[comp.binaries.mac] ABC calculator 1.0

guido@mcvax.cwi.nl (Guido van Rossum) (05/22/87)

[ABC Calculator 1.0 - part 1 of 2]

Here's a Desk Accessory I've written using MPW C. It's copyrighted but
can be freely copied as long as you don't make money for it.  Source
(also copyrighted but free) is available on request; see author's
address, below.

After un-binhex-ing you get a compressed packit file, which unpacks to a
Desk Accessory file and two versions of the documentation: one as ACTA
document, one as text file.  A summary of the documentation is given here.

It's a calculator with a couple of odd features.  First, input consists
of free-form expressions from a simple programming language.  The syntax
is given below.  Second, all operations are carried out with arbitrary
precision, and results printed are exact if representable exactly in
decimal notation.  Even if a variable can't be printed exactly, it is
still represented exactly internally: after "x=1/3" the value of x will
print as ~.33333333333333333333, but x*3 will print as 1. This is
possible because x is represented internally as a pair (numerator,
denominator). 

It also serves as a trivial text file editor, not unlike miniWRITER (wut
without Undo, Find and Print capabilities). 

It's called "ABC Calculator" because the expression syntax is a subset
of the syntax of the ABC programming language.  For more information
about this language, see the January, 1987 issue of "IEEE Software" (and
also an issue of Byte in the near future). 

Here's the syntax of the expressions (using | to separate alternatives,
[ ] to bracket optional parts, and * to indicate 0 or more repetitions):

statement: variable '=' statement | expression expression: number |
variable | '(' statement ')' | formula formula: expression dyadic-op
expression | monadic-op expression dyadic-op: '+' | '-' | '*' | '/' |
'**' |'mod' | 'round' monadic-op: '+' | '-' | '/*' | '*/' | 'round' |
'floor' number: digits ['.' [digits]] [exponent] | '.' digits [exponent]
exponent: letter-e [sign] digits letter-e: 'e' | 'E' sign: '+' | '-'
digits: digit digit* variable: letter letgit* letgit: letter | digit

This syntax is ambiguous: it does not show the priorities of the
operators, which is roughly as follows (listed from high priority to
low):

**
monadic + and -
* and /
dyadic + and -

The more esoteric operators have no fixed priority; parentheses must be
used when they are used in the same expression as other operators.  This
is also true for expressions like a/b/c, a/b*c or a**b**c, which have
more than one interpretation in the human eye. 

Description of individual operators:

x**y: x to the power y; y must be an integer
+, -, *, /: the usual arithmetic operations
floor x: the largest integer not exceeding x; floor -2.2 is -3 round x:
x rounded to the nearest integer; round -1.5 is -2 n round x: x rounded
to n digits; 5 round (2/3) is .66667 x mod y: x modulo y, computed as
x-y*floor(x/y); 2 mod -.3 is -.1
*/x: the denominator of the fraction representing x; */(-2/6) is -1
/*x: the denominator of the fraction representing x; /*(-2/6) is 3

Author's address:

	Guido van Rossum
	CWI, dept. AA
	P.O.Box 4079
	1009 AB Amsterdam
	The Netherlands

Electronic mail: guido@cwi.nl, or guido@mcvax.uucp, or
guido%cwi.nl@seismo.css.gov (from the ARPAnet). 

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--- end of part 1 ---

guido@mcvax.cwi.nl (Guido van Rossum) (05/23/87)

[ABC Calculator 1.0 - part 2 of 2]

---
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--- end of part 2 ---