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## 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
> 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
```

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