Part of it is a bug and part of it is a feature. First the bug, https://github.com/sympy/sympy/blob/7524499458cf114b32e 3aa6e8acdb77e846111f9/sympy/core/evalf.py#L1264 needs to be changed. It should be changed from from_rational(x.p, x.q, prec) to from_rational(x.p, x.q, prec, rnd). Otherwise round down is used instead of round nearest.
This doesn't affect much though. same phenomena happens at 5128 instead of 5158. Now for the feature part. a.n(2) doesn't guarantee you that the result will be rounded nearest to 2 decimal digits. a.n(2) only guarantees that the internal representation of |a-a.n(2)| < 0.5e-2. Here's what sympy does. dps = 2 (digits) is converted to prec=10 (bits) .n routine first evaluates the rational with prec+4 bits and then rounds the result. Larger rational is rounded to p=15977*2**-14 = 0.9751586914... Smaller rational is rounded to q=15966*2**-14 = 0.9750976563... In the round down case 5159 is rounded down to p and 5158 is rounded down to q In the round to nearest case 5129 is rounded to p while 5128 is rounded to q. Then sympy normalizes these mpfs to 10 bits. There are now 2 choices Larger float is rounded nearest to r = 997*2**-10 = 0.9755859375 Smaller float is rounded nearest to s = 996*2**-10 = 0.9746093750 These two are the results you get, but SymPy prints only 2 decimal digits of the numbers and therefore prints 0.98 for the larger and 0.97 for the smaller. There was a similar discussion in issue https://github.com/sympy/sympy/issues/12038 Isuru On Fri, Mar 30, 2018 at 1:37 AM, Chris Smith <smi...@gmail.com> wrote: > Is this expected behavior for evaluating Rationals: > > Rational of a string produces the exact decimal as a fraction: > > >>> Rational('.975159') > 975159/1000000 > > evaluation is going to be affected by rounding > > >>> Rational('.975158').n(2) > 0.97 > >>> Rational('.975159').n(2) > 0.98 > > But why is the digit affecting rounding in the 6th decimal position when > we are trying to evaluate to the 2nd position? And I would have expected > the split to be much closer to 5000 than 5158. > > /c > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/sympy/f9dc2400-5277-4ed1-ad80-00fa5b12bd6e%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/f9dc2400-5277-4ed1-ad80-00fa5b12bd6e%40googlegroups.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CA%2B01voNNwgV9UhUcyPL37K1DSs6PrdiJBa7oPTxN-dO4EYYp5g%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
