I think that Python's float.__round__ is correct. AIUI it rounds correctly based on the true value represented by the float:
In [4]: round(1.05, 1) Out[4]: 1.1 In [5]: import decimal In [6]: decimal.Decimal(1.1) Out[6]: Decimal('1.100000000000000088817841970012523233890533447265625') That's surprising just because the true exact value isn't what we thought it should be. There is a rounding error but it happens in the literal 1.1 that doesn't give us the float we think it should. It's extra confusing because str(1.1) gives '1.1' making it seem like the exact number we requested. The behaviour of round is mathematically correct here though given the input received: it is computing the true exact result correctly rounded (where "correctly rounded" refers to the decimal to binary rounding at the end). For decimals that can be exactly represented in binary the results are as we would intuitively expect: In [7]: round(1.25, 1) Out[7]: 1.2 In [8]: round(1.75, 1) Out[8]: 1.8 (Of course 1.2 and 1.8 are not exactly representable in binary floating point but we have the floats that result from correctly rounding the true numbers 1.2 and 1.8.) -- Oscar On Thu, 11 Apr 2019 at 05:29, Chris Smith <smi...@gmail.com> wrote: > > I am aware of how the numbers are stored but was overly optimistic that the > shift could resolve this in all cases. It can't (and thanks for the > correction). > But my suggested alternative makes a significant difference in how often the > problem arises: > > >>> bad=[] > >>> for i in range(1,1000): > ... n = str(i)+'5' > ... if int(str(round(int(n)/10**len(n),len(n)-1))[-1])%2!=0:bad.append(i) # > e.g. round(0.1235, 3) > ... > >>> len(bad) > 546 > > > >>> bad=[] > >>> for i in range(1,1000): > ... n = str(i)+'5' > ... if round(int(n)/10**len(n)*10**(len(n)-1))%2!=0:bad.append(i) # e.g. > round(0.1235*1000) > ... > >>> len(bad) > 8 > >>> bad # e.g. 0.545*100 != 54.5 > [54, 57, 501, 503, 505, 507, 509, 511] > >> So the question is whether we want to do better and keep the SymPy algorithm. > > -- > 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/b50c0504-ec96-4583-84b1-d5a3902277c2%40googlegroups.com. > 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/CAHVvXxS8kCZRXuXpoHJCWiXOZUjxeAMhY%3DRQPthEKkA_A_tdCQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.