Re: Some improvements to numeric sqrt() and ln()

Dear Dean,

On 2020-03-01 20:47, Dean Rasheed wrote:
> On Fri, 28 Feb 2020 at 08:15, Dean Rasheed <dean.a.rasheed@gmail.com> 
> wrote:
>> 
>> It's possible that there are further gains to be had in the sqrt()
>> algorithm on platforms that support 128-bit integers, but I haven't
>> had a chance to investigate that yet.
>> 
> 
> Rebased patch attached, now using 128-bit integers for part of
> sqrt_var() on platforms that support them. This turned out to be well
> worth it (1.5 to 2 times faster than the previous version if the
> result has less than 30 or 40 digits).

Thank you for these patches, these sound like really nice improvements.
One thing can to my mind while reading the patch:

+     *        If r < 0 Then
+     *            Let r = r + 2*s - 1
+     *            Let s = s - 1

+            /* s is too large by 1; let r = r + 2*s - 1 and s = s - 1 */
+            r_int64 += 2 * s_int64 - 1;
+            s_int64--;

This can be reformulated as:

+     *        If r < 0 Then
+     *            Let r = r + s
+     *            Let s = s - 1
+     *            Let r = r + s

+            /* s is too large by 1; let r = r + 2*s - 1 and s = s - 1 */
+            r_int64 += s_int64;
+            s_int64--;
+            r_int64 += s_int64;

which would remove one mul/shift and the temp. variable. Mind you, I 
have
not benchmarked this, so it might make little difference, but maybe it 
is
worth trying it.

Best regards,

Tels