How to multiply (and divide) BCD numbers by 10 ^ x
I have a large (12-bit) BCD number encoded in an array of 6 bytes - each chunk 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 going left or right on nibble, not bit, but it's a terrible implementation - especially in Javacard, and that's what I'm using. Is there a better way?
Shifting by chunks is the most efficient way.
If performance isn't your concern and you want the most readable version, you can convert your BCD number to a string and move the decimal point around.
If you don't have a decimal point (for example, your number is an integer), you can specify zeros if x> 0, or remove the last -x characters if x <0.
Then convert the string back to BCD. Watch out for overflows and cases where you remove all characters and end up with an empty string.
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You don't need to use bit shift (although this is probably the most efficient way to do it).
For your 12 digit BCD number, assuming there is no overflow, suppose b [5] through b [0] contains your bytes from most significant to least significant, and mod is the modulus (remainder) operation and divs are integer divisions , the following pseudocode will be multiplied 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, this is probably uglier than your bit shifting solution, but as long as you encapsulate any of them into a function, it doesn't really matter.
I suggest having a function line by line:
BcdArray mult10 (BcdArray ba, int shiftAmt);
which would return a modified array applying that cardinality of 10.
Any even power of ten is a simple copy of the bytes (since two nybbles are a byte), while only odd powers of ten need a complex bit-shift or remainder / division code.
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