Greetings,
I have released SLICE-basic-Complex to PharoInbox and created added ISSUE #
1097.
I believe this proposal addresses most of the concerns I have seen.
Thanks again for your review and helpful comments!
A brief discussion follows.
-KenD
=====================================
The SLICE-basic-Complex package (re)adds Complex objects to the Pharo Beta 1
image.
YOU MUST LOAD the SLICE-remove-Complex package BEFORE LOADING THIS PACKAGE !!
==PROBLEMS==
In mathematics, type Complex is a superset of type Real, but in Pharo the
class Complex is unrelated to subclasses of Number. This causes some common
expectations to be disappointed. In particular, the following patterns break
down:
[1] If (A=a) and (B=b) and (A<B) then (a<b)
[2] A squared sqrt = A
[3] A isNumber => (A class) isKindOf: Number
[4] Pharo users and code have expectations that (-1 sqrt) causes an
exception.
[1] | A a B b |
A := 0.
a := A + 0i.
B := 1.
b := B asComplex.
A = a. "true"
B = b. "true"
A < B. "true"
a < b. "ERROR"
[2]
1i squared. "-1 + 0i"
1i squared sqrt. "ERROR"
1i squared real sqrt. "ERROR"
[3] (1.2 + (1/2)i) isNumber. "true"
(1.2 + (1/2)i) class isKindOf: Number. "false"
In particular, isNumber is used in a number of low-level methods which would
not deal well with complex numbers.
E.g. FloatArray>>
*= anObject
^anObject isNumber
ifTrue:[self primMulScalar: anObject asFloat]
ifFalse:[self primMulArray: anObject]
==SOLUTIONS==
[A] SLICE-remove-Complex
Removing the Complex code gives more traditional Smalltalk expectations. In
particular this conservative approach yields the best code backward
compatability because Complex is a relatively recent addition to Squeak and
was not present in many older Smalltalk implementations. In particular,
problems [1][2][3] cannot arise.
[B] SLICE-basic-Complex
[1] is fixed by adding a "formal" method to Complex with selector #< which only
compares real numbers (those whose imaginary component is zero).
[2] is addressed by keeping Complex objects disjoint from Numbers.
Explicit coercion is required
1i squared asComplex sqrt -> 1i
-4 asComplex sqrt -> 2i
The examples shown above continue to yield exceptions.
[3] Complex objects are NOT numbers, but objects with number-like behavior.
Complex instances answer false to isNumber. There is a isNumberOrComplex
predicate which is used in the Number>>= methods in place of isNumber so that
the double dispatch coercions work as expected with Numbers and Complex
instances.
Note that the basicComplex package also adds the hyperbolic trig functions to
Numbers.
-KenDickey [Ken dot Dickey at Whidbey dot Com]
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