[Maxima-discuss] A proposal to solve Re: float(exp(10000)) works, but float(exp(10000/3)) doesn't

[Richard F. <fa...@be...>]

On 1/27/2016 12:33 PM, Stavros Macrakis (Σταῦρος Μακράκης) wrote:
> Is auto-promotion of floats to bfloats a good idea?

There is an argument to be made that machine floats are
just too confusing to use.  We probably all recall newbie questions
about why Maxima floats come up as x.999999999  .  The answer
being  "That's the way binary floats work" in every language.

Here's one alternative.  (Parts were/are? used in Maple).
1. All numeric input is treated as exact decimal and stored as decimal.
2. All internal numbers are, in effect, decimal bigfloats.
3. bigfloat precision is a simple decimal number of digits.
4. underlying representation can be the existing decimal bigfloats
   already in Maxima. (Maxima has both decimal and binary.  The decimal
bigfloats are used for computing output forms.  Multiplying/dividing by 10
is presumably slower than shifting, but what's the hurry?)

Consequences:

1. no newbie questions.
2. no overflow.  The exponent is an arbitrary integer. At least the bound is
what comes with your lisp/hardware.
3. no underflow. The exponent is an arbitrary negative integer.
4. There is a clear separation between very large numbers and "Infinity" 
symbol(s).
5. The discrepancy between lisp implementations will disappear -- we 
will not
see the handling of overflows as exceptions in system 1 and the 
production of In.fty
in system 2.
6. We  could have a set of routines that "converts to machine float and 
calls
numeric libraries" for quadrature, numeric float linear algebra 
subroutines,  etc.

Negative consequences

1. Eh, not so fast?  Would anyone notice the machine float speed in the 
blizzard
of other operations surrounding each operation?
2. The reverse newbie questions,  which is to say, someone says How is 
it that
0.1 is exactly the same as 1/10 on Maxima, when I know they differ by 
5.2e-18
in binary.
3. There is still rounding error, setting precision appropriately matters.
4. Reprogramming, redocumentation,.




Please feel free to comment/ elaborate/implement?

RJF


>
> Are there practical applications, where a user will get a useful 
> answer rather than an error to a substantive problem
> ​ ? I doubt it; I suspect this only happens with
> ​ ​
> artificial problem
> ​ s​
> designed to test Maxima's limit
> ​ s.)​

No, I think people fall into underflow/overflow traps unintentionally.  
Not deliberately
testing Maxima, but at the border of their smarts.  So the purpose would 
be to
give an answer that deserves further thought instead of "darn, it bombed 
out".