getReserveFactor, getDecimals

getReserveFactor

• getReserveFactor, returns the value of reserveFactor as a uint256 variable.

• reserveFactor, amongst other data, is stored within the bitmap ReserveConfigurationMap

The reserve factor is a percentage of protocol interest which goes to the Aave Ecosystem Reserve. The rest of the borrow interest goes to the suppliers.

It does 3 things:

• Bitwise NOT of RESERVE_FACTOR_MASK: ~RESERVE_FACTOR_MASK

• Bitwise AND: data & ~RESERVE_FACTOR_MASK

• Right shift the result of the above by RESERVE_FACTOR_START_BIT_POSITION

RESERVE_FACTOR_MASK

// 64 characters (we ignore the leading 0x)
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0000FFFFFFFFFFFFFFFF

This is a 256-bit hexadecimal number, represented by 64 hexadecimal characters.

• each hex character represents 4 bits => 4 * 64 = 256 bits

In binary: first 176 bits are all 1 (represented by F in hexadecimal), followed by 16 zeros, and ending with another 64 bits of 1.

0xF can be directly interpreted in binary as such:

F = 15 = 8 + 4 + 2 + 1 = 1111

~RESERVE_FACTOR_MASK

The tilde is the bitwise NOT operator -> it flips the bits, changing 0s to 1s and 1s to 0s.

• Notice that only the bits 64-79 are now F, which corresponds to the range of bits that contain the reserveFactor value as seen in ReserveConfigurationMap

• ~RESERVE_FACTOR_MASK: 0x00..FFFF..00

data & ~RESERVE_FACTOR_MASK

• & is the operator for bitwise AND operation

• AND operation returns 1 only if both the bits are 1.

• data AND 0x00..FFFF..00:

  • this means that it is only possible for the result of the operation to contain 1s within the range of 64-79

  • all other bits will be zero, as a bitwise ADD operation with a 0 will result in 0.

  • so we have the possibility of 1s occurring within 64-79 bit, if the corresponding bit in self.data, is also 1.

The purpose of the mask is to wipe out all other irrelevant data, while extracting only the relevant portion of the bitmap

Right shift ( >> )

To illustrate this portion, let us assume the result so far is as follows:

0x00000000000000000000000000000000000000000000 F0FF 0000000000000000 

• The result is right shifted by RESERVE_FACTOR_START_BIT_POSITION

• RESERVE_FACTOR_START_BIT_POSITION = 64

We see that the trailing zeros are dropped off, and replaced as leading zeros. Essentially, the section of bits corresponding to reserveFactor is moved all the way to the end.

Why?

In short, right shifting such that the trailing zeros are removed so that the value is left-padded, results in the proper representation of a number.

In Solidity, strings and bytes are padded on the lower-order (right) side with zero-bytes, while other types (such as numbers and addresses) are padded on the higher-order side.

As an example, this is how we would store the string "abcd" in one full word (32 bytes):

0x6162636400000000000000000000000000000000000000000000000000000000

This is how the number 0x61626364 would be stored:

0x0000000000000000000000000000000000000000000000000000000061626364

uint256 (and other numbers) are left-padded.

getDecimals

• Process is similar to getReserveFactor