Cryptopool price formula

changelog.d/20230809_125756_chanhosuh_crypto_price.rst

@@ -0,0 +1,5 @@
+Added
+-----
+
+- Added spot price methods `dydx` and `dydxfee` to the `CurveCryptoPool`.
+

curvesim/pool/cryptoswap/pool.py

@@ -2,7 +2,7 @@
 Mainly a module to house the `CryptoPool`, a cryptoswap implementation in Python.
 """
 import time
-from math import isqrt
+from math import isqrt, prod
 from typing import List
 
 from curvesim.exceptions import CalculationError, CryptoPoolError
@@ -1029,6 +1029,89 @@ def calc_token_amount(self, amounts: List[int]) -> int:
         d_token -= self._calc_token_fee(amountsp, xp) * d_token // 10**10 + 1
         return d_token
 
+    def dydxfee(self, i, j):
+        """
+        Returns the spot price of i-th coin quoted in terms of j-th coin,
+        i.e. the ratio of output coin amount to input coin amount for
+        an "infinitesimally" small trade.
+
+        Trading fees are deducted.
+
+        Parameters
+        ----------
+        i: int
+            Index of coin to be priced; in a swapping context, this is
+            the "in"-token.
+        j: int
+            Index of quote currency; in a swapping context, this is the
+            "out"-token.
+
+        Returns
+        -------
+        float
+            Price of i-th coin quoted in j-th coin with fees deducted.
+
+        Note
+        ----
+        This is a "view" function; it doesn't change the state of the pool.
+        """
+        return self.dydx(i, j, use_fee=True)
+
+    def dydx(self, i, j, use_fee=False):
+        """
+        Returns the spot price of i-th coin quoted in terms of j-th coin,
+        i.e. the ratio of output coin amount to input coin amount for
+        an "infinitesimally" small trade.
+
+        Defaults to no fees deducted.
+
+        Parameters
+        ----------
+        i: int
+            Index of coin to be priced; in a swapping context, this is
+            the "in"-token.
+        j: int
+            Index of quote currency; in a swapping context, this is the
+            "out"-token.
+
+        Returns
+        -------
+        float
+            Price of i-th coin quoted in j-th coin
+
+        Note
+        ----
+        This is a "view" function; it doesn't change the state of the pool.
+        """
+        xp = self._xp()
+        x_i = xp[i]
+        x_j = xp[j]
+        n = len(xp)
+
+        D = self.D
+        A = self.A
+        A_multiplier = 10**4
+        gamma = self.gamma
+
+        K0 = 10**18 * n**n * prod(xp) / D**n
+
+        coeff = gamma**2 * A / (D * (10**18 + gamma - K0) ** 2) / A_multiplier
+        frac = (10**18 + gamma + K0) * (sum(xp) - D) / (10**18 + gamma - K0)
+        dydx = x_j * (1 + coeff * (x_i + frac)) / (x_i * (1 + coeff * (x_j + frac)))
+
+        if j > 0:
+            price_scale = self.price_scale[j - 1]
+            dydx = dydx * 10**18 / price_scale
+        if i > 0:
+            price_scale = self.price_scale[i - 1]
+            dydx = dydx * price_scale / 10**18
+
+        if use_fee:
+            fee = self._fee(xp)
+            dydx = dydx - dydx * fee / 10**10
+
+        return dydx
+
 
 def _get_unix_timestamp():
     """Get the timestamp in Unix time."""

test/unit/test_cryptopool.py

@@ -755,3 +755,23 @@ def test_multiple_exchange_with_repeg(
         assert pool.price_scale == expected_price_scale
 
         boa.env.time_travel(time_delta)
+
+
+def test_dydxfee(vyper_cryptopool):
+    """Test spot price formula against execution price for small trades."""
+    pool = initialize_pool(vyper_cryptopool)
+
+    # STG, USDC
+    decimals = [18, 6]
+    precisions = [10 ** (18 - d) for d in decimals]
+
+    i = 0
+    j = 1
+    dx = 10**18
+
+    dydx = pool.dydxfee(i, j)
+    dy = vyper_cryptopool.exchange(i, j, dx, 0)
+
+    dx *= precisions[i]
+    dy *= precisions[j]
+    assert abs(dydx - dy / dx) < 1e-6

test/unit/test_tricrypto.py

@@ -4,6 +4,7 @@
 Tests are against the tricrypto-ng contract.
 """
 import os
+from itertools import permutations
 
 import boa
 from hypothesis import HealthCheck, assume, given, settings
@@ -419,3 +420,33 @@ def test__newton_y(vyper_tricrypto, A, gamma, x0, x1, x2, pair, dx_perc):
     y = _newton_y(A, gamma, xp, D, j)
 
     assert y == expected_y
+
+
+def test_dydxfee(vyper_tricrypto):
+    """Test spot price formula against execution price for small trades."""
+    pool = initialize_pool(vyper_tricrypto)
+
+    # USDT, WBTC, WETH
+    decimals = [6, 8, 18]
+    precisions = [10 ** (18 - d) for d in decimals]
+
+    # print("WBTC price:", pool.price_scale[0] / 10**18)
+    # print("WETH price:", pool.price_scale[1] / 10**18)
+
+    dxs = [
+        10**6,
+        10**4,
+        10**15,
+    ]
+
+    for pair in permutations([0, 1, 2], 2):
+        i, j = pair
+
+        dydx = pool.dydxfee(i, j)
+        dx = dxs[i]
+        dy = vyper_tricrypto.exchange(i, j, dx, 0)
+        pool.exchange(i, j, dx, 0)  # update state to match vyper pool
+
+        dx *= precisions[i]
+        dy *= precisions[j]
+        assert abs(dydx - dy / dx) / (dy / dx) < 1e-4