533 lines
13 KiB
Rust
533 lines
13 KiB
Rust
#![allow(unused_variables)]
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//! \[WIP\] Arbitrarily large integers
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use crate::num::Sign::*;
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use crate::num::*;
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use core::ops::{
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Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
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};
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use core::usize;
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use std::convert::TryInto;
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#[derive(Clone, Debug, PartialEq)]
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pub struct BigInt {
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inner: Vec<usize>,
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sign: Sign,
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}
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impl Default for BigInt {
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fn default() -> Self {
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Self {
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inner: vec![0],
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sign: Sign::default(),
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}
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}
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}
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impl From<usize> for BigInt {
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fn from(n: usize) -> Self {
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Self {
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inner: vec![n],
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sign: Sign::default(),
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}
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}
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}
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impl From<&str> for BigInt {
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fn from(s: &str) -> Self {
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Self::from_str_radix(s, 10)
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}
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}
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impl From<String> for BigInt {
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fn from(s: String) -> Self {
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Self::from_str_radix(s, 10)
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}
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}
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impl BigInt {
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/// Create a new Bigint, of value 0
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///
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/// The various `From` implementations are more useful in most cases
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pub fn new() -> Self {
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Self::default()
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}
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fn new_empty() -> Self {
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Self {
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inner: Vec::new(),
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sign: Sign::Positive,
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}
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}
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/// Create a new BigInt, with the specified inner capacity
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pub fn with_capacity(size: usize) -> Self {
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Self {
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inner: Vec::with_capacity(size),
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sign: Positive,
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}
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}
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/// Remove digits that are zero from the internal representation.
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///
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/// Similar to 007 -> 7 in base 10
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pub fn trim_zeros(&mut self) {
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let current_len = self.inner.len();
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if current_len < 2 {
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return;
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}
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let mut trailing_zeros = 0usize;
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for val in self.inner.iter().rev() {
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if *val != 0 {
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break;
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}
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trailing_zeros += 1;
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}
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// Always keep at least one digit
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if trailing_zeros == current_len {
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trailing_zeros -= 1;
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}
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let new_len = current_len - trailing_zeros;
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self.inner.truncate(new_len);
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}
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/// Remove unused digits, and shrink the internal vector
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pub fn shrink_to_fit(&mut self) {
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self.trim_zeros();
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self.inner.shrink_to_fit();
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}
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/// Convert a `&str` or a `String` representing a number in the specified radix to a Bigint.
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///
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/// For radix 10, use the `from` associated function instead.
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pub fn from_str_radix<T: ToString>(s: T, radix: usize) -> BigInt {
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todo!();
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}
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fn get_digit_count(a: &Self, b: &Self) -> usize {
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let a_digits = a.inner.len();
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let b_digits = b.inner.len();
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let digits = if b_digits > a_digits {
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b_digits
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} else {
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a_digits
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};
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if digits > 0 {
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digits
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} else {
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1
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}
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}
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}
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impl Add for BigInt {
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type Output = Self;
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// @TODO: handle signs
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fn add(self, rhs: Self) -> Self::Output {
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if self.sign == Positive && rhs.sign == Negative {
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return self - -rhs;
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}
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let digits = Self::get_digit_count(&self, &rhs) + 1;
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let mut out = BigInt::with_capacity(digits);
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let mut carry = 0usize;
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for i in 0..digits {
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let a = *self.inner.get(i).unwrap_or(&0usize);
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let b = *rhs.inner.get(i).unwrap_or(&0usize);
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let (res, overflowed) = a.overflowing_add(b);
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if res == 0 && !overflowed {
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out.inner.push(res + carry);
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carry = 0;
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continue;
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}
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if overflowed {
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out.inner.push(res + carry);
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carry = 1;
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} else if res < core::usize::MAX {
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out.inner.push(res + carry);
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carry = 0;
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} else {
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out.inner.push(0usize);
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carry = 1;
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}
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}
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out.trim_zeros();
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out
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}
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}
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impl Sub for BigInt {
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type Output = Self;
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// @TODO: handle signs
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fn sub(self, rhs: Self) -> Self::Output {
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let digits = Self::get_digit_count(&self, &rhs);
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let mut out = BigInt::with_capacity(digits);
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let mut borrow = 0usize;
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for i in 0..digits {
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let a = *self.inner.get(i).unwrap_or(&0usize);
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let b = *rhs.inner.get(i).unwrap_or(&0usize);
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if a >= borrow && (a - borrow) >= b {
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let res = a - b - borrow;
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out.inner.push(res);
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borrow = 0;
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} else {
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// To prevent subtraction overflow, the max borrowed
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// value is usize::MAX. The rest of the borrowed value
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// will be added on afterwords.
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// In base ten, this would be like:
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// 18 - 9 = 9-9 + 9
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let rem = (a + 1) - borrow;
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let res = (core::usize::MAX - b) + rem;
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out.inner.push(res);
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borrow = 1;
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}
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}
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out.trim_zeros();
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out
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}
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}
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impl Mul for BigInt {
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type Output = Self;
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fn mul(self, rhs: Self) -> Self::Output {
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// Multiplication can result in twice the number of digits
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let digits = Self::get_digit_count(&self, &rhs) * 2;
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let mut out = BigInt::with_capacity(digits);
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let mut carry = 0usize;
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for i in 0..digits {
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let a = *self.inner.get(i).unwrap_or(&0usize);
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let b = *rhs.inner.get(i).unwrap_or(&0usize);
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if a == 0 || b == 0 {
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out.inner.push(0);
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continue;
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}
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let (res, overflowed) = a.overflowing_mul(b);
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if overflowed {
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todo!()
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} else {
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match res.checked_add(carry) {
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Some(res) => {
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out.inner.push(res);
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carry = 0;
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}
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None => {
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// Well, we have to deal with overflow again
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todo!();
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}
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}
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}
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}
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out.trim_zeros();
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out
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}
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}
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impl Div for BigInt {
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type Output = Self;
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fn div(self, rhs: Self) -> Self::Output {
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todo!()
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}
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}
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impl Rem for BigInt {
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type Output = Self;
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fn rem(self, rhs: Self) -> Self::Output {
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todo!()
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}
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}
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impl AddAssign for BigInt {
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fn add_assign(&mut self, rhs: Self) {
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*self = self.clone() + rhs;
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}
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}
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impl SubAssign for BigInt {
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fn sub_assign(&mut self, rhs: Self) {
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*self = self.clone() - rhs;
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}
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}
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impl MulAssign for BigInt {
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fn mul_assign(&mut self, rhs: Self) {
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*self = self.clone() * rhs;
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}
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}
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impl DivAssign for BigInt {
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fn div_assign(&mut self, rhs: Self) {
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*self = self.clone() / rhs;
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}
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}
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impl RemAssign for BigInt {
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fn rem_assign(&mut self, rhs: Self) {
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*self = self.clone() % rhs;
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}
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}
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impl Neg for BigInt {
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type Output = Self;
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/// Flip the sign of the current `BigInt` value
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fn neg(mut self) -> Self::Output {
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self.sign = !self.sign;
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self
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}
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}
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impl Not for BigInt {
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type Output = Self;
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/// Do a bitwise negation of every digit's value
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fn not(self) -> Self::Output {
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let mut flipped: Vec<usize> = Vec::with_capacity(self.inner.len());
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for val in self.inner.iter() {
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let rev = !*val;
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flipped.push(rev);
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}
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BigInt {
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sign: self.sign,
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inner: flipped,
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}
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}
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}
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macro_rules! impl_from_smaller {
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($(($s: ty, $u: ty)),* ) => {
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$(
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impl From<$s> for BigInt {
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/// Create a `BigInt` from a signed integer primitive
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fn from(n: $s) -> Self {
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let sign = if n < 0 { Sign::Negative } else { Sign::Positive };
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let n = n.abs();
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let raw: usize = <$s>::try_into(n).unwrap();
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Self {
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inner: vec![raw],
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sign,
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}
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}
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}
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impl From<$u> for BigInt {
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/// Create a `BigInt` from an unsigned integer primitive
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fn from(n: $u) -> Self {
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let mut new = Self::new_empty();
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new.inner.push(n as usize);
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new
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}
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}
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)*
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}
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}
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macro_rules! impl_from_larger {
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($(($s: ty, $u: ty)),* ) => {
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$(
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impl From<$s> for BigInt {
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/// Create a `BigInt` from a signed integer primitive
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fn from(n: $s) -> Self {
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todo!();
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}
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}
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impl From<$u> for BigInt {
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/// Create a `BigInt` from an unsigned integer primitive
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fn from(n: $u) -> Self {
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use core::usize::MAX;
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let base_usize_value = n / MAX as $u;
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let rem = n % MAX as $u;
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if base_usize_value == 0 {
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Self::from(rem as usize)
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} else {
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todo!();
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}
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}
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}
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)*
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};
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}
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#[cfg(target_pointer_width = "32")]
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impl_from_larger!((i64, u64), (i128, u128));
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#[cfg(target_pointer_width = "32")]
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impl_from_smaller!((i8, u8), (i16, u16), (i32, u32));
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#[cfg(target_pointer_width = "32")]
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static BITS: usize = 32;
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#[cfg(target_pointer_width = "64")]
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impl_from_larger!((i128, u128));
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#[cfg(target_pointer_width = "64")]
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impl_from_smaller!((i8, u8), (i16, u16), (i32, u32), (i64, u64));
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#[cfg(target_pointer_width = "64")]
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static BITS: usize = 64;
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#[cfg(test)]
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#[cfg_attr(tarpaulin, skip)]
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mod tests {
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use super::*;
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#[test]
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fn sanity_checks() {
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let int = BigInt::from(45u8);
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assert_eq!(int.inner[0], 45usize)
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}
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#[test]
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fn test_trim_zeros() {
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let mut lotsoftrailing = BigInt {
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inner: vec![1, 0, 0, 0, 0, 0, 0, 0, 0],
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sign: Positive,
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};
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lotsoftrailing.trim_zeros();
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assert_eq!(BigInt::from(1), lotsoftrailing);
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}
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#[test]
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fn test_add() {
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// MAX is 2^Bitsize - 1,
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// so the sum should be
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// [MAX -1, 1]
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// Compare base 10: 9 + 9 = 18
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let a = BigInt::from(core::usize::MAX);
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let b = BigInt::from(core::usize::MAX);
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let sum = a + b;
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assert_eq!(
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sum.inner[0],
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core::usize::MAX - 1,
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"least significant place should be MAX - 1"
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);
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assert_eq!(sum.inner[1], 1usize, "most significant place should be 1");
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let a = BigInt::from(core::usize::MAX);
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let b = BigInt::from(1usize);
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let sum = a + b;
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assert_eq!(sum.inner[0], 0usize);
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assert_eq!(sum.inner[1], 1usize);
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}
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#[test]
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fn test_sub() {
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let a = BigInt::from(core::usize::MAX);
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let b = BigInt::from(core::u16::MAX);
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let diff = a - b;
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assert_eq!(
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diff.clone().inner[0],
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core::usize::MAX - core::u16::MAX as usize
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);
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assert_eq!(diff.inner.len(), 1);
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}
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#[test]
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fn test_sub_borrow() {
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let a = BigInt {
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inner: vec![0, 1],
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sign: Positive,
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};
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let b = BigInt::from(2);
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let diff = a - b;
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assert_eq!(diff.clone().inner.len(), 1, "{:#?}", diff.clone());
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assert_eq!(diff.inner[0], core::usize::MAX - 1);
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}
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#[test]
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fn test_sub_assign() {
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let mut a = BigInt {
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inner: vec![1, 0, 1],
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sign: Positive,
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};
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let b = BigInt::from(2);
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a -= b;
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assert_eq!(a.inner, vec![core::usize::MAX, core::usize::MAX]);
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}
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#[test]
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fn test_zeros() {
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let a = BigInt::new();
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let b = BigInt::new();
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let c = a.clone() - b.clone();
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assert_eq!(a.clone(), b.clone());
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assert_eq!(c, a.clone());
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let c = a.clone() + b.clone();
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assert_eq!(a.clone(), b.clone());
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assert_eq!(c, a.clone());
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}
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#[test]
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fn test_not() {
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let a = BigInt::from(0u8);
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let b = !a;
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assert_eq!(b.inner[0], core::usize::MAX);
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}
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#[test]
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fn test_add_assign() {
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let mut a = BigInt::from(core::usize::MAX);
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let b = BigInt::from(core::usize::MAX);
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a += b;
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assert_eq!(
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a.inner[0],
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core::usize::MAX - 1,
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"least significant place should be MAX - 1"
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);
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assert_eq!(a.inner[1], 1usize, "most significant place should be 1");
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}
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#[test]
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fn test_from() {
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// Signed numbers
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assert_eq!(-BigInt::from(2), BigInt::from(-2));
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// Larger than usize
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assert_eq!(BigInt::from(45u128), BigInt::from(45usize));
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}
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}
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