Subject Re: [ib-support] Re: 3 * 1/3 = 0 ??? Raymond Kennington 2002-08-30T19:48:05Z
The C language also treats 1/3 as 0.

rogervellacott wrote:
>
> The issue is not whether it is legitimate to have integer
> operations. It is whether literal values should be interpreted as
> integers by default.
>
> Division by literal values should default to the accurate result, not
> the inaccurate result. So 1/3 should default to 0.3333.. If I have
> declared a variable x as in integer, then it is reasonable that x/3
> (where x = 1) should return 0. But nowhere was I asked to declare
> that 1 was an integer, or that 3 was an integer. So this behaviour

In primary and highschool my maths teachers instilled in us that 3 is not the same as 3.0.

Historically, 3 was a symbol to represent a whole number of objects. Later, notation was
introduced to represent fractional parts of numbers less than one. Today we use the dot or
period.

In Foundations of Mathematics, the development from whole numbers to decimal
representations of fractions has many steps. The notation is not important, but the
representation of 3 is different to the representation of 3.0, although one can propose
several ways to map integers to reals.

The point of this is that 3 is a numeral that represents an integer and an extra symbol is
required to make it otherwise.

Integers and floating-point numbers are stored in different ways in the computer and
operated on with different operators for integers and floats; different registers and
different numbers of registers are used and even a separate floating-point unit is
available in some architectures. In order to operate on integers as floats they must first
be converted.

Now, given that, it is up to the compiler-designer to decide what is to be done when
calculating 1/3, which has the natural computer interpretation of dividing an integer by
an integer. The decision is not whether to treat the numerals as integers or floats, but
whether to treat the division operator / as an integer operator or a floating-point
operator.

What languages do that treat 1/3 as 0 is to interpret the operator as an integer operator
because it operates on integers. This makes it a flexible (or overloaded) operator.

The developer must explicitly inform the compiler to treat the operator as float if that
is desired.

Amongst other things, this is quicker than converting to float, operating and converting
back. Historically, this could have slowed down the operation by a factor of 100 over
doing an integer operation.

However, given that there is an SQL standard, one ought to use it, regardless of any other
argument.

> makes SQL arithmetic quite esoteric, and accident prone.

Quite common, actually. IIRC, FORTRAN and Cobol, as well as C & C++ do the same.

Raymond Kennington