🚀 go-pugleaf

> Some time ago I wrote some procedures for rounding real numbers:
> 
> PROCEDURE round (x:LONGREAL; n:INTEGER): LONGREAL;
> (* Round x to n digits. *)
> 
> PROCEDURE roundp (x:LONGREAL; n:INTEGER): LONGREAL;
> (* Round x to n digits behind the decimal point. *)
> 
> PROCEDURE RealToStr (x:LONGREAL; n:INTEGER; VAR s:ARRAY OF CHAR);
> (* Convert x to s, rounding to a total of n characters.
>    n>0: floating point, else exponential.
> *)
> 
> I am not so happy with my solutions, because I use logarithms and 
> exponential functions to generate power-of-10-factors for left- and 
> right-shifting and ENTIER for truncation. Sometimes arithmetic errors in 
> those functions give me a result of 9.99 when I want to round 10. 
> 
> Does anybody know procedures or algorithms or references about that topic? 

I wrote some routines which implement a rounding function as follows:

   real:=real+FIVE*ipower(TEN, exp-sigFigs);

where exp is the real number's exponent, sigFigs is the number of significant
digits, and ipower raises a floating point number to an integral power using
Knuth's algorithm.  The number's exponent (exp) is extracted as follows:

  exp:=0; x:=ABS(x);
  IF x=ZERO THEN RETURN exp END;  (* exception could be raised here *)
  WHILE x>=TEN DO x:=x/TEN; INC(exp) END;
  WHILE (x>ZERO) & (x<1.0) DO x:=x*TEN; DEC(exp) END;  

> Dr. Frank Hrebabetzky		Fax:	+55 / 48 / 234-1514

I'm not sure if these algorithms will fix your problem but they do not
rely on logarithms or exponential functions so they may work out better
for you.  In general, radix 2 to radix 10 conversions are usually only
approximate except when dealing with integral numbers so errors can be
expected.  Avoid multiplying by the number 0.1 since it is not exactly
representable in radix 2 with a finite number of digits.

If you need exact decimal numbers, I have some routines which implement
these as well (at the expense of not being able to take advantage of
floating point hardware).


Regards,
	Michael
--------------------------------------------------------------
Michael Griebling, P. Eng.		mgriebling@bix.com
Computer Inspirations			grieblm@trt.allied.com