[Issue 366] Adding trailing zeros to a real literal makes it smaller!

[Don Clugston]

Walter Bright wrote:
> Don Clugston wrote:
>>> Conversion from decimal to binary is done using "round to nearest", not
>>> "truncate towards zero". Round to nearest will 50% of the time result 
>>> in larger
>>> numbers than truncating towards 0. Adding 0's to the literal is the 
>>> same as
>>> truncate towards zero.
>>
>> In fact, adding ANY digits to the literal makes it smaller. This one 
>> also fails:
>>
>> static assert(
>> 0.6600_0112_2408_4800_3227e-8L <=
>> 0.6600_0112_2408_4800_3227999999999999999999999999999999e-8L);
> 
> Those extra digits are beyond the precision of the floating point 
> format. Try printing them out in %a format to see the bit pattern. The 
> behavior is governed by C's strtold, and it does the same thing in gcc.
> 
> I can send you the source to strtold if you want to examine it.

Don't worry, I'm a constant user of the %a format!
I've been reading a recent draft of the IEEE 754R standard. It states:
(here μ = real.dig, but could be quadruple.dig if it were expanded).
-----------
If more than μ digits are given for decimal-string to internal 
conversions, the result of the conversion shall be
as if it were carried out in two steps: First round the given number to 
μ decimal digits, and then convert the
resulting μ-digit number to the target format, in both cases rounding 
correctly according to the prevailing
rounding mode.

As a consequence of the foregoing, conversions shall be monotonic: 
increasing the value of an internal
floating-point number shall not decrease its value after conversion to 
an external character sequence, and increasing the value of a external 
character sequence shall not decrease its value after conversion to an
internal floating-point number.
------------
It's the first step (decimal rounding) that appears to be missing.
I don't know how much of a change this is from IEEE 754. Without 
monotonicity, you need to be very careful about increasing the precision 
of constants.