Getting the integer part of a real

[em...@gypsy.uucp]

When we discovered the 'feature' in Ada that an implementor can pick how
he rounds, we discussed various ways to get the integer part of a number.
Here is the 'best' (meaning most portable) way: (p.s. this 'algorithm'
is obviously language-independent)

declare
x : real;
i : integer; -- integer part of x
begin
i := integer(x);
if (i > x) then
-- machine rounded up
i := i - 1;
end if;
end;

Dave Emery
until 7 Nov: ...princeton!siemens!emery
princeton!siemens!em...@seismo.css.gov
after 10 Nov: linus!emery
em...@mitre-bedford.arpa

[Robert Firth]

Given

x : float;
i : integer;

then the line

if (i > x) then ...

won't work, since ">" isn't defined between integers
and floats. This is perhaps what is meant:

if float(i) > x then ...

However, this does not really help the hard-core numerical
programmer, who most likely wants X rounded but left in
FLOATING representation - since otherwise he can use only
a very restricted subrange of float.

What we really need is the set

function FLOOR (X : FLOAT) return FLOAT;
CEIL
ROUND
TRUNC

and let's make them generic in the domain type.

[Arny B. Engelson]

Dave Emery writes:
>
> When we discovered the 'feature' in Ada that an implementor can pick how
> he rounds, we discussed various ways to get the integer part of a number.
> Here is the 'best' (meaning most portable) way: (p.s. this 'algorithm'
> is obviously language-independent)
>
> declare
> x : real;
> i : integer; -- integer part of x
> begin
> i := integer(x);
> if (i > x) then
> -- machine rounded up
> i := i - 1;
> end if;
> end;
>

The above algorithm only works for POSITIVE values of X! For example, if
X = -0.7 this will return -1 instead of 0. The "integer part of a real number"
is a truncate function:

function Trunc (X : Float) return Integer is
I : Integer := Integer (X);
begin
if I > 0 and then
Float(I) > X then
I := I - 1;
elsif I < 0 and then
Float(I) < X then
I := I + 1;
end if;
return I;
end Trunc;

This should return whatever is before the decimal point in a floating point
number.

Arny B. Engelson
{ihnp4 | bonnie | clyde } wayback!arny
(201) 386-4816

[em...@gypsy.uucp]

oops, made a type mismatch mistake in the last note:

comparison should be:

if (real(i) > x) then
i := i - 1; -- machine rounded up

There is no operation ">" (L : integer, R : real)....

Sorry about that, chief...

Dave Emery
Mitre Corp.
em...@mitre-bedford.arpa