FreeBSD-9.3 dc(1)

#####
FIRST
#####
$ dc -xe '50k16o16i.1vp'
0
$ dc -xe '50k10o16i.1vp'
0
$ dc -xe '50k10o10i.1vp'
[0].31622776601683793319988935444327185337195551393252

This should be telling dc(1):

a) scale is 50 (in decimal) digits.
b) output in base16, base10, and base10 respectively.
c) input will be in base16, base16, and base10 respectively.
d) take the square root, and print it to the display.

Of course, the 3rd example above is correct, but the first 2?  Why 0?

######
SECOND
######
$ dc -xe '50k16o16i.4 2^p'
[0].0A
$ dc -xe '50k16o16i.0Avp'
[0].2C572B0D5A1443EC508B9E24D8DF392750959EE138

This should be telling dc(1):

a) scale is 50 (in decimal) digits.
b) output in base16, input is now base16.
c) square "0.4", and print it to the display (result=0.0A).
d) take the square-root of "0.0A", and print it to the display.

Of course, the square-root of a squared number should result in
the orginal number.  But, this is not happening.

#####
THIRD
#####
$ dc -xe '50k16o16i.4 2^p'
[0].0A
$ dc -xe '50k16o16i.40 2^p'
[0].1000
$ dc -xe '50k16o16i.400 2^p'
[0].10000
$ dc -xe '50k16o16i.4000 2^p'
[0].1000000

dc(1) is supposed to be precise in the digits it calculates, but here?
Something is not right about these results, or so it appears to me.

######
FOURTH
######
$ dc -xe '50k16o16i.1vp'
0
$ dc -xe '50k16o16i.10vp'
[0].3EB4F9D9B6D094C33D38373D38777A7D9233A1B0FB
$ dc -xe '50k16o16i.100vp'
[0].3FBE55183CA5ADC8B39B27C6258E4C7E64338B909F
$ dc -xe '50k16o16i.1000vp'
[0].400000000000000000000000000000000000000000

Checking the result of the THIRD example, dc(1) is not outputting to the
scale specified, and despite having all a scale of 50, they are all giving
different results with inputs having a scale of only 1/2/3/4;
Something seems broken to me.

--

GNU's dc(1) is broken too (reported to GNU bc maintainer also):

Thanks!  I really needed a calculator to do squares and square-roots of
hexadecimal fractions, and I use FreeBSD, but their dc(1) is broken too ...

http://lists.freebsd.org/pipermail/freebsd-questions/2016-January/269999.html
http://lists.freebsd.org/pipermail/freebsd-bugs/2016-January/065825.html

I would assert scale is the number of fractional digits displayed regardless
of any base.  Why should anyone care about base10 or whatever other base the
dc(1) author decided to assign as an across-the-board base for the scale
value?  That makes no sense at all for a user of dc(1).  Scale is the number
of fractional digits the dc(1) user wants, not what the author of dc(1)
decided secretly for everybody. I don't think it was ever intended to be the
"base10" fractional digits only, or whatever other scale was used "behind the
scenes".  Scale is a "user demand" for the result, IMHO.

A modern computer should have a working calculator - at least, I think so. 
Thank you so much for your reply, I have some encryption-related software that
depends on it.

> On Tuesday 12 January 2016 23:05:41:
>
> > dc (GNU bc 1.06.95) 1.3.95
> >
> > $ dc -e '50k16o16i.4vp'
> > [0].727C9716FFB764D594A519C0252BE9AE6D00DC9192
> >
> > This is not a 50-digit scale.
>
> It is a 50 digit scale base r10 which is of course shorter base r16.
>
> > $ dc -e '50k16o16i.727C9716FFB764D594A519C0252BE9AE6D00DC9192 2^p'
> > [0].333333333333333333333333333333333325CC2DCA
> >
> > This is not even close to being the original number: 0.4.
>
> This appears to be true.   I'll investigate why the algorithm is wrong.