J3/05-193r1
Date: 9 Aug 2005
To: J3
From: Stan Whitlock
Subject: Precision of operation
NUMBER: F03/0066
TITLE: precision of operation
KEYWORDS: precision, operation
DEFECT TYPE: Interpretation
STATUS: For consideration
QUESTION:
Given
REAL X
X = ... some value ...
IF( (X+3.0) .EQ. 3.0 )...
may the X+3.0 be computed with more range and/or precision than that
of REAL? In other words, is PRECISION(X) .EQ. PRECISION(X+3.0) always
true; or is PRECISION(X) .LT. PRECISION(X+3.0) sometimes true?
References are to J3/04-007.
2.4.1.1 Intrinsic type has "The kind type parameter indicates ... the
decimal precision and exponent range for the real and complex types,
..."
7.1.4.2 Type, type parameters, and shape of the result of an operation
has in (4) "For an expression x1 op x2 where op is a numeric intrinsic
binary operator with both operands of the same type and kind type
parameters, ..., the kind type parameter of the expression is
identical to that of each operand."
Since X and 3.0 are the same type and have the same kind type
parameters, 7.1.4.2 (4) appears to require the X+3.0 have just the
range and precision of REAL; no more, no less (otherwise, the
precision is not identical). But, several members of the J3 email
list have said that the "+" may be done with more precision; using
either 1.4(6) or 7.1.8.3 as the reason.
Perhaps something alone the lines of "The values of floating operands
and of the results of floating expressions may be represented in
greater precision and range than that required by the kind type
parameter; the kind type parameter is not changed thereby." should be
added to 7.1.4.2(4).
QUESTION:
Is PRECISION(X) .EQ. PRECISION(X+3.0) always true?
ANSWER:
Yes, that is the definition of PRECISION. The PRECISION intrinsic has
nothing to do with the precision in which the computation X+3.0 is
computed. 7.1.4.2 (4) only describes the precision of the end result
of the computation.
The weasel words in 1.4 (6) allow the processor to compute this expression
in higher precision than REAL.
EDITS:
None
SUBMITTED BY: Fred Tydeman
HISTORY: 05-193 m173 Submitted
05-193r1 m173 Proposed answer