BancorFormula.sol

Git Source

Inherits: IBancorFormula, Utils, ERC165

Author: https://github.com/AragonBlack/fundraising/blob/master/apps/bancor-formula/contracts/BancorFormula.sol

The sole modification applied to these contracts involves the alteration of the Solidity version and the version-specific removal of the 'public' keyword from the constructor, coinciding with adjustments in the contract import methodology.

State Variables

version

string public version = "0.3";

ONE

uint private constant ONE = 1;

MAX_WEIGHT

uint32 private constant MAX_WEIGHT = 1_000_000;

MIN_PRECISION

uint8 private constant MIN_PRECISION = 32;

MAX_PRECISION

uint8 private constant MAX_PRECISION = 127;

FIXED_1

Auto-generated via 'PrintIntScalingFactors.py'

uint private constant FIXED_1 = 0x080000000000000000000000000000000;

FIXED_2

uint private constant FIXED_2 = 0x100000000000000000000000000000000;

MAX_NUM

uint private constant MAX_NUM = 0x200000000000000000000000000000000;

LN2_NUMERATOR

Auto-generated via 'PrintLn2ScalingFactors.py'

uint private constant LN2_NUMERATOR = 0x3f80fe03f80fe03f80fe03f80fe03f8;

LN2_DENOMINATOR

uint private constant LN2_DENOMINATOR = 0x5b9de1d10bf4103d647b0955897ba80;

OPT_LOG_MAX_VAL

Auto-generated via 'PrintFunctionOptimalLog.py' and 'PrintFunctionOptimalExp.py'

uint private constant OPT_LOG_MAX_VAL = 0x15bf0a8b1457695355fb8ac404e7a79e3;

OPT_EXP_MAX_VAL

uint private constant OPT_EXP_MAX_VAL = 0x800000000000000000000000000000000;

maxExpArray

Auto-generated via 'PrintFunctionConstructor.py'

uint[128] private maxExpArray;

Functions

supportsInterface

See {IERC165-supportsInterface}.

function supportsInterface(bytes4 interfaceId)
    public
    view
    virtual
    override(ERC165)
    returns (bool);

constructor

constructor();

calculatePurchaseReturn

given a token supply, connector balance, weight and a deposit amount (in the connector token), calculates the return for a given conversion (in the main token) Formula: Return = _supply * ((1 + _depositAmount / _connectorBalance) ^ (_connectorWeight / 1000000) - 1)

function calculatePurchaseReturn(
    uint _supply,
    uint _connectorBalance,
    uint32 _connectorWeight,
    uint _depositAmount
) public view returns (uint);

Parameters

Name	Type	Description
_supply	uint256	token total supply
_connectorBalance	uint256	total connector balance
_connectorWeight	uint32	connector weight, represented in ppm, 1-1000000
_depositAmount	uint256	deposit amount, in connector token

Returns

Name	Type	Description
<none>	uint256	purchase return amount

calculateSaleReturn

given a token supply, connector balance, weight and a sell amount (in the main token), calculates the return for a given conversion (in the connector token) Formula: Return = _connectorBalance * (1 - (1 - _sellAmount / _supply) ^ (1 / (_connectorWeight / 1000000)))

function calculateSaleReturn(
    uint _supply,
    uint _connectorBalance,
    uint32 _connectorWeight,
    uint _sellAmount
) public view returns (uint);

Parameters

Name	Type	Description
_supply	uint256	token total supply
_connectorBalance	uint256	total connector
_connectorWeight	uint32	constant connector Weight, represented in ppm, 1-1000000
_sellAmount	uint256	sell amount, in the token itself

Returns

Name	Type	Description
<none>	uint256	sale return amount

calculateCrossConnectorReturn

given two connector balances/weights and a sell amount (in the first connector token), calculates the return for a conversion from the first connector token to the second connector token (in the second connector token) Formula: Return = _toConnectorBalance * (1 - (_fromConnectorBalance / (_fromConnectorBalance + _amount)) ^ (_fromConnectorWeight / _toConnectorWeight))

function calculateCrossConnectorReturn(
    uint _fromConnectorBalance,
    uint32 _fromConnectorWeight,
    uint _toConnectorBalance,
    uint32 _toConnectorWeight,
    uint _amount
) public view returns (uint);

Parameters

Name	Type	Description
_fromConnectorBalance	uint256	input connector balance
_fromConnectorWeight	uint32	input connector weight, represented in ppm, 1-1000000
_toConnectorBalance	uint256	output connector balance
_toConnectorWeight	uint32	output connector weight, represented in ppm, 1-1000000
_amount	uint256	input connector amount

Returns

Name	Type	Description
<none>	uint256	second connector amount

power

General Description: Determine a value of precision. Calculate an integer approximation of (_baseN / _baseD) ^ (_expN / _expD) * 2 ^ precision. Return the result along with the precision used. Detailed Description: Instead of calculating "base ^ exp", we calculate "e ^ (log(base) * exp)". The value of "log(base)" is represented with an integer slightly smaller than "log(base) * 2 ^ precision". The larger "precision" is, the more accurately this value represents the real value. However, the larger "precision" is, the more bits are required in order to store this value. And the exponentiation function, which takes "x" and calculates "e ^ x", is limited to a maximum exponent (maximum value of "x"). This maximum exponent depends on the "precision" used, and it is given by "maxExpArray[precision] >> (MAX_PRECISION - precision)". Hence we need to determine the highest precision which can be used for the given input, before calling the exponentiation function. This allows us to compute "base ^ exp" with maximum accuracy and without exceeding 256 bits in any of the intermediate computations. This functions assumes that "_expN < 2 ^ 256 / log(MAX_NUM - 1)", otherwise the multiplication should be replaced with a "safeMul".

function power(uint _baseN, uint _baseD, uint32 _expN, uint32 _expD)
    internal
    view
    returns (uint, uint8);

generalLog

Compute log(x / FIXED_1) * FIXED_1. This functions assumes that "x >= FIXED_1", because the output would be negative otherwise.

function generalLog(uint x) internal pure returns (uint);

floorLog2

Compute the largest integer smaller than or equal to the binary logarithm of the input.

function floorLog2(uint _n) internal pure returns (uint8);

findPositionInMaxExpArray

The global "maxExpArray" is sorted in descending order, and therefore the following statements are equivalent:

• This function finds the position of [the smallest value in "maxExpArray" larger than or equal to "x"]

• This function finds the highest position of [a value in "maxExpArray" larger than or equal to "x"]

function findPositionInMaxExpArray(uint _x) internal view returns (uint8);

generalExp

This function can be auto-generated by the script 'PrintFunctionGeneralExp.py'. It approximates "e ^ x" via maclaurin summation: "(x^0)/0! + (x^1)/1! + ... + (x^n)/n!". It returns "e ^ (x / 2 ^ precision) * 2 ^ precision", that is, the result is upshifted for accuracy. The global "maxExpArray" maps each "precision" to "((maximumExponent + 1) << (MAX_PRECISION - precision)) - 1". The maximum permitted value for "x" is therefore given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".

function generalExp(uint _x, uint8 _precision) internal pure returns (uint);

optimalLog

Return log(x / FIXED_1) * FIXED_1 Input range: FIXED_1 <= x <= LOG_EXP_MAX_VAL - 1 Auto-generated via 'PrintFunctionOptimalLog.py' Detailed description:

• Rewrite the input as a product of natural exponents and a single residual r, such that 1 < r < 2

• The natural logarithm of each (pre-calculated) exponent is the degree of the exponent

• The natural logarithm of r is calculated via Taylor series for log(1 + x), where x = r - 1

• The natural logarithm of the input is calculated by summing up the intermediate results above

• For example: log(250) = log(e^4 * e^1 * e^0.5 * 1.021692859) = 4 + 1 + 0.5 + log(1 + 0.021692859)

function optimalLog(uint x) internal pure returns (uint);

optimalExp

Return e ^ (x / FIXED_1) * FIXED_1 Input range: 0 <= x <= OPT_EXP_MAX_VAL - 1 Auto-generated via 'PrintFunctionOptimalExp.py' Detailed description:

• Rewrite the input as a sum of binary exponents and a single residual r, as small as possible

• The exponentiation of each binary exponent is given (pre-calculated)

• The exponentiation of r is calculated via Taylor series for e^x, where x = r

• The exponentiation of the input is calculated by multiplying the intermediate results above

• For example: e^5.521692859 = e^(4 + 1 + 0.5 + 0.021692859) = e^4 * e^1 * e^0.5 * e^0.021692859

function optimalExp(uint x) internal pure returns (uint);