Inverse of FAQ 7.31.
On Aug 2, 2011, at 08:02 , Rolf Turner wrote:
Why does R think these numbers ***are*** equal? In a somewhat bizarre set of circumstances I calculated x0 <- 0.03580067 x1 <- 0.03474075 y0 <- 0.4918823 y1 <- 0.4474461 dx <- x1 - x0 dy <- y1 - y0 xx <- (x0 + x1)/2 yy <- (y0 + y1)/2 chk <- yy*dx - xx*dy + x0*dy - y0*dx If you think about it ***very*** carefully ( :-) ) you'll see that ``chk'' ought to be zero. Blow me down, R gets 0. Exactly. To as many significant digits/decimal places as I can get it to print out. But .... I wrote a wee function in C to do the *same* calculation and dyn.load()-ed it and called it with .C(). And I got -1.248844e-19. This is of course zero, to all floating point arithmetic intents and purposes. But if I name the result returned by my call to .C() ``xxx'' and ask xxx >= 0 I get FALSE whereas ``chk >= 0'' returns TRUE (as does ``chk <= 0'', of course). (And inside my C function, the comparison ``xxx >= 0'' yields ``false'' as well.) I was vaguely thinking that raw R arithmetic would be equivalent to C arithmetic. (Isn't R written in C?) Can someone explain to me how it is that R (magically) gets it exactly right, whereas a call to .C() gives the sort of ``approximately right'' answer that one might usually expect? I know that R Core is ***good*** but even they can't make C do infinite precision arithmetic. :-) This is really just idle curiosity --- I realize that this phenomenon is one that I'll simply have to live with. But if I can get some deeper insight as to why it occurs, well, that would be nice.
I think the long and the short of it is that R lost a couple of bits of precision that C retained. This sort of thing happens if R stores things into 64 bit floating point objects while C keeps them in 80 bit CPU registers. In general, floating point calculations do not obey the laws of math, for example the associative law (i.e., (a+b)-c ?= a+(b-c), especially if b and c are large and nearly equal), so any reordering of expressions by the compiler may give a slightly different result.
Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com "D?den skal tape!" --- Nordahl Grieg