function for floating point representation of a number

[jason]

Here's a function that answers the question posed in ​http://groups.google.com/group/sage-devel/browse_thread/thread/c8c75b483f2c47f6 -- give the sign, mantissa, and exponent of a floating point number.

I also cleaned up a few minor other things.

[robertwb]

Looks good. I don't like the name representation() either--maybe parts()?

[jason]

parts() seems too vague. Maybe ieee_754_parts(), except that we support arbitrary precision, not just the set precisions they mention. Maybe floating_point_representation(), or sign_mantissa_exponent().

I'm willing to concede on the naming to make sure this gets in before I start my numerical analysis class in two weeks :).

[robertwb]

Lets go with sign_mantissa_exponent(). Verbose but clear, and one doesn't even have to look at the docstring every time to remember what order the tuple comes in :)

[jason]

apply on top of previous patch

[jason]

Okay, I added a patch which changes the name. This is hopefully ready for a positive review now :).

[cremona]

I see that you have only added this method to mpfr. Should we not preserve as much consistency as possible between the different real types by also adding it to real_double?

[jason]

Very good point. I'll look at this. I might just end up creating an RR number and calling this method behind the scenes

[jason]

apply on top of previous patches

[jason]

I've added a similar function to RDF now.

[robertwb]

​http://en.wikipedia.org/wiki/IEEE_754-1985

The exponent for 0 should be 0. This also avoids the issue of platform dependance for that value, and RDF(0)'s exponent being unrealistically small.

Also, sage/rings/real_mpfr.pyx, line 1890 should be EXAMPLES::

[jason]

apply on top of previous patches

[jason]

The last patch fixes a few other documentation errors and an error in multiplicative_order too. For free.

[robertwb]

all four of the above folded into one

[robertwb]

Looks good.

[jason]

The mantissa and exponent for MPFR is not the same as the mantissa and exponent for IEEE 754. So I'm a little doubtful about the choice to follow IEEE 754 conventions for the exponent value of 0. (but I'm not doubtful enough to change it). I just thought I'd point out that the values from MPFR are different than the conventions from IEEE 754 for the same floating point number.