# sqrt algorithm

Torbjörn Granlund tg at gmplib.org
Thu Aug 13 12:52:23 UTC 2015

```"Marco Bodrato" <bodrato at mail.dm.unipi.it> writes:

Ciao,

On Wed, August 12, 2015 2:03 pm, Torbjörn Granlund wrote:
>   I tested this approach for sqrlo_basecase too, you can find the code
>   enclosed by
>   #ifdef SQRLO_SHORTCUT_MULTIPLICATIONS
>
>   But I'm not sure it is faster, so it is currently disabled.
>
> It will obviously be faster for machines where widening multiplication
> is expensive, and in some other hardware cases.

Ok, I can enable it for sqrlo. Are you working on an improved
mullo_basecase? Otherwise I can change that code using the same criteria I
used for sqrlo...

This is my alternative mullo_basecase:

void
mpn_mullo_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
{
mp_limb_t h;

h = up[0] * vp[n - 1];

if (n != 1)
{
mp_size_t i;
mp_limb_t v0;

v0 = *vp++;
h += mpn_mul_1 (rp, up, n - 1, v0);
h += up[n - 1] * v0;
rp++;

for (i = n - 2; i > 0; i--)
{
v0 = *vp++;
h += mpn_addmul_1 (rp, up, i, v0);
h += up[i] * v0;
rp++;
}
}

rp[0] = h;
}

> I don't recall how we defined mullo/sqrlo wrt the size of the target
> operand.  Can we write above the defined result, i.e., can we write the
> full 2n product if it is convenient?

Current implementation of both mullo and sqrlo do write n limbs only,
possibly by full 2n product in a temporary area followed by MPN_COPY.

IIRC someone proposed the interface mullo(res, x, y, n, tmp); with 2n
limbs in tmp, supporting res == tmp, but we never switched to it.

Regards,
m

--
Torbjörn