Re: How fast does & perform?

• To: mathgroup at smc.vnet.net
• Subject: [mg107325] Re: How fast does & perform?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Tue, 9 Feb 2010 02:45:41 -0500 (EST)

```On 2/8/10 at 3:35 AM, canopus56 at yahoo.com (Canopus56) wrote:

>Setting aside the syntax question of the thread "What does & mean?",
>there appears to be a performance difference between the two syntax
>forms. Looks like the := form is faster:

>data = Table[x, {x, (\[Pi]/8), \[Pi], (\[Pi]/512)}]

>g[x_] := x*Sin[x]

>Timing[Table[g[data[[k]]], {k, 1, Length[data]}]]

>2.71051*10^-17 seconds

>Timing[Map[g, data]]

>0. seconds

>Timing[Map[g[#] &, data]]

>0.016 seconds

>Timing[Map[#*Sin[#] &, data]]

>0.031 seconds

>Timing[#*Sin[#] & /@ data]

>0.032 seconds

To have any real assurance one way is faster than another, you
need longer execution times, at least 1-10 seconds or so to
compensate for the resolution limits on timing. Also, it seems
when mapping these to a data list the pattern matching syntax is
slower. But, consider the following:

In[1]:= data = RandomReal[{-\[Pi], \[Pi]}, 10000000];

In[2]:= g[x_] = x Sin[x];
f = # Sin[#] &;

In[4]:= Timing[g /@ data;]

Out[4]= {14.136,Null}

In[5]:= Timing[f /@ data;]

Out[5]= {2.00905,Null}

In[6]:= Timing[g[data];]

Out[6]= {0.487722,Null}

In[7]:= Timing[f[data];]

Out[7]= {0.487063,Null}

Here it is quite apparent avoiding the use of Map, results in
much faster execution. And when you take advantage of the fact
these function work on lists, it is no longer clear there is any
speed advantage to one form or another.

Note, I realize the timing data above violates my suggestion for
having an execution time of 1-10 seconds for comparison for the
cases where Map is not used. But given memory limits in my
machine, it really isn't practical to obtain such long execution
times for such a simple function.

```

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