Getting the integer part of a real

Getting the integer part of a real

[emery]

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!emery@seismo.css.gov
after 10 Nov:             	linus!emery
		      		emery@mitre-bedford.arpa

Re: Getting the integer part of a real

[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.

Re: Getting the integer part of a real

[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

Re: Getting the integer part of a real

[emery]

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.
			emery@mitre-bedford.arpa

	    

Re: Getting the integer part of a real

[David desJardins]

In article <996@wayback.UUCP> arny@wayback.UUCP (Arny B. Engelson) writes:
>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:

   Not to restart the flame wars (I hope!), but when this topic has been
discussed in the past, the consensus (at least among mathematicians) has
been that "round-down" is preferable to "round-toward-zero."  At the very
least it is not clear that the latter is preferable.

   -- David desJardins

Re: Getting the integer part of a real

[Hazel]

Oops, you got me!  OK, first check if the number is positive or negative, and
do the 'correct' thing.  Obviously, I hadn't thought it all through when
I posted that.  The context of our discussion (at Siemens) on that was 
1.  realizing what the language said, and
2.  coming up with a strategy to get the integer part that didn't depend on
    underlying implementation.  
"The details are left to the reader"  (Meaning, I'm too lazy to work them 
out.  

Thanks, Ken.

				Dave Emery