[Cfp-interest 1927] action item: suggest rewordings for F9.2 of n2596.pdf

[David Hough CFP]

Subject: action item: suggest rewordings for "numerically equal" and "numerically equivalent" in F9.2 of n2596.pdf

Existing:

 F9.2 Expression Transformations
 
 x/2 <-> x * 0.5 page 449  (also in C18)
 Although similar transformations involving inexact constants generally do not
 yield numerically equivalent expressions, if the constants are exact then such transformations can be made on IEC 60559 machines and others that round
 perfectly.

=== suggestion
change "numerically equivalent" to "equivalent"
===
 
 page 450 (added since C18)
 EXAMPLE 1. * x -> x is valid for decimal floating-point expressions x,
 but 1.0 * x -> x is not:
 1. ? 12.34 = (+1, 1, 0) ? (+1, 1234,?2) = (+1, 1234,?2) = 12.34
 1.0 ? 12.34 = (+1, 10,?1) ? (+1, 1234,?2) = (+1, 12340,?3) = 12.340
 The results are numerically equal, but have different quantum exponents,
 hence have different values.

=== suggestion
change "numerically equal" to "equal"
===

 F9.3 Relational operators page 450  (also in C18)
 x < y -> isless(x,y)
 Though numerically equal, these expressions are
 not equivalent because of side effects when x or y is a NaN and the state
 of the FENV_ACCESS pragma is "on".
 This transformation, which would be
 desirable if extra code were required to cause the "invalid" floating-point
 exception for unordered cases, could be performed provided the state of the
 FENV_ACCESS pragma is "off".

=== suggestion
change "numerically equal" to "the same boolean values"
===