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MathGroup Archive 1999

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Re: Block vs. Module

  • To: mathgroup at
  • Subject: [mg15632] Re: [mg15590] Block vs. Module
  • From: David Withoff <withoff>
  • Date: Sat, 30 Jan 1999 04:28:32 -0500 (EST)
  • Sender: owner-wri-mathgroup at

> Recently, while profiling some rather large Mathematica 3.0 programs, my
> colleagues and I discovered that simply exchanging all Module
> statements in a package against Block statements reduced the total
> computation time considerably. In one particular case with a large
> number of function calls and local variables the execution time was
> reduced by almost 50%.
> The Mathematica documentation describes Block as a structure that allows
> for temporarily assigning local values to global names, as opposed to
> Module which defines new local symbols (which obviously takes a lot
> more time). Thus, rather than Module, Block allows to make use of some
> side effects on global symbols, but this should not happen in
> well-structured programs. Due to the extreme speed differences we
> encountered we are now asking ourselves if there is actually any good
> reason against generally using Block instead of Module in Mathematica
> packages. Are there any internal implementation issues that need to be
> taken in account (such as heap management or stack size limitations)?
> Best regards,
>   Eckhard Hennig

Block works by setting aside the values of local variables so that those
variables can be used freely during evaluation of the body of the
Block, and then restoring the original values of the local variables
when the Block finishes.  The overhead of variable localization in
Block is therefore proportional to the number of variables.

Module works by generating new symbols and inserting those symbols where
ever they appear in the body of the Module.  The overhead of variable
localization in Module is therefore proportional to the size of the
body of the Module as well as to the number of variables.

If the body of the Block or Module is large, and the body evaluates
quickly so that the overhead of variable localization is a significant
component of the total time, then Block can be significantly faster
than Module, at least in interpreted functions (uncompiled evaluation).
The analysis is different in compiled code, where Module would in
principle be faster, but that is a separate topic.

Assuming that program correctness is more important than speed (that is,
getting the wrong answer quickly is not an advantage), then the choice
between Module and Block depends on the program.  Block and Module
offer different types of variable localization, and you would
presumably choose the one that is correct for your application.  If it
doesn't matter, then it makes sense to choose Block, at least in
uncompiled code, since Block will usually be faster.

As you pointed out in your message, global variables can lead to
problems in programs based on Block.  For example, a definition such as

In[1]:= f[p_] := p x

that multiples the argument by a global variable x, might give
unexpected behavior if it happens to be called from within a Block that
uses x as a local variable:

In[2]:= x = 2.7; f[5]

Out[2]= 13.5

In[3]:= Block[{x = 99.5}, f[5]]         

Out[3]= 497.5

That conflict won't happen if Module is used:

In[4]:= Module[{x = 99.5}, f[5]]         

Out[4]= 13.5

The other type of difficulty with global variables and Block occurs for
functions that accept symbolic values for function arguments.  Here,
for example, is a function that behaves differently depending on the
name of the argument:

In[5]:= MultiplyByTwo[p_] := Block[{n = 2}, n p]

In[6]:= MultiplyByTwo[z]

Out[6]= 2 z

In[7]:= MultiplyByTwo[n]

Out[7]= 4

Again, that conflict doesn't come up if Block is replaced by Module:

In[8]:= MultiplyByTwo[p_] := Module[{n = 2}, n p]

In[9]:= MultiplyByTwo[n]

Out[9]= 2 n

Probably most programmers would argue that the first example is not, as
you put it, a well-structured program, so you probably don't need to
worry about that.  The second example is of deeper concern, but if your
packages don't use symbolic values for function arguments, or if your
packages use contexts (such as through a package structure involving
BeginPackage and Begin) so that the Block variables are in a private
context, then this type of conflict is unlikely to come up except
internal to the package, which you can watch out for, or if a malicious
user decides to re-use the private package context.

There are not any exotic internal issues (such as "heap management or
stack size limitations") that merit consideration here.  Both Block and
Module are useful in different situations.  It is certainly not
uncommon to prefer Block over Module purely for the speed reason that
you mentioned, but these functions are not terribly complicated, and
the choice in most cases should be based primarily on an understanding
of the type of variable localization that is appropriate for the

Dave Withoff
Wolfram Research

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