CODEWITHSUNDEEP
algorithmmathlargenumberjavacard
Matthew
Matthew

Reputation:

How do I multiply (and divide) BCD numbers by 10^x

I have a large (12 digit) BCD number, encoded in an array of 6 bytes - each nibble is one BCD digit. I need to multiply it by 10^x, where x can be positive or negative.

I know it can be done by shifting left or right by nibble instead of bit, but it's a horrible implementation - especially in Javacard, which is what I'm using. Is there a better way?

Upvotes: 0

Views: 3995

Answers (2)

paxdiablo
paxdiablo

Reputation: 882366

You don't have to use bit-shifting (although that is probably the most efficient way of doing it).

For your 12-digit BCD number, provided there won't be any overflow, assume that b[5] through b[0] holds your bytes from most significant to least significant, and that mod is the modulus (remainder) operation and div is integer division, the following pseudo-code would multiply by 10:

for i = 5 to 1
    b[i] = (b[i] mod 16) * 16 + b[i-1] div 16
b[0] = (b[0] mod 16) * 16

To be honest, that's probably uglier than your bit-shifting solution but, as long as you encapsulate either of them in a function, it shouldn't really matter.

I would suggest having a function along the lines of:

BcdArray mult10 (BcdArray ba, int shiftAmt);

which would return a modified array by applying that power of 10.

Any even power of ten is a simple copy of bytes (since two nybbles is a byte) whilst only the odd powers of ten would need the tricky bit-shifting or remainder/division code.

Upvotes: 1

Nils Pipenbrinck
Nils Pipenbrinck

Reputation: 86393

Shifting by nibbles is the most efficient way.

If performance is not your problem and you want to have the most readable version you may want to convert your BCD-number to a string and move the decimal point around.

In case you don't have a decimal point (e.g. your number is an integer) you can concat zeros if x > 0 or delete the last -x characters if x < 0.

Afterwards convert the string back to BCD. Watch out for overflows and and cases where you delete all characters and end up with an empty string.

Upvotes: 1

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