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https://github.com/darkrenaissance/darkfi.git
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122 lines
3.0 KiB
Python
122 lines
3.0 KiB
Python
import math
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import numpy as np
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import matplotlib.pyplot as plt
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import random
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L = 28948022309329048855892746252171976963363056481941560715954676764349967630337
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# crypsinous original target function
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def target(f, rel_stake):
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T = L * (1 - (1-f)**rel_stake)
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return T
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# naive factorial
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def fact(n):
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assert (n>0)
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n = int(n)
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if n==1:
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return 1
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elif n==2:
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return 2
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else:
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return n * fact(n-1)
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# all inputs to this function are integers
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# sigmas are public
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# stake is private
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def approx_target_in_zk(sigmas, stake):
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# both sigma_1, sigma_2 are constants, if f is a constant.
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# if f is constant then sigma_12, sigma_2
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# this dictates that tuning need to be hardcoded,
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# secondly the reward, or at least the total stake in the network,
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# can't be anonymous, should be public.
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T = [sigma*stake**(i+1) for i, sigma in enumerate(sigmas)]
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return sum(T)
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# approximation of crypsinous targt
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def approx_target(c, stake, Sigma, k):
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sigmas = [int((c/Sigma)**i * (L/fact(i))) for i in range(1, k+1)]
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return -1*approx_target_in_zk(sigmas, stake)
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def approx_target_with_div(c, stake, Sigma, k):
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sigmas = [(c/Sigma)**i * (L/fact(i)) for i in range(1, k+1)]
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return -1*approx_target_in_zk(sigmas, stake)
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f = 0.5
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x = (1-f)
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c = math.log(x)
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# let's assume stakeholde having 1% of the stake, 1/100.
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# each iteration increases stake by value 1.
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TOTAL = 10000
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S = []
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stake = 0
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targets = []
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T = []
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T_approx_2term = []
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T_approx_3term = []
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T_approx_5term = []
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k=7
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START=1
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for i in range(TOTAL):
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if random.random() >= 0.9:
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stake+=1
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S+=[(stake, i+1.0)]
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col = []
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t = target(f, stake/(i+1.0))
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col += [t]
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for j in range(1,k+1):
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t_approx = approx_target_with_div(c, stake, (i+1.0), j)
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col += [t_approx]
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for j in range(1,k+1):
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t_approx = approx_target(c, stake, (i+1.0), j)
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col += [t_approx]
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targets +=[col]
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targets = np.array(targets).T
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plt.subplot(4,1,1)
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plt.plot(targets[0])
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for i in range(START,k+1):
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plt.plot(targets[i])
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plt.legend(["target"] + ["{} terms".format(i) for i in range(START,k+1)], loc='upper right')
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Deltas = []
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for j in range(START+1,k+1):
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diff = np.array(targets[j])-np.array(targets[j-1])
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delta = np.sum(diff)
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Deltas += [delta]
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print(len(Deltas))
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plt.subplot(4,1,2)
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Deltas_derivates = np.poly1d(Deltas)
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plt.plot(Deltas)
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plt.plot(Deltas_derivates.deriv())
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plt.legend(["delta", "derivative"], loc='upper right')
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plt.subplot(4,1,3)
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plt.plot(targets[0])
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for i in range(k,2*(k)+1):
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plt.plot(targets[i])
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plt.legend(["target"] + ["{} terms(with div)".format(i) for i in range(START,k+1)] , loc='upper right')
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Deltas = []
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for j in range(k+2,2*(k)+1):
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diff = np.array(targets[j])-np.array(targets[j-1])
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delta = np.sum(diff)
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Deltas += [delta]
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plt.subplot(4,1,4)
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Deltas_derivates = np.poly1d(Deltas)
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plt.plot(Deltas)
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plt.plot(Deltas_derivates.deriv())
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plt.legend(["delta(with div)", "derivative(with div)"], loc='upper right')
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plt.savefig("target.png")
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