) };
time_t a = tsp->tv_sec, b = usp->tv_sec;
bool borrow;
/*
* Caller is responsible for guaranteeing valid timespec
* inputs. Any user-controlled inputs must be validated or
* adjusted.
*/
KASSERT(tsp->tv_nsec >= 0);
KASSERT(usp->tv_nsec >= 0);
KASSERT(tsp->tv_nsec < 1000000000L);
KASSERT(usp->tv_nsec < 1000000000L);
__CTASSERT(1000000000L <= __type_max(long) - 1000000000L);
/*
* Fail if a - b - borrow overflows TIME_MIN, or if a - b
* overflows TIME_MAX because timespecsub subtracts the borrow
* after computing a - b.
*
* Break it into two mutually exclusive and exhaustive cases:
* I. a < 0
* II. a >= 0
*/
borrow = (tsp->tv_nsec - usp->tv_nsec < 0);
if (a < 0) {
/*
* Case I: a < 0. If b < 0, then -b - 1 >= 0, so
*
* a - b - 1 >= a + 0 >= TIME_MIN,
*
* and, since a <= -1, provided that TIME_MIN <=
* -TIME_MAX - 1 so that TIME_MAX <= -TIME_MIN - 1 (in
* fact, equality holds, under the assumption of
* two's-complement arithmetic),
*
* a - b <= -1 - b = -b - 1 <= TIME_MAX,
*
* so this can't overflow.
*/
__CTASSERT(TIME_MIN <= -TIME_MAX - 1);
/*
* If b >= 0, then a - b - borrow <= a - b < 0, so
* positive results and thus results above TIME_MAX are
* impossible; we need only avoid
*
* a - b - borrow < TIME_MIN,
*
* which we will do by rejecting if
*
* a < TIME_MIN + b + borrow.
*
* The right-hand side is safe to evaluate for any
* values of b and borrow as long as TIME_MIN +
* TIME_MAX + 1 <= TIME_MAX, i.e., TIME_MIN <= -1.
* (Note: If time_t were unsigned, this would fail!)
*
* Note: Unlike Case I in timespecaddok, this criterion
* does not work for b < 0, nor can the roles of a and
* b in the inequality be reversed (e.g., -b < TIME_MIN
* - a + borrow) without extra cases like checking for
* b = TEST_MIN.
*/
__CTASSERT(TIME_MIN < -1);
if (b >= 0 && a < TIME_MIN + b + borrow)
return false;
} else {
/*
* Case II: a >= 0. If b >= 0, then
*
* a - b <= a <= TIME_MAX,
*
* and, provided TIME_MIN <= -TIME_MAX - 1 (in fact,
* equality holds, under the assumption of
* two's-complement arithmetic)
*
* a - b - 1 >= -b - 1 >= -TIME_MAX - 1 >= TIME_MIN,
*
* so this can't overflow.
*/
__CTASSERT(TIME_MIN <= -TIME_MAX - 1);
/*
* If b < 0, then a - b >= a >= 0, so negative results
* and thus results below TIME_MIN are impossible; we
* need only avoid
*
* a - b > TIME_MAX,
*
* which we will do by rejecting if
*
* a > TIME_MAX + b.
*
* (Reminder: The borrow is subtracted afterward in
* timespecsub, so to avoid overflow it is not enough
* to merely reject a - b - borrow > TIME_MAX.)
*
* It is safe to compute the sum TIME_MAX + b because b
* is negative, so the result lies in [0, TIME_MAX).
*/
if (b < 0 && a > TIME_MAX + b)
return false;
}
return true;
}
static bool
timespec2nsok(const struct timespec *ts)
{
return ts->tv_sec < INT64_MAX/1000000000 ||
(ts->tv_sec == INT64_MAX/1000000000 &&
ts->tv_nsec <= INT64_MAX - (INT64_MAX/1000000000)*1000000000);
}
/*
* itimer_transition(it, now, next, &overruns)
*
* Given:
*
* - it: the current state of an itimer (it_value = last expiry
* time, it_interval = periodic rescheduling interval), and
*
* - now: the current time on the itimer's clock;
*
* compute:
*
* - next: the next time the itimer should be scheduled for, and
* - overruns: the number of overruns if we're firing late.
*
* XXX This should maybe also say whether the itimer should expire
* at all.
*/
void
itimer_transition(const struct itimerspec *restrict it,
const struct timespec *restrict now,
struct timespec *restrict next,
int *restrict overrunsp)
{
int64_t last_val, next_val, interval, remainder, now_ns;
int backwards;
/*
* Zero the outputs so we can test assertions in userland
* without undefined behaviour.
*/
timespecclear(next);
*overrunsp = 0;
/*
* Paranoia: Caller should guarantee this.
*/
if (!timespecisset(&it->it_interval)) {
timespecclear(next);
return;
}
/* Did the clock wind backwards? */
backwards = (timespeccmp(&it->it_value, now, >));
/* Valid value and interval guaranteed by itimerfix. */
KASSERT(it->it_value.tv_sec >= 0);
KASSERT(it->it_value.tv_nsec < 1000000000);
KASSERT(it->it_interval.tv_sec >= 0);
KASSERT(it->it_interval.tv_nsec < 1000000000);
/* Nonnegative interval guaranteed by itimerfix. */
KASSERT(it->it_interval.tv_sec >= 0);
KASSERT(it->it_interval.tv_nsec >= 0);
/* Handle the easy case of non-overflown timers first. */
if (__predict_true(!backwards)) {
if (__predict_false(!timespecaddok(&it->it_value,
&it->it_interval)))
goto overflow;
timespecadd(&it->it_value, &it->it_interval, next);
if (__predict_true(timespeccmp(now, next, <)))
return;
}
/*
* If we can't represent the input as a number of nanoseconds,
* bail. This is good up to the year 2262, if we start
* counting from 1970 (2^63 nanoseconds ~ 292 years).
*/
if (__predict_false(!timespec2nsok(now)) ||
__predict_false(!timespec2nsok(&it->it_value)) ||
__predict_false(!timespec2nsok(&it->it_interval)))
goto overflow;
now_ns = timespec2ns(now);
last_val = timespec2ns(&it->it_value);
interval = timespec2ns(&it->it_interval);
KASSERT(now_ns >= 0);
KASSERT(last_val >= 0);
KASSERT(interval >= 0);
/*
* now [backwards] overruns now [forwards]
* | v v v |
* |--+----+-*--x----+----+----|----+----+----+--*-x----+-->
* \/ | \/
* remainder last_val remainder
* (zero or negative) (zero or positive)
*
* Set next_val to last_value + k*interval for some k.
*
* The interval is always positive, and division in C
* truncates, so dividing a positive duration by the interval
* always gives zero or a positive remainder, and dividing a
* negative duration by the interval always gives zero or a
* negative remainder. Hence:
*
* - If now_ns < last_val -- which happens iff backwards, i.e.,
* the clock was wound backwards -- then remainder is zero or
* negative, so subtracting it stays in place or moves
* forward in time, and thus this finds the _earliest_ value
* that is not earlier than now_ns. We will advance this by
* one more interval if we are already firing exactly on the
* interval to find the earliest value _after_ now_ns.
*
* - If now_ns > last_val -- which happens iff !backwards,
* i.e., the clock ran fast -- then remainder is zero or
* positive positive, so this finds the _latest_ value not
* later than now_ns. We will always advance this by one
* more interval to find the earliest value _after_ now_ns.
* We will also count overflows.
*
* (now_ns == last_val is not possible at this point because it
* only happens if the addition of struct timespec would
* overflow, and that is only possible when timespec2ns would
* also overflow for at least one of the inputs.)
*/
KASSERT(last_val != now_ns);
remainder = (now_ns - last_val) % interval;
next_val = now_ns - remainder;
KASSERT((last_val - next_val) % interval == 0);
if (backwards) {
/*
* If the clock was wound back to an exact multiple of
* the interval, so next_val = now_ns, don't demand to
* fire again in the same instant -- advance to the
* next interval. Overflow is not possible; proof is
* asserted.
*/
if (remainder == 0) {
KASSERT(now_ns < last_val);
KASSERT(next_val == now_ns);
KASSERT(last_val - next_val >= interval);
KASSERT(interval <= last_val - next_val);
KASSERT(next_val <= last_val - interval);
KASSERT(next_val <= INT64_MAX - interval);
next_val += interval;
}
} else {
/*
* next_val is the largest integer multiple of interval
* not later than now_ns. Count the number of full
* intervals that were skipped (division should be
* exact here), not counting any partial interval
* between next_val and now_ns, as the number of
* overruns. Advance by one interval -- unless that
* would overflow.
*/
*overrunsp += MIN(INT_MAX - *overrunsp,
(next_val - last_val) / interval);
if (__predict_false(next_val > INT64_MAX - interval))
goto overflow;
next_val += interval;
}
next->tv_sec = next_val / 1000000000;
next->tv_nsec = next_val % 1000000000;
return;
overflow:
next->tv_sec = 0;
next->tv_nsec = 0;
}
