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GNU bc
Ah yes. GNU bc. That useful little calculator program found on most modern Linux
installations that no-one seems to do anything interesting with. Well it's time
for a change. On this page you'll find various bits and pieces to make life with
GNU bc much, much simpler or at least more interesting.
Somewhere below his paragraph there are... (counts for a bit) ...uh, more
than ten bc files and one bash script for starting bc with a special setup.
Each of the scripts/files/programs/libraries/whatevers below are packed with
comments explaining exactly what the file is, what it does and what each of the
functions do. It's not the best way of documenting things, but if you intend to
use or learn from these files, putting the documentation in with the code was
- IMHO - the best way to do things.
This page is currently linked from the bc articles in both the
English
and German
Wikipedias. Welcome and Willkommen to readers heading in from over there!
* If you found this page through an internet search and still can't see what you're
looking for, try the new bc FAQ page - you might find it
there!
Functions Galore
- funcs.bc
- A large number of functions that expand on the standard GNU bc library.
They can be used for doing calculations without having to rederive them every time
bc is started. The first line is a shebang line just so that it can be
started instead of the standard GNU bc interpreter.
- intdiff.bc
- Supplanting the old dfxdx.bc which provided a function to perform simple numerical
differentiation of a single variable function, this also contains the corresponding
numerical integration of a function between two values. The latter comes with a tasty
little function called glai that tries to predict convergence limits.
- logic.bc
- Ever wanted to be able to do logical bitwise operations in bc?
AND, OR, XOR and NOT? Now you can.
- primes.bc
- Originally part of funcs.bc, the prime number functions have now been moved
into their own file. Some algorithms have been rewritten for faster prime
sieving, and there's a new function for generating primes quickly.
Update: added a function to determine whether a number is square-free.
(Or cube-free, or tesseract-free, etc.)
- Other interesting libraries
- collatz.bc
- Some functions for experimenting with the Collatz conjecture. It's unlikely
this library will provide any breakthroughs or insights, but it's fun to play
with every now and again.
- cf.bc
- Want to play with simple Continued Fractions? Start right here.
- complex.bc
- Complex numbers in bc. Yes, that's right; And it works too. OK so it's still
no great shakes, and there's only the most basic of mathematical functions
but I'm still patting myself on the back for this one.
- thermometer.bc
- Twenty functions to convert temperatures between the five most common
temperature scales: Celcius (Centigrade), Farenheit, Kelvin, Reamur and Rankine.
Random Numbers
"What's this?" I hear you cry. Random numbers in bc? Yes and no. GNU bc, let alone
POSIX bc has no access to real-world information that a user can't provide, so while
it's perfectly feasible to implement a random number generator in bc, there's no
way to seed it. i.e. It hasn't got a starter motor to get it going. That's never
stopped me before though.
- rand.bc
- A floating point random number generator of my own devising. It passes all
standard distribution and chi-square testing, and is based entirely around floating
point numbers. This of course makes it much slower than, say, a mersenne twister,
but it's just as good otherwise. Update: added a tweak to prevent random seed decay
that can occur if scale isn't set high enough on loading.
- guess.bc
- It's the old higher-lower guess-the-number game. bc wasn't meant for this sort
of thing so it's time to buck the trend.
- randbc
- A bash shell script that starts rand.bc and seeds the
random number generator using it's own random numbers. i.e. Jump-leads.
Weird Functions
- The 'sum of repeated square roots' function
Okay, so I couldn't come up with a better name for this one. To calculate this
function of/for a number 'n', first take the square root of n, remember it, add it
to a running total and subtract one from the total. Do the same with the square root
remembered from before, repeat until the remembered square root is reduced to 1.
(And thus the running total is getting nothing added to it).
The mathematical formula (assuming your browser will handle this) for the function
is:
Or as simply as possible: ss(x) = sum[n=1..oo] x^(2^(-n))-1
- The Pan-Digital Halving Index
This strange little function returns how many times a number must be divided by
two before all digits, zero to nine, are within the decimal representation of
the result. There's an example in the source file if that's confusing...
- The Angular Logarithm function
Yes, it's true, I suck at naming things. This function and it's inverse (included
in the source) are related to the number sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000,
2000, etc. etc. [See the OEIS's
A037124]
-
Sharp eyed readers might notice that this should be an 'angular exponential'
and not an angular logarithm. I'll get round to changing it eventually.
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