Ada Digits Confusion

Question

I have been doing some reading, and I'm having a tough time understanding how to interpret something that is a "digits x". I.E.

type something is digits 6

I get that it's 6 digits of precision, but I guess what has me mixed up is what does that mean.

1) Y.XXXXXX (6X's),

2) XXX.XXX (Any number of digits, just will always be 6 of them counting both fore and aft the mantissa)

...

I'm just trying to understand what a range of something that is digits 6 (or digits n to be more generic), is there a formula I can simply plug into to determine what my ranges are on a type that is some number of digits?

Answer 1

A type declared with digits is a floating-point type, similar to Float or Long_Float.

The 6 is "the minimum number of significant decimal digits required for the floating point type". For example, all the following will be represented reasonably accurately (but not exactly):

type My_Real is digits 6;
X: My_Real := 1.23456;
Y: My_Real := 12345.6;
Z: My_Real := 1.23456E7;

In practice, there are usually just 2 or 3 underlying floating-point types on a given system. The compiler will choose an appropriate one as the underlying type for your declaration. In practice, two types declared with digits 2 and digits 6 will probably have exactly the same representation and precision.

Understanding the phrase "not exactly" requires an understanding of floating-point that's well beyond the scope of a single question, but if you're familiar with floating-point in other languages, it's the same general idea.

If you want a general understanding of what floating-point is and how it works, the Wikipedia Article isn't bad. A much more advanced treatment is David Goldberg's classic paper "What Every Computer Scientist Should Know About Floating-Point Arithmetic", available here as a web page and here as a PDF.