Maximum number of temporary variables needed for math expressions

ehsan.akhgari@gmail.com
8 Nov 2005 23:37:15 -0500

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Maximum number of temporary variables needed for math expressions ehsan.akhgari@gmail.com (2005-11-08)
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From: ehsan.akhgari@gmail.com
Newsgroups: comp.compilers
Date: 8 Nov 2005 23:37:15 -0500
Organization: Compilers Central
Keywords: arithmetic, comment

Hi all,


Is there any upper bounds on the number of temporary variables that are
needed to translate any given mathematical expression? By intuition, I
guess the answer is 2, but I'm looking for a (possibly formal) proof to
make sure. To make clear what I mean, here is a simple three address
code translation of a math expression using 2 temporary variables:


x+((a+b)*(c/d)-(e*f))


# opcode, operand1, operand2, result
+, a, b, t1
/, c, d, t2
*, t1, t2, t1
*, e, f, t2
-, t1, t2, t1
+, x, t1, t1
# the result is in t1, and t2 is free


Thanks in advance,
Ehsan
[It is my vague recollection that you can use up arbitrarily large
numbers of temporaries by composing operators that aren't commutative
-John]


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