more missing methods: frexp, ldexp, exponent, significand

[laurentbartholdi]

If I want to use ArbField() elements as a shoe-in for Julia's Float64/BigFloat, I'll need these methods. (They actually seem to be easy to implement: exponent(x::ArbFieldElem) = x.mid_exp-1 etc.)

[thofma]

Do these concepts actually make sense for discs? They cannot be used as drop-in replacements for floating point arithmetic (three-valued logic etc).

[laurentbartholdi]

I'm using exponent to scale numbers in a suitable range with guaranteed no loss of precision. I'm always nervous, with balls, that every normalization operation chips some precious bits away.

[thofma]

ldexp we have. For other operations, we need precise rigorous mathematical definition. There is radius exponent, mantissa exponent etc. What is exponent supposed to be mathematically? Also what is frexp to do?

[laurentbartholdi]

I see your point.
The application I have in mind is: I represent elements of P^1(C) as pairs of elements of C, up to common scaling. I cannot normalize them as z/1 or 1/z, because of the box->lozange->box precision loss; and I have to scale them a bit, otherwise the exponents blow off to infty or 0. The simple trick is to scale them so that the largest has real or imag part in [1/2,1].

Do you have a better suggestion on how to do that?

[laurentbartholdi]

ldexp we have. For other operations, we need precise rigorous mathematical definition. There is radius exponent, mantissa exponent etc. What is exponent supposed to be mathematically? Also what is frexp to do?

The semantics could just be: return a pair (mantissa,exponent) such that mantissa*2^exponent = value, with no guarantee as to what mantissa belongs to, except 1/2-radius <= |mantissa|<= 1+radius.