# Maximum number of temporary variables needed for math expressions

## ehsan.akhgari@gmail.com8 Nov 2005 23:37:15 -0500

From comp.compilers

Related articles
Maximum number of temporary variables needed for math expressions ehsan.akhgari@gmail.com (2005-11-08)
Re: Maximum number of temporary variables needed for math expressions RLake@oxfam.org.uk (2005-11-12)
Re: Maximum number of temporary variables needed for math expressions henry@spsystems.net (2005-11-12)
Re: Maximum number of temporary variables needed for math expressions spammer@b2z.com (Omri Barel) (2005-11-12)
Re: Maximum number of temporary variables needed for math expressions n1356597638.ch@chch.demon.co.uk (Charles Bryant) (2005-11-12)
| List of all articles for this month |

 From: ehsan.akhgari@gmail.com Newsgroups: comp.compilers Date: 8 Nov 2005 23:37:15 -0500 Organization: Compilers Central Keywords: arithmetic, comment Posted-Date: 08 Nov 2005 23:37:15 EST

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