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Contract Source Code Verified (Exact Match)
Contract Name:
CurveTwocryptoMathOptimized
Compiler Version
vyper:0.3.10
Contract Source Code (Vyper language format)
# pragma version 0.3.10 # pragma optimize gas # pragma evm-version paris # (c) Curve.Fi, 2020-2023 # AMM Math for 2-coin Curve Cryptoswap Pools # # Unless otherwise agreed on, only contracts owned by Curve DAO or # Swiss Stake GmbH are allowed to call this contract. """ @title CurveTwocryptoMathOptimized @author Curve.Fi @license Copyright (c) Curve.Fi, 2020-2023 - all rights reserved @notice Curve AMM Math for 2 unpegged assets (e.g. ETH <> USD). """ N_COINS: constant(uint256) = 2 A_MULTIPLIER: constant(uint256) = 10000 MIN_GAMMA: constant(uint256) = 10**10 MAX_GAMMA_SMALL: constant(uint256) = 2 * 10**16 MAX_GAMMA: constant(uint256) = 199 * 10**15 # 1.99 * 10**17 MIN_A: constant(uint256) = N_COINS**N_COINS * A_MULTIPLIER / 10 MAX_A: constant(uint256) = N_COINS**N_COINS * A_MULTIPLIER * 1000 version: public(constant(String[8])) = "v2.1.0" # ------------------------ AMM math functions -------------------------------- @internal @pure def _snekmate_log_2(x: uint256, roundup: bool) -> uint256: """ @notice An `internal` helper function that returns the log in base 2 of `x`, following the selected rounding direction. @dev This implementation is derived from Snekmate, which is authored by pcaversaccio (Snekmate), distributed under the AGPL-3.0 license. https://github.com/pcaversaccio/snekmate @dev Note that it returns 0 if given 0. The implementation is inspired by OpenZeppelin's implementation here: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/math/Math.sol. @param x The 32-byte variable. @param roundup The Boolean variable that specifies whether to round up or not. The default `False` is round down. @return uint256 The 32-byte calculation result. """ value: uint256 = x result: uint256 = empty(uint256) # The following lines cannot overflow because we have the well-known # decay behaviour of `log_2(max_value(uint256)) < max_value(uint256)`. if x >> 128 != empty(uint256): value = x >> 128 result = 128 if value >> 64 != empty(uint256): value = value >> 64 result = unsafe_add(result, 64) if value >> 32 != empty(uint256): value = value >> 32 result = unsafe_add(result, 32) if value >> 16 != empty(uint256): value = value >> 16 result = unsafe_add(result, 16) if value >> 8 != empty(uint256): value = value >> 8 result = unsafe_add(result, 8) if value >> 4 != empty(uint256): value = value >> 4 result = unsafe_add(result, 4) if value >> 2 != empty(uint256): value = value >> 2 result = unsafe_add(result, 2) if value >> 1 != empty(uint256): result = unsafe_add(result, 1) if (roundup and (1 << result) < x): result = unsafe_add(result, 1) return result @internal @pure def _cbrt(x: uint256) -> uint256: xx: uint256 = 0 if x >= 115792089237316195423570985008687907853269 * 10**18: xx = x elif x >= 115792089237316195423570985008687907853269: xx = unsafe_mul(x, 10**18) else: xx = unsafe_mul(x, 10**36) log2x: int256 = convert(self._snekmate_log_2(xx, False), int256) # When we divide log2x by 3, the remainder is (log2x % 3). # So if we just multiply 2**(log2x/3) and discard the remainder to calculate our # guess, the newton method will need more iterations to converge to a solution, # since it is missing that precision. It's a few more calculations now to do less # calculations later: # pow = log2(x) // 3 # remainder = log2(x) % 3 # initial_guess = 2 ** pow * cbrt(2) ** remainder # substituting -> 2 = 1.26 ≈ 1260 / 1000, we get: # # initial_guess = 2 ** pow * 1260 ** remainder // 1000 ** remainder remainder: uint256 = convert(log2x, uint256) % 3 a: uint256 = unsafe_div( unsafe_mul( pow_mod256(2, unsafe_div(convert(log2x, uint256), 3)), # <- pow pow_mod256(1260, remainder), ), pow_mod256(1000, remainder), ) # Because we chose good initial values for cube roots, 7 newton raphson iterations # are just about sufficient. 6 iterations would result in non-convergences, and 8 # would be one too many iterations. Without initial values, the iteration count # can go up to 20 or greater. The iterations are unrolled. This reduces gas costs # but takes up more bytecode: a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) a = unsafe_div(unsafe_add(unsafe_mul(2, a), unsafe_div(xx, unsafe_mul(a, a))), 3) if x >= 115792089237316195423570985008687907853269 * 10**18: a = unsafe_mul(a, 10**12) elif x >= 115792089237316195423570985008687907853269: a = unsafe_mul(a, 10**6) return a @internal @pure def _newton_y(ANN: uint256, gamma: uint256, x: uint256[N_COINS], D: uint256, i: uint256, lim_mul: uint256) -> uint256: """ Calculating x[i] given other balances x[0..N_COINS-1] and invariant D ANN = A * N**N This is computationally expensive. """ x_j: uint256 = x[1 - i] y: uint256 = D**2 / (x_j * N_COINS**2) K0_i: uint256 = (10**18 * N_COINS) * x_j / D assert (K0_i >= unsafe_div(10**36, lim_mul)) and (K0_i <= lim_mul) # dev: unsafe values x[i] convergence_limit: uint256 = max(max(x_j / 10**14, D / 10**14), 100) for j in range(255): y_prev: uint256 = y K0: uint256 = K0_i * y * N_COINS / D S: uint256 = x_j + 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): return y raise "Did not converge" @external @pure def newton_y(ANN: uint256, gamma: uint256, x: uint256[N_COINS], D: uint256, i: uint256) -> uint256: # 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 lim_mul: uint256 = 100 * 10**18 # 100.0 if gamma > MAX_GAMMA_SMALL: lim_mul = unsafe_div(unsafe_mul(lim_mul, MAX_GAMMA_SMALL), gamma) # smaller than 100.0 y: uint256 = self._newton_y(ANN, gamma, x, D, i, lim_mul) frac: uint256 = y * 10**18 / D assert (frac >= unsafe_div(10**36 / N_COINS, lim_mul)) and (frac <= unsafe_div(lim_mul, N_COINS)) # dev: unsafe value for y return y @external @pure def get_y( _ANN: uint256, _gamma: uint256, _x: uint256[N_COINS], _D: uint256, i: uint256 ) -> uint256[2]: # 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 lim_mul: uint256 = 100 * 10**18 # 100.0 if _gamma > MAX_GAMMA_SMALL: lim_mul = unsafe_div(unsafe_mul(lim_mul, MAX_GAMMA_SMALL), _gamma) # smaller than 100.0 lim_mul_signed: int256 = convert(lim_mul, int256) ANN: int256 = convert(_ANN, int256) gamma: int256 = convert(_gamma, int256) D: int256 = convert(_D, int256) x_j: int256 = convert(_x[1 - i], int256) gamma2: int256 = unsafe_mul(gamma, gamma) # savediv by x_j done here: y: int256 = D**2 / (x_j * N_COINS**2) # K0_i: int256 = (10**18 * N_COINS) * x_j / D K0_i: int256 = unsafe_div(10**18 * N_COINS * x_j, D) assert (K0_i >= unsafe_div(10**36, lim_mul_signed)) and (K0_i <= lim_mul_signed) # dev: unsafe values x[i] ann_gamma2: int256 = ANN * gamma2 # a = 10**36 / N_COINS**2 a: int256 = 10**32 # b = ANN*D*gamma2/4/10000/x_j/10**4 - 10**32*3 - 2*gamma*10**14 b: int256 = ( D*ann_gamma2/400000000/x_j - convert(unsafe_mul(10**32, 3), int256) - unsafe_mul(unsafe_mul(2, gamma), 10**14) ) # c = 10**32*3 + 4*gamma*10**14 + gamma2/10**4 + 4*ANN*gamma2*x_j/D/10000/4/10**4 - 4*ANN*gamma2/10000/4/10**4 c: int256 = ( unsafe_mul(10**32, convert(3, int256)) + unsafe_mul(unsafe_mul(4, gamma), 10**14) + unsafe_div(gamma2, 10**4) + unsafe_div(unsafe_div(unsafe_mul(4, ann_gamma2), 400000000) * x_j, D) - unsafe_div(unsafe_mul(4, ann_gamma2), 400000000) ) # d = -(10**18+gamma)**2 / 10**4 d: int256 = -unsafe_div(unsafe_add(10**18, gamma) ** 2, 10**4) # delta0: int256 = 3*a*c/b - b delta0: int256 = 3 * a * c / b - b # safediv by b # delta1: int256 = 9*a*c/b - 2*b - 27*a**2/b*d/b delta1: int256 = 3 * delta0 + b - 27*a**2/b*d/b divider: int256 = 1 threshold: int256 = min(min(abs(delta0), abs(delta1)), a) if threshold > 10**48: divider = 10**30 elif threshold > 10**46: divider = 10**28 elif threshold > 10**44: divider = 10**26 elif threshold > 10**42: divider = 10**24 elif threshold > 10**40: divider = 10**22 elif threshold > 10**38: divider = 10**20 elif threshold > 10**36: divider = 10**18 elif threshold > 10**34: divider = 10**16 elif threshold > 10**32: divider = 10**14 elif threshold > 10**30: divider = 10**12 elif threshold > 10**28: divider = 10**10 elif threshold > 10**26: divider = 10**8 elif threshold > 10**24: divider = 10**6 elif threshold > 10**20: divider = 10**2 a = unsafe_div(a, divider) b = unsafe_div(b, divider) c = unsafe_div(c, divider) d = unsafe_div(d, divider) # delta0 = 3*a*c/b - b: here we can do more unsafe ops now: delta0 = unsafe_div(unsafe_mul(unsafe_mul(3, a), c), b) - b # delta1 = 9*a*c/b - 2*b - 27*a**2/b*d/b delta1 = 3 * delta0 + b - unsafe_div(unsafe_mul(unsafe_div(unsafe_mul(27, a**2), b), d), b) # sqrt_arg: int256 = delta1**2 + 4*delta0**2/b*delta0 sqrt_arg: int256 = delta1**2 + unsafe_mul(unsafe_div(4*delta0**2, b), delta0) sqrt_val: int256 = 0 if sqrt_arg > 0: sqrt_val = convert(isqrt(convert(sqrt_arg, uint256)), int256) else: return [ self._newton_y(_ANN, _gamma, _x, _D, i, lim_mul), 0 ] b_cbrt: int256 = 0 if b > 0: b_cbrt = convert(self._cbrt(convert(b, uint256)), int256) else: b_cbrt = -convert(self._cbrt(convert(-b, uint256)), int256) second_cbrt: int256 = 0 if delta1 > 0: # second_cbrt = convert(self._cbrt(convert((delta1 + sqrt_val), uint256) / 2), int256) second_cbrt = convert(self._cbrt(convert(unsafe_add(delta1, sqrt_val), uint256) / 2), int256) else: # second_cbrt = -convert(self._cbrt(convert(unsafe_sub(sqrt_val, delta1), uint256) / 2), int256) second_cbrt = -convert(self._cbrt(unsafe_div(convert(unsafe_sub(sqrt_val, delta1), uint256), 2)), int256) # C1: int256 = b_cbrt**2/10**18*second_cbrt/10**18 C1: int256 = unsafe_div(unsafe_mul(unsafe_div(b_cbrt**2, 10**18), second_cbrt), 10**18) # root: int256 = (10**18*C1 - 10**18*b - 10**18*b*delta0/C1)/(3*a), keep 2 safe ops here. root: int256 = (unsafe_mul(10**18, C1) - unsafe_mul(10**18, b) - unsafe_mul(10**18, b)/C1*delta0)/unsafe_mul(3, a) # y_out: uint256[2] = [ # convert(D**2/x_j*root/4/10**18, uint256), # <--- y # convert(root, uint256) # <----------------------- K0Prev # ] y_out: uint256[2] = [convert(unsafe_div(unsafe_div(unsafe_mul(unsafe_div(D**2, x_j), root), 4), 10**18), uint256), convert(root, uint256)] frac: uint256 = unsafe_div(y_out[0] * 10**18, _D) assert (frac >= unsafe_div(10**36 / N_COINS, lim_mul)) and (frac <= unsafe_div(lim_mul, N_COINS)) # dev: unsafe value for y return y_out @external @view def newton_D(ANN: uint256, gamma: uint256, x_unsorted: uint256[N_COINS], K0_prev: uint256 = 0) -> uint256: """ Finding the invariant using Newton method. ANN is higher by the factor A_MULTIPLIER ANN is already 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 # Initial value of invariant D is that for constant-product invariant x: uint256[N_COINS] = x_unsorted if x[0] < x[1]: x = [x_unsorted[1], x_unsorted[0]] assert x[0] > 10**9 - 1 and x[0] < 10**15 * 10**18 + 1 # dev: unsafe values x[0] assert unsafe_div(x[1] * 10**18, x[0]) > 10**14 - 1 # dev: unsafe values x[i] (input) S: uint256 = unsafe_add(x[0], x[1]) # can unsafe add here because we checked x[0] bounds D: uint256 = 0 if K0_prev == 0: D = N_COINS * isqrt(unsafe_mul(x[0], x[1])) else: # D = isqrt(x[0] * x[1] * 4 / K0_prev * 10**18) D = isqrt(unsafe_mul(unsafe_div(unsafe_mul(unsafe_mul(4, x[0]), x[1]), K0_prev), 10**18)) if S < D: D = S __g1k0: uint256 = gamma + 10**18 diff: uint256 = 0 for i in range(255): D_prev: uint256 = D assert D > 0 # Unsafe division by D and D_prev is now safe # K0: uint256 = 10**18 # for _x in x: # K0 = K0 * _x * N_COINS / D # collapsed for 2 coins K0: uint256 = unsafe_div(unsafe_div((10**18 * N_COINS**2) * x[0], D) * x[1], D) _g1k0: uint256 = __g1k0 if _g1k0 > K0: _g1k0 = unsafe_add(unsafe_sub(_g1k0, K0), 1) # > 0 else: _g1k0 = unsafe_add(unsafe_sub(K0, _g1k0), 1) # > 0 # D / (A * N**N) * _g1k0**2 / gamma**2 mul1: uint256 = unsafe_div(unsafe_div(unsafe_div(10**18 * D, gamma) * _g1k0, gamma) * _g1k0 * A_MULTIPLIER, ANN) # 2*N*K0 / _g1k0 mul2: uint256 = unsafe_div(((2 * 10**18) * N_COINS) * K0, _g1k0) # calculate neg_fprime. here K0 > 0 is being validated (safediv). neg_fprime: uint256 = (S + unsafe_div(S * mul2, 10**18)) + mul1 * N_COINS / K0 - unsafe_div(mul2 * D, 10**18) # D -= f / fprime; neg_fprime safediv being validated D_plus: uint256 = D * (neg_fprime + S) / neg_fprime D_minus: uint256 = unsafe_div(D * D, neg_fprime) if 10**18 > K0: D_minus += unsafe_div(unsafe_div(D * unsafe_div(mul1, neg_fprime), 10**18) * unsafe_sub(10**18, K0), K0) else: D_minus -= unsafe_div(unsafe_div(D * unsafe_div(mul1, neg_fprime), 10**18) * unsafe_sub(K0, 10**18), K0) if D_plus > D_minus: D = unsafe_sub(D_plus, D_minus) else: D = unsafe_div(unsafe_sub(D_minus, D_plus), 2) if D > D_prev: diff = unsafe_sub(D, D_prev) else: diff = unsafe_sub(D_prev, D) if diff * 10**14 < max(10**16, D): # Could reduce precision for gas efficiency here for _x in x: frac: uint256 = _x * 10**18 / D assert (frac > 10**16 / N_COINS - 1) and (frac < 10**20 / N_COINS + 1) # dev: unsafe values x[i] return D raise "Did not converge" @external @view def get_p( _xp: uint256[N_COINS], _D: uint256, _A_gamma: uint256[N_COINS] ) -> uint256: """ @notice Calculates dx/dy. @dev Output needs to be multiplied with price_scale to get the actual value. @param _xp Balances of the pool. @param _D Current value of D. @param _A_gamma Amplification coefficient and gamma. """ assert _D > 10**17 - 1 and _D < 10**15 * 10**18 + 1 # dev: unsafe D values # K0 = P * N**N / D**N. # K0 is dimensionless and has 10**36 precision: K0: uint256 = unsafe_div( unsafe_div(4 * _xp[0] * _xp[1], _D) * 10**36, _D ) # GK0 is in 10**36 precision and is dimensionless. # GK0 = ( # 2 * _K0 * _K0 / 10**36 * _K0 / 10**36 # + (gamma + 10**18)**2 # - (_K0 * _K0 / 10**36 * (2 * gamma + 3 * 10**18) / 10**18) # ) # GK0 is always positive. So the following should never revert: GK0: uint256 = ( unsafe_div(unsafe_div(2 * K0 * K0, 10**36) * K0, 10**36) + pow_mod256(unsafe_add(_A_gamma[1], 10**18), 2) - unsafe_div( unsafe_div(pow_mod256(K0, 2), 10**36) * unsafe_add(unsafe_mul(2, _A_gamma[1]), 3 * 10**18), 10**18 ) ) # NNAG2 = N**N * A * gamma**2 NNAG2: uint256 = unsafe_div(unsafe_mul(_A_gamma[0], pow_mod256(_A_gamma[1], 2)), A_MULTIPLIER) # denominator = (GK0 + NNAG2 * x / D * _K0 / 10**36) denominator: uint256 = (GK0 + unsafe_div(unsafe_div(NNAG2 * _xp[0], _D) * K0, 10**36) ) # p_xy = x * (GK0 + NNAG2 * y / D * K0 / 10**36) / y * 10**18 / denominator # p is in 10**18 precision. return unsafe_div( _xp[0] * ( GK0 + unsafe_div(unsafe_div(NNAG2 * _xp[1], _D) * K0, 10**36) ) / _xp[1] * 10**18, denominator ) @external @pure def wad_exp(x: int256) -> int256: """ @dev Calculates the natural exponential function of a signed integer with a precision of 1e18. @notice Note that this function consumes about 810 gas units. The implementation is inspired by Remco Bloemen's implementation under the MIT license here: https://xn--2-umb.com/22/exp-ln. @param x The 32-byte variable. @return int256 The 32-byte calculation result. """ value: int256 = x # If the result is `< 0.5`, we return zero. This happens when we have the following: # "x <= floor(log(0.5e18) * 1e18) ~ -42e18". if (x <= -42_139_678_854_452_767_551): return empty(int256) # When the result is "> (2 ** 255 - 1) / 1e18" we cannot represent it as a signed integer. # This happens when "x >= floor(log((2 ** 255 - 1) / 1e18) * 1e18) ~ 135". assert x < 135_305_999_368_893_231_589, "Math: wad_exp overflow" # `x` is now in the range "(-42, 136) * 1e18". Convert to "(-42, 136) * 2 ** 96" for higher # intermediate precision and a binary base. This base conversion is a multiplication with # "1e18 / 2 ** 96 = 5 ** 18 / 2 ** 78". value = unsafe_div(x << 78, 5 ** 18) # Reduce the range of `x` to "(-½ ln 2, ½ ln 2) * 2 ** 96" by factoring out powers of two # so that "exp(x) = exp(x') * 2 ** k", where `k` is a signer integer. Solving this gives # "k = round(x / log(2))" and "x' = x - k * log(2)". Thus, `k` is in the range "[-61, 195]". k: int256 = unsafe_add(unsafe_div(value << 96, 54_916_777_467_707_473_351_141_471_128), 2 ** 95) >> 96 value = unsafe_sub(value, unsafe_mul(k, 54_916_777_467_707_473_351_141_471_128)) # Evaluate using a "(6, 7)"-term rational approximation. Since `p` is monic, # we will multiply by a scaling factor later. y: int256 = unsafe_add(unsafe_mul(unsafe_add(value, 1_346_386_616_545_796_478_920_950_773_328), value) >> 96, 57_155_421_227_552_351_082_224_309_758_442) p: int256 = unsafe_add(unsafe_mul(unsafe_add(unsafe_mul(unsafe_sub(unsafe_add(y, value), 94_201_549_194_550_492_254_356_042_504_812), y) >> 96,\ 28_719_021_644_029_726_153_956_944_680_412_240), value), 4_385_272_521_454_847_904_659_076_985_693_276 << 96) # We leave `p` in the "2 ** 192" base so that we do not have to scale it up # again for the division. q: int256 = unsafe_add(unsafe_mul(unsafe_sub(value, 2_855_989_394_907_223_263_936_484_059_900), value) >> 96, 50_020_603_652_535_783_019_961_831_881_945) q = unsafe_sub(unsafe_mul(q, value) >> 96, 533_845_033_583_426_703_283_633_433_725_380) q = unsafe_add(unsafe_mul(q, value) >> 96, 3_604_857_256_930_695_427_073_651_918_091_429) q = unsafe_sub(unsafe_mul(q, value) >> 96, 14_423_608_567_350_463_180_887_372_962_807_573) q = unsafe_add(unsafe_mul(q, value) >> 96, 26_449_188_498_355_588_339_934_803_723_976_023) # The polynomial `q` has no zeros in the range because all its roots are complex. # No scaling is required, as `p` is already "2 ** 96" too large. Also, # `r` is in the range "(0.09, 0.25) * 2**96" after the division. r: int256 = unsafe_div(p, q) # To finalise the calculation, we have to multiply `r` by: # - the scale factor "s = ~6.031367120", # - the factor "2 ** k" from the range reduction, and # - the factor "1e18 / 2 ** 96" for the base conversion. # We do this all at once, with an intermediate result in "2**213" base, # so that the final right shift always gives a positive value. # Note that to circumvent Vyper's safecast feature for the potentially # negative parameter value `r`, we first convert `r` to `bytes32` and # subsequently to `uint256`. Remember that the EVM default behaviour is # to use two's complement representation to handle signed integers. return convert(unsafe_mul(convert(convert(r, bytes32), uint256), 3_822_833_074_963_236_453_042_738_258_902_158_003_155_416_615_667) >>\ convert(unsafe_sub(195, k), uint256), int256)
Contract Security Audit
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[{"stateMutability":"pure","type":"function","name":"newton_y","inputs":[{"name":"ANN","type":"uint256"},{"name":"gamma","type":"uint256"},{"name":"x","type":"uint256[2]"},{"name":"D","type":"uint256"},{"name":"i","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"pure","type":"function","name":"get_y","inputs":[{"name":"_ANN","type":"uint256"},{"name":"_gamma","type":"uint256"},{"name":"_x","type":"uint256[2]"},{"name":"_D","type":"uint256"},{"name":"i","type":"uint256"}],"outputs":[{"name":"","type":"uint256[2]"}]},{"stateMutability":"view","type":"function","name":"newton_D","inputs":[{"name":"ANN","type":"uint256"},{"name":"gamma","type":"uint256"},{"name":"x_unsorted","type":"uint256[2]"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"view","type":"function","name":"newton_D","inputs":[{"name":"ANN","type":"uint256"},{"name":"gamma","type":"uint256"},{"name":"x_unsorted","type":"uint256[2]"},{"name":"K0_prev","type":"uint256"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"view","type":"function","name":"get_p","inputs":[{"name":"_xp","type":"uint256[2]"},{"name":"_D","type":"uint256"},{"name":"_A_gamma","type":"uint256[2]"}],"outputs":[{"name":"","type":"uint256"}]},{"stateMutability":"pure","type":"function","name":"wad_exp","inputs":[{"name":"x","type":"int256"}],"outputs":[{"name":"","type":"int256"}]},{"stateMutability":"view","type":"function","name":"version","inputs":[],"outputs":[{"name":"","type":"string"}]}]
Contract Creation Code
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Multichain Portfolio | 30 Chains
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A contract address hosts a smart contract, which is a set of code stored on the blockchain that runs when predetermined conditions are met. Learn more about addresses in our Knowledge Base.