@polkassembly/util/build/getThresholds.js

Set of utility functions for Polkassembly and more.

"use strict";
// Copyright 2019-2020 @paritytech/polkassembly authors & contributors
// This software may be modified and distributed under the terms
// of the Apache-2.0 license. See the LICENSE file for details.
var __importDefault = (this && this.__importDefault) || function (mod) {
    return (mod && mod.__esModule) ? mod : { "default": mod };
};
Object.defineProperty(exports, "__esModule", { value: true });
var bn_js_1 = __importDefault(require("bn.js"));
var newton_raphson_1 = require("./newton-raphson");
var solveQuadraticEquation_1 = require("./solveQuadraticEquation");
var types_1 = require("./types");
var ONE = new bn_js_1.default(1);
var TWO = new bn_js_1.default(2);
var THREE = new bn_js_1.default(3);
var TEN = new bn_js_1.default(10);
var MAX_ITERATIONS = 20;
var getFAndFp = function (_a) {
    var totalIssuance = _a.totalIssuance, votes = _a.votes, votesWithoutConviction = _a.votesWithoutConviction;
    return {
        f: function (x) {
            // with v: votes, vc: votes without conviction, t: total issuance
            // x^3 + v*x^2 - (vc)^2 * t
            return x.pow(THREE).add(votesWithoutConviction.mul(x.pow(TWO))).sub(votes.pow(TWO).mul(totalIssuance));
        },
        fp: function (x) {
            // 3*x^2 + 2*v*x
            return THREE.mul(x.pow(TWO)).add(TWO.mul(votesWithoutConviction).mul(x));
        }
    };
};
var raphsonIterations = function (f, fp) {
    var initialGuess = ONE;
    var result = { foundRoot: false };
    var i = 1;
    while (!result.foundRoot && i < MAX_ITERATIONS) {
        result = newton_raphson_1.newtonRaphson(f, fp, initialGuess.mul(TEN).pow(new bn_js_1.default(i)));
        i++;
    }
    return result;
};
/**
 * @name getFailingThreshold
 * @summary Calculates amount of nays needed for a referendum to fail
 **/
function getFailingThreshold(_a) {
    var ayes = _a.ayes, ayesWithoutConviction = _a.ayesWithoutConviction, totalIssuance = _a.totalIssuance, threshold = _a.threshold;
    if (ayes.isZero() || ayesWithoutConviction.isZero()) {
        // there is no vote against, any number of aye>0 would work
        return {
            failingThreshold: ONE,
            isValid: true
        };
    }
    // if there are more ayes
    // than the (total issuance) /2 it can't fail
    if (ayesWithoutConviction.gt(totalIssuance.divn(2))) {
        return {
            isValid: false
        };
    }
    if (threshold === types_1.VoteThresholdEnum.Simplemajority) {
        return {
            failingThreshold: ayes,
            isValid: true
        };
    }
    if (threshold === types_1.VoteThresholdEnum.Supermajorityrejection) {
        var _b = getFAndFp({ totalIssuance: totalIssuance, votes: ayes, votesWithoutConviction: ayesWithoutConviction }), f = _b.f, fp = _b.fp;
        var result = raphsonIterations(f, fp);
        return result.foundRoot
            ? {
                failingThreshold: result.result,
                isValid: true
            }
            : {
                isValid: false
            };
    }
    else {
        // SuperMajorityRejection
        // with v: votes, vc: votes without conviction, t: total issuance
        // -t*x^2 + v^2*x + (v)^2*vc
        var res = solveQuadraticEquation_1.solveQuadraticEquation(totalIssuance.neg(), ayes.pow(TWO), ayes.pow(TWO).mul(ayesWithoutConviction));
        return {
            failingThreshold: bn_js_1.default.max(res[0], res[1]),
            isValid: true
        };
    }
}
exports.getFailingThreshold = getFailingThreshold;
/**
 * @name getPassingThreshold
 * @summary Calculates amount of ayes needed for a referendum to pass
 **/
function getPassingThreshold(_a) {
    var nays = _a.nays, naysWithoutConviction = _a.naysWithoutConviction, totalIssuance = _a.totalIssuance, threshold = _a.threshold;
    if (nays.isZero() || naysWithoutConviction.isZero()) {
        // there is no vote against, any number of aye>0 would work
        return {
            isValid: true,
            passingThreshold: ONE
        };
    }
    // if there are more nays
    // than the (total issuance) /2 it can't pass
    if (naysWithoutConviction.gt(totalIssuance.divn(2))) {
        return {
            isValid: false
        };
    }
    if (threshold === types_1.VoteThresholdEnum.Simplemajority) {
        return {
            isValid: true,
            passingThreshold: nays
        };
    }
    if (threshold === types_1.VoteThresholdEnum.Supermajorityapproval) {
        var _b = getFAndFp({ totalIssuance: totalIssuance, votes: nays, votesWithoutConviction: naysWithoutConviction }), f = _b.f, fp = _b.fp;
        var result = raphsonIterations(f, fp);
        return result.foundRoot
            ? {
                isValid: true,
                passingThreshold: result.result
            }
            : {
                isValid: false
            };
    }
    else {
        // SuperMajorityRejection
        // with v: votes, vc: votes without conviction, t: total issuance
        // -t*x^2 + v^2*x + (v)^2*vc
        var res = solveQuadraticEquation_1.solveQuadraticEquation(totalIssuance.neg(), nays.pow(TWO), nays.pow(TWO).mul(naysWithoutConviction));
        return {
            isValid: true,
            passingThreshold: bn_js_1.default.max(res[0], res[1])
        };
    }
}
exports.getPassingThreshold = getPassingThreshold;