On Thu, 15 Oct 2009, Raymond Toy wrote:
< reyssat wrote:
< > Hi,
< >
< > I have some questions and remarks about precision of floats and bigfloats.
< >
< > I construct
< >
< > f(i):=block([u], u:sqrt(10^(2*i)+1)/10^i, print(bfloat(u)),print(float(u)));
< >
< > then :
< > (%i3) f(2);
< > 1.000049998750063b0
< > 1.000049998750062
< >
< > **** this is ok, just slightly strange that float gives a better result
< > than bfloat (the right answer is 1.000049998750062496..., so should be
< > rounded to ...0062 and not ...0063).
< >
< I think bfloats try to be accurate, but there's no guarantee that it is
< accurate to the last bit, especially for the special functions.
< > By the way, I cannot find in the documentation (at least in chapter 10,
< > floating point) the definition and precision of a float.
< >
< The precision of a float depends on the double-float type of the
< underlying lisp. But I think everyone uses IEEE double-floats, so the
< precision is well defined.
< >
< > (%i5) f(200);
< > 1.0b0
< > Maxima encountered a Lisp error:
< >
< > Error in PROGN [or a callee]: Can't print a non-number.
< >
< > Automatically continuing.
< > To reenable the Lisp debugger set *debugger-hook* to nil.
< >
< > **** bfloat is ok. But float cannot calculate this since some
< > intermediate result is too big (once again, is the limit for the
< > exponent given in the documentation ?), although the result itself is a
< >
< No I don't think the limit is in the documentation. But the largest
< IEEE number is 2^1024 minus one bit. There is some package that has
< this information, but I can't remember the name of the package.
Ray, do you mean the lisp constants
most-positive-double-float
most-positive-fixnum
etc.? These are accessible in the ususal way from within maxima:
:lisp most-positive-fixnum
536870911
:lisp most-positive-double-float
1.7976931348623157e308
Leo
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