Although using sed expression is great it has its limitations. For example following fails:
$ echo "1000000000000000000000000000000+1" | sed -e 's/\([0-9]*\)+\([0-9]*\)/expr \1 + \2/e'
expr: 1000000000000000000000000000000: Numerical result out of range
To overcome this limitation one my simply turn to the built in power of pure sed and implement following arbitrary length decimal adder:
#!/bin/sed -f
s/+/\n/g
s/$/\n\n0/
:LOOP
s/^\(.*\)\(.\)\n\(.*\)\(.\)\n\(.*\)\n\(.\)$/0\1\n0\3\n\5\n\6\2\4/
h
s/^.*\n.*\n.*\n\(...\)$/\1/
# decimal full adder module
# INPUT: 3digits (Carry in, A, B,)
# OUTPUT: 2bits (Carry, Sum)
s/$/;000=00001=01002=02003=03004=04005=05006=06007=07008=08009=09010=01011=02012=03013=04014=05015=06016=07017=08018=09019=10020=02021=03022=04023=05024=06025=07026=08027=09028=10029=11030=03031=04032=05033=06034=07035=08036=09037=10038=11039=12040=04041=05042=06043=07044=08045=09046=10047=11048=12049=13050=05051=06052=07053=08054=09055=10056=11057=12058=13059=14060=06061=07062=08063=09064=10065=11066=12067=13068=14069=15070=07071=08072=09073=10074=11075=12076=13077=14078=15079=16080=08081=09082=10083=11084=12085=13086=14087=15088=16089=17090=09091=10092=11093=12094=13095=14096=15097=16098=17099=18100=01101=02102=03103=04104=05105=06106=07107=08108=09109=10110=02111=03112=04113=05114=06115=07116=08117=09118=10119=11120=03121=04122=05123=06124=07125=08126=09127=10128=11129=12130=04131=05132=06133=07134=08135=09136=10137=11138=12139=13140=05141=06142=07143=08144=09145=10146=11147=12148=13149=14150=06151=07152=08153=09154=10155=11156=12157=13158=14159=15160=07161=08162=09163=10164=11165=12166=13167=14168=15169=16170=08171=09172=10173=11174=12175=13176=14177=15178=16179=17180=09181=10182=11183=12184=13185=14186=15187=16188=17189=18190=10191=11192=12193=13194=14195=15196=16197=17198=18199=19/
s/^\(...\)[^;]*;[^;]*\1=\(..\).*/\2/
H
g
s/^\(.*\)\n\(.*\)\n\(.*\)\n...\n\(.\)\(.\)$/\1\n\2\n\5\3\n\4/
/^\([0]*\)\n\([0]*\)\n/ {
s/^.*\n.*\n\(.*\)\n\(.\)/\2\1/
s/^0\(.*\)/\1/
q
}
b LOOP
The way it works is by implementing decimal adder module that adds two input digits (A and B) as well as Carry Bit and produces a Sum and Carry bit. The idea is borrowed from electronic where binary adder does the same for binary numbers. All we have to do is loop the adder over all digits and we can add arbitrary length numbers (limited by memory). Below is the adder in action:
./decAdder.sed
666666666666666666666666666666999999999999991111111112222+1100000000000000000000011111111111111111111111111111111111
1766666666666666666666677777778111111111111102222222223333
In exactly the same way one can implement binary (or any other base) adder. All you have to do is replace the line that starts with s/$/;000=00001...
with proper substitution pattern for given base. For example: s/$/;000=00001=01010=01011=10100=01101=10110=10111=11/
is substitution pattern for arbitrary length binary adder.
You can fit the code documented on my github.
sed
to do math