Python speed vs csharp

[David M. Cooke]

At some point, "Terry Reedy" <tjreedy at udel.edu> wrote:

> "David M. Cooke" <cookedm+news at physics.mcmaster.ca> wrote in message
> news:qnkn0eutndk.fsf at arbutus.physics.mcmaster.ca...
>> At some point, Mike <mike at nospam.com> wrote:
>> > Here's the chunk of code that I'm spending most of my time
> executing:
>> >
>> > # Rational approximation for erfc(x) (Abramowitz & Stegun, Sec.
> 7.1.26)
>> > # Fifth order approximation. |error| <= 1.5e-7 for all x
>> > #
>> > def erfc( x ):
>> >    p  =  0.3275911
>> >    a1 =  0.254829592
>> >    a2 = -0.284496736
>> >    a3 =  1.421413741
>> >    a4 = -1.453152027
>> >    a5 =  1.061405429
>> >
>> >    t = 1.0 / (1.0 + p*float(x))
>> >    erfcx = ( (a1 + (a2 + (a3 +
>> >              (a4 + a5*t)*t)*t)*t)*t ) * math.exp(-(x**2))
>> >    return erfcx
>
> Does inlining the constants give any speedup?  or is local lookup so
> fast that it does not matter?

Should've thought of that too :-). It runs in 6.07 s now (my previous
version was 6.45 s, and the unmodified version above was 8.23 s).

Here's my best version:

exp = math.exp
def erfc( x ):
   t = 1.0 + 0.3275911*x 
   return ( (0.254829592 + (
             (1.421413741 + (-1.453152027 + 1.061405429/t)/t)/t - 0.284496736)
             /t)/t ) * exp(-(x**2))


The reversal of the order of the a2 evaluation is because looking at
the bytecodes (using the dis module) it turns out that -0.284 was
being stored as 0.284, then negated. However, -1.45 is stored as that.
This runs in 5.77 s. You could speed that up a little if you're
willing to manipulate the bytecode directly :-)

-- 
|>|\/|<
/--------------------------------------------------------------------------\
|David M. Cooke
|cookedm(at)physics(dot)mcmaster(dot)ca