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Worksheets related to Applied Discrete Structures

def random_n_bit_prime(n):
    return random_prime(2^n-1,lbound=2^(n-1))

def factor_time(bits):
    return timeit('factor(random_n_bit_prime('+bits.str()+')*random_n_bit_prime('+bits.str()+'))',seconds=True)
for k in srange(10,90,10):
8.05362701416e-05 0.000219452667236 0.00155693435669 0.00596276092529 0.0131066799164 0.0466529846191 0.213326597214 0.866991996765
map(lambda k:[k,factor_time(k)],srange(5,30,5))
4.76112365723e-05 8.1022644043e-05 0.00013451385498 0.000207384109497 0.000469622421265 [[5, None], [10, None], [15, None], [20, None], [25, None]]
g=lambda k:[k,factor_time(k)]
0.00633575248718 [40, None]
File: /cocalc/lib/python2.7/site-packages/smc_sagews/
Signature : timeit(*args, **kwds)
Docstring :
Time execution of a command or block of commands.

This command has been enhanced for Salvus so you may use it as a
block decorator as well, e.g.,

   %timeit 2+3


   %timeit(number=10, preparse=False)  2^3

   %timeit(number=10, seconds=True)  2^3



   [rest of the cell]

Here is the original docstring for timeit:

nodetex Accurately measure the wall time required to execute


* "stmt" -- a text string.

* "globals_dict" -- a dictionary or "None" (default). Evaluate
  "stmt" in the context of the globals dictionary. If not set, the
  current "globals()" dictionary is used.

* "preparse" -- (default: use globals preparser default) if
  "True" preparse "stmt" using the Sage preparser.

* "number" -- integer, (optional, default: 0), number of loops.

* "repeat" -- integer, (optional, default: 3), number of

* "precision" -- integer, (optional, default: 3), precision of
  output time.

* "seconds" -- boolean (default: "False"). Whether to just return
  time in seconds.


An instance of "SageTimeitResult" unless the optional parameter
"seconds=True" is passed. In that case, the elapsed time in seconds
is returned as a floating-point number.


   sage: from sage.misc.sage_timeit import sage_timeit
   sage: sage_timeit('3^100000', globals(), preparse=True, number=50)      # random output
   '50 loops, best of 3: 1.97 ms per loop'
   sage: sage_timeit('3^100000', globals(), preparse=False, number=50)     # random output
   '50 loops, best of 3: 67.1 ns per loop'
   sage: a = 10
   sage: sage_timeit('a^2', globals(), number=50)                            # random output
   '50 loops, best of 3: 4.26 us per loop'

If you only want to see the timing and not have access to
additional information, just use the "timeit" object:

   sage: timeit('10^2', number=50)
   50 loops, best of 3: ... per loop

Using sage_timeit gives you more information though:

   sage: s = sage_timeit('10^2', globals(), repeat=1000)
   sage: len(s.series)
   sage: mean(s.series)   # random output
   sage: min(s.series)    # random output
   sage: t = stats.TimeSeries(s.series)
   sage: t.scale(10^6).plot_histogram(bins=20,figsize=[12,6], ymax=2)
   Graphics object consisting of 20 graphics primitives

The input expression can contain newlines (but doctests cannot, so
we use "os.linesep" here):

   sage: from sage.misc.sage_timeit import sage_timeit
   sage: from os import linesep as CR
   sage: # sage_timeit(r'a = 2nb=131nfactor(a^b-1)')
   sage: sage_timeit('a = 2' + CR + 'b=131' + CR + 'factor(a^b-1)',
   ....:             globals(), number=10)
   10 loops, best of 3: ... per loop

Test to make sure that "timeit" behaves well with output:

   sage: timeit("print 'Hi'", number=50)
   50 loops, best of 3: ... per loop

If you want a machine-readable output, use the "seconds=True"

   sage: timeit("print 'Hi'", seconds=True)   # random output
   sage: t = timeit("print 'Hi'", seconds=True)
   sage: t     #r random output