# stable-swap-sim 0.1.4

Simulations of the StableSwap invariant compared to Curve's reference implementation.
Documentation
``````# Source from: https://github.com/curvefi/curve-contract/blob/master/tests/simulation.py

class Curve:

"""
Python model of Curve pool math.
"""

def __init__(self, A, D, n, p=None, tokens=None):
"""
A: Amplification coefficient
D: Total deposit size
n: number of currencies
p: target prices
"""
self.A = A  # actually A * n ** (n - 1) because it's an invariant
self.n = n
self.fee = 10 ** 7
if p:
self.p = p
else:
self.p = [10 ** 18] * n
if isinstance(D, list):
self.x = D
else:
self.x = [D // n * 10 ** 18 // _p for _p in self.p]
self.tokens = tokens

def xp(self):
return [x * p // 10 ** 18 for x, p in zip(self.x, self.p)]

def D(self):
"""
D invariant calculation in non-overflowing integer operations
iteratively

A * sum(x_i) * n**n + D = A * D * n**n + D**(n+1) / (n**n * prod(x_i))

Converging solution:
D[j+1] = (A * n**n * sum(x_i) - D[j]**(n+1) / (n**n prod(x_i))) / (A * n**n - 1)
"""
Dprev = 0
xp = self.xp()
S = sum(xp)
D = S
Ann = self.A * self.n
while abs(D - Dprev) > 1:
D_P = D
for x in xp:
D_P = D_P * D // (self.n * x)
Dprev = D
D = (Ann * S + D_P * self.n) * D // ((Ann - 1) * D + (self.n + 1) * D_P)

return D

def y(self, i, j, x):
"""
Calculate x[j] if one makes x[i] = x

Done by solving quadratic equation iteratively.
x_1**2 + x1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
x_1**2 + b*x_1 = c

x_1 = (x_1**2 + c) / (2*x_1 + b)
"""
D = self.D()
xx = self.xp()
xx[i] = x  # x is quantity of underlying asset brought to 1e18 precision
xx = [xx[k] for k in range(self.n) if k != j]
Ann = self.A * self.n
c = D
for y in xx:
c = c * D // (y * self.n)
c = c * D // (self.n * Ann)
b = sum(xx) + D // Ann - D
y_prev = 0
y = D
while abs(y - y_prev) > 1:
y_prev = y
y = (y ** 2 + c) // (2 * y + b)
return y  # the result is in underlying units too

def y_D(self, i, _D):
"""
Calculate x[j] if one makes x[i] = x

Done by solving quadratic equation iteratively.
x_1**2 + x1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
x_1**2 + b*x_1 = c

x_1 = (x_1**2 + c) / (2*x_1 + b)
"""
xx = self.xp()
xx = [xx[k] for k in range(self.n) if k != i]
S = sum(xx)
Ann = self.A * self.n
c = _D
for y in xx:
c = c * _D // (y * self.n)
c = c * _D // (self.n * Ann)
b = S + _D // Ann
y_prev = 0
y = _D
while abs(y - y_prev) > 1:
y_prev = y
y = (y ** 2 + c) // (2 * y + b - _D)
return y  # the result is in underlying units too

def dy(self, i, j, dx):
# dx and dy are in underlying units
xp = self.xp()
return xp[j] - self.y(i, j, xp[i] + dx)

def exchange(self, i, j, dx):
xp = self.xp()
x = xp[i] + dx
y = self.y(i, j, x)
dy = xp[j] - y
fee = dy * self.fee // 10 ** 10
assert dy > 0
self.x[i] = x * 10 ** 18 // self.p[i]
self.x[j] = (y + fee) * 10 ** 18 // self.p[j]
return dy - fee

def remove_liquidity_imbalance(self, amounts):
_fee = self.fee * self.n // (4 * (self.n - 1))

old_balances = self.x
new_balances = self.x[:]
D0 = self.D()
for i in range(self.n):
new_balances[i] -= amounts[i]
self.x = new_balances
D1 = self.D()
self.x = old_balances
fees = [0] * self.n
for i in range(self.n):
ideal_balance = D1 * old_balances[i] // D0
difference = abs(ideal_balance - new_balances[i])
fees[i] = _fee * difference // 10 ** 10
new_balances[i] -= fees[i]
self.x = new_balances
D2 = self.D()
self.x = old_balances

token_amount = (D0 - D2) * self.tokens // D0

def calc_withdraw_one_coin(self, token_amount, i):
xp = self.xp()
xp_reduced = list(xp)

D0 = self.D()
D1 = D0 - token_amount * D0 // self.tokens
new_y = self.y_D(i, D1)

fee = self.fee * self.n // (4 * (self.n - 1))
for j in range(self.n):
dx_expected = 0
if j == i:
dx_expected = xp[j] * D1 // D0 - new_y
else:
dx_expected = xp[j] - xp[j] * D1 // D0
xp_reduced[j] -= fee * dx_expected // 10 ** 10

self.x = [x * 10 ** 18 // p for x, p in zip(xp_reduced, self.p)]
dy = xp_reduced[i] - self.y_D(i, D1) - 1    # Withdraw less to account for rounding errors
self.x = [x * 10 ** 18 // p for x, p in zip(xp, self.p)]
dy_0 = xp[i] - new_y

return dy, dy_0 - dy
``````