path: root/src/passwordmaker/base_conversion/iterative_conversion_impl.rs

//! Implementation of iterative conversion support for the types we need it for: u128 and [u32;N].
//! Beware that all functions in this module are optimized for the use cases of passwordmaker-rs. They may or may not
//! be suitable for anything else.

//let's start with the simple case: u128
//we do need a NewType here, because actual u128 already has a Mul<&usize> implementation that does not match the version we want.

use std::ops::{DivAssign, Mul};
use std::convert::{TryFrom, TryInto};
use std::fmt::Display;
use std::error::Error;
use std::iter::once;

use super::iterative_conversion::RemAssignWithQuotient;

//Type to be used as V, with usize as B.
pub(crate) struct SixteenBytes(u128);

impl SixteenBytes{
    pub(super) fn new(value : u128) -> Self {
        SixteenBytes(value)
    }
}

//just for convenience
impl From<u128> for SixteenBytes{
    fn from(x: u128) -> Self {
        SixteenBytes(x)
    }
}
impl From<&usize> for SixteenBytes{
    fn from(x: &usize) -> Self {
        SixteenBytes(*x as u128)
    }
}
impl DivAssign<&usize> for SixteenBytes{
    fn div_assign(&mut self, rhs: &usize) {
        self.0 /= *rhs as u128
    }
}
impl RemAssignWithQuotient for SixteenBytes{
    fn rem_assign_with_quotient(&mut self, divisor : &Self) -> Self {
        let quotient = self.0 / divisor.0;
        self.0 %= divisor.0;
        Self(quotient)
    }
}
impl TryFrom<SixteenBytes> for usize{
    type Error = std::num::TryFromIntError;
    fn try_from(value: SixteenBytes) -> Result<Self, Self::Error> {
        value.0.try_into()
    }
}
impl Mul<&usize> for &SixteenBytes{
    type Output = Option<SixteenBytes>;
    fn mul(self, rhs: &usize) -> Self::Output {
        self.0.checked_mul(*rhs as u128).map(Into::into)
    }
}

impl Mul<&SixteenBytes> for &SixteenBytes{
    type Output = Option<SixteenBytes>;

    fn mul(self, rhs: &SixteenBytes) -> Self::Output {
        self.0.checked_mul(rhs.0).map(Into::into)
    }
}

//--------------------------------------------------------------------------------------------------------------------------------------
//and now the hard part: The same for [u32;N].
//We cannot directly implement all the Foreign traits on arrays directly. So, newtypes again.

#[derive(PartialEq, PartialOrd, Ord, Eq, Clone)]
pub(crate) struct ArbitraryBytes<const N : usize>([u32;N]);

//Const generics are still a bit limited -> let's just implement From for the exact types we need.
impl From<&usize> for ArbitraryBytes<5>{
    fn from(x: &usize) -> Self {
        Self([
            0,//(*x >> 32*4) as u32, //zero on all target platforms
            0,//(*x >> 32*3) as u32, //zero on all target platforms
            0,//(*x >> 32*2) as u32, //zero on all target platforms
            x.checked_shr(32).map(|x| x as u32).unwrap_or_default(),
            *x as u32,
        ])
    }
}

impl From<&usize> for ArbitraryBytes<8>{
    fn from(x: &usize) -> Self {
        Self([
            0,//(*x >> 32*7) as u32, //zero on all target platforms
            0,//(*x >> 32*6) as u32, //zero on all target platforms
            0,//(*x >> 32*5) as u32, //zero on all target platforms
            0,//(*x >> 32*4) as u32, //zero on all target platforms
            0,//(*x >> 32*3) as u32, //zero on all target platforms
            0,//(*x >> 32*2) as u32, //zero on all target platforms
            x.checked_shr(32).map(|x| x as u32).unwrap_or_default(),
            *x as u32,
        ])
    }
}

impl From<&u32> for ArbitraryBytes<5>{
    fn from(x: &u32) -> Self {
        Self([
            0,
            0,
            0,
            0,
            *x,
        ])
    }
}

impl From<&u32> for ArbitraryBytes<8>{
    fn from(x: &u32) -> Self {
        Self([
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            *x,
        ])
    }
}

//workaround for lack of proper const-generic support.
pub(crate) trait PadWithAZero{
    type Output;
    fn pad_with_a_zero(&self) -> Self::Output;
}

impl PadWithAZero for ArbitraryBytes<5>{
    type Output = ArbitraryBytes<6>;
    fn pad_with_a_zero(&self) -> Self::Output {
        ArbitraryBytes::<6>([
            0,
            self.0[0],
            self.0[1],
            self.0[2],
            self.0[3],
            self.0[4],
        ])
    }
}

impl PadWithAZero for ArbitraryBytes<8>{
    type Output = ArbitraryBytes<9>;
    fn pad_with_a_zero(&self) -> Self::Output {
        ArbitraryBytes::<9>([
            0,
            self.0[0],
            self.0[1],
            self.0[2],
            self.0[3],
            self.0[4],
            self.0[5],
            self.0[6],
            self.0[7],
        ])
    }
}

impl<const N : usize> DivAssign<&usize> for ArbitraryBytes<N>{
    //just do long division.
    fn div_assign(&mut self, rhs: &usize) {
        self.div_assign_with_remainder_usize(rhs);
    }
}

#[derive(Debug, Clone, Copy)]
pub(crate) struct ArbitraryBytesToUsizeError;
impl Display for ArbitraryBytesToUsizeError{
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "conversion from arbitrary sized int-array to usize failed")
    }
}
impl Error for ArbitraryBytesToUsizeError{}

impl<const N : usize> TryFrom<ArbitraryBytes<N>> for usize{
    type Error = ArbitraryBytesToUsizeError;

    fn try_from(value: ArbitraryBytes<N>) -> Result<Self, Self::Error> {
        usize::try_from(&value)
    }
}

impl<const N : usize> TryFrom<&ArbitraryBytes<N>> for usize{
    type Error = ArbitraryBytesToUsizeError;
    #[cfg(target_pointer_width = "64")]
    fn try_from(value: &ArbitraryBytes<N>) -> Result<Self, Self::Error> {
        //64 bits.
        if value.0[0..N.saturating_sub(2)].iter().any(|x| *x != 0) {
            Err(ArbitraryBytesToUsizeError)
        } else {
            //failing to get last_bit is an actual error.
            let last_bit = value.0.get(N-1).ok_or(ArbitraryBytesToUsizeError).copied();
            //second-last is not an error though.
            let second_last_bit = value.0.get(N-2).copied().unwrap_or_default();
            last_bit.map(|last_bit| u64_from_u32s(second_last_bit, last_bit) as usize)
        }
    }
    #[cfg(not(target_pointer_width = "64"))]
    fn try_from(value: &ArbitraryBytes<N>) -> Result<Self, Self::Error> {
        //16 or 32 bits.
        if value.0[0..N.saturating_sub(1)].iter().any(|x| *x != 0) {
            Err(ArbitraryBytesToUsizeError)
        } else {
            value.0.get(N-1).and_then(|x| (*x).try_into().ok()).ok_or(ArbitraryBytesToUsizeError)
        }
    }
}

#[derive(Debug, Clone, Copy)]
pub(crate) struct ArbitraryBytesToU32Error;
impl Display for ArbitraryBytesToU32Error{
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "conversion from arbitrary sized int-array to u32 failed")
    }
}
impl Error for ArbitraryBytesToU32Error{}

impl<const N : usize> TryFrom<&ArbitraryBytes<N>> for u32{
    type Error = ArbitraryBytesToU32Error;

    fn try_from(value: &ArbitraryBytes<N>) -> Result<Self, Self::Error> {
        if value.0[0..N.saturating_sub(1)].iter().any(|x| *x != 0) {
            Err(ArbitraryBytesToU32Error)
        } else {
            value.0.get(N-1).copied().ok_or(ArbitraryBytesToU32Error)
        }
    }
}

macro_rules! make_mul {
    ($t:ty, $long_t:ty) => {
        impl<const N : usize> Mul<$t> for ArbitraryBytes<N>{
            type Output = Option<ArbitraryBytes<N>>;
            fn mul(mut self, rhs: $t) -> Self::Output {
                let carry = self.0.iter_mut().rev().fold(<$long_t>::default(), |carry, digit|{
                    debug_assert_eq!(carry, carry & (<$t>::MAX as $long_t)); //carry always has to fit in usize, otherwise something is terribly wrong.
                    let res = (*digit as $long_t) * (rhs as $long_t) + carry;
                    *digit = res as u32;
                    res >> 32
                });
                if carry != 0 { //if there's still carry after we hit the last digit, well, didn't fit obviously.
                    None
                } else {
                    Some(self)
                }
            }
        }
    };
}
make_mul!(u32,u64);
#[cfg(target_pointer_width = "64")]
make_mul!(usize, u128);
#[cfg(not(target_pointer_width = "64"))]
make_mul!(usize, u64);

impl<const N : usize> Mul<&usize> for &ArbitraryBytes<N>{
    type Output = Option<ArbitraryBytes<N>>;
    fn mul(self, rhs: &usize) -> Self::Output {
        (*self).clone() * (*rhs)
    }
}

impl<const N : usize> Mul<&ArbitraryBytes<N>> for &ArbitraryBytes<N> where ArbitraryBytes<N> : for<'a> From<&'a usize> {
    type Output = Option<ArbitraryBytes<N>>;
    ///School method. I haven't tried Karatsuba, but rule of thumb is that it only gets faster at about 32 digits. We have 8 digits max.
    fn mul(self, rhs: &ArbitraryBytes<N>) -> Self::Output {
        let mut result : ArbitraryBytes<N> = (&0_usize).into();
        let no_overflow = rhs.0.iter().enumerate().filter(|(_,b)| **b != 0).try_for_each(|(i,b)|{
            let p : Option<ArbitraryBytes<N>> = self.clone() * *b;
            let p = p.filter(|p| p.0[0..(N-1-i)].iter().all(|&i| i == 0));
            let carry = p.map(|p|{
                //for some reason it's faster to use slices than iterators here.
                slice_overflowing_add_assign(&mut result.0[0..(i+1)], &p.0[(N-1-i)..])
            });
            carry.filter(|x| !x).map(|_|())
        });
        no_overflow.map(|_| result)
    }
}

impl<const N : usize, const M : usize> RemAssignWithQuotient for ArbitraryBytes<N> 
    where Self : for<'a> From<&'a usize> + for<'a> From<&'a u32> + PadWithAZero<Output = ArbitraryBytes<M>>
{
    fn rem_assign_with_quotient(&mut self, divisor : &Self) -> Self{

        //This is based on Knuth, TAOCP vol 2 section 4.3, algorithm D.
        //First, check if we can get away without doing a division.
        match Ord::cmp(self, divisor){
            std::cmp::Ordering::Less => Self::from(&0_usize), //leave self unchanged, it's the remainder.
            std::cmp::Ordering::Equal => { *self = Self::from(&0_usize); Self::from(&1_usize) },
            std::cmp::Ordering::Greater => {
                //If a single digit division suffices, do a single digit division.
                if let Ok(divisor_as_u32) = divisor.try_into() {
                    self.rem_assign_with_quotient_u32(&divisor_as_u32)
                } else {
                    self.rem_assign_with_quotient_knuth(divisor)
                }
            },
        }
    }
}

macro_rules! make_div_assign_with_remainder {
    ($name:ident, $t_divisor:ty, $t_long:ty) => {
        /// Replaces self with Quotient and returns Remainder
        fn $name(&mut self, rhs: &$t_divisor) -> $t_divisor {
            debug_assert!((<$t_long>::MAX >> 32) as u128 >= <$t_divisor>::MAX as u128);

            let divisor = *rhs as $t_long;
            let remainder = self.0.iter_mut().fold(0 as $t_long,|carry, current| {
                debug_assert_eq!(carry, carry & (<$t_divisor>::MAX as $t_long)); //carry has to be lower than divisor, and divisor is $t_divisor.
                let carry_shifted = carry << 32;
                let dividend = (carry_shifted) | (*current as $t_long);
                let remainder = dividend % divisor;
                let ratio = dividend / divisor;
                debug_assert_eq!(ratio, ratio & 0xffff_ffff); //this is fine. The first digit after re-adding the carry is alwys zero.
                *current = (ratio) as u32; 
                remainder
            });
            debug_assert_eq!(remainder, remainder & (<$t_divisor>::MAX as $t_long));
            remainder as $t_divisor
        }
    };
}

impl<const N : usize> ArbitraryBytes<N>{
    pub(super) fn new(data : [u32;N]) -> Self {
        ArbitraryBytes(data)
    }

    #[cfg(target_pointer_width = "64")]
    make_div_assign_with_remainder!(div_assign_with_remainder_usize, usize, u128);

    #[cfg(not(target_pointer_width = "64"))]
    make_div_assign_with_remainder!(div_assign_with_remainder_usize, usize, u64);

    make_div_assign_with_remainder!(div_assign_with_remainder_u32, u32, u64);

    fn rem_assign_with_quotient_u32(&mut self, divisor: &u32) -> Self where Self : for<'a> From<&'a u32> {
        let remainder = self.div_assign_with_remainder_u32(divisor);
        std::mem::replace(self, Self::from(&remainder))
    }
    
    //This is Knuth, The Art of Computer Programming Volume 2, Section 4.3, Algorithm D.
    fn rem_assign_with_quotient_knuth<const M : usize>(&mut self, divisor : &Self) -> Self
        where Self : PadWithAZero<Output = ArbitraryBytes<M>> +
                     for<'a> From<&'a usize>
    {
        debug_assert!(M == N+1);
        //first we need to find n (number of digits in divisor)
        let n_digits_divisor= N - divisor.find_first_nonzero_digit();
        debug_assert!(n_digits_divisor > 1);
        //and same in the non-normalized dividend
        let m_plus_n_digits_dividend = N - self.find_first_nonzero_digit();
        let m_extra_digits_dividend = m_plus_n_digits_dividend - n_digits_divisor;

        //step D1: Normalize. This brings the maximum error for each digit down to no more than 2.
        let normalize_shift = divisor.get_digit_from_right(n_digits_divisor - 1).leading_zeros() as usize;
        //again, missing const generics ruin all the fun.
        let mut dividend = self.shift_left(normalize_shift);
        let divisor = divisor.shift_left(normalize_shift);
        debug_assert_eq!(divisor.get_digit_from_right(n_digits_divisor - 1).leading_zeros(),0);

        let mut quotient : Self = (&0_usize).into();

        //needed for Step D3, but is the same for all iterations -> factored out.
        let guess_divisor = divisor.get_digit_from_right(n_digits_divisor - 1) as u64;
        let divisor_second_significant_digit = divisor.get_digit_from_right(n_digits_divisor-2) as u64;

        //step D2, D7: the loop.
        for j in (0..=m_extra_digits_dividend).rev() {
            //Step D3: Guess a digit
            let guess_dividend = u64_from_u32s(dividend.get_digit_from_right(j+n_digits_divisor), dividend.get_digit_from_right(j + n_digits_divisor - 1));
            let mut guesstimate = guess_dividend/guess_divisor;
            let mut guess_reminder = guess_dividend % guess_divisor;
            //refine our guesstimate (still step D3). Ensures that error of guesstimate is either 0 or +1.
            while guess_reminder <= u32::MAX as u64
                && (guesstimate > u32::MAX as u64
                    || divisor_second_significant_digit * guesstimate
                        > (guess_reminder << 32) | (dividend.get_digit_from_right(j + n_digits_divisor - 2) as u64)
                ) {
                guesstimate -= 1;
                guess_reminder += guess_divisor;
            }
            //Step D4: Pretend the guess was correct and subtract guesstimate * divisor from dividend.
            debug_assert!(guesstimate & (u32::MAX as u64) == guesstimate, "The while above should have made guesstimate a one-digit number. Debug!");
            let mut guesstimate = guesstimate as u32;
            let s = (divisor.clone() * guesstimate).expect("Multipliation by a digit cannot overflow for a padded type.");
            let s_range = (M - 1 - n_digits_divisor)..M;
            let d_range = (s_range.start - j)..(s_range.end - j);
            let did_overflow = slice_overflowing_sub_assign(&mut dividend.0[d_range.clone()], &s.0[s_range.clone()]);
            //Step D5: If guesstimate was incorrect, the subtraction has overflown. The result is wrapped in such a case.
            if did_overflow {
                //Step D6: We have to correct our guesstimate. It was too large by one. We also have to fix the overflow that has occured.
                guesstimate -= 1;
                //The addition must overflow again. The two overflows cancel out, and since we are using wrapping arithmetics, the result becomes correct again.
                let did_overflow = slice_overflowing_add_assign(&mut dividend.0[d_range.clone()], &divisor.0[s_range.clone()]);
                debug_assert!(did_overflow, "Knuth, TAOCP Vol 2, Chap 4.3.1 exercise 21 says: if this fails, the while above is wrong. Debug.")
            }
            quotient.set_digit_from_right(guesstimate, j);
        }

        //Steop D8: Compute Remainder.
        self.0 = dividend.shift_right(normalize_shift).0[1..].try_into()
            .expect("Conversion of what should have been an N-element slice into an N-element array failed.");
        quotient
        
    }

    fn find_first_nonzero_digit(&self) -> usize{
        self.0.iter().enumerate().skip_while(|(_,v)| **v == 0).next().map(|(x,_)| x).unwrap_or(N)
    }

    fn get_digit_from_right(&self, i : usize) -> u32{
        self.0[N-i-1]
    }
    fn set_digit_from_right(&mut self, val: u32, i : usize){
        self.0[N-i-1] = val;
    }

    fn shift_left<const M : usize>(&self, s : usize) -> <Self as PadWithAZero>::Output
        where Self : PadWithAZero<Output = ArbitraryBytes<M>>
    {
        debug_assert!(s < 32);
        let mut res = self.pad_with_a_zero();
        if s != 0{
            res.0.iter_mut().zip(self.0.iter().chain(once(&0))).for_each(|(current, next)| *current = (*current << s) | (*next >> (32-s)));
        }
        res
    }

    fn shift_right(mut self, s : usize) -> Self {
        debug_assert!(s < 32);
        if s != 0 {
            let _ = self.0.iter_mut().fold(0u32, |carry, val| {
                let c = *val << (32-s);
                *val >>= s;
                debug_assert!(*val & carry == 0);
                *val |= carry;
                c
            });
        }
        self
    }
}

fn slice_overflowing_sub_assign(lhs : &mut [u32], rhs: &[u32]) -> bool{
    debug_assert_eq!(lhs.len(), rhs.len());
    lhs.iter_mut().zip(rhs.iter()).rev().fold(false,|carry,(a,b)| {
        let r = b.overflowing_add(carry as u32);
        let s = a.overflowing_sub(r.0);
        *a = s.0;
        r.1 || s.1
    })
}

fn slice_overflowing_add_assign(lhs : &mut [u32], rhs : &[u32]) -> bool {
    debug_assert_eq!(lhs.len(), rhs.len());
    lhs.iter_mut().zip(rhs.iter()).rev().fold(false, |carry, (a, b)| {
        let r = b.overflowing_add(carry as u32);
        let s = a.overflowing_add(r.0);
        *a = s.0;
        r.1 || s.1
    })
}

fn u64_from_u32s(msb : u32, lsb : u32) -> u64{
    let msb = msb as u64;
    let lsb = lsb as u64;
    (msb << 32) | lsb
}

#[cfg(test)]
mod arbitrary_bytes_tests{
    use super::*;
    use rand::RngCore;
    use rand_xoshiro::rand_core::SeedableRng;
    use rand_xoshiro::Xoshiro256Plus;

    /// Tests specifically the case that will_overflow is true.
    #[test]
    fn knuth_add_back_test(){
        let mut dividend = ArbitraryBytes::new([
            //m = 3, n=5
            u32::MAX,
            u32::MAX,
            u32::MAX-1,
            u32::MAX,
            u32::MAX,
            0,
            0,
            3
        ]);
        let divisor = ArbitraryBytes::new([
            0,
            0,
            0,
            0,
            0,
            u32::MAX,
            u32::MAX,
            u32::MAX,
        ]);
        let result = dividend.rem_assign_with_quotient(&divisor);
        assert_eq!(dividend.0, [0,0,0,0,0,0,0,2]);
        assert_eq!(result.0, [0,0,0,u32::MAX,u32::MAX, u32::MAX, u32::MAX, u32::MAX]);
    }


    fn prepare_many_numbers(max_dividend_digits : u32, min_dividend_digits : u32, max_divisor_digits : u32, min_divisor_digits : u32) -> Vec<(ArbitraryBytes<5>,ArbitraryBytes<5>, u128, u128)>{
        assert!(max_dividend_digits < 5);
        assert!(min_dividend_digits <= max_dividend_digits);
        assert!(max_divisor_digits < 5);
        assert!(min_divisor_digits <= max_divisor_digits);
        let mut rng = Xoshiro256Plus::seed_from_u64(0);
        let mut res = Vec::new();
        for _i in 0..1000000 {
            let dx = rng.next_u32() % (max_dividend_digits + 1 - min_dividend_digits) + min_dividend_digits;
            let dy = rng.next_u32() % (max_divisor_digits + 1 -  min_divisor_digits) +  min_divisor_digits;
            let ds = dx.min(dy);
            let dl = dx.max(dy);
            let dividendx = [
                0,
                if dl >= 4 { rng.next_u32() } else { 0 },
                if dl >= 3 { rng.next_u32() } else { 0 },
                if dl >= 2 { rng.next_u32() } else { 0 },
                if dl >= 1 { rng.next_u32() } else { 0 },
            ];
            let divisorx = [
                0,
                if ds >= 4 { rng.next_u32() } else { 0 },
                if ds >= 3 { rng.next_u32() } else { 0 },
                if ds >= 2 { rng.next_u32() } else { 0 },
                if ds >= 1 { rng.next_u32() } else { 0 },
            ];
            let needs_swap = ds == dl && dividendx[5-ds as usize] < divisorx[5-ds as usize];
            let dividend = ArbitraryBytes::new(if needs_swap {divisorx} else {dividendx});
            let divisor  = ArbitraryBytes::new(if needs_swap {dividendx} else {divisorx});
            assert!(dividend.ge(&divisor));

            let td = 
                ((dividend.0[1] as u128)<<96)
              + ((dividend.0[2] as u128)<<64)
              + ((dividend.0[3] as u128)<<32)
              + (dividend.0[4] as u128);
            let tn = 
                ((divisor.0[1] as u128)<<96)
              + ((divisor.0[2] as u128)<<64)
              + ((divisor.0[3] as u128)<<32)
              + (divisor.0[4] as u128);


            res.push((dividend, divisor, td/tn, td%tn));
        }
        res
    }

    /// Just tests a bunch of procedurally generated numbers (all within u128 for easy comparison.)
    #[test]
    fn rem_assign_with_quotient_knuth_many_numbers_test() {
        let input = prepare_many_numbers(4,2, 4, 2);
        for (mut dividend, divisor, expected_quotient, expexted_remainder) in input {
            let quotient = dividend.rem_assign_with_quotient_knuth(&divisor);
            let remainder = dividend;
            let quotient = ((quotient.0[1] as u128)<<(96)) + ((quotient.0[2] as u128)<<64) + ((quotient.0[3] as u128)<<32) + (quotient.0[4] as u128);
            let remainder = ((remainder.0[1] as u128)<<(96)) + ((remainder.0[2] as u128)<<64) + ((remainder.0[3] as u128)<<32) + (remainder.0[4] as u128);
            assert_eq!(quotient, expected_quotient);
            assert_eq!(remainder, expexted_remainder);
        }
    }
    /// Just tests a bunch of procedurally generated numbers (all within u128 for easy comparison.)
    #[test]
    fn rem_assign_with_quotient_many_numbers_test() {
        let input = prepare_many_numbers(4,1, 4, 1);
        for (mut dividend, divisor, expected_quotient, expexted_remainder) in input {
            let quotient = dividend.rem_assign_with_quotient(&divisor);
            let remainder = dividend;
            let quotient = ((quotient.0[1] as u128)<<(96)) + ((quotient.0[2] as u128)<<64) + ((quotient.0[3] as u128)<<32) + (quotient.0[4] as u128);
            let remainder = ((remainder.0[1] as u128)<<(96)) + ((remainder.0[2] as u128)<<64) + ((remainder.0[3] as u128)<<32) + (remainder.0[4] as u128);
            assert_eq!(quotient, expected_quotient);
            assert_eq!(remainder, expexted_remainder);
        }
    }

    #[test]
    fn rem_assign_with_quotient_u32_many_numbers_test() {
        let input = prepare_many_numbers(4,1, 1, 1);
        for (mut dividend, divisor, expected_quotient, expexted_remainder) in input {
            let quotient = dividend.rem_assign_with_quotient_u32(&divisor.0.last().unwrap());
            let remainder = dividend;
            let quotient = ((quotient.0[1] as u128)<<(96)) + ((quotient.0[2] as u128)<<64) + ((quotient.0[3] as u128)<<32) + (quotient.0[4] as u128);
            let remainder = ((remainder.0[1] as u128)<<(96)) + ((remainder.0[2] as u128)<<64) + ((remainder.0[3] as u128)<<32) + (remainder.0[4] as u128);
            assert_eq!(quotient, expected_quotient);
            assert_eq!(remainder, expexted_remainder);
        }
    }

    #[test]
    fn rem_assign_with_quotient_u32_test(){
        let mut a = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let quotient = a.rem_assign_with_quotient_u32(&0x12345);
        assert_eq!(quotient.0, [0x9A10,0xB282B7BA,0xE4948E98,0x2AE63D74,0xE6FDFF4A]);
        assert_eq!(a.0, [0,0,0,0,0x6882]);
    }

    #[test]
    fn rem_assign_with_quotient_u32_test2(){
        let mut a = ArbitraryBytes::new([0,0,0,0,0x1234]);
        let quotient = a.rem_assign_with_quotient_u32(&0x12345);
        assert_eq!(quotient.0, [0,0,0,0,0]);
        assert_eq!(a.0, [0,0,0,0,0x1234]);
    }

    #[test]
    fn div_assign_with_remainder_usize_test(){
        let mut a = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let remainder = a.div_assign_with_remainder_usize(&0x1234_usize);
        assert_eq!(a.0, [0x9A135,0x79AA8650,0xD251DC7A,0x9AA8C1F2,0x8B9729EF]);
        assert_eq!(remainder, 0x2E8);
    }

    #[test]
    fn div_assign_with_remainder_usize_test2(){
        let mut a = ArbitraryBytes::new([0,0,0,0,0x1234]);
        let remainder = a.div_assign_with_remainder_usize(&0x1235_usize);
        assert_eq!(a.0, [0,0,0,0,0]);
        assert_eq!(remainder, 0x1234);
    }

    #[cfg(target_pointer_width = "64")]
    #[test]
    fn div_assign_with_remainder_usize_test3(){
        let mut a = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let remainder = a.div_assign_with_remainder_usize(&0x123456789ab_usize);
        assert_eq!(a.0, [0,0x9A107B,0xBEC8B35A,0xEC9D3B43,0x056F803A]);
        assert_eq!(remainder, 0xD7537A4B6);
    }

    #[test]
    fn sub_assign_test() {
        let mut a = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let b = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let carry = slice_overflowing_sub_assign(&mut a.0,&b.0);
        assert!(!carry);
        assert_eq!(a.0, [0x6CA2C267,0xb414f734,0xb30ddbf2,0x35b61c9c,0x4fd97562]);
    }

    #[test]
    fn sub_assign_test2() {
        let mut a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let carry = slice_overflowing_sub_assign(&mut a.0,&b.0);
        assert!(carry);
        assert_eq!(a.0, [0x935D3D98,0x4BEB08CB,0x4CF2240D,0xCA49E363,0xB0268A9E]);
    }

    #[test]
    fn add_assign_test() {
        let mut a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = ArbitraryBytes::new([0xaf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let carry = slice_overflowing_add_assign(&mut a.0,&b.0);
        assert!(!carry);
        assert_eq!(a.0, [0xF1F2406D,0xB414F734,0x4134F39C,0x5A1EC98D,0xA7753586]);
    }
    #[test]
    fn add_assign_test2() {
        let mut a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = ArbitraryBytes::new([0xbf4a816a,0xb414f734,0x7a2167c7,0x47ea7314,0xfba75574]);
        let carry = slice_overflowing_add_assign(&mut a.0,&b.0);
        assert!(carry);
        assert_eq!(a.0, [0x01F2406D,0xB414F734,0x4134F39C,0x5A1EC98D,0xA7753586]);
    }

    #[test]
    fn shift_left_test() {
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = a.shift_left(7);
        assert_eq!(b.0,[0x21, 0x53DF817F,0xFFFFFFE3, 0x89C5EA89, 0x1A2B3C55, 0xE6F00900]);
    }
    
    #[test]
    fn shift_right_test() {
        let a = ArbitraryBytes::new([0x21, 0x53DF817F,0xFFFFFFE3, 0x89C5EA89, 0x1A2B3C55, 0xE6F00900]);
        let b = a.shift_right(7);
        assert_eq!(b.0,[0, 0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
    }

    #[test]
    fn get_digit_from_right_test(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        assert_eq!(a.get_digit_from_right(3), 0xffffffff);
    }

    #[test]
    fn set_digit_from_right_test(){
        let mut a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        a.set_digit_from_right(0xdeadbeef, 4);
        assert_eq!(a.0[0], 0xdeadbeef);
    }

    #[test]
    fn find_first_nonzero_digit_test() {
        let a = ArbitraryBytes::new([0,0,0,0x12345678,0xabcde012]);
        assert_eq!(a.find_first_nonzero_digit(),3);
    }

    #[test]
    fn mul_arbitrary_test(){
        let a = ArbitraryBytes::new([0,0,0,0x47ea7314,0xfba75574]);
        let b = ArbitraryBytes::new([0,0,0,0x12345678,0xabcde012]);
        let a_big = (0x47ea7314_u128 << 32) | 0xfba75574u128;
        let b_big = (0x12345678_u128 << 32) | 0xabcde012u128;
        let c_big = a_big*b_big;
        let c = (&a * &b).unwrap();
        assert_eq!(c_big & 0xffff_ffff, c.0[4] as u128 );
        assert_eq!((c_big >> 32 ) & 0xffff_ffff, c.0[3] as u128);
        assert_eq!((c_big >> 64 ) & 0xffff_ffff, c.0[2] as u128);
        assert_eq!((c_big >> 96 ) & 0xffff_ffff, c.0[1] as u128);
        assert_eq!(0, c.0[0]);
    }
    #[test]
    fn mul_arbitrary_test_2(){
        let a = ArbitraryBytes::new([0x2763ac9f,0xd1ae1f38,0x1753a5c7,0x47ea7314,0xfba75574]);
        let b = ArbitraryBytes::new([0,0,0,0,2]);
        let c = (&a * &b).unwrap();
        assert_eq!(0x4EC7593F, c.0[0]);
        assert_eq!(0xA35C3E70, c.0[1]);
        assert_eq!(2*0x1753a5c7, c.0[2]);
        assert_eq!(0x8fd4e629, c.0[3]);
        assert_eq!(0xf74eaae8, c.0[4]);
    }
    #[test]
    fn mul_arbitrary_test_3(){
        let a = ArbitraryBytes::new([0,0,0,0,2]);
        let b = ArbitraryBytes::new([0x2763ac9f,0xd1ae1f38,0x1753a5c7,0x47ea7314,0xfba75574]);
        let c = (&a * &b).unwrap();
        assert_eq!(0x4EC7593F, c.0[0]);
        assert_eq!(0xA35C3E70, c.0[1]);
        assert_eq!(2*0x1753a5c7, c.0[2]);
        assert_eq!(0x8fd4e629, c.0[3]);
        assert_eq!(0xf74eaae8, c.0[4]);
    }
    #[test]
    fn mul_arbitrary_test_4(){
        let a = ArbitraryBytes::new([0,0,0,0,8]);
        let b = ArbitraryBytes::new([0x2763ac9f,0xd1ae1f38,0x1753a5c7,0x47ea7314,0xfba75574]);
        let c = &a * &b;
        assert!(c.is_none())
    }
    #[test]
    fn mul_arbitrary_test_5(){
        let a = ArbitraryBytes::new([0,0,0,1,0]);
        let b = ArbitraryBytes::new([0x2763ac9f,0xd1ae1f38,0x1753a5c7,0x47ea7314,0xfba75574]);
        let c = &a * &b;
        assert!(c.is_none())
    }
    #[test]
    fn mul_arbitrary_test_6(){
        let a = ArbitraryBytes::new([0,0,0,1,1]);
        let b = ArbitraryBytes::new([0,0xffffffff,0x1753a5c7,0x47ea7314,0xfba75574]);
        let c = &a * &b;
        assert!(c.is_none())
    }

    #[test]
    fn mul_with_u32_test(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = 3u32;
        let product = a*b;
        assert_eq!(product.unwrap().0, [0xC7F73D08,0xFFFFFFFF,0x553AA37F,0x369D036A,0x0369A036])
    }
    #[test]
    fn mul_with_u32_test2(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = 4u32;
        let product = a*b;
        assert!(product.is_none())
    }
    #[test]
    fn mul_with_usize_test_working(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = 3usize;
        let product = a*b;
        assert_eq!(product.unwrap().0, [0xC7F73D08,0xFFFFFFFF,0x553AA37F,0x369D036A,0x0369A036])
    }
    #[test]
    fn mul_with_usize_test_overflow(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = 4usize;
        let product = a*b;
        assert!(product.is_none())
    }
    #[cfg(target_pointer_width = "64")]
    #[test]
    fn mul_with_usize_test_64bit_works(){
        let a = ArbitraryBytes::new([0,0,0xc7138bd5,0x12345678,0xabcde012]);
        let b = 0x123456789ausize;
        let product = a*b;
        assert_eq!(product.unwrap().0, [0xE,0x28130BBC,0x7442D257,0x1FEDDF10,0xC8ED3AD4])
    }
    #[cfg(target_pointer_width = "64")]
    #[test]
    fn mul_with_usize_test_64bit_overflow(){
        let a = ArbitraryBytes::new([0,0x1,0xc7138bd5,0x12345678,0xabcde012]);
        let b = usize::MAX;
        let product = a*b;
        assert!(product.is_none())
    }
    #[test]
    fn try_into_u32_test(){
        let a = ArbitraryBytes::new([0,0,0,0,0xabcde012]);
        let b : u32 = (&a).try_into().unwrap();
        assert_eq!(b, 0xabcde012);
    }
    #[test]
    fn try_into_u32_test_overflows(){
        let a = ArbitraryBytes::new([0,0,0,0x1,0xabcde012]);
        let b : Result<u32,_> = (&a).try_into();
        assert!(b.is_err())
    }
    #[test]
    fn try_into_usize_test(){
        let a = ArbitraryBytes::new([0,0,0,0,0xe012]);
        let b : usize = (&a).try_into().unwrap();
        assert_eq!(b, 0xe012);
    }
    #[test]
    fn try_into_usize_test_overflows(){
        let a = ArbitraryBytes::new([0,0,0x1,0,0xabcde012]);
        let b : Result<usize,_> = (&a).try_into();
        assert!(b.is_err())
    }
    #[cfg(target_pointer_width = "64")]
    #[test]
    fn try_into_usize_test_on_64_bits(){
        let a = ArbitraryBytes::new([0,0,0,0x54a,0xabcde012]);
        let b : usize= (&a).try_into().unwrap();
        assert_eq!(b, 0x54aabcde012);
    }
    #[cfg(target_pointer_width = "32")]
    #[test]
    fn try_into_usize_test_on_64_bits(){
        let a = ArbitraryBytes::new([0,0,0,0x54a,0xabcde012]);
        let b : Result<usize,_> = (&a).try_into();
        assert!(b.is_err())
    }
    #[test]
    fn pad_with_a_zero_5(){
        let a = ArbitraryBytes::new([0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = a.pad_with_a_zero();
        assert_eq!(*b.0.first().unwrap(),0);
        assert_eq!(b.0[1..], a.0);
    }
    #[test]
    fn pad_with_a_zero_8(){
        let a = ArbitraryBytes::new([0x4631abcd,0x35a40be4,0x074c4d0a,0x42a7bf02,0xffffffff,0xc7138bd5,0x12345678,0xabcde012]);
        let b = a.pad_with_a_zero();
        assert_eq!(*b.0.first().unwrap(),0);
        assert_eq!(b.0[1..], a.0);
    }
    #[cfg(target_pointer_width = "64")]
    #[test]
    fn from_usize_5_large(){
        let a : ArbitraryBytes<5> = (&0x7246abcd705aef_usize).into();
        assert_eq!(a.0[4], 0xcd705aef);
        assert_eq!(a.0[3], 0x007246ab);
        assert!(a.0[..3].iter().all(|x| *x==0));
    }
    #[test]
    fn from_usize_5(){
        let a : ArbitraryBytes<5> = (&0xcd705aef_usize).into();
        assert_eq!(a.0[4], 0xcd705aef);
        assert!(a.0[..4].iter().all(|x| *x==0));
    }
    #[cfg(target_pointer_width = "64")]
    #[test]
    fn from_usize_8_large(){
        let a : ArbitraryBytes<8> = (&0x7246abcd705aef_usize).into();
        assert_eq!(a.0[7], 0xcd705aef);
        assert_eq!(a.0[6], 0x007246ab);
        assert!(a.0[..6].iter().all(|x| *x==0));
    }
    #[test]
    fn from_usize_8(){
        let a : ArbitraryBytes<8> = (&0xcd705aef_usize).into();
        assert_eq!(a.0[7], 0xcd705aef);
        assert!(a.0[..7].iter().all(|x| *x==0));
    }
}