Warning! Contract bytecode has been changed and doesn't match the verified one. Therefore, interaction with this smart contract may be risky.
- Contract name:
- Vyper_contract
- Optimization enabled
- false
- Compiler version
- v0.2.12
- Verified at
- 2023-07-14T14:37:21.361072Z
Contract source code
# @version 0.2.12
# (c) Curve.Fi, 2021
# Math for crypto pools
#
# Unless otherwise agreed on, only contracts owned by Curve DAO or
# Swiss Stake GmbH are allowed to call this contract.
N_COINS: constant(int128) = 3 # <- change
A_MULTIPLIER: constant(uint256) = 10000
MIN_GAMMA: constant(uint256) = 10**10
MAX_GAMMA: constant(uint256) = 5 * 10**16
MIN_A: constant(uint256) = N_COINS**N_COINS * A_MULTIPLIER / 100
MAX_A: constant(uint256) = N_COINS**N_COINS * A_MULTIPLIER * 1000
@internal
@pure
def sort(A0: uint256[N_COINS]) -> uint256[N_COINS]:
"""
Insertion sort from high to low
"""
A: uint256[N_COINS] = A0
for i in range(1, N_COINS):
x: uint256 = A[i]
cur: uint256 = i
for j in range(N_COINS):
y: uint256 = A[cur-1]
if y > x:
break
A[cur] = y
cur -= 1
if cur == 0:
break
A[cur] = x
return A
@internal
@view
def _geometric_mean(unsorted_x: uint256[N_COINS], sort: bool = True) -> uint256:
"""
(x[0] * x[1] * ...) ** (1/N)
"""
x: uint256[N_COINS] = unsorted_x
if sort:
x = self.sort(x)
D: uint256 = x[0]
diff: uint256 = 0
for i in range(255):
D_prev: uint256 = D
tmp: uint256 = 10**18
for _x in x:
tmp = tmp * _x / D
D = D * ((N_COINS - 1) * 10**18 + tmp) / (N_COINS * 10**18)
if D > D_prev:
diff = D - D_prev
else:
diff = D_prev - D
if diff <= 1 or diff * 10**18 < D:
return D
raise "Did not converge"
@external
@view
def geometric_mean(unsorted_x: uint256[N_COINS], sort: bool = True) -> uint256:
return self._geometric_mean(unsorted_x, sort)
@external
@view
def reduction_coefficient(x: uint256[N_COINS], fee_gamma: uint256) -> uint256:
"""
fee_gamma / (fee_gamma + (1 - K))
where
K = prod(x) / (sum(x) / N)**N
(all normalized to 1e18)
"""
K: uint256 = 10**18
S: uint256 = 0
for x_i in x:
S += x_i
# Could be good to pre-sort x, but it is used only for dynamic fee,
# so that is not so important
for x_i in x:
K = K * N_COINS * x_i / S
if fee_gamma > 0:
K = fee_gamma * 10**18 / (fee_gamma + 10**18 - K)
return K
@external
@view
def newton_D(ANN: uint256, gamma: uint256, x_unsorted: uint256[N_COINS]) -> uint256:
"""
Finding the invariant using Newton method.
ANN is higher by the factor A_MULTIPLIER
ANN is already A * N**N
Currently uses 60k gas
"""
# Safety checks
assert ANN > MIN_A - 1 and ANN < MAX_A + 1 # dev: unsafe values A
assert gamma > MIN_GAMMA - 1 and gamma < MAX_GAMMA + 1 # dev: unsafe values gamma
# Initial value of invariant D is that for constant-product invariant
x: uint256[N_COINS] = self.sort(x_unsorted)
assert x[0] > 10**9 - 1 and x[0] < 10**15 * 10**18 + 1 # dev: unsafe values x[0]
for i in range(1, N_COINS):
frac: uint256 = x[i] * 10**18 / x[0]
assert frac > 10**11-1 # dev: unsafe values x[i]
D: uint256 = N_COINS * self._geometric_mean(x, False)
S: uint256 = 0
for x_i in x:
S += x_i
for i in range(255):
D_prev: uint256 = D
K0: uint256 = 10**18
for _x in x:
K0 = K0 * _x * N_COINS / D
_g1k0: uint256 = gamma + 10**18
if _g1k0 > K0:
_g1k0 = _g1k0 - K0 + 1
else:
_g1k0 = K0 - _g1k0 + 1
# D / (A * N**N) * _g1k0**2 / gamma**2
mul1: uint256 = 10**18 * D / gamma * _g1k0 / gamma * _g1k0 * A_MULTIPLIER / ANN
# 2*N*K0 / _g1k0
mul2: uint256 = (2 * 10**18) * N_COINS * K0 / _g1k0
neg_fprime: uint256 = (S + S * mul2 / 10**18) + mul1 * N_COINS / K0 - mul2 * D / 10**18
# D -= f / fprime
D_plus: uint256 = D * (neg_fprime + S) / neg_fprime
D_minus: uint256 = D*D / neg_fprime
if 10**18 > K0:
D_minus += D * (mul1 / neg_fprime) / 10**18 * (10**18 - K0) / K0
else:
D_minus -= D * (mul1 / neg_fprime) / 10**18 * (K0 - 10**18) / K0
if D_plus > D_minus:
D = D_plus - D_minus
else:
D = (D_minus - D_plus) / 2
diff: uint256 = 0
if D > D_prev:
diff = D - D_prev
else:
diff = D_prev - D
if diff * 10**14 < max(10**16, D): # Could reduce precision for gas efficiency here
# Test that we are safe with the next newton_y
for _x in x:
frac: uint256 = _x * 10**18 / D
assert (frac > 10**16 - 1) and (frac < 10**20 + 1) # dev: unsafe values x[i]
return D
raise "Did not converge"
@external
@view
def newton_y(ANN: uint256, gamma: uint256, x: uint256[N_COINS], D: uint256, i: uint256) -> uint256:
"""
Calculating x[i] given other balances x[0..N_COINS-1] and invariant D
ANN = A * N**N
"""
# Safety checks
assert ANN > MIN_A - 1 and ANN < MAX_A + 1 # dev: unsafe values A
assert gamma > MIN_GAMMA - 1 and gamma < MAX_GAMMA + 1 # dev: unsafe values gamma
assert D > 10**17 - 1 and D < 10**15 * 10**18 + 1 # dev: unsafe values D
for k in range(3):
if k != i:
frac: uint256 = x[k] * 10**18 / D
assert (frac > 10**16 - 1) and (frac < 10**20 + 1) # dev: unsafe values x[i]
y: uint256 = D / N_COINS
K0_i: uint256 = 10**18
S_i: uint256 = 0
x_sorted: uint256[N_COINS] = x
x_sorted[i] = 0
x_sorted = self.sort(x_sorted) # From high to low
convergence_limit: uint256 = max(max(x_sorted[0] / 10**14, D / 10**14), 100)
for j in range(2, N_COINS+1):
_x: uint256 = x_sorted[N_COINS-j]
y = y * D / (_x * N_COINS) # Small _x first
S_i += _x
for j in range(N_COINS-1):
K0_i = K0_i * x_sorted[j] * N_COINS / D # Large _x first
for j in range(255):
y_prev: uint256 = y
K0: uint256 = K0_i * y * N_COINS / D
S: uint256 = S_i + y
_g1k0: uint256 = gamma + 10**18
if _g1k0 > K0:
_g1k0 = _g1k0 - K0 + 1
else:
_g1k0 = K0 - _g1k0 + 1
# D / (A * N**N) * _g1k0**2 / gamma**2
mul1: uint256 = 10**18 * D / gamma * _g1k0 / gamma * _g1k0 * A_MULTIPLIER / ANN
# 2*K0 / _g1k0
mul2: uint256 = 10**18 + (2 * 10**18) * K0 / _g1k0
yfprime: uint256 = 10**18 * y + S * mul2 + mul1
_dyfprime: uint256 = D * mul2
if yfprime < _dyfprime:
y = y_prev / 2
continue
else:
yfprime -= _dyfprime
fprime: uint256 = yfprime / y
# y -= f / f_prime; y = (y * fprime - f) / fprime
# y = (yfprime + 10**18 * D - 10**18 * S) // fprime + mul1 // fprime * (10**18 - K0) // K0
y_minus: uint256 = mul1 / fprime
y_plus: uint256 = (yfprime + 10**18 * D) / fprime + y_minus * 10**18 / K0
y_minus += 10**18 * S / fprime
if y_plus < y_minus:
y = y_prev / 2
else:
y = y_plus - y_minus
diff: uint256 = 0
if y > y_prev:
diff = y - y_prev
else:
diff = y_prev - y
if diff < max(convergence_limit, y / 10**14):
frac: uint256 = y * 10**18 / D
assert (frac > 10**16 - 1) and (frac < 10**20 + 1) # dev: unsafe value for y
return y
raise "Did not converge"
@external
@view
def halfpow(power: uint256, precision: uint256) -> uint256:
"""
1e18 * 0.5 ** (power/1e18)
Inspired by: https://github.com/balancer-labs/balancer-core/blob/master/contracts/BNum.sol#L128
"""
intpow: uint256 = power / 10**18
otherpow: uint256 = power - intpow * 10**18
if intpow > 59:
return 0
result: uint256 = 10**18 / (2**intpow)
if otherpow == 0:
return result
term: uint256 = 10**18
x: uint256 = 5 * 10**17
S: uint256 = 10**18
neg: bool = False
for i in range(1, 256):
K: uint256 = i * 10**18
c: uint256 = K - 10**18
if otherpow > c:
c = otherpow - c
neg = not neg
else:
c -= otherpow
term = term * (c * x / 10**18) / K
if neg:
S -= term
else:
S += term
if term < precision:
return result * S / 10**18
raise "Did not converge"
@external
@view
def sqrt_int(x: uint256) -> uint256:
"""
Originating from: https://github.com/vyperlang/vyper/issues/1266
"""
if x == 0:
return 0
z: uint256 = (x + 10**18) / 2
y: uint256 = x
for i in range(256):
if z == y:
return y
y = z
z = (x * 10**18 / z + z) / 2
raise "Did not converge"
Contract ABI
[{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"geometric_mean","inputs":[{"type":"uint256[3]","name":"unsorted_x"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"geometric_mean","inputs":[{"type":"uint256[3]","name":"unsorted_x"},{"type":"bool","name":"sort"}]},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"reduction_coefficient","inputs":[{"type":"uint256[3]","name":"x"},{"type":"uint256","name":"fee_gamma"}],"gas":4063},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"newton_D","inputs":[{"type":"uint256","name":"ANN"},{"type":"uint256","name":"gamma"},{"type":"uint256[3]","name":"x_unsorted"}],"gas":3318199},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"newton_y","inputs":[{"type":"uint256","name":"ANN"},{"type":"uint256","name":"gamma"},{"type":"uint256[3]","name":"x"},{"type":"uint256","name":"D"},{"type":"uint256","name":"i"}],"gas":1859387},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"halfpow","inputs":[{"type":"uint256","name":"power"},{"type":"uint256","name":"precision"}],"gas":513767},{"type":"function","stateMutability":"view","outputs":[{"type":"uint256","name":""}],"name":"sqrt_int","inputs":[{"type":"uint256","name":"x"}],"gas":199003}]
Contract Creation Code
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