[EMAIL PROTECTED] wrote: > On Oct 2, 1:12 am, Robert Kern <[EMAIL PROTECTED]> wrote: >> [EMAIL PROTECTED] wrote:
>>> How does gmpy make the conversion from float to rational? >> gmpy has a configurable transformation between floats and the internal >> representation. I believe the default goes through str(). > > How do you do that? Is it configurable at run time or something that > has to be done when compiled? Run-time. Use gmpy.set_fcoform(). There is documentation: http://gmpy.googlecode.com/svn/trunk/doc/gmpydoc.txt However, it appears I was wrong about the default. The default will simply extract the C double and call mpf_set_d() on it to convert it to the appropriate internal mpf format. This faithfully gives: In [26]: gmpy.mpf(0.6) Out[26]: mpf('5.9999999999999998e-1') The real conversion to mpq rational numbers takes place in using gmpy.f2q(): In [28]: gmpy.f2q? Type: builtin_function_or_method Base Class: <type 'builtin_function_or_method'> Namespace: Interactive Docstring: f2q(x[,err]): returns the 'best' mpq approximating x to within relative error err (default, x's precision); 'best' rationals as per Stern-Brocot tree; mpz if denom is 1. If err<0, error sought is 2.0 ** err. In [44]: d = gmpy.mpf(0.6) In [45]: d Out[45]: mpf('5.9999999999999998e-1') In [46]: d.getrprec() Out[46]: 53 In [47]: gmpy.f2q(d) Out[47]: mpq(3,5) In [48]: gmpy.f2q(d, -53) Out[48]: mpq(3,5) In [49]: gmpy.f2q(d, -54) Out[49]: mpq(3,5) In [50]: gmpy.f2q(d, -55) Out[50]: mpq(6002194384070353L,10003657306783922L) The procedure followed here finds mpq(3,5) because evaluating "3.0/5.0" in as binary floating point numbers in double precision gives you the same thing as evaluating "0.6". So mpq(3,5) is the most parsimonious rational number *approximating* Python's float("0.6") to within the default double-precision of binary floating point arithmetic. However, float("0.6") is a rational number that has the precise value of mpq(6002194384070353L,10003657306783922L). > But it is still wrong to say "0.6 is definitely not the same as 3/5". In the context in which it was said, I don't think it's wrong though it is incomplete and confusing if taken out of that context. > One can say 0.6 doesn't have an exact float representation and that > inexact representation is not the same as 3/5. And I suppose one can > be surprised that when this inexact representation is coerced to a > rational the result is now exact. > > Would that be a fairer way of putting it? Yes. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco -- http://mail.python.org/mailman/listinfo/python-list
