[Maxima-bugs] [ maxima-Bugs-620070 ] rat->float loses 9 digits of precision!

[<no...@so...>]

Bugs item #620070, was opened at 2002-10-08 00:30
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=620070&group_id=4933

Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: rat->float loses 9 digits of precision!

Initial Comment:
Maxima 5.5 / gcl 2-3.6 / Windows 2000 / Athlon

num: 1099511627775 $
den:  1099511627776 $

fnfd : float(num)/float(den) => 0.9999999999990905 
(correct)
but
fnd: float(num/den) => 0.9999999403953552

That is, we're only getting 7 digits of precision when our 
floating point actually supports 16!

The problem is in Fpcofrat1, with the value of machine-
mantissa-precision, which is substituted at read-time, 
and is defined as:

(eval-when (compile load)
(defconstant machine-mantissa-precision
  (float-digits 1d0))
)

Apparently when Maxima was built, this evaluated to 24, 
not to 53 as it should have.

Correcting machine-mantissa-precision to 53 and 
redefining fpcofrat1 with the correct value gives the 
correct result.

Why does machine-mantissa-precision have the wrong 
value?  Is Maxima cross-compiled for Windows?

Anyway, while looking at the fpcofrat1 code, I realized 
that it could be simplified and optimized at the same 
time.  Here is my code.  Does someone want to look it 
over and check it in?

-----------

The following code takes advantage of modern floating 
point's extended range for the common case, and 
Maxima's bfloat routines to simplify the (very rare) case 
where a numerator or denominator has more than 300 
digits.

;; Convert rational number NU/D to float
(defun fpcofrat1 (nu d)
  (if (and (< (abs nu) most-positive-double-float)
	   (< (abs d) most-positive-double-float))
      ;; Machine arithmetic is excellent
      (/ (float nu) d)
    ;; ...except in the rare case where nu or d are huge
    (let ((fpprec #.(+ machine-mantissa-precision 3)))
      (fp2flo ($bfloat (list '(rat simp) nu d))))))


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>Comment By: Raymond Toy (rtoy)
Date: 2002-10-15 12:51

Message:
Logged In: YES 
user_id=28849

This appears to be fixed in the CVS sources.

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You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=620070&group_id=4933