/*
* ntp_calendar.c - calendar and helper functions
*
* Written by Juergen Perlinger (perlinger@ntp.org) for the NTP project.
* The contents of 'html/copyright.html' apply.
*
* --------------------------------------------------------------------
* Some notes on the implementation:
*
* Calendar algorithms thrive on the division operation, which is one of
* the slowest numerical operations in any CPU. What saves us here from
* abysmal performance is the fact that all divisions are divisions by
* constant numbers, and most compilers can do this by a multiplication
* operation. But this might not work when using the div/ldiv/lldiv
* function family, because many compilers are not able to do inline
* expansion of the code with following optimisation for the
* constant-divider case.
*
* Also div/ldiv/lldiv are defined in terms of int/long/longlong, which
* are inherently target dependent. Nothing that could not be cured with
* autoconf, but still a mess...
*
* Furthermore, we need floor division in many places. C either leaves
* the division behaviour undefined (< C99) or demands truncation to
* zero (>= C99), so additional steps are required to make sure the
* algorithms work. The {l,ll}div function family is requested to
* truncate towards zero, which is also the wrong direction for our
* purpose.
*
* For all this, all divisions by constant are coded manually, even when
* there is a joined div/mod operation: The optimiser should sort that
* out, if possible. Most of the calculations are done with unsigned
* types, explicitely using two's complement arithmetics where
* necessary. This minimises the dependecies to compiler and target,
* while still giving reasonable to good performance.
*
* The implementation uses a few tricks that exploit properties of the
* two's complement: Floor division on negative dividents can be
* executed by using the one's complement of the divident. One's
* complement can be easily created using XOR and a mask.
*
* Finally, check for overflow conditions is minimal. There are only two
* calculation steps in the whole calendar that potentially suffer from
* an internal overflow, and these are coded in a way that avoids
* it. All other functions do not suffer from internal overflow and
* simply return the result truncated to 32 bits.
*/
#include <config.h>
#include <sys/types.h>
#include "ntp_types.h"
#include "ntp_calendar.h"
#include "ntp_stdlib.h"
#include "ntp_fp.h"
#include "ntp_unixtime.h"
#include "ntpd.h"
#include "lib_strbuf.h"
/* For now, let's take the conservative approach: if the target property
* macros are not defined, check a few well-known compiler/architecture
* settings. Default is to assume that the representation of signed
* integers is unknown and shift-arithmetic-right is not available.
*/
#ifndef TARGET_HAS_2CPL
# if defined(__GNUC__)
# if defined(__i386__) || defined(__x86_64__) || defined(__arm__)
# define TARGET_HAS_2CPL 1
# else
# define TARGET_HAS_2CPL 0
# endif
# elif defined(_MSC_VER)
# if defined(_M_IX86) || defined(_M_X64) || defined(_M_ARM)
# define TARGET_HAS_2CPL 1
# else
# define TARGET_HAS_2CPL 0
# endif
# else
# define TARGET_HAS_2CPL 0
# endif
#endif
#ifndef TARGET_HAS_SAR
# define TARGET_HAS_SAR 0
#endif
#if !defined(HAVE_64BITREGS) && defined(UINT64_MAX) && (SIZE_MAX >= UINT64_MAX)
# define HAVE_64BITREGS
#endif
/*
*---------------------------------------------------------------------
* replacing the 'time()' function
*---------------------------------------------------------------------
*/
static systime_func_ptr systime_func = &time;
static inline time_t now(void);
systime_func_ptr
ntpcal_set_timefunc(
systime_func_ptr nfunc
)
{
systime_func_ptr res;
res = systime_func;
if (NULL == nfunc)
nfunc = &time;
systime_func = nfunc;
return res;
}
static inline time_t
now(void)
{
return (*systime_func)(NULL);
}
/*
*---------------------------------------------------------------------
* Get sign extension mask and unsigned 2cpl rep for a signed integer
*---------------------------------------------------------------------
*/
static inline uint32_t
int32_sflag(
const int32_t v)
{
# if TARGET_HAS_2CPL && TARGET_HAS_SAR && SIZEOF_INT >= 4
/* Let's assume that shift is the fastest way to get the sign
* extension of of a signed integer. This might not always be
* true, though -- On 8bit CPUs or machines without barrel
* shifter this will kill the performance. So we make sure
* we do this only if 'int' has at least 4 bytes.
*/
return (uint32_t)(v >> 31);
# else
/* This should be a rather generic approach for getting a sign
* extension mask...
*/
return UINT32_C(0) - (uint32_t)(v < 0);
# endif
}
static inline int32_t
uint32_2cpl_to_int32(
const uint32_t vu)
{
int32_t v;
# if TARGET_HAS_2CPL
/* Just copy through the 32 bits from the unsigned value if
* we're on a two's complement target.
*/
v = (int32_t)vu;
# else
/* Convert to signed integer, making sure signed integer
* overflow cannot happen. Again, the optimiser might or might
* not find out that this is just a copy of 32 bits on a target
* with two's complement representation for signed integers.
*/
if (vu > INT32_MAX)
v = -(int32_t)(~vu) - 1;
else
v = (int32_t)vu;
# endif
return v;
}
/*
*---------------------------------------------------------------------
* Convert between 'time_t' and 'vint64'
*---------------------------------------------------------------------
*/
vint64
time_to_vint64(
const time_t * ptt
)
{
vint64 res;
time_t tt;
tt = *ptt;
# if SIZEOF_TIME_T <= 4
res.D_s.hi = 0;
if (tt < 0) {
res.D_s.lo = (uint32_t)-tt;
M_NEG(res.D_s.hi, res.D_s.lo);
} else {
res.D_s.lo = (uint32_t)tt;
}
# elif defined(HAVE_INT64)
res.q_s = tt;
# else
/*
* shifting negative signed quantities is compiler-dependent, so
* we better avoid it and do it all manually. And shifting more
* than the width of a quantity is undefined. Also a don't do!
*/
if (tt < 0) {
tt = -tt;
res.D_s.lo = (uint32_t)tt;
res.D_s.hi = (uint32_t)(tt >> 32);
M_NEG(res.D_s.hi, res.D_s.lo);
} else {
res.D_s.lo = (uint32_t)tt;
res.D_s.hi = (uint32_t)(tt >> 32);
}
# endif
return res;
}
time_t
vint64_to_time(
const vint64 *tv
)
{
time_t res;
# if SIZEOF_TIME_T <= 4
res = (time_t)tv->D_s.lo;
# elif defined(HAVE_INT64)
res = (time_t)tv->q_s;
# else
res = ((time_t)tv->d_s.hi << 32) | tv->D_s.lo;
# endif
return res;
}
/*
*---------------------------------------------------------------------
* Get the build date & time
*---------------------------------------------------------------------
*/
int
ntpcal_get_build_date(
struct calendar * jd
)
{
/* The C standard tells us the format of '__DATE__':
*
* __DATE__ The date of translation of the preprocessing
* translation unit: a character string literal of the form "Mmm
* dd yyyy", where the names of the months are the same as those
* generated by the asctime function, and the first character of
* dd is a space character if the value is less than 10. If the
* date of translation is not available, an
* implementation-defined valid date shall be supplied.
*
* __TIME__ The time of translation of the preprocessing
* translation unit: a character string literal of the form
* "hh:mm:ss" as in the time generated by the asctime
* function. If the time of translation is not available, an
* implementation-defined valid time shall be supplied.
*
* Note that MSVC declares DATE and TIME to be in the local time
* zone, while neither the C standard nor the GCC docs make any
* statement about this. As a result, we may be +/-12hrs off
* UTC. But for practical purposes, this should not be a
* problem.
*
*/
# ifdef MKREPRO_DATE
static const char build[] = MKREPRO_TIME "/" MKREPRO_DATE;
# else
static const char build[] = __TIME__ "/" __DATE__;
# endif
static const char mlist[] = "JanFebMarAprMayJunJulAugSepOctNovDec";
char monstr[4];
const char * cp;
unsigned short hour, minute, second, day, year;
/* Note: The above quantities are used for sscanf 'hu' format,
* so using 'uint16_t' is contra-indicated!
*/
# ifdef DEBUG
static int ignore = 0;
# endif
ZERO(*jd);
jd->year = 1970;
jd->month = 1;
jd->monthday = 1;
# ifdef DEBUG
/* check environment if build date should be ignored */
if (0 == ignore) {
const char * envstr;
envstr = getenv("NTPD_IGNORE_BUILD_DATE");
ignore = 1 + (envstr && (!*envstr || !strcasecmp(envstr, "yes")));
}
if (ignore > 1)
return FALSE;
# endif
if (6 == sscanf(build, "%hu:%hu:%hu/%3s %hu %hu",
&hour, &minute, &second, monstr, &day, &year)) {
cp = strstr(mlist, monstr);
if (NULL != cp) {
jd->year = year;
jd->month = (uint8_t)((cp - mlist) / 3 + 1);
jd->monthday = (uint8_t)day;
jd->hour = (uint8_t)hour;
jd->minute = (uint8_t)minute;
jd->second = (uint8_t)second;
return TRUE;
}
}
return FALSE;
}
/*
*---------------------------------------------------------------------
* basic calendar stuff
*---------------------------------------------------------------------
*/
/*
* Some notes on the terminology:
*
* We use the proleptic Gregorian calendar, which is the Gregorian
* calendar extended in both directions ad infinitum. This totally
* disregards the fact that this calendar was invented in 1582, and
* was adopted at various dates over the world; sometimes even after
* the start of the NTP epoch.
*
* Normally date parts are given as current cycles, while time parts
* are given as elapsed cycles:
*
* 1970-01-01/03:04:05 means 'IN the 1970st. year, IN the first month,
* ON the first day, with 3hrs, 4minutes and 5 seconds elapsed.
*
* The basic calculations for this calendar implementation deal with
* ELAPSED date units, which is the number of full years, full months
* and full days before a date: 1970-01-01 would be (1969, 0, 0) in
* that notation.
*
* To ease the numeric computations, month and day values outside the
* normal range are acceptable: 2001-03-00 will be treated as the day
* before 2001-03-01, 2000-13-32 will give the same result as
* 2001-02-01 and so on.
*
* 'rd' or 'RD' is used as an abbreviation for the latin 'rata die'
* (day number). This is the number of days elapsed since 0000-12-31
* in the proleptic Gregorian calendar. The begin of the Christian Era
* (0001-01-01) is RD(1).
*/
/*
* ====================================================================
*
* General algorithmic stuff
*
* ====================================================================
*/
/*
*---------------------------------------------------------------------
* fast modulo 7 operations (floor/mathematical convention)
*---------------------------------------------------------------------
*/
int
u32mod7(
uint32_t x
)
{
/* This is a combination of tricks from "Hacker's Delight" with
* some modifications, like a multiplication that rounds up to
* drop the final adjustment stage.
*
* Do a partial reduction by digit sum to keep the value in the
* range permitted for the mul/shift stage. There are several
* possible and absolutely equivalent shift/mask combinations;
* this one is ARM-friendly because of a mask that fits into 16
* bit.
*/
x = (x >> 15) + (x & UINT32_C(0x7FFF));
/* Take reminder as (mod 8) by mul/shift. Since the multiplier
* was calculated using ceil() instead of floor(), it skips the
* value '7' properly.
* M <- ceil(ldexp(8/7, 29))
*/
return (int)((x * UINT32_C(0x24924925)) >> 29);
}
int
i32mod7(
int32_t x
)
{
/* We add (2**32 - 2**32 % 7), which is (2**32 - 4), to negative
* numbers to map them into the postive range. Only the term '-4'
* survives, obviously.
*/
uint32_t ux = (uint32_t)x;
return u32mod7((x < 0) ? (ux - 4u) : ux);
}
uint32_t
i32fmod(
int32_t x,
uint32_t d
)
{
uint32_t ux = (uint32_t)x;
uint32_t sf = UINT32_C(0) - (x < 0);
ux = (sf ^ ux ) % d;
return (d & sf) + (sf ^ ux);
}
/*
*---------------------------------------------------------------------
* Do a periodic extension of 'value' around 'pivot' with a period of
* 'cycle'.
*
* The result 'res' is a number that holds to the following properties:
*
* 1) res MOD cycle == value MOD cycle
* 2) pivot <= res < pivot + cycle
* (replace </<= with >/>= for negative cycles)
*
* where 'MOD' denotes the modulo operator for FLOOR DIVISION, which
* is not the same as the '%' operator in C: C requires division to be
* a truncated division, where remainder and dividend have the same
* sign if the remainder is not zero, whereas floor division requires
* divider and modulus to have the same sign for a non-zero modulus.
*
* This function has some useful applications:
*
* + let Y be a calendar year and V a truncated 2-digit year: then
* periodic_extend(Y-50, V, 100)
* is the closest expansion of the truncated year with respect to
* the full year, that is a 4-digit year with a difference of less
* than 50 years to the year Y. ("century unfolding")
*
* + let T be a UN*X time stamp and V be seconds-of-day: then
* perodic_extend(T-43200, V, 86400)
* is a time stamp that has the same seconds-of-day as the input
* value, with an absolute difference to T of <= 12hrs. ("day
* unfolding")
*
* + Wherever you have a truncated periodic value and a non-truncated
* base value and you want to match them somehow...
*
* Basically, the function delivers 'pivot + (value - pivot) % cycle',
* but the implementation takes some pains to avoid internal signed
* integer overflows in the '(value - pivot) % cycle' part and adheres
* to the floor division convention.
*
* If 64bit scalars where available on all intended platforms, writing a
* version that uses 64 bit ops would be easy; writing a general
* division routine for 64bit ops on a platform that can only do
* 32/16bit divisions and is still performant is a bit more
* difficult. Since most usecases can be coded in a way that does only
* require the 32bit version a 64bit version is NOT provided here.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_periodic_extend(
int32_t pivot,
int32_t value,
int32_t cycle
)
{
/* Implement a 4-quadrant modulus calculation by 2 2-quadrant
* branches, one for positive and one for negative dividers.
* Everything else can be handled by bit level logic and
* conditional one's complement arithmetic. By convention, we
* assume
*
* x % b == 0 if |b| < 2
*
* that is, we don't actually divide for cycles of -1,0,1 and
* return the pivot value in that case.
*/
uint32_t uv = (uint32_t)value;
uint32_t up = (uint32_t)pivot;
uint32_t uc, sf;
if (cycle > 1)
{
uc = (uint32_t)cycle;
sf = UINT32_C(0) - (value < pivot);
uv = sf ^ (uv - up);
uv %= uc;
pivot += (uc & sf) + (sf ^ uv);
}
else if (cycle < -1)
{
uc = ~(uint32_t)cycle + 1;
sf = UINT32_C(0) - (value > pivot);
uv = sf ^ (up - uv);
uv %= uc;
pivot -= (uc & sf) + (sf ^ uv);
}
return pivot;
}
/*---------------------------------------------------------------------
* Note to the casual reader
*
* In the next two functions you will find (or would have found...)
* the expression
*
* res.Q_s -= 0x80000000;
*
* There was some ruckus about a possible programming error due to
* integer overflow and sign propagation.
*
* This assumption is based on a lack of understanding of the C
* standard. (Though this is admittedly not one of the most 'natural'
* aspects of the 'C' language and easily to get wrong.)
*
* see
* http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf
* "ISO/IEC 9899:201x Committee Draft — April 12, 2011"
* 6.4.4.1 Integer constants, clause 5
*
* why there is no sign extension/overflow problem here.
*
* But to ease the minds of the doubtful, I added back the 'u' qualifiers
* that somehow got lost over the last years.
*/
/*
*---------------------------------------------------------------------
* Convert a timestamp in NTP scale to a 64bit seconds value in the UN*X
* scale with proper epoch unfolding around a given pivot or the current
* system time. This function happily accepts negative pivot values as
* timestamps before 1970-01-01, so be aware of possible trouble on
* platforms with 32bit 'time_t'!
*
* This is also a periodic extension, but since the cycle is 2^32 and
* the shift is 2^31, we can do some *very* fast math without explicit
* divisions.
*---------------------------------------------------------------------
*/
vint64
ntpcal_ntp_to_time(
uint32_t ntp,
const time_t * pivot
)
{
vint64 res;
# if defined(HAVE_INT64)
res.q_s = (pivot != NULL)
? *pivot
: now();
res.Q_s -= 0x80000000u; /* unshift of half range */
ntp -= (uint32_t)JAN_1970; /* warp into UN*X domain */
ntp -= res.D_s.lo; /* cycle difference */
res.Q_s += (uint64_t)ntp; /* get expanded time */
# else /* no 64bit scalars */
time_t tmp;
tmp = (pivot != NULL)
? *pivot
: now();
res = time_to_vint64(&tmp);
M_SUB(res.D_s.hi, res.D_s.lo, 0, 0x80000000u);
ntp -= (uint32_t)JAN_1970; /* warp into UN*X domain */
ntp -= res.D_s.lo; /* cycle difference */
M_ADD(res.D_s.hi, res.D_s.lo, 0, ntp);
# endif /* no 64bit scalars */
return res;
}
/*
*---------------------------------------------------------------------
* Convert a timestamp in NTP scale to a 64bit seconds value in the NTP
* scale with proper epoch unfolding around a given pivot or the current
* system time.
*
* Note: The pivot must be given in the UN*X time domain!
*
* This is also a periodic extension, but since the cycle is 2^32 and
* the shift is 2^31, we can do some *very* fast math without explicit
* divisions.
*---------------------------------------------------------------------
*/
vint64
ntpcal_ntp_to_ntp(
uint32_t ntp,
const time_t *pivot
)
{
vint64 res;
# if defined(HAVE_INT64)
res.q_s = (pivot)
? *pivot
: now();
res.Q_s -= 0x80000000u; /* unshift of half range */
res.Q_s += (uint32_t)JAN_1970; /* warp into NTP domain */
ntp -= res.D_s.lo; /* cycle difference */
res.Q_s += (uint64_t)ntp; /* get expanded time */
# else /* no 64bit scalars */
time_t tmp;
tmp = (pivot)
? *pivot
: now();
res = time_to_vint64(&tmp);
M_SUB(res.D_s.hi, res.D_s.lo, 0, 0x80000000u);
M_ADD(res.D_s.hi, res.D_s.lo, 0, (uint32_t)JAN_1970);/*into NTP */
ntp -= res.D_s.lo; /* cycle difference */
M_ADD(res.D_s.hi, res.D_s.lo, 0, ntp);
# endif /* no 64bit scalars */
return res;
}
/*
* ====================================================================
*
* Splitting values to composite entities
*
* ====================================================================
*/
/*
*---------------------------------------------------------------------
* Split a 64bit seconds value into elapsed days in 'res.hi' and
* elapsed seconds since midnight in 'res.lo' using explicit floor
* division. This function happily accepts negative time values as
* timestamps before the respective epoch start.
*---------------------------------------------------------------------
*/
ntpcal_split
ntpcal_daysplit(
const vint64 *ts
)
{
ntpcal_split res;
uint32_t Q, R;
# if defined(HAVE_64BITREGS)
/* Assume we have 64bit registers an can do a divison by
* constant reasonably fast using the one's complement trick..
*/
uint64_t sf64 = (uint64_t)-(ts->q_s < 0);
Q = (uint32_t)(sf64 ^ ((sf64 ^ ts->Q_s) / SECSPERDAY));
R = (uint32_t)(ts->Q_s - Q * SECSPERDAY);
# elif defined(UINT64_MAX) && !defined(__arm__)
/* We rely on the compiler to do efficient 64bit divisions as
* good as possible. Which might or might not be true. At least
* for ARM CPUs, the sum-by-digit code in the next section is
* faster for many compilers. (This might change over time, but
* the 64bit-by-32bit division will never outperform the exact
* division by a substantial factor....)
*/
if (ts->q_s < 0)
Q = ~(uint32_t)(~ts->Q_s / SECSPERDAY);
else
Q = (uint32_t)( ts->Q_s / SECSPERDAY);
R = ts->D_s.lo - Q * SECSPERDAY;
# else
/* We don't have 64bit regs. That hurts a bit.
*
* Here we use a mean trick to get away with just one explicit
* modulo operation and pure 32bit ops.
*
* Remember: 86400 <--> 128 * 675
*
* So we discard the lowest 7 bit and do an exact division by
* 675, modulo 2**32.
*
* First we shift out the lower 7 bits.
*
* Then we use a digit-wise pseudo-reduction, where a 'digit' is
* actually a 16-bit group. This is followed by a full reduction
* with a 'true' division step. This yields the modulus of the
* full 64bit value. The sign bit gets some extra treatment.
*
* Then we decrement the lower limb by that modulus, so it is
* exactly divisible by 675. [*]
*
* Then we multiply with the modular inverse of 675 (mod 2**32)
* and voila, we have the result.
*
* Special Thanks to Henry S. Warren and his "Hacker's delight"
* for giving that idea.
*
* (Note[*]: that's not the full truth. We would have to
* subtract the modulus from the full 64 bit number to get a
* number that is divisible by 675. But since we use the
* multiplicative inverse (mod 2**32) there's no reason to carry
* the subtraction into the upper bits!)
*/
uint32_t al = ts->D_s.lo;
uint32_t ah = ts->D_s.hi;
/* shift out the lower 7 bits, smash sign bit */
al = (al >> 7) | (ah << 25);
ah = (ah >> 7) & 0x00FFFFFFu;
R = (ts->d_s.hi < 0) ? 239 : 0;/* sign bit value */
R += (al & 0xFFFF);
R += (al >> 16 ) * 61u; /* 2**16 % 675 */
R += (ah & 0xFFFF) * 346u; /* 2**32 % 675 */
R += (ah >> 16 ) * 181u; /* 2**48 % 675 */
R %= 675u; /* final reduction */
Q = (al - R) * 0x2D21C10Bu; /* modinv(675, 2**32) */
R = (R << 7) | (ts->d_s.lo & 0x07F);
# endif
res.hi = uint32_2cpl_to_int32(Q);
res.lo = R;
return res;
}
/*
*---------------------------------------------------------------------
* Split a 64bit seconds value into elapsed weeks in 'res.hi' and
* elapsed seconds since week start in 'res.lo' using explicit floor
* division. This function happily accepts negative time values as
* timestamps before the respective epoch start.
*---------------------------------------------------------------------
*/
ntpcal_split
ntpcal_weeksplit(
const vint64 *ts
)
{
ntpcal_split res;
uint32_t Q, R;
/* This is a very close relative to the day split function; for
* details, see there!
*/
# if defined(HAVE_64BITREGS)
uint64_t sf64 = (uint64_t)-(ts->q_s < 0);
Q = (uint32_t)(sf64 ^ ((sf64 ^ ts->Q_s) / SECSPERWEEK));
R = (uint32_t)(ts->Q_s - Q * SECSPERWEEK);
# elif defined(UINT64_MAX) && !defined(__arm__)
if (ts->q_s < 0)
Q = ~(uint32_t)(~ts->Q_s / SECSPERWEEK);
else
Q = (uint32_t)( ts->Q_s / SECSPERWEEK);
R = ts->D_s.lo - Q * SECSPERWEEK;
# else
/* Remember: 7*86400 <--> 604800 <--> 128 * 4725 */
uint32_t al = ts->D_s.lo;
uint32_t ah = ts->D_s.hi;
al = (al >> 7) | (ah << 25);
ah = (ah >> 7) & 0x00FFFFFF;
R = (ts->d_s.hi < 0) ? 2264 : 0;/* sign bit value */
R += (al & 0xFFFF);
R += (al >> 16 ) * 4111u; /* 2**16 % 4725 */
R += (ah & 0xFFFF) * 3721u; /* 2**32 % 4725 */
R += (ah >> 16 ) * 2206u; /* 2**48 % 4725 */
R %= 4725u; /* final reduction */
Q = (al - R) * 0x98BBADDDu; /* modinv(4725, 2**32) */
R = (R << 7) | (ts->d_s.lo & 0x07F);
# endif
res.hi = uint32_2cpl_to_int32(Q);
res.lo = R;
return res;
}
/*
*---------------------------------------------------------------------
* Split a 32bit seconds value into h/m/s and excessive days. This
* function happily accepts negative time values as timestamps before
* midnight.
*---------------------------------------------------------------------
*/
static int32_t
priv_timesplit(
int32_t split[3],
int32_t ts
)
{
/* Do 3 chained floor divisions by positive constants, using the
* one's complement trick and factoring out the intermediate XOR
* ops to reduce the number of operations.
*/
uint32_t us, um, uh, ud, sf32;
sf32 = int32_sflag(ts);
us = (uint32_t)ts;
um = (sf32 ^ us) / SECSPERMIN;
uh = um / MINSPERHR;
ud = uh / HRSPERDAY;
um ^= sf32;
uh ^= sf32;
ud ^= sf32;
split[0] = (int32_t)(uh - ud * HRSPERDAY );
split[1] = (int32_t)(um - uh * MINSPERHR );
split[2] = (int32_t)(us - um * SECSPERMIN);
return uint32_2cpl_to_int32(ud);
}
/*
*---------------------------------------------------------------------
* Given the number of elapsed days in the calendar era, split this
* number into the number of elapsed years in 'res.hi' and the number
* of elapsed days of that year in 'res.lo'.
*
* if 'isleapyear' is not NULL, it will receive an integer that is 0 for
* regular years and a non-zero value for leap years.
*---------------------------------------------------------------------
*/
ntpcal_split
ntpcal_split_eradays(
int32_t days,
int *isleapyear
)
{
/* Use the fast cycle split algorithm here, to calculate the
* centuries and years in a century with one division each. This
* reduces the number of division operations to two, but is
* susceptible to internal range overflow. We take some extra
* steps to avoid the gap.
*/
ntpcal_split res;
int32_t n100, n001; /* calendar year cycles */
uint32_t uday, Q;
/* split off centuries first
*
* We want to execute '(days * 4 + 3) /% 146097' under floor
* division rules in the first step. Well, actually we want to
* calculate 'floor((days + 0.75) / 36524.25)', but we want to
* do it in scaled integer calculation.
*/
# if defined(HAVE_64BITREGS)
/* not too complicated with an intermediate 64bit value */
uint64_t ud64, sf64;
ud64 = ((uint64_t)days << 2) | 3u;
sf64 = (uint64_t)-(days < 0);
Q = (uint32_t)(sf64 ^ ((sf64 ^ ud64) / GREGORIAN_CYCLE_DAYS));
uday = (uint32_t)(ud64 - Q * GREGORIAN_CYCLE_DAYS);
n100 = uint32_2cpl_to_int32(Q);
# else
/* '4*days+3' suffers from range overflow when going to the
* limits. We solve this by doing an exact division (mod 2^32)
* after caclulating the remainder first.
*
* We start with a partial reduction by digit sums, extracting
* the upper bits from the original value before they get lost
* by scaling, and do one full division step to get the true
* remainder. Then a final multiplication with the
* multiplicative inverse of 146097 (mod 2^32) gives us the full
* quotient.
*
* (-2^33) % 146097 --> 130717 : the sign bit value
* ( 2^20) % 146097 --> 25897 : the upper digit value
* modinv(146097, 2^32) --> 660721233 : the inverse
*/
uint32_t ux = ((uint32_t)days << 2) | 3;
uday = (days < 0) ? 130717u : 0u; /* sign dgt */
uday += ((days >> 18) & 0x01FFFu) * 25897u; /* hi dgt (src!) */
uday += (ux & 0xFFFFFu); /* lo dgt */
uday %= GREGORIAN_CYCLE_DAYS; /* full reduction */
Q = (ux - uday) * 660721233u; /* exact div */
n100 = uint32_2cpl_to_int32(Q);
# endif
/* Split off years in century -- days >= 0 here, and we're far
* away from integer overflow trouble now. */
uday |= 3;
n001 = uday / GREGORIAN_NORMAL_LEAP_CYCLE_DAYS;
uday -= n001 * GREGORIAN_NORMAL_LEAP_CYCLE_DAYS;
/* Assemble the year and day in year */
res.hi = n100 * 100 + n001;
res.lo = uday / 4u;
/* Possibly set the leap year flag */
if (isleapyear) {
uint32_t tc = (uint32_t)n100 + 1;
uint32_t ty = (uint32_t)n001 + 1;
*isleapyear = !(ty & 3)
&& ((ty != 100) || !(tc & 3));
}
return res;
}
/*
*---------------------------------------------------------------------
* Given a number of elapsed days in a year and a leap year indicator,
* split the number of elapsed days into the number of elapsed months in
* 'res.hi' and the number of elapsed days of that month in 'res.lo'.
*
* This function will fail and return {-1,-1} if the number of elapsed
* days is not in the valid range!
*---------------------------------------------------------------------
*/
ntpcal_split
ntpcal_split_yeardays(
int32_t eyd,
int isleap
)
{
/* Use the unshifted-year, February-with-30-days approach here.
* Fractional interpolations are used in both directions, with
* the smallest power-of-two divider to avoid any true division.
*/
ntpcal_split res = {-1, -1};
/* convert 'isleap' to number of defective days */
isleap = 1 + !isleap;
/* adjust for February of 30 nominal days */
if (eyd >= 61 - isleap)
eyd += isleap;
/* if in range, convert to months and days in month */
if (eyd >= 0 && eyd < 367) {
res.hi = (eyd * 67 + 32) >> 11;
res.lo = eyd - ((489 * res.hi + 8) >> 4);
}
return res;
}
/*
*---------------------------------------------------------------------
* Convert a RD into the date part of a 'struct calendar'.
*---------------------------------------------------------------------
*/
int
ntpcal_rd_to_date(
struct calendar *jd,
int32_t rd
)
{
ntpcal_split split;
int leapy;
u_int ymask;
/* Get day-of-week first. It's simply the RD (mod 7)... */
jd->weekday = i32mod7(rd);
split = ntpcal_split_eradays(rd - 1, &leapy);
/* Get year and day-of-year, with overflow check. If any of the
* upper 16 bits is set after shifting to unity-based years, we
* will have an overflow when converting to an unsigned 16bit
* year. Shifting to the right is OK here, since it does not
* matter if the shift is logic or arithmetic.
*/
split.hi += 1;
ymask = 0u - ((split.hi >> 16) == 0);
jd->year = (uint16_t)(split.hi & ymask);
jd->yearday = (uint16_t)split.lo + 1;
/* convert to month and mday */
split = ntpcal_split_yeardays(split.lo, leapy);
jd->month = (uint8_t)split.hi + 1;
jd->monthday = (uint8_t)split.lo + 1;
return ymask ? leapy : -1;
}
/*
*---------------------------------------------------------------------
* Convert a RD into the date part of a 'struct tm'.
*---------------------------------------------------------------------
*/
int
ntpcal_rd_to_tm(
struct tm *utm,
int32_t rd
)
{
ntpcal_split split;
int leapy;
/* get day-of-week first */
utm->tm_wday = i32mod7(rd);
/* get year and day-of-year */
split = ntpcal_split_eradays(rd - 1, &leapy);
utm->tm_year = split.hi - 1899;
utm->tm_yday = split.lo; /* 0-based */
/* convert to month and mday */
split = ntpcal_split_yeardays(split.lo, leapy);
utm->tm_mon = split.hi; /* 0-based */
utm->tm_mday = split.lo + 1; /* 1-based */
return leapy;
}
/*
*---------------------------------------------------------------------
* Take a value of seconds since midnight and split it into hhmmss in a
* 'struct calendar'.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_daysec_to_date(
struct calendar *jd,
int32_t sec
)
{
int32_t days;
int ts[3];
days = priv_timesplit(ts, sec);
jd->hour = (uint8_t)ts[0];
jd->minute = (uint8_t)ts[1];
jd->second = (uint8_t)ts[2];
return days;
}
/*
*---------------------------------------------------------------------
* Take a value of seconds since midnight and split it into hhmmss in a
* 'struct tm'.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_daysec_to_tm(
struct tm *utm,
int32_t sec
)
{
int32_t days;
int32_t ts[3];
days = priv_timesplit(ts, sec);
utm->tm_hour = ts[0];
utm->tm_min = ts[1];
utm->tm_sec = ts[2];
return days;
}
/*
*---------------------------------------------------------------------
* take a split representation for day/second-of-day and day offset
* and convert it to a 'struct calendar'. The seconds will be normalised
* into the range of a day, and the day will be adjusted accordingly.
*
* returns >0 if the result is in a leap year, 0 if in a regular
* year and <0 if the result did not fit into the calendar struct.
*---------------------------------------------------------------------
*/
int
ntpcal_daysplit_to_date(
struct calendar *jd,
const ntpcal_split *ds,
int32_t dof
)
{
dof += ntpcal_daysec_to_date(jd, ds->lo);
return ntpcal_rd_to_date(jd, ds->hi + dof);
}
/*
*---------------------------------------------------------------------
* take a split representation for day/second-of-day and day offset
* and convert it to a 'struct tm'. The seconds will be normalised
* into the range of a day, and the day will be adjusted accordingly.
*
* returns 1 if the result is in a leap year and zero if in a regular
* year.
*---------------------------------------------------------------------
*/
int
ntpcal_daysplit_to_tm(
struct tm *utm,
const ntpcal_split *ds ,
int32_t dof
)
{
dof += ntpcal_daysec_to_tm(utm, ds->lo);
return ntpcal_rd_to_tm(utm, ds->hi + dof);
}
/*
*---------------------------------------------------------------------
* Take a UN*X time and convert to a calendar structure.
*---------------------------------------------------------------------
*/
int
ntpcal_time_to_date(
struct calendar *jd,
const vint64 *ts
)
{
ntpcal_split ds;
ds = ntpcal_daysplit(ts);
ds.hi += ntpcal_daysec_to_date(jd, ds.lo);
ds.hi += DAY_UNIX_STARTS;
return ntpcal_rd_to_date(jd, ds.hi);
}
/*
* ====================================================================
*
* merging composite entities
*
* ====================================================================
*/
#if !defined(HAVE_INT64)
/* multiplication helper. Seconds in days and weeks are multiples of 128,
* and without that factor fit well into 16 bit. So a multiplication
* of 32bit by 16bit and some shifting can be used on pure 32bit machines
* with compilers that do not support 64bit integers.
*
* Calculate ( hi * mul * 128 ) + lo
*/
static vint64
_dwjoin(
uint16_t mul,
int32_t hi,
int32_t lo
)
{
vint64 res;
uint32_t p1, p2, sf;
/* get sign flag and absolute value of 'hi' in p1 */
sf = (uint32_t)-(hi < 0);
p1 = ((uint32_t)hi + sf) ^ sf;
/* assemble major units: res <- |hi| * mul */
res.D_s.lo = (p1 & 0xFFFF) * mul;
res.D_s.hi = 0;
p1 = (p1 >> 16) * mul;
p2 = p1 >> 16;
p1 = p1 << 16;
M_ADD(res.D_s.hi, res.D_s.lo, p2, p1);
/* mul by 128, using shift: res <-- res << 7 */
res.D_s.hi = (res.D_s.hi << 7) | (res.D_s.lo >> 25);
res.D_s.lo = (res.D_s.lo << 7);
/* fix up sign: res <-- (res + [sf|sf]) ^ [sf|sf] */
M_ADD(res.D_s.hi, res.D_s.lo, sf, sf);
res.D_s.lo ^= sf;
res.D_s.hi ^= sf;
/* properly add seconds: res <-- res + [sx(lo)|lo] */
p2 = (uint32_t)-(lo < 0);
p1 = (uint32_t)lo;
M_ADD(res.D_s.hi, res.D_s.lo, p2, p1);
return res;
}
#endif
/*
*---------------------------------------------------------------------
* Merge a number of days and a number of seconds into seconds,
* expressed in 64 bits to avoid overflow.
*---------------------------------------------------------------------
*/
vint64
ntpcal_dayjoin(
int32_t days,
int32_t secs
)
{
vint64 res;
# if defined(HAVE_INT64)
res.q_s = days;
res.q_s *= SECSPERDAY;
res.q_s += secs;
# else
res = _dwjoin(675, days, secs);
# endif
return res;
}
/*
*---------------------------------------------------------------------
* Merge a number of weeks and a number of seconds into seconds,
* expressed in 64 bits to avoid overflow.
*---------------------------------------------------------------------
*/
vint64
ntpcal_weekjoin(
int32_t week,
int32_t secs
)
{
vint64 res;
# if defined(HAVE_INT64)
res.q_s = week;
res.q_s *= SECSPERWEEK;
res.q_s += secs;
# else
res = _dwjoin(4725, week, secs);
# endif
return res;
}
/*
*---------------------------------------------------------------------
* get leap years since epoch in elapsed years
*---------------------------------------------------------------------
*/
int32_t
ntpcal_leapyears_in_years(
int32_t years
)
{
/* We use the in-out-in algorithm here, using the one's
* complement division trick for negative numbers. The chained
* division sequence by 4/25/4 gives the compiler the chance to
* get away with only one true division and doing shifts otherwise.
*/
uint32_t sf32, sum, uyear;
sf32 = int32_sflag(years);
uyear = (uint32_t)years;
uyear ^= sf32;
sum = (uyear /= 4u); /* 4yr rule --> IN */
sum -= (uyear /= 25u); /* 100yr rule --> OUT */
sum += (uyear /= 4u); /* 400yr rule --> IN */
/* Thanks to the alternation of IN/OUT/IN we can do the sum
* directly and have a single one's complement operation
* here. (Only if the years are negative, of course.) Otherwise
* the one's complement would have to be done when
* adding/subtracting the terms.
*/
return uint32_2cpl_to_int32(sf32 ^ sum);
}
/*
*---------------------------------------------------------------------
* Convert elapsed years in Era into elapsed days in Era.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_days_in_years(
int32_t years
)
{
return years * DAYSPERYEAR + ntpcal_leapyears_in_years(years);
}
/*
*---------------------------------------------------------------------
* Convert a number of elapsed month in a year into elapsed days in year.
*
* The month will be normalized, and 'res.hi' will contain the
* excessive years that must be considered when converting the years,
* while 'res.lo' will contain the number of elapsed days since start
* of the year.
*
* This code uses the shifted-month-approach to convert month to days,
* because then there is no need to have explicit leap year
* information. The slight disadvantage is that for most month values
* the result is a negative value, and the year excess is one; the
* conversion is then simply based on the start of the following year.
*---------------------------------------------------------------------
*/
ntpcal_split
ntpcal_days_in_months(
int32_t m
)
{
ntpcal_split res;
/* Add ten months with proper year adjustment. */
if (m < 2) {
res.lo = m + 10;
res.hi = 0;
} else {
res.lo = m - 2;
res.hi = 1;
}
/* Possibly normalise by floor division. This does not hapen for
* input in normal range. */
if (res.lo < 0 || res.lo >= 12) {
uint32_t mu, Q, sf32;
sf32 = int32_sflag(res.lo);
mu = (uint32_t)res.lo;
Q = sf32 ^ ((sf32 ^ mu) / 12u);
res.hi += uint32_2cpl_to_int32(Q);
res.lo = mu - Q * 12u;
}
/* Get cummulated days in year with unshift. Use the fractional
* interpolation with smallest possible power of two in the
* divider.
*/
res.lo = ((res.lo * 979 + 16) >> 5) - 306;
return res;
}
/*
*---------------------------------------------------------------------
* Convert ELAPSED years/months/days of gregorian calendar to elapsed
* days in Gregorian epoch.
*
* If you want to convert years and days-of-year, just give a month of
* zero.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_edate_to_eradays(
int32_t years,
int32_t mons,
int32_t mdays
)
{
ntpcal_split tmp;
int32_t res;
if (mons) {
tmp = ntpcal_days_in_months(mons);
res = ntpcal_days_in_years(years + tmp.hi) + tmp.lo;
} else
res = ntpcal_days_in_years(years);
res += mdays;
return res;
}
/*
*---------------------------------------------------------------------
* Convert ELAPSED years/months/days of gregorian calendar to elapsed
* days in year.
*
* Note: This will give the true difference to the start of the given
* year, even if months & days are off-scale.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_edate_to_yeardays(
int32_t years,
int32_t mons,
int32_t mdays
)
{
ntpcal_split tmp;
if (0 <= mons && mons < 12) {
if (mons >= 2)
mdays -= 2 - is_leapyear(years+1);
mdays += (489 * mons + 8) >> 4;
} else {
tmp = ntpcal_days_in_months(mons);
mdays += tmp.lo
+ ntpcal_days_in_years(years + tmp.hi)
- ntpcal_days_in_years(years);
}
return mdays;
}
/*
*---------------------------------------------------------------------
* Convert elapsed days and the hour/minute/second information into
* total seconds.
*
* If 'isvalid' is not NULL, do a range check on the time specification
* and tell if the time input is in the normal range, permitting for a
* single leapsecond.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_etime_to_seconds(
int32_t hours,
int32_t minutes,
int32_t seconds
)
{
int32_t res;
res = (hours * MINSPERHR + minutes) * SECSPERMIN + seconds;
return res;
}
/*
*---------------------------------------------------------------------
* Convert the date part of a 'struct tm' (that is, year, month,
* day-of-month) into the RD of that day.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_tm_to_rd(
const struct tm *utm
)
{
return ntpcal_edate_to_eradays(utm->tm_year + 1899,
utm->tm_mon,
utm->tm_mday - 1) + 1;
}
/*
*---------------------------------------------------------------------
* Convert the date part of a 'struct calendar' (that is, year, month,
* day-of-month) into the RD of that day.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_date_to_rd(
const struct calendar *jd
)
{
return ntpcal_edate_to_eradays((int32_t)jd->year - 1,
(int32_t)jd->month - 1,
(int32_t)jd->monthday - 1) + 1;
}
/*
*---------------------------------------------------------------------
* convert a year number to rata die of year start
*---------------------------------------------------------------------
*/
int32_t
ntpcal_year_to_ystart(
int32_t year
)
{
return ntpcal_days_in_years(year - 1) + 1;
}
/*
*---------------------------------------------------------------------
* For a given RD, get the RD of the associated year start,
* that is, the RD of the last January,1st on or before that day.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_rd_to_ystart(
int32_t rd
)
{
/*
* Rather simple exercise: split the day number into elapsed
* years and elapsed days, then remove the elapsed days from the
* input value. Nice'n sweet...
*/
return rd - ntpcal_split_eradays(rd - 1, NULL).lo;
}
/*
*---------------------------------------------------------------------
* For a given RD, get the RD of the associated month start.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_rd_to_mstart(
int32_t rd
)
{
ntpcal_split split;
int leaps;
split = ntpcal_split_eradays(rd - 1, &leaps);
split = ntpcal_split_yeardays(split.lo, leaps);
return rd - split.lo;
}
/*
*---------------------------------------------------------------------
* take a 'struct calendar' and get the seconds-of-day from it.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_date_to_daysec(
const struct calendar *jd
)
{
return ntpcal_etime_to_seconds(jd->hour, jd->minute,
jd->second);
}
/*
*---------------------------------------------------------------------
* take a 'struct tm' and get the seconds-of-day from it.
*---------------------------------------------------------------------
*/
int32_t
ntpcal_tm_to_daysec(
const struct tm *utm
)
{
return ntpcal_etime_to_seconds(utm->tm_hour, utm->tm_min,
utm->tm_sec);
}
/*
*---------------------------------------------------------------------
* take a 'struct calendar' and convert it to a 'time_t'
*---------------------------------------------------------------------
*/
time_t
ntpcal_date_to_time(
const struct calendar *jd
)
{
vint64 join;
int32_t days, secs;
days = ntpcal_date_to_rd(jd) - DAY_UNIX_STARTS;
secs = ntpcal_date_to_daysec(jd);
join = ntpcal_dayjoin(days, secs);
return vint64_to_time(&join);
}
/*
* ====================================================================
*
* extended and unchecked variants of caljulian/caltontp
*
* ====================================================================
*/
int
ntpcal_ntp64_to_date(
struct calendar *jd,
const vint64 *ntp
)
{
ntpcal_split ds;
ds = ntpcal_daysplit(ntp);
ds.hi += ntpcal_daysec_to_date(jd, ds.lo);
return ntpcal_rd_to_date(jd, ds.hi + DAY_NTP_STARTS);
}
int
ntpcal_ntp_to_date(
struct calendar *jd,
uint32_t ntp,
const time_t *piv
)
{
vint64 ntp64;
/*
* Unfold ntp time around current time into NTP domain. Split
* into days and seconds, shift days into CE domain and
* process the parts.
*/
ntp64 = ntpcal_ntp_to_ntp(ntp, piv);
return ntpcal_ntp64_to_date(jd, &ntp64);
}
vint64
ntpcal_date_to_ntp64(
const struct calendar *jd
)
{
/*
* Convert date to NTP. Ignore yearday, use d/m/y only.
*/
return ntpcal_dayjoin(ntpcal_date_to_rd(jd) - DAY_NTP_STARTS,
ntpcal_date_to_daysec(jd));
}
uint32_t
ntpcal_date_to_ntp(
const struct calendar *jd
)
{
/*
* Get lower half of 64bit NTP timestamp from date/time.
*/
return ntpcal_date_to_ntp64(jd).d_s.lo;
}
/*
* ====================================================================
*
* day-of-week calculations
*
* ====================================================================
*/
/*
* Given a RataDie and a day-of-week, calculate a RDN that is reater-than,
* greater-or equal, closest, less-or-equal or less-than the given RDN
* and denotes the given day-of-week
*/
int32_t
ntpcal_weekday_gt(
int32_t rdn,
int32_t dow
)
{
return ntpcal_periodic_extend(rdn+1, dow, 7);
}
int32_t
ntpcal_weekday_ge(
int32_t rdn,
int32_t dow
)
{
return ntpcal_periodic_extend(rdn, dow, 7);
}
int32_t
ntpcal_weekday_close(
int32_t rdn,
int32_t dow
)
{
return ntpcal_periodic_extend(rdn-3, dow, 7);
}
int32_t
ntpcal_weekday_le(
int32_t rdn,
int32_t dow
)
{
return ntpcal_periodic_extend(rdn, dow, -7);
}
int32_t
ntpcal_weekday_lt(
int32_t rdn,
int32_t dow
)
{
return ntpcal_periodic_extend(rdn-1, dow, -7);
}
/*
* ====================================================================
*
* ISO week-calendar conversions
*
* The ISO8601 calendar defines a calendar of years, weeks and weekdays.
* It is related to the Gregorian calendar, and a ISO year starts at the
* Monday closest to Jan,1st of the corresponding Gregorian year. A ISO
* calendar year has always 52 or 53 weeks, and like the Grogrian
* calendar the ISO8601 calendar repeats itself every 400 years, or
* 146097 days, or 20871 weeks.
*
* While it is possible to write ISO calendar functions based on the
* Gregorian calendar functions, the following implementation takes a
* different approach, based directly on years and weeks.
*
* Analysis of the tabulated data shows that it is not possible to
* interpolate from years to weeks over a full 400 year range; cyclic
* shifts over 400 years do not provide a solution here. But it *is*
* possible to interpolate over every single century of the 400-year
* cycle. (The centennial leap year rule seems to be the culprit here.)
*
* It can be shown that a conversion from years to weeks can be done
* using a linear transformation of the form
*
* w = floor( y * a + b )
*
* where the slope a must hold to
*
* 52.1780821918 <= a < 52.1791044776
*
* and b must be chosen according to the selected slope and the number
* of the century in a 400-year period.
*
* The inverse calculation can also be done in this way. Careful scaling
* provides an unlimited set of integer coefficients a,k,b that enable
* us to write the calulation in the form
*
* w = (y * a + b ) / k
* y = (w * a' + b') / k'
*
* In this implementation the values of k and k' are chosen to be the
* smallest possible powers of two, so the division can be implemented
* as shifts if the optimiser chooses to do so.
*
* ====================================================================
*/
/*
* Given a number of elapsed (ISO-)years since the begin of the
* christian era, return the number of elapsed weeks corresponding to
* the number of years.
*/
int32_t
isocal_weeks_in_years(
int32_t years
)
{
/*
* use: w = (y * 53431 + b[c]) / 1024 as interpolation
*/
static const uint16_t bctab[4] = { 157, 449, 597, 889 };
int32_t cs, cw;
uint32_t cc, ci, yu, sf32;
sf32 = int32_sflag(years);
yu = (uint32_t)years;
/* split off centuries, using floor division */
cc = sf32 ^ ((sf32 ^ yu) / 100u);
yu -= cc * 100u;
/* calculate century cycles shift and cycle index:
* Assuming a century is 5217 weeks, we have to add a cycle
* shift that is 3 for every 4 centuries, because 3 of the four
* centuries have 5218 weeks. So '(cc*3 + 1) / 4' is the actual
* correction, and the second century is the defective one.
*
* Needs floor division by 4, which is done with masking and
* shifting.
*/
ci = cc * 3u + 1;
cs = uint32_2cpl_to_int32(sf32 ^ ((sf32 ^ ci) >> 2));
ci = ci & 3u;
/* Get weeks in century. Can use plain division here as all ops
* are >= 0, and let the compiler sort out the possible
* optimisations.
*/
cw = (yu * 53431u + bctab[ci]) / 1024u;
return uint32_2cpl_to_int32(cc) * 5217 + cs + cw;
}
/*
* Given a number of elapsed weeks since the begin of the christian
* era, split this number into the number of elapsed years in res.hi
* and the excessive number of weeks in res.lo. (That is, res.lo is
* the number of elapsed weeks in the remaining partial year.)
*/
ntpcal_split
isocal_split_eraweeks(
int32_t weeks
)
{
/*
* use: y = (w * 157 + b[c]) / 8192 as interpolation
*/
static const uint16_t bctab[4] = { 85, 130, 17, 62 };
ntpcal_split res;
int32_t cc, ci;
uint32_t sw, cy, Q;
/* Use two fast cycle-split divisions again. Herew e want to
* execute '(weeks * 4 + 2) /% 20871' under floor division rules
* in the first step.
*
* This is of course (again) susceptible to internal overflow if
* coded directly in 32bit. And again we use 64bit division on
* a 64bit target and exact division after calculating the
* remainder first on a 32bit target. With the smaller divider,
* that's even a bit neater.
*/
# if defined(HAVE_64BITREGS)
/* Full floor division with 64bit values. */
uint64_t sf64, sw64;
sf64 = (uint64_t)-(weeks < 0);
sw64 = ((uint64_t)weeks << 2) | 2u;
Q = (uint32_t)(sf64 ^ ((sf64 ^ sw64) / GREGORIAN_CYCLE_WEEKS));
sw = (uint32_t)(sw64 - Q * GREGORIAN_CYCLE_WEEKS);
# else
/* Exact division after calculating the remainder via partial
* reduction by digit sum.
* (-2^33) % 20871 --> 5491 : the sign bit value
* ( 2^20) % 20871 --> 5026 : the upper digit value
* modinv(20871, 2^32) --> 330081335 : the inverse
*/
uint32_t ux = ((uint32_t)weeks << 2) | 2;
sw = (weeks < 0) ? 5491u : 0u; /* sign dgt */
sw += ((weeks >> 18) & 0x01FFFu) * 5026u; /* hi dgt (src!) */
sw += (ux & 0xFFFFFu); /* lo dgt */
sw %= GREGORIAN_CYCLE_WEEKS; /* full reduction */
Q = (ux - sw) * 330081335u; /* exact div */
# endif
ci = Q & 3u;
cc = uint32_2cpl_to_int32(Q);
/* Split off years; sw >= 0 here! The scaled weeks in the years
* are scaled up by 157 afterwards.
*/
sw = (sw / 4u) * 157u + bctab[ci];
cy = sw / 8192u; /* sw >> 13 , let the compiler sort it out */
sw = sw % 8192u; /* sw & 8191, let the compiler sort it out */
/* assemble elapsed years and downscale the elapsed weeks in
* the year.
*/
res.hi = 100*cc + cy;
res.lo = sw / 157u;
return res;
}
/*
* Given a second in the NTP time scale and a pivot, expand the NTP
* time stamp around the pivot and convert into an ISO calendar time
* stamp.
*/
int
isocal_ntp64_to_date(
struct isodate *id,
const vint64 *ntp
)
{
ntpcal_split ds;
int32_t ts[3];
uint32_t uw, ud, sf32;
/*
* Split NTP time into days and seconds, shift days into CE
* domain and process the parts.
*/
ds = ntpcal_daysplit(ntp);
/* split time part */
ds.hi += priv_timesplit(ts, ds.lo);
id->hour = (uint8_t)ts[0];
id->minute = (uint8_t)ts[1];
id->second = (uint8_t)ts[2];
/* split days into days and weeks, using floor division in unsigned */
ds.hi += DAY_NTP_STARTS - 1; /* shift from NTP to RDN */
sf32 = int32_sflag(ds.hi);
ud = (uint32_t)ds.hi;
uw = sf32 ^ ((sf32 ^ ud) / DAYSPERWEEK);
ud -= uw * DAYSPERWEEK;
ds.hi = uint32_2cpl_to_int32(uw);
ds.lo = ud;
id->weekday = (uint8_t)ds.lo + 1; /* weekday result */
/* get year and week in year */
ds = isocal_split_eraweeks(ds.hi); /* elapsed years&week*/
id->year = (uint16_t)ds.hi + 1; /* shift to current */
id->week = (uint8_t )ds.lo + 1;
return (ds.hi >= 0 && ds.hi < 0x0000FFFF);
}
int
isocal_ntp_to_date(
struct isodate *id,
uint32_t ntp,
const time_t *piv
)
{
vint64 ntp64;
/*
* Unfold ntp time around current time into NTP domain, then
* convert the full time stamp.
*/
ntp64 = ntpcal_ntp_to_ntp(ntp, piv);
return isocal_ntp64_to_date(id, &ntp64);
}
/*
* Convert a ISO date spec into a second in the NTP time scale,
* properly truncated to 32 bit.
*/
vint64
isocal_date_to_ntp64(
const struct isodate *id
)
{
int32_t weeks, days, secs;
weeks = isocal_weeks_in_years((int32_t)id->year - 1)
+ (int32_t)id->week - 1;
days = weeks * 7 + (int32_t)id->weekday;
/* days is RDN of ISO date now */
secs = ntpcal_etime_to_seconds(id->hour, id->minute, id->second);
return ntpcal_dayjoin(days - DAY_NTP_STARTS, secs);
}
uint32_t
isocal_date_to_ntp(
const struct isodate *id
)
{
/*
* Get lower half of 64bit NTP timestamp from date/time.
*/
return isocal_date_to_ntp64(id).d_s.lo;
}
/*
* ====================================================================
* 'basedate' support functions
* ====================================================================
*/
static int32_t s_baseday = NTP_TO_UNIX_DAYS;
static int32_t s_gpsweek = 0;
int32_t
basedate_eval_buildstamp(void)
{
struct calendar jd;
int32_t ed;
if (!ntpcal_get_build_date(&jd))
return NTP_TO_UNIX_DAYS;
/* The time zone of the build stamp is unspecified; we remove
* one day to provide a certain slack. And in case somebody
* fiddled with the system clock, we make sure we do not go
* before the UNIX epoch (1970-01-01). It's probably not possible
* to do this to the clock on most systems, but there are other
* ways to tweak the build stamp.
*/
jd.monthday -= 1;
ed = ntpcal_date_to_rd(&jd) - DAY_NTP_STARTS;
return (ed < NTP_TO_UNIX_DAYS) ? NTP_TO_UNIX_DAYS : ed;
}
int32_t
basedate_eval_string(
const char * str
)
{
u_short y,m,d;
u_long ned;
int rc, nc;
size_t sl;
sl = strlen(str);
rc = sscanf(str, "%4hu-%2hu-%2hu%n", &y, &m, &d, &nc);
if (rc == 3 && (size_t)nc == sl) {
if (m >= 1 && m <= 12 && d >= 1 && d <= 31)
return ntpcal_edate_to_eradays(y-1, m-1, d)
- DAY_NTP_STARTS;
goto buildstamp;
}
rc = sscanf(str, "%lu%n", &ned, &nc);
if (rc == 1 && (size_t)nc == sl) {
if (ned <= INT32_MAX)
return (int32_t)ned;
goto buildstamp;
}
buildstamp:
msyslog(LOG_WARNING,
"basedate string \"%s\" invalid, build date substituted!",
str);
return basedate_eval_buildstamp();
}
uint32_t
basedate_get_day(void)
{
return s_baseday;
}
int32_t
basedate_set_day(
int32_t day
)
{
struct calendar jd;
int32_t retv;
/* set NTP base date for NTP era unfolding */
if (day < NTP_TO_UNIX_DAYS) {
msyslog(LOG_WARNING,
"baseday_set_day: invalid day (%lu), UNIX epoch substituted",
(unsigned long)day);
day = NTP_TO_UNIX_DAYS;
}
retv = s_baseday;
s_baseday = day;
ntpcal_rd_to_date(&jd, day + DAY_NTP_STARTS);
msyslog(LOG_INFO, "basedate set to %04hu-%02hu-%02hu",
jd.year, (u_short)jd.month, (u_short)jd.monthday);
/* set GPS base week for GPS week unfolding */
day = ntpcal_weekday_ge(day + DAY_NTP_STARTS, CAL_SUNDAY)
- DAY_NTP_STARTS;
if (day < NTP_TO_GPS_DAYS)
day = NTP_TO_GPS_DAYS;
s_gpsweek = (day - NTP_TO_GPS_DAYS) / DAYSPERWEEK;
ntpcal_rd_to_date(&jd, day + DAY_NTP_STARTS);
msyslog(LOG_INFO, "gps base set to %04hu-%02hu-%02hu (week %d)",
jd.year, (u_short)jd.month, (u_short)jd.monthday, s_gpsweek);
return retv;
}
time_t
basedate_get_eracenter(void)
{
time_t retv;
retv = (time_t)(s_baseday - NTP_TO_UNIX_DAYS);
retv *= SECSPERDAY;
retv += (UINT32_C(1) << 31);
return retv;
}
time_t
basedate_get_erabase(void)
{
time_t retv;
retv = (time_t)(s_baseday - NTP_TO_UNIX_DAYS);
retv *= SECSPERDAY;
return retv;
}
uint32_t
basedate_get_gpsweek(void)
{
return s_gpsweek;
}
uint32_t
basedate_expand_gpsweek(
unsigned short weekno
)
{
/* We do a fast modulus expansion here. Since all quantities are
* unsigned and we cannot go before the start of the GPS epoch
* anyway, and since the truncated GPS week number is 10 bit, the
* expansion becomes a simple sub/and/add sequence.
*/
#if GPSWEEKS != 1024
# error GPSWEEKS defined wrong -- should be 1024!
#endif
uint32_t diff;
diff = ((uint32_t)weekno - s_gpsweek) & (GPSWEEKS - 1);
return s_gpsweek + diff;
}
/*
* ====================================================================
* misc. helpers
* ====================================================================
*/
/* --------------------------------------------------------------------
* reconstruct the centrury from a truncated date and a day-of-week
*
* Given a date with truncated year (2-digit, 0..99) and a day-of-week
* from 1(Mon) to 7(Sun), recover the full year between 1900AD and 2300AD.
*/
int32_t
ntpcal_expand_century(
uint32_t y,
uint32_t m,
uint32_t d,
uint32_t wd)
{
/* This algorithm is short but tricky... It's related to
* Zeller's congruence, partially done backwards.
*
* A few facts to remember:
* 1) The Gregorian calendar has a cycle of 400 years.
* 2) The weekday of the 1st day of a century shifts by 5 days
* during a great cycle.
* 3) For calendar math, a century starts with the 1st year,
* which is year 1, !not! zero.
*
* So we start with taking the weekday difference (mod 7)
* between the truncated date (which is taken as an absolute
* date in the 1st century in the proleptic calendar) and the
* weekday given.
*
* When dividing this residual by 5, we obtain the number of
* centuries to add to the base. But since the residual is (mod
* 7), we have to make this an exact division by multiplication
* with the modular inverse of 5 (mod 7), which is 3:
* 3*5 === 1 (mod 7).
*
* If this yields a result of 4/5/6, the given date/day-of-week
* combination is impossible, and we return zero as resulting
* year to indicate failure.
*
* Then we remap the century to the range starting with year
* 1900.
*/
uint32_t c;
/* check basic constraints */
if ((y >= 100u) || (--m >= 12u) || (--d >= 31u))
return 0;
if ((m += 10u) >= 12u) /* shift base to prev. March,1st */
m -= 12u;
else if (--y >= 100u)
y += 100u;
d += y + (y >> 2) + 2u; /* year share */
d += (m * 83u + 16u) >> 5; /* month share */
/* get (wd - d), shifted to positive value, and multiply with
* 3(mod 7). (Exact division, see to comment)
* Note: 1) d <= 184 at this point.
* 2) 252 % 7 == 0, but 'wd' is off by one since we did
* '--d' above, so we add just 251 here!
*/
c = u32mod7(3 * (251u + wd - d));
if (c > 3u)
return 0;
if ((m > 9u) && (++y >= 100u)) {/* undo base shift */
y -= 100u;
c = (c + 1) & 3u;
}
y += (c * 100u); /* combine into 1st cycle */
y += (y < 300u) ? 2000 : 1600; /* map to destination era */
return (int)y;
}
char *
ntpcal_iso8601std(
char * buf,
size_t len,
TcCivilDate * cdp
)
{
if (!buf) {
LIB_GETBUF(buf);
len = LIB_BUFLENGTH;
}
if (len) {
len = snprintf(buf, len, "%04u-%02u-%02uT%02u:%02u:%02u",
cdp->year, cdp->month, cdp->monthday,
cdp->hour, cdp->minute, cdp->second);
if (len < 0)
*buf = '\0';
}
return buf;
}
/* -*-EOF-*- */