half-life calc for DA Exp

half-life-calc.ts

import { BigNumber, utils } from "ethers";

// SUMMARY
// This script calculates the half-life in seconds for a given
// startPrice, endPrice, startTime, and endTime.
// The calculation accounts for the Art Blocks pseudo-exponential pricing curve
// used in DAExp minters.

// INPUTS
const startPrice = utils.parseUnits("10", "ether");
const endPrice = utils.parseUnits("0.8", "ether");
const startTime = BigNumber.from("1681530920"); // 2023-04-14 20:55:20
const endTime = startTime.add(3600); // 1 hour later

// calc intermediate terms
// use EXTRA_DECIMALS to gain precision for decimal values (BigNumber doesn't support decimals)
const EXTRA_DECIMALS = 10 ** 5;
const priceRatio =
  startPrice.mul(EXTRA_DECIMALS).div(endPrice).toNumber() / EXTRA_DECIMALS;
const completedHalfLives = Math.floor(Math.log(priceRatio) / Math.log(2));
const _denominator = BigNumber.from(2).pow(completedHalfLives);
const y1 = startPrice.div(_denominator);
const y2 = y1.div(2);
const zNumerator = endPrice.sub(y1);
const zDenominator = y2.sub(y1);
const z =
  zNumerator.mul(EXTRA_DECIMALS).div(zDenominator).toNumber() / EXTRA_DECIMALS;
// half-life is a fallout
const halfLifeSeconds = Math.round(
  endTime.sub(startTime).toNumber() /
    ((completedHalfLives + 1) * z + completedHalfLives * (1 - z))
);
console.log("halfLifeSeconds:", halfLifeSeconds.toString());