Thoughts on IEEE P754

Waldemar Horwat waldemar at google.com
Fri Aug 22 11:39:57 PDT 2008


Sam Ruby wrote:
>> - We should not print the trailing zeroes.  IEEE P754 does not
>> require it, and it breaks things such as array lookup.  There is
>> precedence for this in ECMAScript:  -0 and +0 both print as "0".  If
>> someone really wants to distinguish among equal numbers, he can do it
>> with a function call to one of the mandated functions.
> 
> Please explain the breakage?

It's already explained in the other emails here.


> When dealing with currency, having 0.05 + 0.05 produce 0.10 is a feature.

Contrary to some beliefs, the different cohort members in IEEE P754 are *not* a valid indicator of precision.  To prove this, assume that the different cohort members are an indicator of precision.  Then evaluate:

  3.00 + 1.00000

IEEE P754 returns 4.00000, while the result is actually precise to only two digits after the decimal point.  Hence a contradiction.  QED.


It gets worse.  If you insist on distinguishing cohort members while printing then you'll really confuse users who print the result of:

1m/.1m

Hint:  The result is equal to 10 but could not print as "10".  Scroll down to see the actual value that distinguishing cohort members would require to be printed.



















































Answer:  Were we to distinguish cohort members, that value of 10 would be required to print as "1e1".  This is unacceptable and, as mentioned before, breaks array indexing.

    Waldemar


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