ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 04 Apr 2013 13:34:40 -0500What are the differences between RealDoubleField() and RealField(53) ?https://ask.sagemath.org/question/9991/what-are-the-differences-between-realdoublefield-and-realfield53/Hi,
This question is related to
[question 2402](http://ask.sagemath.org/question/2402/what-are-the-different-real-numbers-in-sage)
(still open!) and tries to collect differences between RDF=RealDoubleField() and RR=RealField(53).
These are two floating point real number fields with both 53 bits of precision. The first one comes from the processor floating-point arithmetic, the second one is "emulated" by mpfr. They are assumed to follow the same rounding standards (to the nearest, according to the [sagebook](http://sagebook.gforge.inria.fr/), but i may be wrong).
However, we can see some differences between them:
sage: RDF(1/10)*10 == RDF(1)
False
sage: RDF(1/10)*10 - RDF(1)
-1.11022302463e-16
sage: RR(1/10)*10 == RR(1)
True
sage: sage: RR(1/10)*10 - RR(1)
0.000000000000000
Could you explain that ?
**EDIT: this was a bug and it is now fixed**, see [trac ticket 14416](http://trac.sagemath.org/ticket/14416).
There are also some specificities on which field should be used for some
methods.
- For example, it seems that the eignevalues are not well computed on RR, but are
correctly computed on RDF ([see trac #13660](http://trac.sagemath.org/sage_trac/ticket/13660)). What is the reason for that ?
- Also, it seems that when dealing with huge matrices, the fast atlas library in
only used when entries are in RDF, not in RR
([see trac #10815](http://trac.sagemath.org/sage_trac/ticket/10815)).
Are there other difference that should be known between both implementations of floating point numbers in Sage ?
ThierrytmonteilThu, 04 Apr 2013 13:34:40 -0500https://ask.sagemath.org/question/9991/