/*
* Function multiplies a multiple-digit number (array of digits) by a fixed number,
* while a applying a shift (this is a base operation in the standard multiplocation
* algorithm)
* Additionally, there is a truncation of the result to a certain number of digits
*/
function truncatedMultiplyByNumber(array, number, shift, truncationThreshold) {
const newArray = [];
let uebertrag = 0;
for (let nullindex = 0; nullindex < shift; nullindex++) {
if (nullindex >= truncationThreshold) { return newArray }
newArray.push(0)
}
for (let index = 0; index < array.length; index++) {
if (index + shift >= truncationThreshold) {uebertrag = 0; break}
const wert = (uebertrag + array[index] * number)
newArray.push(wert % 10);
uebertrag = (wert - (wert % 10)) / 10;
}
while (uebertrag > 0) {
newArray.push(uebertrag % 10);
uebertrag = (uebertrag - (uebertrag % 10)) / 10;
}
return newArray;
}
/*
* Function inmplements a summation while truncating the result to a certain
* number of digits
*/
function truncatedAddition(array1, array2, truncationThreshold) {
const resultArray = [];
let i = 0;
uebertrag = 0;
while (array1[i] != undefined || array2[i] != undefined || uebertrag > 0) {
if (i >= truncationThreshold) {break}
const value = (array1[i] || 0) + (array2[i] || 0) + uebertrag;
resultArray.push(value % 10);
uebertrag = (value - value % 10) / 10
i += 1;
}
return resultArray;
}
/*
* Function implements the full multiplication of two multi-digit numbers (arrays)
* while truncating all the steps in the algorithm to be performed with truncated
* numbers
*/
function truncatedMultiplication(array1, array2, truncationThreshold) {
let result = [0]
array1.forEach((x, index) => { result = truncatedAddition(result, truncatedMultiplyByNumber(array2, x, index, truncationThreshold), truncationThreshold)})
return result;
}
/*
* Function implements a truncated version of the power function. All calculations
* are essentially carried out with numbers truncated to a certain number of digits
*/
function truncatedSelfPower(number, truncationThreshold,) {
const numberArr = number.toString().split('').map(x => parseInt(x)).reverse()
let resultArr = [...numberArr];
for (let i = 1; i < number; i++) {
resultArr = truncatedMultiplication(numberArr, resultArr, truncationThreshold )
}
return resultArr
}
function calculateSelfPowerSum(number, truncationThreshold) {
result = [0];
for (let i= 1; i <= number; i++) {
result = truncatedAddition(result, truncatedSelfPower(i, truncationThreshold), truncationThreshold)
}
return result
}
console.log(calculateSelfPowerSum(1000, 10).reduce((a,b,index) => a + b * 10 ** (index)))
