8 Nov 2005 23:37:15 -0500

Related articles |
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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) |

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

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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