Accurate timing information for Sage commands#

This is an implementation of nice timeit functionality, like the %timeit magic command in IPython. To use it, use the timeit command. This command then calls sage_timeit(), which you can find below.

EXAMPLES:

sage: timeit('1+1')    # random output
625 loops, best of 3: 314 ns per loop

>>> from sage.all import *
>>> timeit('1+1')    # random output
625 loops, best of 3: 314 ns per loop

AUTHOR:

– William Stein, based on code by Fernando Perez included in IPython

class sage.misc.sage_timeit.SageTimeitResult(stats, series=None)[source]#

Bases: object

Represent the statistics of a timeit() command.

Prints as a string so that it can be easily returned to a user.

INPUT:

  • stats – tuple of length 5 containing the following information:

    • integer, number of loops

    • integer, repeat number

    • Python integer, number of digits to print

    • number, best timing result

    • str, time unit

EXAMPLES:

sage: from sage.misc.sage_timeit import SageTimeitResult
sage: SageTimeitResult( (3, 5, int(8), pi, 'ms') )                              # needs sage.symbolic
3 loops, best of 5: 3.1415927 ms per loop

>>> from sage.all import *
>>> from sage.misc.sage_timeit import SageTimeitResult
>>> SageTimeitResult( (Integer(3), Integer(5), int(Integer(8)), pi, 'ms') )                              # needs sage.symbolic
3 loops, best of 5: 3.1415927 ms per loop

sage: units = [u"s", u"ms", u"μs", u"ns"]
sage: scaling = [1, 1e3, 1e6, 1e9]
sage: number = 7
sage: repeat = 13
sage: precision = int(5)
sage: best = pi / 10 ^ 9                                                        # needs sage.symbolic
sage: order = 3
sage: stats = (number, repeat, precision, best * scaling[order], units[order])  # needs sage.symbolic
sage: SageTimeitResult(stats)                                                   # needs sage.symbolic
7 loops, best of 13: 3.1416 ns per loop

>>> from sage.all import *
>>> units = [u"s", u"ms", u"μs", u"ns"]
>>> scaling = [Integer(1), RealNumber('1e3'), RealNumber('1e6'), RealNumber('1e9')]
>>> number = Integer(7)
>>> repeat = Integer(13)
>>> precision = int(Integer(5))
>>> best = pi / Integer(10) ** Integer(9)                                                        # needs sage.symbolic
>>> order = Integer(3)
>>> stats = (number, repeat, precision, best * scaling[order], units[order])  # needs sage.symbolic
>>> SageTimeitResult(stats)                                                   # needs sage.symbolic
7 loops, best of 13: 3.1416 ns per loop

If the third argument is not a Python integer, a TypeError is raised:

sage: SageTimeitResult( (1, 2, 3, 4, 's') )
<repr(<sage.misc.sage_timeit.SageTimeitResult at 0x...>) failed: TypeError: * wants int>

>>> from sage.all import *
>>> SageTimeitResult( (Integer(1), Integer(2), Integer(3), Integer(4), 's') )
<repr(<sage.misc.sage_timeit.SageTimeitResult at 0x...>) failed: TypeError: * wants int>
sage.misc.sage_timeit.sage_timeit(stmt, globals_dict=None, preparse=None, number=0, repeat=3, precision=3, seconds=False)[source]#

Accurately measure the wall time required to execute stmt.

INPUT:

  • 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, (default: 0), number of loops.

  • repeat – integer, (default: 3), number of repetition.

  • precision – integer, (default: 3), precision of output time.

  • seconds – boolean (default: False). Whether to just return time in seconds.

OUTPUT:

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.

EXAMPLES:

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'

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

>>> from sage.all import *
>>> timeit('10^2', number=Integer(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)
1000
sage: mean(s.series)   # random output                                          # needs sage.modules
3.1298141479492283e-07
sage: min(s.series)    # random output
2.9258728027343752e-07
sage: t = stats.TimeSeries(s.series)                                            # needs numpy sage.modules
sage: t.scale(10^6).plot_histogram(bins=20,figsize=[12,6], ymax=2)              # needs numpy sage.modules sage.plot
Graphics object consisting of 20 graphics primitives

>>> from sage.all import *
>>> s = sage_timeit('10^2', globals(), repeat=Integer(1000))
>>> len(s.series)
1000
>>> mean(s.series)   # random output                                          # needs sage.modules
3.1298141479492283e-07
>>> min(s.series)    # random output
2.9258728027343752e-07
>>> t = stats.TimeSeries(s.series)                                            # needs numpy sage.modules
>>> t.scale(Integer(10)**Integer(6)).plot_histogram(bins=Integer(20),figsize=[Integer(12),Integer(6)], ymax=Integer(2))              # needs numpy sage.modules sage.plot
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 = 2\nb=131\nfactor(a^b-1)')
sage: sage_timeit('a = 2' + CR + 'b=131' + CR + 'factor(a^b-1)',                # needs sage.libs.pari
....:             globals(), number=10)
10 loops, best of 3: ... per loop

>>> from sage.all import *
>>> from sage.misc.sage_timeit import sage_timeit
>>> from os import linesep as CR
>>> # sage_timeit(r'a = 2\nb=131\nfactor(a^b-1)')
>>> sage_timeit('a = 2' + CR + 'b=131' + CR + 'factor(a^b-1)',                # needs sage.libs.pari
...             globals(), number=Integer(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

>>> from sage.all import *
>>> timeit("print('Hi')", number=Integer(50))
50 loops, best of 3: ... per loop

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

sage: timeit("print('Hi')", seconds=True)   # random output
1.42555236816e-06
sage: t = timeit("print('Hi')", seconds=True)
sage: t     #r random output
3.6010742187499999e-07

>>> from sage.all import *
>>> timeit("print('Hi')", seconds=True)   # random output
1.42555236816e-06
>>> t = timeit("print('Hi')", seconds=True)
>>> t     #r random output
3.6010742187499999e-07