├── __init__.py ├── tests ├── __init__.py ├── __pycache__ │ ├── __init__.cpython-37.pyc │ ├── __init__.cpython-39.pyc │ ├── conftest.cpython-37-pytest-6.2.5.pyc │ ├── conftest.cpython-39-pytest-6.2.5.pyc │ └── test_ratios.cpython-37-pytest-6.2.5.pyc ├── conftest.py └── test_ratios.py ├── .gitignore ├── pytest.ini ├── README.md ├── examples ├── test_balancer_math.py └── balancer_math.cairo ├── contracts └── ratio.cairo └── LICENSE /__init__.py: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /tests/__init__.py: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /.hypothesis/ 2 | /__pycache__/ 3 | /.vscode/ 4 | /.pytest_cache/ -------------------------------------------------------------------------------- /pytest.ini: -------------------------------------------------------------------------------- 1 | # pytest.ini 2 | [pytest] 3 | addopts = -ra --disable-warnings --verbose 4 | testpaths = 5 | tests -------------------------------------------------------------------------------- /tests/__pycache__/__init__.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/0xtonysprocket/ratios_cairo/HEAD/tests/__pycache__/__init__.cpython-37.pyc -------------------------------------------------------------------------------- /tests/__pycache__/__init__.cpython-39.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/0xtonysprocket/ratios_cairo/HEAD/tests/__pycache__/__init__.cpython-39.pyc -------------------------------------------------------------------------------- /tests/__pycache__/conftest.cpython-37-pytest-6.2.5.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/0xtonysprocket/ratios_cairo/HEAD/tests/__pycache__/conftest.cpython-37-pytest-6.2.5.pyc -------------------------------------------------------------------------------- /tests/__pycache__/conftest.cpython-39-pytest-6.2.5.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/0xtonysprocket/ratios_cairo/HEAD/tests/__pycache__/conftest.cpython-39-pytest-6.2.5.pyc -------------------------------------------------------------------------------- /tests/__pycache__/test_ratios.cpython-37-pytest-6.2.5.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/0xtonysprocket/ratios_cairo/HEAD/tests/__pycache__/test_ratios.cpython-37-pytest-6.2.5.pyc -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # ratios_cairo 2 | repository that defines a cairo struct called ratio that represents a rational number in order to calculate exponents. 3 | 4 | Ratio is x/y where x and y in Z mod p 5 | 6 | Current functionality: 7 | 8 | - multiply ratios 9 | - divide ratios 10 | - raise ratio to power 11 | - take nth root of ratio 12 | - add ratios 13 | - absolute value of difference between ratios 14 | - check if one ratio is less than or equal to another 15 | 16 | Todo: 17 | 18 | - add testing 19 | - add overflow protection 20 | -------------------------------------------------------------------------------- /tests/conftest.py: -------------------------------------------------------------------------------- 1 | import os 2 | import asyncio 3 | import pytest 4 | 5 | from starkware.starknet.testing.starknet import Starknet 6 | 7 | # contract and library paths 8 | RATIO_CONTRACT = os.path.join(os.path.dirname(__file__), "../contracts/ratio.cairo") 9 | 10 | 11 | @pytest.fixture(scope="module") 12 | def event_loop(): 13 | return asyncio.new_event_loop() 14 | 15 | 16 | # contract and object factories 17 | @pytest.fixture(scope="module") 18 | async def starknet_factory(): 19 | starknet = await Starknet.empty() 20 | return starknet 21 | 22 | 23 | @pytest.fixture(scope="module") 24 | async def ratio_factory(starknet_factory): 25 | starknet = starknet_factory 26 | 27 | # Deploy the account contract 28 | ratio_contract = await starknet.deploy(source=RATIO_CONTRACT) 29 | 30 | return ratio_contract 31 | -------------------------------------------------------------------------------- /tests/test_ratios.py: -------------------------------------------------------------------------------- 1 | import pytest 2 | import math 3 | from hypothesis import given, strategies as st, settings 4 | 5 | # from OZ utils.py 6 | def to_uint(a): 7 | """Takes in value, returns uint256-ish tuple.""" 8 | return (a & ((1 << 128) - 1), a >> 128) 9 | 10 | 11 | def from_uint(uint): 12 | """Takes in uint256-ish tuple, returns value.""" 13 | return uint[0] + (uint[1] << 128) 14 | 15 | 16 | @given( 17 | x=st.integers(min_value=1, max_value=100000), 18 | y=st.integers(min_value=1, max_value=100000), 19 | z=st.integers(min_value=1, max_value=100000), 20 | k=st.integers(min_value=1, max_value=100000), 21 | ) 22 | @settings(deadline=None) 23 | @pytest.mark.asyncio 24 | async def test_ratio_diff(ratio_factory, x, y, z, k): 25 | ratio = ratio_factory 26 | 27 | base = (to_uint(x), to_uint(y)) # x/y 28 | other = (to_uint(z), to_uint(k)) # z/k 29 | 30 | root = await ratio.ratio_diff(base, other).call() 31 | assert (from_uint(root.result[0][0]), from_uint(root.result[0][1])) == ( 32 | ( 33 | abs(z * y - x * k), 34 | k * y, 35 | ) 36 | if k != y 37 | else (abs(z - x), k) 38 | ) 39 | 40 | 41 | @given( 42 | x=st.integers(min_value=1, max_value=100000), 43 | y=st.integers(min_value=1, max_value=100000), 44 | z=st.integers(min_value=1, max_value=100000), 45 | k=st.integers(min_value=1, max_value=100000), 46 | ) 47 | @settings(deadline=None) 48 | @pytest.mark.asyncio 49 | async def test_ratio_le_eq(ratio_factory, x, y, z, k): 50 | ratio = ratio_factory 51 | 52 | base = (to_uint(x), to_uint(y)) # x/y 53 | other = (to_uint(z), to_uint(k)) # z/k 54 | 55 | root = await ratio.ratio_less_than_or_eq(base, other).call() 56 | print(root.result) 57 | print(root.result[0]) 58 | assert root.result[0] == (1 if x / y <= z / k else 0) 59 | 60 | 61 | @given( 62 | x=st.integers(min_value=1, max_value=100000), 63 | y=st.integers(min_value=1, max_value=100000), 64 | z=st.integers(min_value=1, max_value=100000), 65 | k=st.integers(min_value=1, max_value=100000), 66 | ) 67 | @settings(deadline=None) 68 | @pytest.mark.asyncio 69 | async def test_ratio_mul(ratio_factory, x, y, z, k): 70 | ratio = ratio_factory 71 | 72 | base = (to_uint(x), to_uint(y)) # x/y 73 | other = (to_uint(z), to_uint(k)) # exponent 74 | 75 | root = await ratio.ratio_mul(base, other).call() 76 | assert (from_uint(root.result[0][0]), from_uint(root.result[0][1])) == ( 77 | x * z, 78 | y * k, 79 | ) 80 | 81 | 82 | @given( 83 | x=st.integers(min_value=1, max_value=100), 84 | y=st.integers(min_value=1, max_value=100), 85 | z=st.integers(min_value=1, max_value=9), 86 | ) 87 | @settings(deadline=None) 88 | @pytest.mark.asyncio 89 | async def test_ratio_pow(ratio_factory, x, y, z): 90 | ratio = ratio_factory 91 | 92 | base = (to_uint(x), to_uint(y)) # x/y 93 | power = to_uint(z) # exponent 94 | 95 | root = await ratio.ratio_pow(base, power).call() 96 | assert (from_uint(root.result[0][0]), from_uint(root.result[0][1])) == ( 97 | x ** z, 98 | y ** z, 99 | ) 100 | 101 | 102 | """ 103 | 104 | """ 105 | 106 | 107 | @given( 108 | x=st.integers(min_value=1, max_value=100000), 109 | y=st.integers(min_value=1, max_value=100000), 110 | z=st.integers(min_value=1, max_value=100000), 111 | k=st.integers(min_value=1, max_value=100000), 112 | ) 113 | @settings(deadline=None) 114 | @pytest.mark.asyncio 115 | async def test_ratio_add(ratio_factory, x, y, z, k): 116 | ratio = ratio_factory 117 | 118 | base = (to_uint(x), to_uint(y)) # x/y 119 | other = (to_uint(z), to_uint(k)) # exponent 120 | 121 | root = await ratio.ratio_add(base, other).call() 122 | assert (from_uint(root.result[0][0]), from_uint(root.result[0][1])) == ( 123 | (x * k + y * z, y * k) if y != k else (x + z, y) 124 | ) 125 | 126 | 127 | @given( 128 | x=st.integers(min_value=1, max_value=10000), 129 | y=st.integers(min_value=1, max_value=10000), 130 | m=st.integers(min_value=1, max_value=7), 131 | p=st.integers(min_value=5, max_value=11), 132 | ) 133 | @settings(deadline=None) 134 | @pytest.mark.asyncio 135 | async def test_nth_root_by_digit(ratio_factory, x, y, m, p): 136 | ratio = ratio_factory 137 | 138 | base = (to_uint(x), to_uint(y)) # x/y 139 | root = to_uint(m) # which root 140 | precision = p # how many digits 141 | 142 | root = await ratio.nth_root_by_digit(base, root, precision).call() 143 | res = math.floor(((x / y) ** (1 / m)) * 10 ** p) / (10 ** p) 144 | assert (from_uint(root.result[0][0]) / from_uint(root.result[0][1]) - res) < ( 145 | 5 / (10 ** p) 146 | ) 147 | -------------------------------------------------------------------------------- /examples/test_balancer_math.py: -------------------------------------------------------------------------------- 1 | import pytest 2 | from .conftest import DECIMALS 3 | 4 | # from OZ utils.py 5 | 6 | 7 | def to_uint(a): 8 | """Takes in value, returns uint256-ish tuple.""" 9 | return (a & ((1 << 128) - 1), a >> 128) 10 | 11 | 12 | def from_uint(uint): 13 | """Takes in uint256-ish tuple, returns value.""" 14 | return uint[0] + (uint[1] << 128) 15 | 16 | 17 | @pytest.mark.asyncio 18 | async def test_get_spot_price(balancer_factory): 19 | balancer_contract, _ = balancer_factory 20 | 21 | a_balance = to_uint(10 * DECIMALS) 22 | a_weight = (to_uint(1), to_uint(2)) # 1/2 23 | b_balance = to_uint(4 * DECIMALS) 24 | b_weight = (to_uint(1), to_uint(3)) # 1/3 25 | fee = (to_uint(1), to_uint(100)) # 1% 26 | 27 | spot_price = await balancer_contract.get_spot_price( 28 | a_balance, a_weight, b_balance, b_weight, fee 29 | ).call() 30 | assert (from_uint(spot_price.result[0][0]), from_uint(spot_price.result[0][1])) == ( 31 | 3000 * DECIMALS, 32 | 792 * DECIMALS, 33 | ) 34 | 35 | 36 | @pytest.mark.asyncio 37 | async def test_get_pool_minted_given_single_in(balancer_factory): 38 | balancer_contract, _ = balancer_factory 39 | 40 | amount_of_a_in = to_uint(21376 * DECIMALS) 41 | a_balance = to_uint(45789 * DECIMALS) 42 | supply = to_uint(10000 * DECIMALS) 43 | a_weight = (to_uint(1), to_uint(3)) # 1/3 44 | total_weight = (to_uint(1), to_uint(1)) # 1/1 45 | swap_fee = (to_uint(1), to_uint(100)) # 1/100 46 | 47 | pool_minted = await balancer_contract.get_pool_minted_given_single_in( 48 | amount_of_a_in, a_balance, supply, a_weight, total_weight, swap_fee 49 | ).call() 50 | assert ( 51 | from_uint(pool_minted.result[0][0]) / 52 | from_uint(pool_minted.result[0][1]) 53 | - (1354.11112 * DECIMALS) 54 | ) < 5 / (10 ** 6) 55 | 56 | 57 | @pytest.mark.asyncio 58 | async def test_get_single_out_given_pool_in(balancer_factory): 59 | balancer_contract, _ = balancer_factory 60 | 61 | pool_amount_in = to_uint(1000 * DECIMALS) 62 | a_balance = to_uint(5324 * DECIMALS) 63 | supply = to_uint(1234567 * DECIMALS) 64 | a_weight = (to_uint(1), to_uint(3)) 65 | total_weight = (to_uint(1), to_uint(1)) 66 | swap_fee = (to_uint(1), to_uint(100)) 67 | exit_fee = (to_uint(1), to_uint(100)) 68 | 69 | pool_minted = await balancer_contract.get_single_out_given_pool_in( 70 | pool_amount_in, a_balance, supply, a_weight, total_weight, swap_fee, exit_fee 71 | ).call() 72 | assert from_uint(pool_minted.result[0][0]) / from_uint( 73 | pool_minted.result[0][1] 74 | ) - (12.712370 * DECIMALS) < 5 / (10 ** 6) 75 | 76 | 77 | @pytest.mark.asyncio 78 | async def test_get_out_given_in(balancer_factory): 79 | balancer_contract, _ = balancer_factory 80 | 81 | amount_of_a_in = to_uint(100 * DECIMALS) 82 | a_balance = to_uint(2324 * DECIMALS) 83 | a_weight = (to_uint(1), to_uint(3)) 84 | b_balance = to_uint(1234 * DECIMALS) 85 | b_weight = (to_uint(1), to_uint(3)) 86 | swap_fee = (to_uint(1), to_uint(100)) 87 | 88 | pool_minted = await balancer_contract.get_out_given_in( 89 | amount_of_a_in, a_balance, a_weight, b_balance, b_weight, swap_fee 90 | ).call() 91 | assert from_uint(pool_minted.result[0][0]) / from_uint( 92 | pool_minted.result[0][1] 93 | ) - (50.4193149 * DECIMALS) < 5 / (10 ** 7) 94 | 95 | 96 | @pytest.mark.asyncio 97 | async def test_get_proportional_deposits_given_pool_out(balancer_factory): 98 | balancer_contract, _ = balancer_factory 99 | 100 | pool_supply_ratio = (to_uint(10000 * DECIMALS), to_uint(578347 * DECIMALS)) 101 | token_list_input = [ 102 | (1, # token 1 103 | to_uint(200 * DECIMALS)), # Uint balance of token 1 104 | (2, # token 2 105 | to_uint(1111 * DECIMALS)), # balance 106 | (3, # token 3 107 | to_uint(7777 * DECIMALS)), # balance 108 | ] 109 | 110 | list_of_deposits = await balancer_contract.get_proportional_deposits_given_pool_out(pool_supply_ratio, token_list_input).call() 111 | assert list_of_deposits.result[0][0][0] == 1 112 | assert from_uint(list_of_deposits.result[0][0][1]) - \ 113 | (((10000 * DECIMALS) / (578347 * DECIMALS)) * (200 * DECIMALS)) < 5 / (10**5) 114 | 115 | assert list_of_deposits.result[0][1][0] == 2 116 | assert from_uint(list_of_deposits.result[0][1][1]) - \ 117 | (((10000 * DECIMALS) / (578347 * DECIMALS)) 118 | * (1111 * DECIMALS)) < 5 / (10**5) 119 | 120 | assert list_of_deposits.result[0][2][0] == 3 121 | assert from_uint(list_of_deposits.result[0][2][1]) - \ 122 | (((10000 * DECIMALS) / (578347 * DECIMALS)) 123 | * (7777 * DECIMALS)) < 5 / (10**5) 124 | 125 | 126 | @pytest.mark.asyncio 127 | async def test_get_proportional_withdraw_given_pool_in(balancer_factory): 128 | balancer_contract, _ = balancer_factory 129 | 130 | pool_total_supply = to_uint(578347 * DECIMALS) 131 | amount_in = to_uint(10000 * DECIMALS) 132 | exit_fee = (to_uint(1), to_uint(1000)) 133 | token_list_input = [ 134 | (1, # token 1 135 | to_uint(200 * DECIMALS)), # Uint balance of token 1 136 | (2, # token 2 137 | to_uint(1111 * DECIMALS)), # balance 138 | (3, # token 3 139 | to_uint(7777 * DECIMALS)), # balance 140 | ] 141 | 142 | list_of_deposits = await balancer_contract.get_proportional_withdraw_given_pool_in(pool_total_supply, amount_in, exit_fee, token_list_input).call() 143 | assert list_of_deposits.result[0][0][0] == 1 144 | assert from_uint(list_of_deposits.result[0][0][1]) - \ 145 | ((((10000 * DECIMALS) - (10000 * DECIMALS / 1000)) / 146 | (578347 * DECIMALS)) * (200 * DECIMALS)) < 5 / (10**5) 147 | 148 | assert list_of_deposits.result[0][1][0] == 2 149 | assert from_uint(list_of_deposits.result[0][1][1]) - \ 150 | ((((10000 * DECIMALS) - (10000 * DECIMALS / 1000)) / 151 | (578347 * DECIMALS)) * (578347 * DECIMALS)) * (1111 * DECIMALS) < 5 / (10**5) 152 | 153 | assert list_of_deposits.result[0][2][0] == 3 154 | assert from_uint(list_of_deposits.result[0][2][1]) - \ 155 | ((((10000 * DECIMALS) - (10000 * DECIMALS / 1000)) / 156 | (578347 * DECIMALS)) * (7777 * DECIMALS)) < 5 / (10**5) 157 | -------------------------------------------------------------------------------- /contracts/ratio.cairo: -------------------------------------------------------------------------------- 1 | %lang starknet 2 | %builtins pedersen range_check ecdsa 3 | 4 | from starkware.cairo.common.registers import get_fp_and_pc 5 | from starkware.cairo.common.cairo_builtins import HashBuiltin, SignatureBuiltin 6 | from starkware.cairo.common.math_cmp import is_le 7 | from starkware.cairo.common.math import assert_not_zero, assert_le 8 | from starkware.cairo.common.uint256 import ( 9 | Uint256, uint256_add, uint256_sub, uint256_mul, uint256_le, uint256_lt, uint256_signed_nn 10 | ) 11 | 12 | ########## 13 | # STRUCTS 14 | ########## 15 | 16 | # n -> numerator 17 | # d -> denominator 18 | struct Ratio: 19 | member n : Uint256 20 | member d : Uint256 21 | end 22 | 23 | ########## 24 | # MATH 25 | ########## 26 | 27 | # x * y where x and y in rationals return z in rationals 28 | @view 29 | func ratio_mul{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 30 | x : Ratio, y : Ratio) -> (z : Ratio): 31 | alloc_locals 32 | 33 | # needed for dereferencing ratios 34 | let (__fp__, _) = get_fp_and_pc() 35 | 36 | let (local n: Uint256, _) = uint256_mul(x.n, y.n) 37 | let (local d: Uint256, _) = uint256_mul(x.d, y.d) 38 | local z: Ratio = Ratio(n, d) 39 | 40 | return (z) 41 | end 42 | 43 | # divide x/y 44 | @view 45 | func ratio_div{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 46 | x : Ratio, y : Ratio) -> (z : Ratio): 47 | alloc_locals 48 | 49 | # needed for dereferencing ratios 50 | let (__fp__, _) = get_fp_and_pc() 51 | 52 | let (local n: Uint256, _) = uint256_mul(x.n, y.d) 53 | let (local d: Uint256, _) = uint256_mul(x.d, y.n) 54 | 55 | return (Ratio(n, d)) 56 | end 57 | 58 | # x^m where x is element of rationals and m is element of naturals -> element of rationals 59 | @view 60 | func ratio_pow{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 61 | x : Ratio, m : Uint256) -> (z : Ratio): 62 | alloc_locals 63 | 64 | if m.low == 0: 65 | return (Ratio(Uint256(1, 0), Uint256(1, 0))) 66 | end 67 | 68 | # needed for dereferencing ratios 69 | let (__fp__, _) = get_fp_and_pc() 70 | 71 | let (local y : Uint256) = uint256_sub(m, Uint256(1, 0)) 72 | 73 | let (local rest_of_product : Ratio) = ratio_pow(x, y) 74 | let (local z: Ratio) = ratio_mul(x, rest_of_product) 75 | 76 | return (z) 77 | end 78 | 79 | 80 | @view 81 | func pow{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 82 | base : felt, exponent : felt) -> (result : felt): 83 | if exponent == 0: 84 | return (1) 85 | end 86 | 87 | let rest_of_product : felt = pow(base, exponent - 1) 88 | let z : felt = base * rest_of_product 89 | 90 | return (z) 91 | end 92 | 93 | @view 94 | func diff{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 95 | x : felt, y : felt) -> (result : felt): 96 | let le : felt = is_le(y, x) 97 | if le == 1: 98 | let diff : felt = x - y 99 | return (diff) 100 | else: 101 | let diff : felt = y - x 102 | return (diff) 103 | end 104 | end 105 | 106 | # add x + y 107 | @view 108 | func ratio_add{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 109 | first_ratio : Ratio, second_ratio : Ratio) -> (sum : Ratio): 110 | alloc_locals 111 | 112 | # needed for dereferencing ratios 113 | let (__fp__, _) = get_fp_and_pc() 114 | 115 | if first_ratio.d.low == second_ratio.d.low: 116 | if first_ratio.d.high == second_ratio.d.high: 117 | let (local a: Uint256, is_overflow) = uint256_add(first_ratio.n, second_ratio.n) 118 | assert (is_overflow) = 0 119 | local sum : Ratio = Ratio(a, first_ratio.d) 120 | return (sum) 121 | end 122 | end 123 | 124 | let (local x: Uint256, _) = uint256_mul(first_ratio.n, second_ratio.d) 125 | let (local y: Uint256, _) = uint256_mul(second_ratio.n, first_ratio.d) 126 | 127 | let (local i: Uint256, _) = uint256_add(x, y) 128 | let (local j: Uint256, _) = uint256_mul(first_ratio.d, second_ratio.d) 129 | local sum : Ratio = Ratio( 130 | i, 131 | j) 132 | return (sum) 133 | end 134 | 135 | # absolute value of base - other 136 | @view 137 | func ratio_diff{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 138 | base_ratio : Ratio, other_ratio : Ratio) -> (diff : Ratio): 139 | alloc_locals 140 | 141 | # needed for dereferencing ratios 142 | let (__fp__, _) = get_fp_and_pc() 143 | 144 | if base_ratio.d.low == other_ratio.d.low: 145 | if base_ratio.d.high == other_ratio.d.high: 146 | let le : felt = uint256_le(other_ratio.n, base_ratio.n) 147 | if le == 1: 148 | let z: Uint256 = uint256_sub(base_ratio.n, other_ratio.n) 149 | let diff : Ratio = Ratio(z, base_ratio.d) 150 | return (diff) 151 | else: 152 | let z: Uint256 = uint256_sub(other_ratio.n, base_ratio.n) 153 | let diff : Ratio = Ratio(z, base_ratio.d) 154 | return (diff) 155 | end 156 | end 157 | end 158 | 159 | let (local x: Uint256, _) = uint256_mul(other_ratio.n, base_ratio.d) 160 | let (local y: Uint256, _) = uint256_mul(base_ratio.n, other_ratio.d) 161 | let r_le : felt = uint256_le(x, y) 162 | if r_le == 1: 163 | let (local m: Uint256, _) = uint256_mul(base_ratio.n, other_ratio.d) 164 | let (local n: Uint256, _) = uint256_mul(other_ratio.n, base_ratio.d) 165 | let o: Uint256 = uint256_sub(m, n) 166 | let (local p: Uint256, _) = uint256_mul(base_ratio.d, other_ratio.d) 167 | let diff : Ratio = Ratio( 168 | o, 169 | p) 170 | return (diff) 171 | else: 172 | let (local i: Uint256, _) = uint256_mul(other_ratio.n, base_ratio.d) 173 | let (local j: Uint256, _) = uint256_mul(base_ratio.n, other_ratio.d) 174 | let k: Uint256 = uint256_sub(i, j) 175 | let (local l: Uint256, _) = uint256_mul(base_ratio.d, other_ratio.d) 176 | let diff : Ratio = Ratio( 177 | k, 178 | l) 179 | return (diff) 180 | end 181 | end 182 | 183 | @view 184 | func ratio_less_than_or_eq{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 185 | first_ratio : Ratio, second_ratio : Ratio) -> (bool : felt): 186 | alloc_locals 187 | 188 | # needed for dereferencing ratios 189 | let (__fp__, _) = get_fp_and_pc() 190 | 191 | let (local x: Uint256, _) = uint256_mul(first_ratio.n, second_ratio.d) 192 | let (local y: Uint256, _) = uint256_mul(second_ratio.n, first_ratio.d) 193 | let r_le : felt = uint256_le(x, y) 194 | if r_le == 1: 195 | return (1) 196 | end 197 | 198 | return (0) 199 | end 200 | 201 | # take nth root digit by digit until get to desired precision assuming 18 digits of decimals 202 | @view 203 | func nth_root_by_digit{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 204 | x : Ratio, m : Uint256, precision : felt) -> (z : Ratio): 205 | alloc_locals 206 | 207 | # needed for dereferencing ratios 208 | let (__fp__, _) = get_fp_and_pc() 209 | 210 | # edge case if m == 1 211 | if m.low == 1: 212 | return (x) 213 | end 214 | 215 | # edge case if ratio is 1 216 | if x.n.low == x.d.low: 217 | if x.n.high == x.d.high: 218 | return (Ratio(Uint256(1, 0), Uint256(1, 0))) 219 | end 220 | end 221 | 222 | # calculate integer part 223 | local digit : felt = 0 224 | let (local base : felt) = pow(10, digit) 225 | local initial_guess : Ratio = Ratio(Uint256(1, 0), Uint256(base, 0)) 226 | let (local integer_part_non_adjusted : Ratio) = recursive_find_integer_part(x, m, initial_guess) 227 | 228 | let (local z : Ratio) = find_precision_part(x, m, precision, digit, integer_part_non_adjusted) 229 | # let z : Ratio = Ratio(numerator.n, precision_digits) 230 | return (z) 231 | end 232 | 233 | func recursive_find_integer_part{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 234 | x : Ratio, m : Uint256, guess : Ratio) -> (z : Ratio): 235 | alloc_locals 236 | 237 | # needed for dereferencing ratios 238 | let (__fp__, _) = get_fp_and_pc() 239 | 240 | let (local guess_to_m : Ratio) = ratio_pow(guess, m) 241 | let (local le : felt) = ratio_less_than_or_eq(x, guess_to_m) 242 | 243 | if le == 1: 244 | let (local k: Uint256) = uint256_sub(guess.n, Uint256(1, 0)) 245 | local z : Ratio = Ratio(k, Uint256(1, 0)) 246 | return (z) 247 | else: 248 | let (local y: Uint256, is_overflow) = uint256_add(guess.n, Uint256(1, 0)) 249 | assert (is_overflow) = 0 250 | local new_guess : Ratio = Ratio(y, guess.d) 251 | let (local z : Ratio) = recursive_find_integer_part(x, m, new_guess) 252 | return (z) 253 | end 254 | end 255 | 256 | func recursive_find_part{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 257 | x : Ratio, m : Uint256, guess : Ratio, count : felt) -> (z : Ratio): 258 | alloc_locals 259 | 260 | # needed for dereferencing ratios 261 | let (__fp__, _) = get_fp_and_pc() 262 | 263 | if count == 10: 264 | let (local y: Uint256) = uint256_sub(guess.n, Uint256(1, 0)) 265 | return (Ratio(y, guess.d)) 266 | end 267 | 268 | let (local guess_to_m : Ratio) = ratio_pow(guess, m) 269 | let (local le : felt) = ratio_less_than_or_eq(guess_to_m, x) 270 | let r_le: felt = ratio_less_than_or_eq(x, guess_to_m) 271 | 272 | if le == 1: 273 | if r_le == 1: 274 | return (guess) 275 | end 276 | 277 | local new_count : felt = count + 1 278 | let (local q: Uint256, _) = uint256_add(guess.n, Uint256(1,0)) 279 | local new_guess : Ratio = Ratio(q, guess.d) 280 | let (local z : Ratio) = recursive_find_part(x, m, new_guess, new_count) 281 | return (z) 282 | else: 283 | let (local q: Uint256) = uint256_sub(guess.n, Uint256(1,0)) 284 | local z : Ratio = Ratio(q, guess.d) 285 | return (z) 286 | end 287 | end 288 | 289 | func find_precision_part{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 290 | current_x : Ratio, m : Uint256, precision : felt, digit : felt, current_root : Ratio) -> ( 291 | z : Ratio): 292 | alloc_locals 293 | 294 | # needed for dereferencing ratios 295 | let (__fp__, _) = get_fp_and_pc() 296 | 297 | local current_digit : felt = digit + 1 298 | let (local base : felt) = pow(10, current_digit) 299 | let (local x: Uint256, _) = uint256_mul(current_root.n, Uint256(10, 0)) 300 | let (local w: Uint256, _) = uint256_add(x, Uint256(1,0)) 301 | local initial_guess : Ratio = Ratio(w, Uint256(base, 0)) 302 | local count : felt = 1 303 | let (local current_part : Ratio) = recursive_find_part(current_x, m, initial_guess, count) 304 | 305 | let le : felt = is_le(precision, current_digit) 306 | 307 | if le == 1: 308 | return (current_part) 309 | else: 310 | let (local z : Ratio) = find_precision_part(current_x, m, precision, current_digit, current_part) 311 | return (z) 312 | end 313 | end 314 | -------------------------------------------------------------------------------- /examples/balancer_math.cairo: -------------------------------------------------------------------------------- 1 | %lang starknet 2 | 3 | from starkware.cairo.common.cairo_builtins import HashBuiltin, SignatureBuiltin 4 | from starkware.starknet.common.syscalls import get_caller_address, get_contract_address 5 | from starkware.cairo.common.alloc import alloc 6 | from starkware.cairo.common.registers import get_fp_and_pc 7 | from starkware.cairo.common.math import assert_not_zero, assert_le, unsigned_div_rem 8 | from starkware.cairo.common.math_cmp import is_le 9 | from starkware.cairo.common.uint256 import ( 10 | Uint256, uint256_add, uint256_sub, uint256_mul, uint256_le, uint256_lt, 11 | uint256_unsigned_div_rem) 12 | 13 | from contracts.lib.ratios.contracts.ratio import ( 14 | Ratio, ratio_mul, ratio_div, ratio_add, ratio_diff, nth_root_by_digit, pow, ratio_pow, 15 | ratio_less_than_or_eq) 16 | 17 | from openzeppelin.security.safemath import SafeUint256 18 | 19 | ######### 20 | # STRUCT 21 | ######### 22 | 23 | struct TokenAndAmount: 24 | member erc_address : felt 25 | member amount : Uint256 26 | end 27 | 28 | ######### 29 | # BALANCER STYLE MATH 30 | # CONSTANT VALUE INVARIANT 31 | ######### 32 | 33 | # Cairo implementation of https://github.com/balancer-labs/balancer-core/blob/master/contracts/BMath.sol 34 | 35 | namespace Balancer_Math: 36 | # 37 | # a_balance/a_weight fee.denominator 38 | # / * / 39 | # b_balance/b_weight fee.denominator - fee.numerator 40 | # 41 | @view 42 | func get_spot_price{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 43 | a_balance : Uint256, a_weight : Ratio, b_balance : Uint256, b_weight : Ratio, 44 | fee : Ratio) -> (spot_price : Ratio): 45 | alloc_locals 46 | 47 | # needed for dereferencing ratios 48 | let (__fp__, _) = get_fp_and_pc() 49 | 50 | let (local x : Uint256) = SafeUint256.mul(a_balance, a_weight.n) 51 | let (local y : Uint256) = SafeUint256.mul(b_balance, b_weight.n) 52 | let fee_adj : Uint256 = SafeUint256.sub_le(fee.d, fee.n) 53 | 54 | local num_ratio : Ratio = Ratio(n=x, d=a_weight.d) 55 | local den_ratio : Ratio = Ratio(n=y, d=b_weight.d) 56 | 57 | let (local z : Uint256) = SafeUint256.mul(num_ratio.n, den_ratio.d) 58 | let (local z_fee : Uint256) = SafeUint256.mul(z, fee.d) 59 | let (local k : Uint256) = SafeUint256.mul(den_ratio.n, num_ratio.d) 60 | let (local k_fee : Uint256) = SafeUint256.mul(fee_adj, k) 61 | 62 | local spot_price : Ratio = Ratio(n=z_fee, d=k_fee) 63 | 64 | return (spot_price) 65 | end 66 | 67 | ########################### 68 | # DEPOSITS AND WITHDRAWALS 69 | ########################### 70 | 71 | # ********************************************************************************************** 72 | # calcPoolOutGivenSingleIn // 73 | # pAo = poolAmountOut / \ // 74 | # tAi = tokenAmountIn /// / // wI \ \\ \ wI \ // 75 | # wI = tokenWeightIn //| tAi *| 1 - || 1 - -- | * sF || + tBi \ -- \ // 76 | # tW = totalWeight pAo=|| \ \ \\ tW / // | ^ tW | * pS - pS // 77 | # tBi = tokenBalanceIn \\ ------------------------------------- / / // 78 | # pS = poolSupply \\ tBi / / // 79 | # sF = swapFee \ / // 80 | # **********************************************************************************************/ 81 | @view 82 | func get_pool_minted_given_single_in{ 83 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 84 | amount_of_a_in : Uint256, a_balance : Uint256, supply : Uint256, a_weight : Ratio, 85 | total_weight : Ratio, swap_fee : Ratio) -> (pool_tokens_out : Ratio): 86 | alloc_locals 87 | 88 | # needed for dereferencing ratios 89 | let (__fp__, _) = get_fp_and_pc() 90 | 91 | let (local divide_weights : Ratio) = ratio_div(a_weight, total_weight) 92 | 93 | # TODO: add sanity check that 1/1 > divide_weights 94 | let (local step_one : Ratio) = ratio_diff( 95 | Ratio(Uint256(1, 0), Uint256(1, 0)), divide_weights) 96 | 97 | let (local step_one_times_fee : Ratio) = ratio_mul(step_one, swap_fee) 98 | 99 | let (local i : Uint256) = SafeUint256.sub_le(step_one_times_fee.d, step_one_times_fee.n) 100 | local one_minus : Ratio = Ratio(i, step_one_times_fee.d) 101 | let (local times_amount : Ratio) = ratio_mul( 102 | Ratio(amount_of_a_in, Uint256(1, 0)), one_minus) 103 | let (local plus_token_balance : Ratio) = ratio_add( 104 | times_amount, Ratio(a_balance, Uint256(1, 0))) 105 | let (local divided_by_balance : Ratio) = ratio_div( 106 | plus_token_balance, Ratio(a_balance, Uint256(1, 0))) 107 | 108 | let (local exponent : Ratio) = ratio_div(a_weight, total_weight) 109 | 110 | let (local raised_to_exponent : Ratio) = ratio_pow(divided_by_balance, exponent.n) 111 | 112 | # nth root accurate to 9 digits 113 | with_attr error_message( 114 | "ERROR WHEN TAKING THE NTH ROOT : LIKELY FRACTION REDUCTION PROBLEM; TRY SLIGHTLY ADJUSTING NUMBERS"): 115 | let (local take_root_of_exponent : Ratio) = nth_root_by_digit( 116 | raised_to_exponent, exponent.d, 9) 117 | end 118 | let (local times_pool_supply : Ratio) = ratio_mul( 119 | take_root_of_exponent, Ratio(supply, Uint256(1, 0))) 120 | let (local amount_pool_tokens_out : Ratio) = ratio_diff( 121 | times_pool_supply, Ratio(supply, Uint256(1, 0))) 122 | 123 | return (amount_pool_tokens_out) 124 | end 125 | 126 | # IMPLEMENT LATER 127 | # @view 128 | # func get_single_in_given_pool_out{ 129 | # syscall_ptr : felt*, 130 | # pedersen_ptr : HashBuiltin*, 131 | # range_check_ptr 132 | # }(erc20_address: felt, pool_amount_out: felt) -> (amount_of_a_in: felt): 133 | # end 134 | 135 | # ********************************************************************************************** 136 | # calcSingleOutGivenPoolIn // 137 | # tAo = tokenAmountOut / / \\ // 138 | # bO = tokenBalanceOut / // pS - (pAi * (1 - eF)) \ / 1 \ \\ // 139 | # pAi = poolAmountIn | bO - || ----------------------- | ^ | --------- | * b0 || // 140 | # ps = poolSupply \ \\ pS / \(wO / tW)/ // // 141 | # wI = tokenWeightIn tAo = \ \ // // 142 | # tW = totalWeight / / wO \ \ // 143 | # sF = swapFee * | 1 - | 1 - ---- | * sF | // 144 | # eF = exitFee \ \ tW / / // 145 | # **********************************************************************************************/ 146 | @view 147 | func get_single_out_given_pool_in{ 148 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 149 | pool_amount_in : Uint256, a_balance : Uint256, supply : Uint256, a_weight : Ratio, 150 | total_weight : Ratio, swap_fee : Ratio, exit_fee : Ratio) -> (amount_token_out : Ratio): 151 | alloc_locals 152 | 153 | # needed for dereferencing ratios 154 | let (__fp__, _) = get_fp_and_pc() 155 | 156 | let x : Uint256 = SafeUint256.sub_le(exit_fee.d, exit_fee.n) 157 | 158 | # calculate main ratio 159 | local one_minus_exit_fee : Ratio = Ratio(x, exit_fee.d) 160 | let times_pool_in : Ratio = ratio_mul( 161 | one_minus_exit_fee, Ratio(pool_amount_in, Uint256(1, 0))) 162 | 163 | let (local y : Uint256) = SafeUint256.mul(supply, times_pool_in.d) 164 | let y_adj : Uint256 = SafeUint256.sub_le(y, times_pool_in.n) 165 | local pool_supply_minus : Ratio = Ratio(y_adj, times_pool_in.d) 166 | let divided_by_ps : Ratio = ratio_div(pool_supply_minus, Ratio(supply, Uint256(1, 0))) 167 | 168 | let exponent : Ratio = ratio_div(total_weight, a_weight) 169 | 170 | let raised_to_exponent : Ratio = ratio_pow(divided_by_ps, exponent.n) 171 | 172 | with_attr error_message( 173 | "ERROR WHEN TAKING THE NTH ROOT : LIKELY FRACTION REDUCTION PROBLEM; TRY SLIGHTLY ADJUSTING NUMBERS"): 174 | let take_root_of_exponent : Ratio = nth_root_by_digit(raised_to_exponent, exponent.d, 9) 175 | end 176 | 177 | let times_balance_out : Ratio = ratio_mul( 178 | take_root_of_exponent, Ratio(a_balance, Uint256(1, 0))) 179 | 180 | let (local z : Uint256) = SafeUint256.mul(a_balance, times_balance_out.d) 181 | let z_adj : Uint256 = SafeUint256.sub_le(z, times_balance_out.n) 182 | let first_ratio : Ratio = Ratio(z_adj, times_balance_out.d) 183 | 184 | # calculate other ratio 185 | let step_one : Ratio = ratio_diff(total_weight, a_weight) 186 | 187 | let step_one_times_fee : Ratio = ratio_mul(step_one, swap_fee) 188 | 189 | let k : Uint256 = SafeUint256.sub_le(step_one_times_fee.d, step_one_times_fee.n) 190 | local second_ratio : Ratio = Ratio(k, step_one_times_fee.d) 191 | 192 | # multiply together 193 | let amount_token_out : Ratio = ratio_mul(first_ratio, second_ratio) 194 | 195 | return (amount_token_out) 196 | end 197 | 198 | # IMPLEMENT LATER 199 | # @view 200 | # func get_pool_in_given_single_out{ 201 | # syscall_ptr : felt*, 202 | # pedersen_ptr : HashBuiltin*, 203 | # range_check_ptr 204 | # }(erc20_address: felt, amount_of_a_out: felt) -> (pool_tokens_in: felt): 205 | # end 206 | 207 | ########################### 208 | # SWAPS 209 | ########################### 210 | 211 | # ********************************************************************************************** 212 | # calcOutGivenIn // 213 | # aO = tokenAmountOut // 214 | # bO = tokenBalanceOut // 215 | # bI = tokenBalanceIn / / bI \ (wI / wO) \ // 216 | # aI = tokenAmountIn aO = bO * | 1 - | -------------------------- | ^ | // 217 | # wI = tokenWeightIn \ \ ( bI + ( aI * ( 1 - sF )) / / // 218 | # wO = tokenWeightOut // 219 | # sF = swapFee // 220 | # **********************************************************************************************/ 221 | @view 222 | func get_out_given_in{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 223 | amount_of_a_in : Uint256, a_balance : Uint256, a_weight : Ratio, b_balance : Uint256, 224 | b_weight : Ratio, swap_fee : Ratio) -> (amount_of_b_out : Ratio): 225 | alloc_locals 226 | 227 | # needed for dereferencing ratios 228 | let (__fp__, _) = get_fp_and_pc() 229 | 230 | local token_balance_in : Ratio = Ratio(a_balance, Uint256(1, 0)) 231 | local token_amount_in : Ratio = Ratio(amount_of_a_in, Uint256(1, 0)) 232 | local token_balance_out : Ratio = Ratio(b_balance, Uint256(1, 0)) 233 | local one_ratio : Ratio = Ratio(Uint256(1, 0), Uint256(1, 0)) 234 | 235 | let x : Uint256 = SafeUint256.sub_le(swap_fee.d, swap_fee.n) 236 | local one_minus_swap_fee : Ratio = Ratio(x, swap_fee.d) 237 | let times_tai : Ratio = ratio_mul(one_minus_swap_fee, token_amount_in) 238 | let plus_balance_in : Ratio = ratio_add(token_balance_in, times_tai) 239 | let balance_in_divided_by : Ratio = ratio_div(token_balance_in, plus_balance_in) 240 | 241 | let exponent : Ratio = ratio_div(a_weight, b_weight) 242 | 243 | let raised_to_exponent : Ratio = ratio_pow(balance_in_divided_by, exponent.n) 244 | 245 | with_attr error_message( 246 | "ERROR WHEN TAKING THE NTH ROOT : LIKELY FRACTION REDUCTION PROBLEM; TRY SLIGHTLY ADJUSTING NUMBERS"): 247 | let take_root_of_exponent : Ratio = nth_root_by_digit(raised_to_exponent, exponent.d, 9) 248 | end 249 | 250 | let (local one_minus_all : Ratio) = ratio_diff(one_ratio, take_root_of_exponent) 251 | let amount_of_b_out : Ratio = ratio_mul(token_balance_out, one_minus_all) 252 | 253 | return (amount_of_b_out) 254 | end 255 | 256 | @view 257 | func get_proportional_withdraw_given_pool_in{ 258 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 259 | pool_total_supply : Uint256, pool_amount_in : Uint256, exit_fee : Ratio, 260 | token_list_len : felt, token_list : TokenAndAmount*) -> ( 261 | output_arr_len : felt, output_arr : TokenAndAmount*): 262 | alloc_locals 263 | 264 | local ratio_in : Ratio = Ratio(pool_amount_in, Uint256(1, 0)) 265 | let (local fee_adj : Ratio) = ratio_mul(ratio_in, exit_fee) 266 | let (local adj_in : Ratio) = ratio_diff(ratio_in, fee_adj) 267 | local ratio_total_supply : Ratio = Ratio(pool_total_supply, Uint256(1, 0)) 268 | let (local adj_pool_supply_ratio : Ratio) = ratio_div(adj_in, ratio_total_supply) 269 | 270 | let (local output_arr : TokenAndAmount*) = alloc() 271 | 272 | let (local return_arr_len : felt, 273 | local return_arr : TokenAndAmount*) = _recursive_get_balance_needed( 274 | adj_pool_supply_ratio, token_list_len, token_list, 0, output_arr, 0) 275 | 276 | return (return_arr_len, return_arr) 277 | end 278 | 279 | @view 280 | func get_proportional_deposits_given_pool_out{ 281 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 282 | pool_supply_ratio : Ratio, token_list_len : felt, token_list : TokenAndAmount*) -> ( 283 | output_arr_len : felt, output_arr : TokenAndAmount*): 284 | alloc_locals 285 | 286 | let (local output_arr : TokenAndAmount*) = alloc() 287 | 288 | let (local return_arr_len : felt, 289 | local return_arr : TokenAndAmount*) = _recursive_get_balance_needed( 290 | pool_supply_ratio, token_list_len, token_list, 0, output_arr, 0) 291 | 292 | return (return_arr_len, return_arr) 293 | end 294 | 295 | func _recursive_get_balance_needed{ 296 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 297 | pool_supply_ratio : Ratio, input_arr_len : felt, input_arr : TokenAndAmount*, 298 | output_arr_len : felt, output_arr : TokenAndAmount*, counter : felt) -> ( 299 | list_len : felt, list : TokenAndAmount*): 300 | alloc_locals 301 | 302 | # needed for dereferencing struct 303 | let (__fp__, _) = get_fp_and_pc() 304 | 305 | if input_arr_len == 0: 306 | return (output_arr_len, output_arr) 307 | end 308 | 309 | let current_struct : TokenAndAmount* = [&input_arr] 310 | let (local amount_in : Uint256) = _get_balance_needed_from_pool_supply( 311 | pool_supply_ratio, current_struct.amount) 312 | 313 | # assert used for assignment 314 | assert output_arr[counter] = TokenAndAmount(current_struct.erc_address, amount_in) 315 | 316 | let (local _output_arr_len : felt, 317 | _output_arr : TokenAndAmount*) = _recursive_get_balance_needed( 318 | pool_supply_ratio, 319 | input_arr_len - 1, 320 | input_arr + TokenAndAmount.SIZE, 321 | output_arr_len + 1, 322 | output_arr, 323 | counter + 1) 324 | 325 | return (_output_arr_len, _output_arr) 326 | end 327 | 328 | func _get_balance_needed_from_pool_supply{ 329 | syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_check_ptr}( 330 | pool_supply_ratio : Ratio, current_balance : Uint256) -> (balance_needed : Uint256): 331 | alloc_locals 332 | 333 | local ratio_current_balance : Ratio = Ratio(current_balance, Uint256(1, 0)) 334 | let (local curr_times_supply_ratio : Ratio) = ratio_mul( 335 | ratio_current_balance, pool_supply_ratio) 336 | let (local amount_required : Uint256, _) = SafeUint256.div_rem( 337 | curr_times_supply_ratio.n, curr_times_supply_ratio.d) 338 | 339 | return (amount_required) 340 | end 341 | end 342 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------