On 2020-07-13 at 08:23, Greg Wooledge wrote:
> On Mon, Jul 13, 2020 at 06:47:51AM -0400, The Wanderer wrote:
>
>> In some contexts it could even need fewer; for example, calc (as
>> shipped in Debian) provides the built-in function 'pi()', which
>> takes a precision - expressed as a value between zero and one - and
>> returns pi to that level of precision.
>
> I do not understand this description. How many decimal places do
> you get for a precision of, say, 0.5?
(It turns out I got the specification of what the precision can be
expressed as wrong, and "precision" may not be the correct term for it
anyway; see below.)
I don't understand the full algorithm myself, but the output seems
coherent:
$ calc
C-style arbitrary precision calculator (version 2.12.7.2)
Calc is open software. For license details type: help copyright
[Type "exit" to exit, or "help" for help.]
; pi(.5)
3
; pi(.1)
3.1
; pi(.9)
2.7
; pi(.05)
3.15
; pi(.0005)
3.1415
; pi(.00005)
3.1416
; pi(.00001)
3.14159
; pi(.00009)
3.1416
I generally just use something like 'pi(.0000000000000001)' (i.e., hold
down the 0 key for a while in between . and 1), and that produces all
the precision I could really care for. The limit that gets printed (at
least with default configuration) appears to be
; pi(.0000000000000000000000000000000000000000000000000001)
~3.14159265358979323846
and you can get that same visible result with a much shorter precision
value. I expect that there are configuration settings which will
increase the displayed precision, but I've never needed to find them.
Also, it turns out that it accepts values >=1 and <=0 as well:
; pi(5)
5
; pi(10)
0
; pi(50)
0
; pi(3)
3
; pi(4)
4
; pi(2)
4
; pi(-1)
3
; pi(0)
zero epsilon value for pi
; pi(1)
3
The results just aren't very useful.
>> The list of built-in functions in the bc man page is very short,
>> and doesn't include any such thing, so unless something has added
>> one without the man page getting updated anything that needs to use
>> pi is going to take more typing than with calc.
>
> True. But it's not a *huge* amount of typing.
>
> unicorn:~$ bc -l
Yep - as soon as I saw someone point out what this flag did, I figured
this would be in there somewhere. (I didn't figure it out from looking
the flag up in the man page, but that's me.)
> bc 1.07.1
> Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006, 2008, 2012-2017 Free Software Foundation, Inc.
> This is free software with ABSOLUTELY NO WARRANTY.
> For details type `warranty'.
> 4*a(1)
> 3.14159265358979323844
Definitely convenient, but also requires knowing more about math than
I've managed to internalize over the decades to figure out. I would not
have thought of multiplying by the arctangent of 1 (or of anything) to
arrive at pi.
--
The Wanderer
The reasonable man adapts himself to the world; the unreasonable one
persists in trying to adapt the world to himself. Therefore all
progress depends on the unreasonable man. -- George Bernard Shaw
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