# [time-nuts] GPS seconds conversion on an Arduino

paul swed paulswedb at gmail.com
Sun May 14 13:12:15 EDT 2017

```The goal I had was to convert GPS to UTC to minutes from 1980 to create the
wwvb time message.
Much of it was reasonable but then the funnies came in. The WWVB contains a
part of the message that says DST is coming and dst is here.. Tables took
care of that nicely.
I used 64 bit words because that nicely line up with seconds in a minute.
Good comments by everyone.
Regards
Paul
WB8TSL

On Sun, May 14, 2017 at 12:15 PM, Nick Sayer via time-nuts <
time-nuts at febo.com> wrote:

> I wouldn’t expect floating point to enter into it.
>
> Add the leap second correction in, then take seconds modulo 86400 and you
> get the second-within-the-day. Divide seconds by 86400 and you get the day
> number.
>
> With the day number, it’s quite straightforward to figure out gregorian
> date given a 0 date in modern times (GPS’ epoch is in 1980). You do have to
> figure out externally what 1024 week GPS cycle you’re in. You can start
> with a firmware default and increment an EEPROM value every zero-crossing.
> As long as the user gets a fix at least once every 1024 weeks, you’ll be
> good.
>
> You figure out the year by subtracting 365 or 366 and incrementing the
> year number until the day is less than either 366 or 365. Picking which of
> those is tricky, but it’s not particularly onerous. You figure out the
> month by comparing the remaining days to a list of day-of-year-for-month
> values (again, being careful to increment by 1 during leap years if the
> month is > 2). Subtract that out, add 1, and the remainder is the
> day-of-month.
>
> Turning a second-within-the-day value into H:M:S is child’s play. The only
> nuance left is 23:59:60 when a leap second occurs.
>
> All of that is enough to go from GPS second number to the NMEA UTC output.
>
> Going from NMEA UTC output to DST corrected local time is actually an
> exercise I’ve done for my GPS clock. You can take a look at my C code for
> that on GitHub: https://github.com/nsayer/GPS_clock
>
> Now, going to Sidereal time, *that’s* a floating-point bitch.
>
>
> > On May 13, 2017, at 6:58 PM, Mark Sims <holrum at hotmail.com> wrote:
> >
> > Converting GPS seconds to Gregorian date/time on the Arduino will be an
> arduous task.  You take GPS seconds and add it to the GPS starring epoch to
> get a Julian date.  Then add in the number of leap seconds as a fraction of
> a day to get UTC and possibly add in a time zone offset for local time.
> Don't forget to do daylight savings time conversion...  Then convert the
> result to Gregorian date/time for display.
> >
> > The problem is the Arduino floating point library is single precision
> only and does not have the resolution needed to handle the numbers
> involved.  Doing it with integer arithmetic (long longs) opens up a whole
> new can of worms.
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