Question

I can plot a function with variable values as large as I need in gnuplot 4.4:

gnuplot> t = 10000*365.25*24*3600
gnuplot> f(x) = alpha*delta*exp(-alpha*x)*(sin(omega*t-alpha*x)-cos(omega*t-alpha*x))
gnuplot> plot f(x)

But If I instead want to iterate over t using similar values as above, by using the `plot for’ command, I get segfaults or it doesn’t seem to end (I waited a long time and still no response):

tau = int(40000*365.25*24*3600)
step = int(10000*365.25*24*3600)
f(x,t) = alpha*delta*exp(-alpha*x)*(sin(omega*t-alpha*x)-cos(omega*t-alpha*x))
plot for [t=0:tau:step] f(x,t)

If I have tau = 1000, and step = 10 then there is no problem, so I’m assuming that the size of the iterables is the issue. Is there some way around this or am I doing something wrong?

Some more info following @mgilson’s answer:
My system is 64-bit, and python can handle some very large integers:

>>> import sys
>>> sys.maxint
9223372036854775807
>>> tau = int(40000*365.25*24*3600)
>>> print tau
1262304000000

While gnuplot cannot:

gnuplot> tau = int(40000*365.25*24*3600)
gnuplot> print tau
-2147483648

Here’s the plot file if you want to try it:

tau   = int(40000*365.25*24*3600)
delta = 10
kappa = 1e-6
omega = 2*pi/tau  # angular frequency
alpha = sqrt(omega/(2*kappa))  # a simplifying factor

# set the range of x and time, t
set xrange[0:3000]
step = int(10000*365.25*24*3600)

f(x,t) = alpha*delta*exp(-alpha*x)*(sin(omega*t-alpha*x)-cos(omega*t-alpha*x))
plot for [t=0:tau:step] f(x,t)

Answer 1

quickly putting some of this into the python interpreter:

>>> tau = int(40000*365.25*24*3600)
>>> tau
1262304000000L
>>> step = int(10000*365.25*24*3600)
>>> step
315576000000L

Notice the L at the end of the integers? That means that these numbers overflowed the system’s maximum integer size which is:

>>> import sys
>>> sys.maxint   #2**31 - 1
2147483647

for my system. Python handles this gracefully by using a custom type (long) which allows the integer to occupy an unlimited number of bytes. The way gnuplot handles this is that the overflow wraps around …

gnuplot> tau = int(40000*365.25*24*3600)
gnuplot> print tau
-2147483648

Now you have negative numbers where you expected positive ones.

EDIT

It appears that gnuplot uses 4-byte integers no matter what python’s sys.maxint is. On my ubuntu x86_64 machine, python’s sys.maxint is much larger than gnuplot’s integer can handle (which is still capped at 2**31-1).