BigMathMinified
the number is divided into two parts: a coefficient and an exponent. This comes at a cost of losing some precision at the end of the number because the exponent simply fills it with zeroes. This precision is oftentimes negligible and can result in significant gas cost reduction due to storage space reduction. Also note, a valid big number is as follows: if the exponent is > 0, then coefficient last bits should be occupied to have max precision.
roundUp is more like a increase 1, which happens everytime for the same number. roundDown simply sets trailing digits after coefficientSize to zero (floor), only once for the same number.
ROUND_DOWN
bool ROUND_DOWNconstants to use for roundUp input param to increase readability
ROUND_UP
bool ROUND_UPtoBigNumber
function toBigNumber(uint256 normal, uint256 coefficientSize, uint256 exponentSize, bool roundUp) internal pure returns (uint256 bigNumber)converts normal number to BigNumber with exponent and coefficient (or precision).
e.g.:
5035703444687813576399599 (normal) = (coefficient32bits, exponent8bits)40bits
5035703444687813576399599 (decimal) => 10000101010010110100000011111011110010100110100000000011100101001101001101011101111 (binary)
=> 10000101010010110100000011111011000000000000000000000000000000000000000000000000000
^-------------------- 51(exponent) -------------- ^
coefficient = 1000,0101,0100,1011,0100,0000,1111,1011 (2236301563)
exponent = 0011,0011 (51)
bigNumber = 1000,0101,0100,1011,0100,0000,1111,1011,0011,0011 (572493200179)
Parameters
| Name | Type | Description |
|---|---|---|
| normal | uint256 | number which needs to be converted into Big Number |
| coefficientSize | uint256 | at max how many bits of precision there should be (64 = uint64 (64 bits precision)) |
| exponentSize | uint256 | at max how many bits of exponent there should be (8 = uint8 (8 bits exponent)) |
| roundUp | bool | signals if result should be rounded down or up |
Return Values
| Name | Type | Description |
|---|---|---|
| bigNumber | uint256 | converted bigNumber (coefficient << exponent) |
fromBigNumber
function fromBigNumber(uint256 bigNumber, uint256 exponentSize, uint256 exponentMask) internal pure returns (uint256 normal)get normal number from bigNumber, exponentSize and exponentMask
mostSignificantBit
function mostSignificantBit(uint256 normal) internal pure returns (uint256 lastBit)gets the most significant bit lastBit of a normal number (length of given number of binary format).
e.g.
5035703444687813576399599 = 10000101010010110100000011111011110010100110100000000011100101001101001101011101111
lastBit = ^--------------------------------- 83 ----------------------------------------^