BigMathVault

Git Source

this is an optimized version mainly created by taking Fluid vault's codebase into consideration so it's use is limited for other cases.

State Variables

COEFFICIENT_SIZE_DEBT_FACTOR

uint256 private constant COEFFICIENT_SIZE_DEBT_FACTOR = 35;

EXPONENT_SIZE_DEBT_FACTOR

uint256 private constant EXPONENT_SIZE_DEBT_FACTOR = 15;

COEFFICIENT_MAX_DEBT_FACTOR

uint256 private constant COEFFICIENT_MAX_DEBT_FACTOR = (1 << COEFFICIENT_SIZE_DEBT_FACTOR) - 1;

EXPONENT_MAX_DEBT_FACTOR

uint256 private constant EXPONENT_MAX_DEBT_FACTOR = (1 << EXPONENT_SIZE_DEBT_FACTOR) - 1;

DECIMALS_DEBT_FACTOR

uint256 private constant DECIMALS_DEBT_FACTOR = 16384;

MAX_MASK_DEBT_FACTOR

uint256 internal constant MAX_MASK_DEBT_FACTOR = (1 << (COEFFICIENT_SIZE_DEBT_FACTOR + EXPONENT_SIZE_DEBT_FACTOR)) - 1;

PRECISION

uint256 internal constant PRECISION = 64;

TWO_POWER_64

uint256 internal constant TWO_POWER_64 = 1 << PRECISION;

TWO_POWER_69_MINUS_1

uint256 internal constant TWO_POWER_69_MINUS_1 = (1 << 69) - 1;

COEFFICIENT_PLUS_PRECISION

uint256 private constant COEFFICIENT_PLUS_PRECISION = COEFFICIENT_SIZE_DEBT_FACTOR + PRECISION;

COEFFICIENT_PLUS_PRECISION_MINUS_1

uint256 private constant COEFFICIENT_PLUS_PRECISION_MINUS_1 = COEFFICIENT_PLUS_PRECISION - 1;

TWO_POWER_COEFFICIENT_PLUS_PRECISION_MINUS_1

uint256 private constant TWO_POWER_COEFFICIENT_PLUS_PRECISION_MINUS_1 = (1 << COEFFICIENT_PLUS_PRECISION_MINUS_1) - 1;

TWO_POWER_COEFFICIENT_PLUS_PRECISION_MINUS_1_MINUS_1

uint256 private constant TWO_POWER_COEFFICIENT_PLUS_PRECISION_MINUS_1_MINUS_1 =
    (1 << (COEFFICIENT_PLUS_PRECISION_MINUS_1 - 1)) - 1;

Functions

mulDivNormal

multiplies a normal number with a bigNumber1 and then divides by bigNumber2.

*For vault's use case MUST always:

• bigNumbers have exponent size 15 bits
• bigNumbers have coefficient size 35 bits and have 35th bit always 1 (when exponent > 0 BigMath numbers have max precision) so coefficients must always be in range 17179869184 <= coefficient <= 34359738367.
• bigNumber1 (debt factor) always have exponent >= 1 & <= 16384
• bigNumber2 (connection factor) always have exponent >= 1 & <= 32767 (15 bits)
• bigNumber2 always >= bigNumber1 (connection factor can never be < base branch debt factor)
• as a result of previous points, numbers must never be 0
• normal is positionRawDebt and is always within 10000 and type(int128).max*

function mulDivNormal(uint256 normal, uint256 bigNumber1, uint256 bigNumber2) internal pure returns (uint256);

Returns

mulDivBigNumber

multiplies a bigNumber with normal number1 and then divides by TWO_POWER_64.

*For vault's use case (calculating new branch debt factor after liquidation):

• number1 is debtFactor, intialized as TWO_POWER_64 and reduced from there, hence it's always <= TWO_POWER_64 and always > 0.
• bigNumber is branch debt factor, which starts as ((X35 << 15) | (1 << 14)) and reduces from there.
• bigNumber must have have exponent size 15 bits and be >= 1 & <= 16384
• bigNumber must have coefficient size 35 bits and have 35th bit always 1 (when exponent > 0 BigMath numbers have max precision) so coefficients must always be in range 17179869184 <= coefficient <= 34359738367.*

function mulDivBigNumber(uint256 bigNumber, uint256 number1) internal pure returns (uint256 result);

Parameters

Returns

mulBigNumber

multiplies a bigNumber1 with another bigNumber2.

*For vault's use case (calculating connection factor of merged branches userTickDebtFactor * connectionDebtFactor *... connectionDebtFactor):

• bigNumbers must have have exponent size 15 bits and be >= 1 & <= 32767
• bigNumber must have coefficient size 35 bits and have 35th bit always 1 (when exponent > 0 BigMath numbers have max precision) so coefficients must always be in range 17179869184 <= coefficient <= 34359738367.*

sum of exponents from bigNumber1 bigNumber2 should be > 16384. e.g. res = bigNumber1 * bigNumber2 = (coe1, exp1) * (coe2, exp2) >> decimal = (coe1coe2>>overflow, exp1+exp2+overflow-decimal)*

function mulBigNumber(uint256 bigNumber1, uint256 bigNumber2) internal pure returns (uint256);

Parameters

Returns

divBigNumber

divides a bigNumber1 by bigNumber2.

*For vault's use case (calculating connectionFactor_ = baseBranchDebtFactor / currentBranchDebtFactor) bigNumbers MUST always:

• have exponent size 15 bits and be >= 1 & <= 16384
• have coefficient size 35 bits and have 35th bit always 1 (when exponent > 0 BigMath numbers have max precision) so coefficients must always be in range 17179869184 <= coefficient <= 34359738367.
• as a result of previous points, numbers must never be 0 e.g. res = bigNumber1 / bigNumber2 = (coe1, exp1) / (coe2, exp2) << decimal = ((coe1<<precision_)/coe2, exp1+decimal-exp2-precision_)*

function divBigNumber(uint256 bigNumber1, uint256 bigNumber2) internal pure returns (uint256);

Parameters

Returns