Algorithm

The integer is composed of mantissa and exponent part of encoding, and pack algorithm is:

integer = mantissa * (exponent_base^exponent)

where the exponent_base is 10. This compression algorithm is mainly targeted at two types of data fee and amount:

• fee: 11 bits of mantissa and 5bits of exponent, total in 2 bytes

• amount: 35 bits of mantissa and 5bits of exponent, total in 5 bytes

max value limitation of algorithm

For the amount, the max mantissa is 2^35 - 1, and the max exponent is 2^5 - 1 or 31. According to the pack algorithm, when exponent larger than 30, the result will exceed u128, so we use 30 as the max value of exponent, the max value of amount is

max_amount = (2^35 - 1) * 10^30 = 34359738367000000000000000000000000000

For the fee, the max mantissa is 2^11 - 1, and the max exponent is 2^5 - 1 or 31, which make the max value of fee is

max_fee = (2^11 - 1) * 10^31 = 20470000000000000000000000000000000

Numerical precision loss

According to the formula, it can be seen that the compression algorithm will be numerical precision loss. For the numbers smaller than 2^128 will be changed after compression and cannot be recovered. For example, a fee integer is (2^10+1)*10^2+1 = 102501 where the mantissa is 2^10+1=101 and the exponent is 2, the pack result will be (2^10+1)*10^2 = 102500 which results in a 1 numerical precision loss.

version: 4457a91