ISO 8601 Repeating Interval: every last day of month - time

Is it possible to define repeating interval for every last day of month in terms of ISO 8601?
I need this for several Mesos/Chronos jobs.

ISO 8601:2004 does not specify.
ISO 8601-1:2019 and in particular ISO 8601-2:2019 (not freely available afaik) apparently clarifies in section 14 and Appendix D that if an interval specifies a non-existing data then you back up to the last available day. I take this to mean that R/2021-01-31P1M specifies the intervals 2021-01-31P1M, 2021-02-28P1M, 2021-03-31P1M etc.

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Is there any way by which I can get TimeZone value using time stamp

This is the value which I have,
Sun Mar 29 2020 02:55:00 GMT+0530
and I want to get,for example
Asia/Calcutta
as ouput. Thanks in advance.
Offset does not indicate zone
get TimeZone value using time stamp
No.
You cannot determine a time zone from an offset.
Many time zones can share the same offset-from-UTC (the number of hours-minutes-seconds ahead or behind the prime meridian).
See the list of time zone names in Wikipedia. Click on the column header to sort by offset. Notice how often several zones share the same offset.
Specific to your example, notice how we currently have two zones that coincidentally share an offset of five and a half hours ahead of UTC:
Asia/Kolkata (India)
Asia/Colombo (Sri Lanka)
So, without further input, there is no way to know if the author of your input string intended India time or Sri Lanka time.
By the way, the name Asia/Calcutta has been changed to Asia/Kolkata. If your system has no such name, then your tzdata is several years out of date. Always keep all the copies of tzdata up-to-date in OSes, database servers such as Postgres, and runtimes such as Java.
Another complication: politicians frequently change the offset used in their jurisdictions.
So while all of India today uses the same offset of +05:30, that has not always been the case, nor is it likely to always be true in the future (based on the history of how often zones change around the world).
ISO 8601
The ISO 8601 standard defines many sensible formats for representing date-time values as text.
2020-01-23T12:34:56.123456789+05:30
The java.time framework built into Java 8 and later extends one of those format wisely by appending the name of the time zone in square brackets. I suggest using this format if feasible.
2020-01-23T12:34:56.123456789+05:30[Asia/Kolkata]

Is there a one to one and onto relation between ISO-8601 UTC and Unix Timestamp?

Time Formats
A point in time is often represented as Unix Time, or as a human-readable ISO 8601 date in UTC time string.
For example:
Unix Time
Seconds since Epoch, or Unix timestamp, in seconds or milliseconds:
1529325705
1529325705000
ISO 8601 Date
2018-06-18T15:41:45+00:00
My question
Is there a one-to-one and onto relationship between the two? In other words, is there a point in time with a single representation in one format, and more than one, or zero, representations in the other?
Yes, it is possible to find such a date. From the wiki article on Unix time:
Every day is treated as if it contains exactly 86400 seconds,[2] so leap seconds are not applied to seconds since the Epoch.
That means that the leap seconds themselves cannot be represented in Unix time.
For example, the latest leap second occurred at the end of 2016, so 2016-12-31T23:59:60+00:00 is a valid ISO 8601 time stamp. However, the Unix time stamp for the second before, at 23:59:59, is represented as 1483228799 and the second after, 00:00:00 (on January 1 2017) is 1483228800, so there is no Unix timestamp that represents the leap second.
In practice, this is probably not a problem for you; there has only been 27 leap seconds since they were introduced in 1972.
It might be worthwhile to mention that most software implementations of ISO 8601 does not take leap seconds into account either, but will do something else if asked to parse "2016-12-31T23:59:60+00:00". The System.DateTime class in .NET throws an exception, while it's also conceivable that a library would return 2017-01-01 00:00:00.
No. there is a nice correspondence between the two, but the relationship is 1 to many, and strictly speaking there may not even exist a precise Unix millisecond for a given ISO date-time string. Some issues are:
There are some freedoms in the ISO 8601 format, so the same Unix millisecond may be written in several ways even when we require that the time be in UTC (the offset is zero).
Seconds and fraction of seconds are optional, and there may be a varying number of decimals on the seconds. So a milliseconds value of 1 529 381 160 000, for example, could be written as for example
2018-06-19T04:06:00.000000000Z
2018-06-19T04:06:00.00Z
2018-06-19T04:06:00Z
2018-06-19T04:06Z
The offset of 0 would normally be written as Z, but may also be written as you do in the question, +00:00. I think the forms +00 and +0000 are OK too (forms with a minus are not).
Since there may be more than three decimals on the seconds in ISO 8601, no exact Unix millisecond may match. So you will have to accept truncation (or rounding) to convert to Unix time. Of course the error will be still greater if you convert to Unix seconds rather than milliseconds.
As Thomas Lycken noted, leap seconds can be represented in ISO 8601, but not in Unix time.
In other words, is there a point in time with a single representation in one format, and more than one, or zero, representations in the other?
No. The UTC time depends on your geographic location, ie. your latitude and longitude. However, the UNIX timestamp is a way to track time as a running total of seconds. This count starts at the Unix Epoch on January 1st, 1970 at UTC.
From Unix TimeStamp,
It should also be pointed out that this point in time technically does not change no
matter where you are located on the globe.

ISO 8601 hour number inconsistency

ISO 8601, section 5.3 specifies
hours are represented by two digits from [01] to [24]
But below, section 5.3.2 permits both "00:00:00" and "24:00:00" for midnight.
I also know from experience that the midnight hour is commonly represented by the digits [00], and never by [24] except at the exact second of midnight. So this appears to be an error in the specification. Surely someone has noticed this before me. Is there published errata? Am I missing something?
I don't know a section 5.3 in latest ISO-8601-paper, but see this:
4.2.3 Midnight
The complete representations in basic and extended format for midnight, in accordance with 4.2.2, shall be expressed in
either of the two following ways:
Basic format Extended format
a) 000000 00:00:00 (the beginning of a calendar day)
b) 240000 24:00:00 (the end of a calendar day)
The representations may have reduced
accuracy in accordance with 4.2.2.3 or may be designated as a time
expression in accordance with 4.2.2.5. To represent midnight the
representations may be expanded with a decimal fraction containing
only zeros in accordance with 4.2.2.4.
NOTE 1 Midnight will normally be represented as [00:00] or [24:00].
NOTE 2 The end of one calendar day [24:00] coincides with [00:00] at the start of the next calendar
day, e.g. [24:00] on 12 April 1985 is the same as [00:00] on 13 April
1985. If there is no association with a date or a time interval both a) and b) represent the same local time in the 24-hour timekeeping
system.
NOTE 3 The choice of representation a) or b) will depend upon
any association with a date, or a time interval. Representations where
[hh] has the value [24] are only preferred to represent the end of a time interval in accordance with 4.4 or recurring time interval in accordance with 4.5.
So I think all is fine, no inconsistency.
By the way, I have adapted this special value 24:00 in my Java time library Time4J (see class net.time4j.PlainTime) to enable more elegant time interval descriptions. And I also know from real life that such a hour value is not unusual (for example in shop opening times).

How to represent dates before epoch as a UNIX timestamp

It occurred to me that I'm not aware of a mechanism to store dates before 1970 jan. 1 as Unix timestamps. Since that date is the Unix "epoch" this isn't much of a surprise.
But - even though it's not designed for that - I still wish to store dates in the far past in Unix format.I need this for reasons.
So my question is: how would one go about making unix-timestamps contain "invalid" but still working dates? Would storing a negative amount of seconds work? Can we even store negative amounts of seconds in a unix-timestamp? I mean isn't it unsigned?
Also if I'm correct then I could only store dates as far back as 1901. dec. 13 20:45:52 could this be extended any further back in history by any means?
Unix Time is usually a 32-bit number of whole seconds from the first moment of 1970 in UTC, the epoch being 1 January 1970 00:00:00 UTC. That means a range of about 136 years with about half on either side of the epoch. Negative numbers are earlier, zero is the epoch, and positive are later. For a signed 32-bit integer, the values range from 1901-12-13 to 2038-01-19 03:14:07 UTC.
This is not written in stone. Well, it is written, but in a bunch of different stones. Older ones say 32-bit, newer ones 64-bit. Some specifications says that the meaning is "implementation-defined". Some Unix systems use an unsigned int to extend only into the future past the epoch, but usual practice has been a signed number. Some use a float rather than an integer. For details, see Wikipedia article on Unix Time, and this Question.
So, basically, your Question makes no sense. You have to know the context of your programming language (standard C, other C, Java, etc.), environment (POSIX-compliant), particular software library, or database store, or application.
Avoid Count-From-Epoch
Add to this lack of specificity the fact that a couple dozen other epochs have been used by various software systems, some extremely popular and common. Examples include January 1, 1601 for NTFS file system & COBOL, January 1, 1980 for various FAT file systems, January 1, 2001 for Apple Cocoa, and January 0, 1900 for Excel & Lotus 1-2-3 spreadsheets.
Further add the fact that different granularities of count have been used. Besides whole seconds, some systems use milliseconds, microseconds, or nanoseconds.
I recommend against tracking date-time as a count-from-epoch. Instead use specific data types where available in your programming language or database.
ISO 8601
When data types are not available, or when exchanging data, follow the ISO 8601 standard which defines sensible string formats for various kinds of date-time values.
Date
2015-07-29
A date-time with an offset from UTC (Z is zero/Zulu for UTC) (note padding zero on offset)
2015-07-29T14:59:08Z
2001-02-13T12:34:56.123+05:30
Week (with or without day of week)
2015-W31
2015-W31-3
Ordinal date (day-of-year)
2015-210
Interval
"2007-03-01T13:00:00Z/2008-05-11T15:30:00Z"
Duration (format of PnYnMnDTnHnMnS)
P3Y6M4DT12H30M5S = "period of three years, six months, four days, twelve hours, thirty minutes, and five seconds"
Search StackOverflow.com for many more Questions and Answers on these topics.

Efficient algorithm for determining if a date is in DST

I'm looking for a better than O(n) algorithm to determine if a date in the future will have daylight savings time applied (and how much). Given a year, month, day, hour, minute and time zone (and a copy of the Olsen Time Zone database) how does one efficiently determine if that date will be in DST? I'm looking for the algorithm, not a library function to call.
Thank you.
FURTHER EXPLANATION: The date library I'm using is very slow when you create an object with a date in the future and a time zone. It turns out its doing a linear calculation to calculate if the date is in daylight savings time. Not only that, its doing this at object creation time. Obviously it could wait until asked, but it should also be more efficient.
Sure, DST rules change and a date library can't predict the future, but the alternative is to put an arbitrary upper limit on localized dates.
Everybody's already commented on the problems with always-changing DSTs. But I can accept the premise that we just pretend the currently known rules will apply forever.
To get your DST information, the first thing to do is to calculate the year/month/day for your future date (if it isn't in that form already). Then you look up your time zone and pull out the variation against UTC, the DST on/off rule and offset. There could be several different rules depending on which year, you want to be sure to grab the right one for your "target" year. For reasons explained below, it may be handy to also be aware of the rules for the preceding year.
The on/off rules will have a funny spec like "Oct lastSun": That means the switch occurs in the night of the last Sunday in October.
What you need to do is gather up all of these tersely formatted "rules" and develop a bit of code for each to determine the last date indicated by that rule. It's currently December, so given a couple of rules like "Mar lastSun" and "Oct lastSun" for my time zone, those dates would be March 29, 2009 and October 25, 2009. Which of these dates is more recent? October. October is associated with an "off", so we must currently have NO DST.
You can calculate the DST on/off dates for the current (i.e. target) year regardless of whether the target date is before or after those dates; if the on/off date is in the future of your target date, then simply do the rule calculation again for the previous year. Note that the rules may have changed during the interval, so be sure to apply the correct one for the year you're looking at.
Worst case for this calculation is, you have to repeat your two rule calculations for the previous year. But there's no searching going on otherwise, so it's strictly O(1).
I found a Local/DST/Tz calculator here: http://home-4.tiscali.nl/~t876506/WhatDay.html and as it's a JavaScript applet you should be able to simply crib the code. It doesn't handle all rules, though, so you will need to add some code for the remaining rules.
Update: I just noticed you have an hour and minute in your time as well. That complicates matters just a little. If your date is not on a "switch" date then the instructions I gave above will do you fine. Otherwise, you need to consider the time. I guess the cleanest thing to do would be to include the time in your determination of "most recent". I.e. if your target time is 00:30 UTC and switch time for the given zone is 01:00, then the target year's switch time is still in the future and you have to use the previous year's switch time instead. For practical purposes, this will mean that the "other" switch time was the most recent, and its on/off status applies.
Your number one problem is daylight savings rules that are set by the local authorities. The latter can pass almost any law at any time and therefore change the rules in a way you can't possibly predict.
As far as I know DST changes that are known start and end on a fixed day each year (first weekend in april, last weekend in october, stuff like that). So you could ese the Doomsday Algorithm to find the days of the week for the given year and calculate the conversion dates from that. Then you can determine if DST is in effect in source and/or destination locale. The converion itself is simply a matter of adding and/or subtracting an hour to compensate for DST and then factor in the timezone difference.
Hmm, as I see the problematic point is to determine weekday for a given day, far in the future.
For that, I suggest something like that:
after every 400 years, the complete system turns around, so first divide the number of years with 400, take the integral part. In 400 years, there are 99 leap years and 301 simple ones. If an arbitrary day is Monday, then the same day 400 years later will be 301+2x99 = 499 (mod 7) ---> Monday+2 ---> Wednesday. So you have to say something like that:
wday = (ref_day + 2 * (int)((target_year - ref_year) / 400)) mod 7
then you can do further optimizations, but I guess you can go year-by-year, that will do it. At most you make 399 simple operations, if (leap_year) then ++ else +=2, mod 7.
After you have the weekday for Jan 1 that year, you can calculate DST switching dates, as Carl Smotricz has written.

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