R help - Nov 1998 - seq() in 0.62.4 and 0.63

Solaris 2.6, R Version 0.63.0  (November 14, 1998)
               Version 0.62.4  (October 24, 1998)
> seq(0.15, 0.70, 0.05)
 [1] 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

The much reviled (on r-help) 0.62.3 got such simple cases right (even if
0.62.1 did not). 

Jim Lindsey insisted that such bugs are reported here, so I am.  And yes,
this is a real example and leads to an incorrect analysis of the dataset in
question. 

The problem is the lines

                            if (by > 0) 
                                    while (from + n * by > to) n <- n - 1
                            else while (from + n * by < to) n <- n - 1

One should try to avoid exact comparisons on floating-point quantities.
Given the work above to choose a suitable tolerance, we can attach a
tolerance here, say

      if (by > 0)  while (from + n * (1 - eps) * by > to) n <- n - 1
      else         while (from + n * (1 - eps) * by < to) n <- n - 1   

although I suspect eps is actually rather too small for safety (I would
suggest 10 x machine precision to allow for a number of lfoating point
operations).

However, I think there is a much simpler approach:

	    n <- as.integer(n + 0.1) # make sure n is not too small
            tol <- abs(to - from) * 10 * .Machine$double.eps
	    if(by > 0)	while(from + n*by > to + tol) n <- n - 1
	    else	while(from + n*by < to - tol) n <- n - 1


Brian

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Prof Brian D Ripley <ripley at stats.ox.ac.uk> writes:
> Solaris 2.6, R Version 0.63.0  (November 14, 1998)
>                Version 0.62.4  (October 24, 1998)
> 
> > seq(0.15, 0.70, 0.05)
>  [1] 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65
> 
> The much reviled (on r-help) 0.62.3 got such simple cases right (even if
> 0.62.1 did not). 
Argh!!!! We've been discussing alternative ways of getting seq right,
but didn't get around to follow it through.
> although I suspect eps is actually rather too small for safety (I would
> suggest 10 x machine precision to allow for a number of lfoating point
> operations).
The : operator already uses 1e-7... (just like S does)
> However, I think there is a much simpler approach:
> 
> 	    n <- as.integer(n + 0.1) # make sure n is not too small
>             tol <- abs(to - from) * 10 * .Machine$double.eps
> 	    if(by > 0)	while(from + n*by > to + tol) n <- n - 1
> 	    else	while(from + n*by < to - tol) n <- n - 1
I've been advocating by*(from/by):(to/by), so as to have the fuzz-fix
in one place, and:
> .05*(.15/.05):(.70/.05) 
 [1] 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

Of course one needs to get the sign things right as well...

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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