I have some questions about the REAL type and constrained REAL types.
References to
the standard are to X.680 (07/2002):
1) According to 20.5 NOTE 1 the values
R ::= REAL
a R ::= {mantissa 1, base 2, exponent 0}
b R ::= {mantissa 1, base 10, exponent 0}
are different abstract values even if they both represent the
mathematical real 1.
That's right.
What about two forms expressed in the same base? Is
c R ::= {mantissa 1024, base 2, exponent -10}
the same abstract value as a?
Yes.
2) Is it legal to have constraints on mantissa and/or exponent? For example:
Rm ::= REAL (WITH COMPONENTS {..., mantissa (-999 .. 999)})
Yes, it's legal.
Would the value c from above fulfill this constraint? (It should if it
is the same abstract value as a)
Section B.3.2.5.e reads as follows:
e) Each real value defined with base 2 is normalized
so that the mantissa is odd, and each real value
defined with base 10 is normalized so that the last
digit of the mantissa is not 0.
As I understand it, value c should not violate the constraint since, when
normalized, the mantissa is within bounds. Nonetheless, I wouldn't say
that such a constraint makes much sense.
If this really matters (that is, is not purely an academic question),
please let me know and I'll investigate it further.
3) Does a REAL type with base constraint allow the special real values
PLUS-INFINTY and MINUS-INFINITY? In other words, is this legal:
Rb ::= REAL (WITH COMPONENTS {..., base(10)})
d Rb ::= MINUS-INFINITY
Yes, it's fine.
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