Re: understanding floating point types

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Sun, 22 Aug 2010 12:05:33 -0700 (PDT), Ada novice wrote:

> 1. You used: type My_Float is digits 3; I tend to confuse the fact
> that digits 3 means 3 digits of precision after the decimal point? So
> when I consider 2.33 or 3.45, then both numbers are with digits 2 in
> my mind. Or does digits 3 mean 3 significant digits which will include
> the leading 2 in 2.33 and the leading 3 in 3.45 as well?

Yes, it is relative, in the case of floating-point numbers. Ada has another
model of real numbers, the fixed point numbers, they have an absolute
precision.

> 2. In your example, you have:
> 
> Model view: 8.04E+00
> The reality: 8.03850E+00
> 
> If I understand correctly, model view represents the number that is
> exactly representable by the computer.

Yes, the model number is your requirement. The machine number is an
implementation that fulfills your requirement.

> In our case here, we can get
> the reality number since Float has higher precision digits than
> My_Float. However if My_float used the same precision digits as Float
> (i.e. 6) then this would also represent the number that could be
> represented by the computer. If both a and b had a hypothetical 30
> digits of precision, then neither Float (6 digits) nor Long_Float (15
> digits), nor Long_Long_Float (18 digits) would give the right value
> that would represent the model number of the multiplication result
> a*b.

Neither they would a or b. 30 digits precision require 101 bits of machine
mantissa.

> I mentioned the word hypothetical, as we would not able to use a
> number with 30 digits of precision anyway on a computer. But my point
> was to say that Model view doesn't have to have less precision digits
> as the reality number.

The machine number precision must be equal or greater than the model one.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de