[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: Immediate doubles (up to 2^256) and rationals coming to Guile 3
From: |
Arne Babenhauserheide |
Subject: |
Re: Immediate doubles (up to 2^256) and rationals coming to Guile 3 |
Date: |
Sat, 08 Jun 2019 10:07:45 +0200 |
User-agent: |
mu4e 1.2.0; emacs 26.1 |
Mark H Weaver <address@hidden> writes:
> Mark H Weaver <address@hidden> writes:
>
>> Here's the format of fixrats on 64-bit systems:
…
> This allows for an elegant packing operation:
>
> if (SCM_I_INUMP (numerator) && SCM_I_INUMP (denominator))
> {
> union { double f; uint64_t u; } u;
> u.f = SCM_I_INUM (numerator);
> u.u += SCM_I_INUM (denominator);
Wow, I didn’t know that you could do that.
However: "The details of that allocation are implementation-defined, and
it's undefined behavior to read from the member of the union that wasn't
most recently written." https://en.cppreference.com/w/cpp/language/union
Can you guarantee that this works?
> if ((scm_t_inum) u.f == SCM_I_INUM (numerator))
> {
> u.u += 0xc010000000000000;
> u.u = (u.u << 6) | (u.u >> 58);
> if ((u.u & 0x1f) == 0)
> return SCM_PACK (u.u | scm_fixrat_tag);
> }
> }
>
> We start by converting the numerator into an IEEE double. We then use
> unsigned integer addition to add the denominator to the 64-bit
> representation of that double. We now check that this new IEEE double
> has integer part equal to the numerator. If it doesn't, this indicates
> either that the numerator is too large to be represented exactly, or
> that the denominator is too large to fit in the remaining bits.
>
> The only thing that remains to be done at this point is to rotate left 6
> bits, so that the 5 highest exponent bits become the lowest 5 bits,
> where the fixrat tag will go, and to add a value which adjusts the IEEE
> biased exponent field to be 0 when the numerator is 1 or -1.
It is really cool to read these deep details — is there a chance that
when this lands you could re-vamp the emails you wrote here into a
blog-post we can easily link to?
Best wishes,
Arne
--
Unpolitisch sein
heißt politisch sein
ohne es zu merken
signature.asc
Description: PGP signature
- Re: Immediate doubles (up to 2^256) and rationals coming to Guile 3, (continued)
Re: Immediate doubles (up to 2^256) and rationals coming to Guile 3, Mark H Weaver, 2019/06/07