Unix Tip: Using bc for big calculations

For sysadmins who want to perform simple calculations on the command line, there's a considerably more useful tool than expr. Try bc. Like expr, the bc command allows you to do simple math. Here are some examples:

boson> echo 6*6-3 | bc
33
boson> amt=`echo 6*6-3 | bc`
boson> echo $amt
33

You can also go into calculator mode by typing bc on the command line by itself and then feed it as many calculations as you want:

boson% bc
7*7*7
343
256*256
65536
256*256*256
16777216
256*256*256*256
4294967296
256*256*256*256*256*256*256*256
18446744073709551616
quit

Notice that you can calculate some very large values! You can also achieve a high degree of precision by setting the number of places you want to see following the decimal point.

boson% bc
scale=4
177/7
25.2857
quit

The "scale" setting, as you can see from the example above, determines the number of decimal places to save. You can, therefore, get considerably more useful values than the rounded down results of expr. Using bc, you don't have to escape multiplication operations and computing powers of 2 (or any arbitrary number for that matter) is simple, fast and accurate as shown below.

boson% expr 3 \* 3
9
boson% echo 3*3 | bc
9
boson% bc
2^8
256
2^32
4294967296
quit

Look how quickly we can calculate the number of IP addresses that will be available in IPv6 as opposed to IPv4:

boson% bc
2^32
4294967296
2^128
340282366920938463463374607431768211456
quit

That's one staggering large number, but bc can generate even larger numbers with ease and speed:

boson% bc
2^256
11579208923731619542357098500868790785326998466564056403945758400791\
3129639936
2^512
13407807929942597099574024998205846127479365820592393377723561443721\
76403007354697680187429816690342769003185818648605085375388281194656\
9946433649006084096
2^1024
17976931348623159077293051907890247336179769789423065727343008115773\
26758055009631327084773224075360211201138798713933576587897688144166\
22492847430639474124377767893424865485276302219601246094119453082952\
08500576883815068234246288147391311054082723716335051068458629823994\
7245938479716304835356329624224137216
quit

The numbers wrap around in 68-digit segments until the complete number has been printed on the screen. The bc command is also useful for doing base conversions. Say you want to know the hexadecimal equivalent of 255. Just do this:

boson% bc
obase=16
255
FF
quit

Maybe that's too easy. Let's try some larger numbers:

boson% bc
obase=16
4294967296
100000000
340282366920938463463374607431768211456
100000000000000000000000000000000
quit

No surprise there, right? Since we fed bc the decimal values of 2^32 and 2^128, we would expect a number starting with 1 and followed by a long string of zeroes. If we want to see the largest values (in hex) that we can hold in 32 and 128 bits, we can do this:

boson% bc
obase=16
4294967296-1
FFFFFFFF
340282366920938463463374607431768211456-1
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
quit

We can also feed arbitrarily long numbers into bc using the same continuation line form that bc uses to display long numbers:

boson% bc
obase=16
13407807929942597099574024998205846127479365820592393377723561443721\
76403007354697680187429816690342769003185818648605085375388281194656\
9946433649006084096
1000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000
quit

Other numeric bases can be selected as well. In the example below, we're electing to use octal and then ... septal?

boson% bc
obase=8
12
14
obase=7
8
11
quit

While bc has tremendous functionality for quick math, you probably don't want to use it for every bit of math you do in every script you write since many languages have math skills of their own. On the other hand, bc will beat the socks off most desktop calculators and it's fun to get some expert help with those base conversions.