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GNU bc FAQ

Looking through my site logs, I realise that many people who find the GNU bc page are looking for something that isn't actually here. This page is for precisely those things that people apparently want answers to.

Without further ado, here are some of the questions asked of search engines that people haven't found the answer to on the GNU bc page:

1. How do I do a square root in bash?
2. How do I do a square root in GNU bc?
3. How do I do floating point numbers in GNU bc?
4. How do I do a logarithm in bash?
5. How do I do a cube root in GNU bc?

How do I do a square root in bash?

I reckon this is a trick question - do you guys want to use bc or not? :) Okay... Lets assume both and work from there:

bash square roots - the hard way - no bc!

You really honestly and truthfully don't want to do this, surely? The bash shell is only capable of integer arithmetic, so even if you could take a square root, you'll only get the integer portion of the answer... i.e. sqrt(10) = 3 to the nearest whole number. If that's all you need, then this shell function is for you:

sqrt() { local x=$1 s=$1 os=0;while ((s!=os));do os=$s;s=$(((s+x/s)/2));done;echo $s; }

Once you've entered the above into a script or your interactive session, the command sqrt {number} will output the square root of {number}. e.g. sqrt 123456 will print 351.

Be warned though, the above contains no checking for negative numbers, and the function will crash with an error when given one. This is probably for the best.

bash square roots - the easy way - using bc

The simplest way to do this is to pipe some bc syntax to bc -l:

echo 'sqrt({number})' | bc -l

How do I do a square root in GNU bc?

If you've been paying attention class, the answer to this has already been used in the previous answer!

bc has its own built in sqrt() function. You don't even need to include the standard library - it's right there when you run the program... Which leads us on to the next question...

How do I do floating point numbers in GNU bc?

It concerns me greatly the number of people who don't know about the scale variable in bc. With scale, the number of decimal places of floating point precision can be set. Including the standard library (with the -l flag) automatically sets the scale to 20. This site's funcs.bc library sets the same to 100 for increased accuracy.

For instance; The example from the question before last might have been written:

echo 'scale=20;sqrt({number})' | bc

How do I do a logarithm in bash?

Again... not sure whether the requestor wants bash or bc code, so it's twice the work for me :):

bash logarithms - the hard way - no bc!

Bearing in mind that bash is integer-only, this shell function will return the rounded down logarithm in bash:

log(){ local x=$1 n=2 l=-1;if [ "$2" != "" ];then n=$x;x=$2;fi;while((x));do let l+=1 x/=n;done;echo $l; }

Once you've entered the above into a script or your interactive session, the command log {number} will output the logarithm of {number} to base 2. e.g. log 123456 will print 16 (even though the log to base 2 of 123456 is nearer to 17!)

The 'clever' bit is that the command log {n1} {n2} will output the logarithm of {n2} to base {n1}, so log 10 10000 will print 4, and log 3 9923 will print 8, etc.

Beware again - this works only when fed positive integers. Anything else is not checked for and may cause this function to behave bizarrely.

bash logarithms - the easy way - using bc

Guess what? You can pipe some bc syntax to bc -l!:

echo 'l({number})' | bc -l

echo 'l({n1})/l({n2})' | bc -l

How do I do a cube root in GNU bc?

The easiest way to do a cube root in bc is to use the pow() and root() functions from this site's funcs.bc library; pow({number},1/3) and root({number},3) both achieving the required result. ;)

Of course, you may just want to use the following quick-and-dirty trick that both of those functions are based upon. Again, this example is for the bash shell:

echo 'e(l({number})/3)' | bc -l

ⁿ√x = x^(1/n) = e^{(ln x)/n}

define cbrt(x) { return e(l(x)/3)) }

As you might guess then, the e() and l() used above are the GNU bc exponential and natural logarithm functions respectively. Both are only available as part of the standard library, so the -l flag is absolutely essential for them to be usable.