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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

2007.0. "Precedence of Exponentiation" by AD::DEVER () Fri Oct 27 1995 10:46

	Does exponentiation take precedence from right to left or from left
    to right?  In other words, is the expression
    
		      z
		     y	      
		    X

	   	   (y^z)	    z
    equivalent to x      or to (x^y) ?

	My guess is right to left.  I've found only two references, neither
    of them mathematically authoritative: both HP (HP-48) and Casio
    calculators use left to right precedence, and Fortran uses the opposite.

	Any reply would be appreciated, but, since I need to know by Monday
    evening, a quick reply would be helpful.  References would be
    particularly helpful.

    /Dan

T.R	Title	User	Personal Name	Date	Lines
2007.1	FORTRAN was right	EVMS::HALLYB	Fish have no concept of fire	`Fri Oct 27 1995 12:13`	4
	> (y^z) z > equivalent to x or to (x^y) ? The former.
2007.2	the logic behind it	WIBBIN::NOYCE	EV5 issues 4 instructions per meter	`Fri Oct 27 1995 14:19`	3
	Left-to right would have made a^b^c the same as a^(b*c), which is considered pointless. So that's why it's right-to-left, and a^b^c = a^(b^c).
2007.3	Looking for Law, not Truth	AD::DEVER		`Fri Oct 27 1995 14:58`	8
	To clarify a bit, I'm looking for a reference to use as an authority to prevent a potential dispute. Something along the lines of "The Annals of the International Math Board," if there is such a thing. I have found another reference: _CRC_Handbook_of_Mathematical_Sciences_. Does this carry a lot of weight? (It agrees with right to left.) /Dan
2007.4	CRC should cite references for each section	EVMS::HALLYB	Fish have no concept of fire	`Fri Oct 27 1995 16:10`	9
	Well, where's the authority that says multiplication has higher precedence than addition? Or that subtraction associates left-to-right? Hmm, a little PostScript and I could have a reference card wiht all sorts of official-looking endorsements. Will that do? :-) John
2007.5		AUSSIE::GARSON	achtentachtig kacheltjes	`Sat Oct 28 1995 04:58`	26
	re .3 I don't think there is an applicable ISO standard. Can you elaborate on the potential dispute and perhaps we can advise you on the most appropriate reference source or standard? By the way, precedence is not the same thing as associativity. It is the latter to which you are referring in .0. For the reasons stated in .2 the more sensible associativity for the exponentiation operator is right to left. However any programming language is entitled to define its operators to have whatever precedence and associativity is seen fit for that language and indeed programming languages do differ in this area. The calculators are presumably using the non-standard left-to-right associativity for reasons of technical limitations. A simplistic calculator would simply evaluate each operator in the order entered without regard to precedence or associativity. This minimises the need for intermediate storage. A more sophisticated calculator might define a limited number of precedences and be able to store that number of intermediate values. However implementing right-to-left associativity would potentially require an unlimited amount of intermediate storage. This is barely an issue on modern computers but could be an issue with a calculator (or at least not worth designing for).