Monday, November 27, 2006

operations on numeric types

First a bit of info about the built-in numeric types, in case you never saw them before or in case you have forgotten. The floating point types: 'single', 'double' and 'real' (not the subject of this article). The integral types: 'byte', 'nat16', 'nat32', 'nat64', 'int16', 'int32', 'int64' and 'int'. A 'byte' is unsigned and 8 bits. The 'int*' types are signed integer types (specified size or native int type), 'nat*' are unsigned integer types (again, of the specified size or else the native size). The native ones, 'int' and 'nat' are equal in size and have the size of the target platform (32 or 64 bit).

I am still somewhat unsure about the operations on those types. For example: what type should the result of a unary minus on a 'nat16' be? I would say 'int32', because the result can require 17 bits and that would not fit into a 'int16'. And I want to avoid unexpected overflows as much as I can. But this leaves me with some unpleasant consequences. I have no type to use for the unary minus on a 'nat64'. And neither I have for the native 'nat', because it would require one more bit than the 'int' has. So at this time there is no unary minus available for those two types. This problem of course doesn't exist for the 'int*' types; for example the unary minus operation on a 'int16' returns an 'int16' again.

I propose the following 'solution': I give the 'nat*' types a member function 'truncateToSigned', or something like that, which discards the most significant bit and then returns a signed type of the same size as the original. Like this:

class nat16
# (...)
const procedure truncateToSigned() : int16
# truncate and convert to signed

This allows the programmer to do what he/she wants, but allows for data loss. But at least the 'corruption' is visible by looking at the name of the function!

I already provided the 'int*' types with a function to turn the sign. This is a way to write assignments like 'delta = -delta' like this: 'delta.turnSign' (will be available in the next compiler version). This function doesn't return a result and changes the value of the object itself. (So it is different from the unary minus, which does not change its object and instead returns a value.) I wasn't completely sure about the name, maybe I could have used something like 'negate' instead but I am not sure if that means what's intended (I am not a native English speaker).

I am thinking about a signed byte type. At this type the literal -1 has type int16. That looks like a bit of a waste for such a small number. So it would maybe be nice to add a type (e.g. 'sbyte') for unsigned 8-bit values. Then I could add to 'byte' also a member 'truncateToSigned' to return a signed equivalent. But to avoid loss the unary minus of 'byte' would still return an 'int16'.

Another proposition. We now have a way to make a signed from an unsigned but not the other way around. So I would like to add a member 'abs' (= absolute value) that gives the unsigned value. I don't really like 'abs' because it looks to short. But on the other hand, something like 'absoluteValue' looks too long. Suggestions and argumentations for a name are of course welcome :-)

P.S.: I converted my blog to the new Blogger Beta, and it looks like the RSS of the old articles is a bit messed up now

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