[J3] Question on TINY example

Steven G. Kargl kargl at uw.edu
Wed Jun 22 18:19:03 UTC 2022

On Wed, Jun 22, 2022 at 05:40:37PM +0000, Mark LeAir via J3 wrote:
> Another one of our compiler engineers pointed this out to me.  Do we agree this example needs fixing?
> In F'2018, 16.9.191, the example has TINY(x) == 2**(-127) for default real.  I think that should be 2**(-126).
> 32-bit IEEE-754 has an exponent bias of 127.  For example, 1.0 is 0x3f800000, whose exponent field is 127.  So the smallest normal value, which has an exponent field of 1, is 2**(-126) times 1.0.  And TINY() is the smallest normal (full precision) value.
> If this example is fixed, then so should the example for RANGE (16.9.158).
> If the example for TINY() is not wrong, then the floating-point model used for examples is not IEEE-754, and if that's the case, that should be fixed.
> The example for TINY() in draft F'202X is the same (16.9.209).

The description of TINY is correct with respect to the model given
in 16.4 NOTE 1.  I cannot find any text that claims the model in
NOTE 1 represents to IEEE-754 binary24. 


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