formula.py

import math

from fastnumbers import fast_float

def calculate(new, old, net_worth):
    new = fast_float(new)
    old = fast_float(old)
    net_worth = fast_float(net_worth)

    # Treat anything below 0 upvotes as 0 upvotes
    if old < 0:
        old = 0
    if new < 0:
        new = 0

    # Compute gain
    delta = new - old

    # Treat negative gain as no gain
    if delta < 0:
        delta = 0

    # Compute the maximum of the sigmoid
    sig_max = sigmoid_max(old)

    # Compute the midpoint of the sigmoid
    sig_mp = sigmoid_midpoint(old)

    # Compute the steepness of the sigmoid
    sig_stp = sigmoid_steepness(old)

    # Calculate return
    factor = sigmoid(delta, sig_max, sig_mp, sig_stp)

    # Normalize between -1 and 1
    factor = factor - 1

    # Adjust based on net worth
    factor = factor * net_worth_coefficient(net_worth)

    # Return investment amount multiplier (change + 1)
    return factor + 1

def sigmoid(x, maxvalue, midpoint, steepness):
    arg = -(steepness * (x - midpoint))
    y = fast_float(maxvalue) / ( 1 + math.exp(arg) )
    return y

def sigmoid_max(old):
    return 1.2 + 0.6 / ((old / 10) + 1)

def sigmoid_midpoint(old):
    sig_mp_0 = 10
    sig_mp_1 = 500
    return linear_interpolate(old, 0, 25000, sig_mp_0, sig_mp_1)

def sigmoid_steepness(old):
    return 0.06 / ((old / 100) + 1)

def linear_interpolate(x, x_0, x_1, y_0, y_1):
    m = (y_1 - y_0) / fast_float(x_1 - x_0)
    c = y_0
    y = (m * x) + c
    return y

def net_worth_coefficient(net_worth):
    return net_worth ** -0.155 * 6