big_num_math/

lib.rs

//! Allows to compute on big integer numbers. No negative numbers support.

type RawRow = Vec<u8>;
type Row = PlacesRow;

#[macro_use]
mod macroinstruction;
mod nth_root;

pub use nth_root::root;

/// `PlacesRow` represents row of decimal places starting at ones (`0` index).
#[derive(Clone, PartialEq, Debug)]
pub struct PlacesRow {
    row: RawRow,
}

use core::{cmp::Ordering, ops::Deref};
impl Deref for PlacesRow {
    type Target = [u8];

    /// View into internal storage.
    fn deref(&self) -> &[u8] {
        self.row.as_slice()
    }
}

impl PlacesRow {
    /// Strong ctor for usage with prebuilded raw places row.
    ///
    /// Only ones are allowed in `row`.
    /// Places in `row` have to be ordered from ones over tens, hundreds, … to highest place;
    /// from 0-index to last-index.
    ///
    /// Leading zeros are truncated. Does not change capacity.
    ///
    /// Returns `PlacesRow` or index where place > `9` was
    /// encountered. `None` for 0-len `row`.
    pub fn new_from_vec(mut row: Vec<u8>) -> Result<Self, Option<usize>> {
        if row.len() == 0 {
            return Err(None);
        }

        let row_len = len_without_leading_raw(&row, 0, 1);

        let mut ix = 0;
        while ix < row_len {
            if row[ix] > 9 {
                return Err(Some(ix));
            }

            ix += 1;
        }

        row.truncate(row_len);
        Ok(Row { row })
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_u8(num: u8) -> Self {
        new_from_num!(num)
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_u16(num: u16) -> Self {
        new_from_num!(num)
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_u32(num: u32) -> Self {
        new_from_num!(num)
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_u64(num: u64) -> Self {
        new_from_num!(num)
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_u128(num: u128) -> Self {
        new_from_num!(num)
    }

    /// Handy ctor for usage with primitive numeric data type.
    pub fn new_from_usize(num: usize) -> Self {
        new_from_num!(num)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_u8(&self) -> Option<u8> {
        try_into_num!(&self.row, u8, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_u16(&self) -> Option<u16> {
        try_into_num!(&self.row, u16, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_u32(&self) -> Option<u32> {
        try_into_num!(&self.row, u32, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_u64(&self) -> Option<u64> {
        try_into_num!(&self.row, u64, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_u128(&self) -> Option<u128> {
        try_into_num!(&self.row, u128, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_usize(&self) -> Option<usize> {
        try_into_num!(&self.row, usize, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_i8(&self) -> Option<i8> {
        try_into_num!(&self.row, i8, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_i16(&self) -> Option<i16> {
        try_into_num!(&self.row, i16, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_i32(&self) -> Option<i32> {
        try_into_num!(&self.row, i32, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_i64(&self) -> Option<i64> {
        try_into_num!(&self.row, i64, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_i128(&self) -> Option<i128> {
        try_into_num!(&self.row, i128, &mut 0)
    }

    /// Convertor method.
    ///
    /// Returns `None` if `PlacesRow` cannot fit into target type.
    pub fn try_into_isize(&self) -> Option<isize> {
        try_into_num!(&self.row, isize, &mut 0)
    }

    /// Handy ctor for usage with long numbers.
    ///
    /// Only digits are allowed in `s`. Leading zeros are omitted.
    ///
    /// Returns `PlacesRow` or index in `s` where uncovertable `char` was
    /// encountered. `None` for empty string.
    pub fn new_from_str(s: &str) -> Result<Self, Option<usize>> {
        let row = new_from_str_raw(s);
        if let Ok(row) = row {
            Ok(Self { row })
        } else {
            Err(row.unwrap_err())
        }
    }

    /// Returns `String` representation.
    pub fn to_number(&self) -> String {
        let row = &self.row;
        let len = row.len();
        let mut number = String::new();
        number.reserve_exact(len);
        for i in row.iter().rev() {
            let digit = to_digit(*i);
            number.push(digit);
        }

        number
    }

    /// `true` if and only if `PlacesRow` is _unity_ value.
    pub fn is_unity(&self) -> bool {
        is_unity_raw(&self.row)
    }

    /// `true` if and only if `PlacesRow` is _nought_ value.
    pub fn is_nought(&self) -> bool {
        is_nought_raw(&self.row)
    }

    /// Returns unity `PlacesRow`.
    pub fn unity() -> PlacesRow {
        Row { row: unity_raw() }
    }

    /// Returns nought `PlacesRow`.
    pub fn nought() -> PlacesRow {
        Row { row: nought_raw() }
    }

    #[deprecated(since = "2.2.0", note = "Pick `fn nought` instead.")]
    /// Returns zero `PlacesRow`.
    pub fn zero() -> PlacesRow {
        Self::nought()
    }

    /// Returns decimal places count.
    ///
    /// Check with [`DecCnt`] for detail on count properties.
    pub fn places(&self) -> usize {
        dec_pla_cnt_raw(&self.row)
    }
}

fn new_from_str_raw(mut s: &str) -> Result<RawRow, Option<usize>> {
    let s_len_orig = s.len();
    if s_len_orig == 0 {
        return Err(None);
    }

    s = s.trim_start_matches('0');
    let s_len = s.len();

    let row = if s_len == 0 {
        nought_raw()
    } else {
        let mut row = Vec::new();
        row.reserve_exact(s_len);

        let mut err_inx = s_len_orig;
        for (c, sc) in s.chars().rev().zip(row.spare_capacity_mut()) {
            err_inx -= 1;
            if c.is_ascii_digit() {
                let n = from_digit(c);
                sc.write(n);
            } else {
                return Err(Some(err_inx));
            }
        }

        unsafe { row.set_len(s_len) }
        row
    };

    Ok(row)
}

fn truncate_leading_raw(row: &mut RawRow, lead: u8, ex_to: usize) {
    let new_len = len_without_leading_raw(row, lead, ex_to);
    row.truncate(new_len);
}

fn len_without_leading_raw(row: &[u8], lead: u8, ex_to: usize) -> usize {
    let mut row_len = row.len();
    while row_len > ex_to {
        row_len -= 1;
        if lead != row[row_len] {
            row_len += 1;
            break;
        }
    }

    row_len
}

fn unity_raw() -> RawRow {
    vec![1; 1]
}

fn nought_raw() -> RawRow {
    vec![0; 1]
}

const fn is_unity_raw(row: &[u8]) -> bool {
    is_one_raw(row, 1)
}

const fn is_nought_raw(row: &[u8]) -> bool {
    is_one_raw(row, 0)
}

const fn is_one_raw(row: &[u8], one: u8) -> bool {
    row.len() == 1 && row[0] == one
}

fn from_digit(c: char) -> u8 {
    match c {
        '0' => 0,
        '1' => 1,
        '2' => 2,
        '3' => 3,
        '4' => 4,
        '5' => 5,
        '6' => 6,
        '7' => 7,
        '8' => 8,
        '9' => 9,
        _ => panic!("Unsupported char `{c}` conversion."),
    }
}

fn to_digit(n: u8) -> char {
    match n {
        0 => '0',
        1 => '1',
        2 => '2',
        3 => '3',
        4 => '4',
        5 => '5',
        6 => '6',
        7 => '7',
        8 => '8',
        9 => '9',
        _ => panic!("Only number < 10 supported."),
    }
}

impl std::string::ToString for PlacesRow {
    /// Returns `String` representation.
    fn to_string(&self) -> String {
        self.to_number()
    }
}

use core::convert::From;
use std::cmp::max;
use std::time::{Duration, Instant};

impl From<u8> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: u8) -> Self {
        Self::new_from_u8(value)
    }
}

impl From<u16> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: u16) -> Self {
        Self::new_from_u16(value)
    }
}

impl From<u32> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: u32) -> Self {
        Self::new_from_u32(value)
    }
}

impl From<u64> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: u64) -> Self {
        Self::new_from_u64(value)
    }
}

impl From<u128> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: u128) -> Self {
        Self::new_from_u128(value)
    }
}

impl From<usize> for PlacesRow {
    /// Converts `value` into `PlacesRow`.
    fn from(value: usize) -> Self {
        Self::new_from_usize(value)
    }
}

/// Represents 1,000 numbers of √10 ≈ 3.16.
///
/// Check with `fn` [`ord_of_mag`].
pub const SQUARE_ROOT_TEN_COMPARATOR: &str = "3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880014690519596700153903344921657179259940659150153474113339484124085316929577090471576461044369257879062037808609941828371711548406328552999118596824564203326961604691314336128949791890266529543612676178781350061388186278580463683134952478031143769334671973819513185678403231241795402218308045872844614600253577579702828644029024407977896034543989163349222652612067792651676031048436697793756926155720500369894909469421850007358348844643882731109289109042348054235653403907274019786543725939641726001306990000955784463109626790694418336130181302894541703315807731626386395193793704654765220632063686587197822049312426053454111609356979828132452297000798883523759585328579251362964686511497675217123459559238039375625125369855194955325099947038843990336466165470647234999796132343403021857052187836676345789510732982875157945215771652139626324438399018484560935762602";

/// Order of magnitude computational variants.
#[derive(Clone, PartialEq, Debug)]
pub enum OomClass {
    /// Uses `√10` for relation.
    ///
    /// Check with [`SQUARE_ROOT_TEN_COMPARATOR`].
    Strict,
    /// Uses `5` for relation.
    Loose,
}

/// Order of magnitude variants enumeration.
#[derive(Clone, PartialEq, Debug)]
pub enum Oom {
    /// Order of magnitude is not defined for nought `PlacesRow`.
    Undefined,
    /// Precise _oom_.
    ///
    /// Check with `Approx(usize)` variant.
    Precise(usize),
    /// Approximated _oom_ is result of operation on `PlacesRow` requiring
    /// greater precision than provided by `SQUARE_ROOT_TEN_COMPARATOR`.
    ///
    /// Check with `fn` [`ord_of_mag`].
    Approx(usize),
}

/// Computes order of magnitude for `num` and `class`.
///
/// OOM is defined for number _n_ as follows:
///
/// n = u ⋅ 10ⁱ, v ÷10 ≤ u < v, v = √10 ∨ v = 5
///
/// Then _i_ is order of magnitude of such number.
///
/// `Strict` variant evaluation is precise up to 1,000 numbers of [`SQUARE_ROOT_TEN_COMPARATOR`].
/// Any `num` requiring higher precision is considered to be of higher order. That
/// means its order of magnitude is arranged equal to its decimal places count
/// and is reported as `Oom::Approx(usize)`.
///
/// Returns `Oom` enumeration.
pub fn ord_of_mag(num: &PlacesRow, class: OomClass) -> Oom {
    let row = &num.row;
    if is_nought_raw(row) {
        return Oom::Undefined;
    }

    let cmp = match class {
        OomClass::Strict => SQUARE_ROOT_TEN_COMPARATOR.chars().map(from_digit).collect(),
        OomClass::Loose => vec![5],
    };

    let row_len = row.len();
    let cmp_len = cmp.len();

    let mut row_ix = row_len;
    let mut cmp_ix = 0;

    let mut num_less = None;

    loop {
        if row_ix == 0 || cmp_ix == cmp_len {
            break;
        }

        row_ix = row_ix - 1;

        if row[row_ix] < cmp[cmp_ix] {
            num_less = Some(true);
            break;
        }

        if row[row_ix] > cmp[cmp_ix] {
            num_less = Some(false);
            break;
        }

        cmp_ix = cmp_ix + 1;
    }

    let (num_less, precise) = if let Some(l) = num_less {
        (l, true)
    } else {
        let ord = row_len.cmp(&cmp_len);
        match ord {
            Ordering::Greater => (false, class == OomClass::Loose),
            Ordering::Less => (true, true),
            _ => (false, true),
        }
    };

    let oom = if num_less { row_len - 1 } else { row_len };

    match precise {
        true => Oom::Precise(oom),
        false => Oom::Approx(oom),
    }
}

/// Relation enumeration.
///
/// ```
/// use big_num_math::{rel, PlacesRow, Rel, DecCnt};
/// let num_1 = PlacesRow::new_from_usize(100);
/// let num_2 = PlacesRow::new_from_usize(101);
/// let num_3 = PlacesRow::new_from_usize(1);
///
/// assert_eq!(Rel::Lesser(None), rel(&num_1, &num_2));
/// let cnt_1_cnt_2_dif: DecCnt = (1,3,2);
/// assert_eq!(Rel::Lesser(Some(cnt_1_cnt_2_dif)), rel(&num_3, &num_1));
/// ```
#[derive(Debug, PartialEq, Clone)]
pub enum Rel {
    /// Greater than comparand. Holds information about decimal difference, if there is some.
    Greater(Option<DecCnt>),
    /// Equal to comparand.
    Equal,
    /// Lesser than comparand. Holds information about decimal difference, if there is some.
    Lesser(Option<DecCnt>),
}

/// Checks relation of `num` to `comparand`.
///
/// Returns `Rel` relation.
pub fn rel(num: &PlacesRow, comparand: &PlacesRow) -> Rel {
    let r1 = &num.row;
    let r2 = &comparand.row;

    rel_raw(r1, r2)
}

const fn rel_raw(r1: &[u8], r2: &[u8]) -> Rel {
    match rel_dec_raw(r1, r2) {
        RelDec::Greater(c) => Rel::Greater(Some(c)),
        RelDec::Lesser(c) => Rel::Lesser(Some(c)),
        RelDec::Equal(mut inx) => {
            let mut rel = Rel::Equal;

            while inx > 0 {
                inx -= 1;
                if r1[inx] > r2[inx] {
                    rel = Rel::Greater(None);
                    break;
                } else if r1[inx] < r2[inx] {
                    rel = Rel::Lesser(None);
                    break;
                }
            }

            rel
        }
    }
}

/// Decimal places count.
///
/// Tuple fields describe places count and are defined as follows.
/// |Name|Meaning    |
/// |:--:|:--------- |
/// |0   |number     |
/// |1   |comparand  |
/// |2   |difference |
///
/// Count relates to power of ten as table evinces.
/// |  Count |    Relation                  |
/// |:------:|:------------:                |
/// | 0      | number < 10⁰ ⇒ number = 0    |
/// | 1      | number < 10¹ ∧ number ≥ 10⁰  |
/// | 2      | number < 10² ∧ number ≥ 10¹  |
/// | ⋮      |   ⋮                          |
/// | n      | number < 10ⁿ ∧ number ≥ 10ⁿ⁻¹|
pub type DecCnt = (usize, usize, usize);

/// Decimal relation enumeration.
///
/// Expresses relation of numbers in decimal places count.
///
/// ```
/// use big_num_math::{rel_dec, PlacesRow, RelDec, DecCnt};
/// let num_1 = PlacesRow::new_from_usize(333);
/// let num_2 = PlacesRow::new_from_usize(777);
/// let num_3 = PlacesRow::new_from_usize(1);
///
/// assert_eq!(RelDec::Equal(3), rel_dec(&num_1, &num_2));
/// let cnt_1_cnt_2_dif: DecCnt = (1,3,2);
/// assert_eq!(RelDec::Lesser(cnt_1_cnt_2_dif), rel_dec(&num_3, &num_1));
/// ```
#[derive(Debug, PartialEq, Clone)]
pub enum RelDec {
    /// Count greater than comparand has. Holds information about respective counts.
    Greater(DecCnt),
    /// Count equal to comparand count. Holds count information.
    Equal(usize),
    /// Count lesser than comparand has. Holds information about respective counts.
    Lesser(DecCnt),
}

/// Compares decimal places count of `num` and `comparand`.
///
/// Beware of nought values comparison. `fn deref` allows to view internal
/// storage and for nought it has some length, exactly 1, but count would be `0` exactly.
///
/// Returns `RelDec` relation.
pub fn rel_dec(num: &PlacesRow, comparand: &PlacesRow) -> RelDec {
    let r1 = &num.row;
    let r2 = &comparand.row;

    rel_dec_raw(r1, r2)
}

// ⟺ no leading zeros
// num.len() > comparand.len() ⇒ num > comparand
// num.len() < comparand.len() ⇒ num < comparand
// num.len() = comparand.len() ⇒ num ⪒ comparand
const fn rel_dec_raw(r1: &[u8], r2: &[u8]) -> RelDec {
    let r1_cnt = dec_pla_cnt_raw(r1);
    let r2_cnt = dec_pla_cnt_raw(r2);

    if r1_cnt == r2_cnt {
        return RelDec::Equal(r1_cnt);
    }

    let mut cnts = (r1_cnt, r2_cnt, 0);

    return if r1_cnt > r2_cnt {
        cnts.2 = r1_cnt - r2_cnt;
        RelDec::Greater(cnts)
    } else {
        cnts.2 = r2_cnt - r1_cnt;
        RelDec::Lesser(cnts)
    };
}

const fn dec_pla_cnt_raw(r: &[u8]) -> usize {
    if is_nought_raw(r) {
        0
    } else {
        r.len()
    }
}

/// Computes `addend1` and `addend2` sum.
///
/// Returns `PlacesRow` with result.
pub fn add(addend1: &PlacesRow, addend2: &PlacesRow) -> PlacesRow {
    let r1 = &addend1.row;
    let r2 = &addend2.row;

    let max_len = max(r1.len(), r2.len());

    // avoids repetitive reallocations
    // +1 stands for contigent new place
    let mut sum = Vec::new();
    sum.reserve_exact(max_len + 1);

    #[cfg(test)]
    let sum_ptr = sum.as_ptr();

    addition_two(r1, r2, &mut sum);

    #[cfg(test)]
    assert!(sum_ptr == sum.as_ptr());

    Row { row: sum }
}

/// Computes `minuend` and `subtrahend` difference.
///
/// Returns difference `PlacesRow` if `minuend` ≥ `subtrahend`, `None` otherwise.
pub fn sub(minuend: &PlacesRow, subtrahend: &PlacesRow) -> Option<PlacesRow> {
    let minuend = &minuend.row;
    let subtrahend = &subtrahend.row;

    match rel_raw(minuend, subtrahend) {
        Rel::Equal => return Some(Row::nought()),
        Rel::Lesser(_) => return None,
        _ => {}
    };

    let mut minuend = minuend.clone();
    _ = subtraction_arithmetical(&mut minuend, &subtrahend);

    minuend.shrink_to_fit();

    Some(Row { row: minuend })
}

/// Computes `factor1` and `factor2` product.
///
/// Returns `PlacesRow` with result.
pub fn mul(factor1: &PlacesRow, factor2: &PlacesRow) -> PlacesRow {
    let factor1 = &factor1.row;
    let factor2 = &factor2.row;

    let row = mul_raw(factor1, factor2, true);
    PlacesRow { row }
}

fn mul_raw(factor1: &[u8], factor2: &[u8], shrink: bool) -> RawRow {
    if let Some(row) = mul_shortcut(factor1, factor2) {
        row
    } else {
        let mut row = multiplication(factor1, factor2);

        if shrink {
            row.shrink_to_fit();
        }

        row
    }
}

// x ⋅0 = 0
// 0 ⋅x = 0
//
// 1 ⋅x = x
// x ⋅1 = x
fn mul_shortcut(factor1: &[u8], factor2: &[u8]) -> Option<RawRow> {
    if is_nought_raw(factor1) || is_nought_raw(factor2) {
        Some(nought_raw())
    } else if is_unity_raw(factor1) {
        Some(factor2.to_vec())
    } else if is_unity_raw(factor2) {
        Some(factor1.to_vec())
    } else {
        None
    }
}

/// Computes `power` of `base`.
///
/// Returns `PlacesRow` with result.
pub fn pow(base: &PlacesRow, power: u16) -> PlacesRow {
    let base = &base.row;

    let row = pow_raw(base, power, true);
    Row { row }
}

fn pow_raw(base: &RawRow, pow: u16, shrink: bool) -> RawRow {
    if let Some(pow) = pow_shortcut(base, pow) {
        return pow;
    }

    let mut pow = power(base, pow);
    if shrink {
        pow.shrink_to_fit();
    }

    pow
}

// x⁰ = 1
// x¹ = x
// 0ⁿ = 0 n∊ℕ﹥₀
// 1ⁿ = 1 n∊ℕ₀
fn pow_shortcut(base: &[u8], pow: u16) -> Option<RawRow> {
    if pow == 0 {
        Some(unity_raw())
    } else if pow == 1 {
        Some(base.to_vec())
    } else if is_nought_raw(base) {
        Some(nought_raw())
    } else if is_unity_raw(base) {
        Some(unity_raw())
    } else {
        None
    }
}

/// Computes `dividend` and `divisor` ratio and remainder.
///
/// Returns tuple with `PlacesRow` ratio and `PlacesRow` remainder in order or `None` when `divisor` is nought.
pub fn divrem(dividend: &PlacesRow, divisor: &PlacesRow) -> Option<(PlacesRow, PlacesRow)> {
    let dividend = &dividend.row;
    let divisor = &divisor.row;

    match divrem_shortcut(dividend, divisor) {
        Some(res) => return res,
        None => {}
    }

    let remratio = division(
        &dividend,
        &divisor,
        #[cfg(test)]
        &mut vec![],
    );

    let mut rem = remratio.0;
    rem.shrink_to_fit();

    Some((Row { row: remratio.1 }, Row { row: rem }))
}

// x ÷0, illegal
// x ÷1 = x
// a ÷b = 0Ra, a < b
fn divrem_shortcut(dividend: &RawRow, divisor: &RawRow) -> Option<Option<(Row, Row)>> {
    if is_nought_raw(divisor) {
        return Some(None);
    }

    let end_clone = || Row {
        row: dividend.clone(),
    };

    let shortcut = if is_unity_raw(divisor) {
        (end_clone(), Row::nought())
    } else {
        match rel_raw(dividend, divisor) {
            Rel::Lesser(_) => (Row::nought(), end_clone()),
            _ => return None,
        }
    };

    Some(Some(shortcut))
}

#[cfg(test)]
use tests_of_units::prime_ck::{PrimeCkEscCode, PrimeCkTestGauges};

/// Examines `num` primality.
///
/// Unity is not considered to be prime number.
///
/// Computation is intemperately time consuming on large numbers, especially large prime numbers, or
/// generally on numbers having large divisor only.
///
/// Optionally, allows for time-limited computation. Early interruption can be insubstantially delayed
/// due nature of limit verification.
///
/// Returns `None` for computation with exhausted timeframe.
pub fn prime_ck(
    num: &PlacesRow,
    lim: Option<Duration>,
    #[cfg(test)] tg: &mut PrimeCkTestGauges,
) -> Option<bool> {
    let row = &num.row;

    {
        if is_one_raw(row, 2) || is_one_raw(row, 3) || is_one_raw(row, 5) || is_one_raw(row, 7) {
            #[cfg(test)]
            {
                tg.esc = PrimeCkEscCode::Ar;
            }
            return Some(true);
        }

        let one = row[0];
        if one % 2 == 0 || one == 5 || is_unity_raw(&row) {
            #[cfg(test)]
            {
                tg.esc = PrimeCkEscCode::Ob;
            }
            return Some(false);
        }
    }

    {
        let mut sum = nought_raw();
        let mut ix = 0;

        let len = row.len();
        while ix < len {
            addition_sum(&vec![row[ix]], &mut sum, 0);
            ix += 1;
        }

        let rem = division_dynamo(
            sum,
            &vec![3],
            #[cfg(test)]
            &mut vec![],
        )
        .0;

        if is_nought_raw(&rem) {
            #[cfg(test)]
            {
                tg.esc = PrimeCkEscCode::Dt;
            }
            return Some(false);
        }
    }

    // 1 < a ≤ b < num, num = a ⋅b = √num ⋅√num
    //  ⇒ a=b=√num ∨ a < b ⇒ a < √num ∧ b > √num
    let sqrt = heron_sqrt_raw(&row);

    #[cfg(test)]
    {
        if let Some(n) = try_into_num!(&sqrt, usize, &mut 0) {
            tg.sqrt = n
        }
    }

    // counters initial state when starting at 7
    let mut accel_cnt: [isize; 25] = [
        1,   // 3
        -1,  // 7   +2 ⋅2
        -3,  // 11  +2 ⋅2
        -4,  // 13  +2 ⋅1
        -6,  // 17  +2 ⋅2
        -7,  // 19  +2 ⋅1
        -9,  // 23  +2 ⋅2
        -12, // 29  +2 ⋅3
        -13, // 31  +2 ⋅1
        -16, // 37  +2 ⋅3
        -18, // 41  +2 ⋅2
        -19, // 43  +2 ⋅1
        -21, // 47  +2 ⋅2
        -24, // 53  +2 ⋅3
        -27, // 59  +2 ⋅3
        -28, // 61  +2 ⋅1
        -31, // 67  +2 ⋅3
        -33, // 71  +2 ⋅2
        -34, // 73  +2 ⋅1
        -37, // 79  +2 ⋅3
        -39, // 83  +2 ⋅2
        -42, // 89  +2 ⋅3
        -46, // 97  +2 ⋅4
        -48, // 101 +2 ⋅2
        -49, // 103 +2 ⋅1
    ];

    let then = Instant::now();
    let (limited, limit) = if let Some(d) = lim {
        (true, d)
    } else {
        (false, Duration::ZERO)
    };

    let increment = vec![2];
    let mut probe = vec![5];
    loop {
        if limited && limit <= then.elapsed() {
            return None;
        }

        addition_sum(&increment, &mut probe, 0);

        if let Rel::Greater(_) = rel_raw(&probe, &sqrt) {
            #[cfg(test)]
            {
                if !tg.check_starts {
                    tg.esc = PrimeCkEscCode::Pn;
                }
            }

            return Some(true);
        }

        accel_cnt[0] += 1;
        accel_cnt[1] += 1;
        accel_cnt[2] += 1;
        accel_cnt[3] += 1;
        accel_cnt[4] += 1;

        accel_cnt[5] += 1;
        accel_cnt[6] += 1;
        accel_cnt[7] += 1;
        accel_cnt[8] += 1;
        accel_cnt[9] += 1;

        accel_cnt[10] += 1;
        accel_cnt[11] += 1;
        accel_cnt[12] += 1;
        accel_cnt[13] += 1;
        accel_cnt[14] += 1;

        accel_cnt[15] += 1;
        accel_cnt[16] += 1;
        accel_cnt[17] += 1;
        accel_cnt[18] += 1;
        accel_cnt[19] += 1;

        accel_cnt[20] += 1;
        accel_cnt[21] += 1;
        accel_cnt[22] += 1;
        accel_cnt[23] += 1;
        accel_cnt[24] += 1;

        #[cfg(test)]
        {
            if tg.check_starts {
                let probe_val = try_into_num!(probe, usize, &mut 0).unwrap();
                if accel_cnt[0] == 3 {
                    tg.esc = PrimeCkEscCode::Hit_3_Start;
                    tg.peekhole = probe_val;
                }

                if probe[0] == 5 {
                    tg.esc = PrimeCkEscCode::Hit_5_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[1] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_7_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[2] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_11_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[3] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_13_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[4] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_17_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[5] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_19_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[6] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_23_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[7] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_29_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[8] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_31_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[9] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_37_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[10] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_41_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[11] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_43_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[12] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_47_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[13] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_53_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[14] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_59_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[15] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_61_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[16] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_67_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[17] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_71_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[18] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_73_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[19] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_79_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[20] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_83_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[21] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_89_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[22] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_97_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[23] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_101_Start;
                    tg.peekhole = probe_val;
                }

                if accel_cnt[24] == 0 {
                    tg.esc = PrimeCkEscCode::Hit_103_Start;
                    tg.peekhole = probe_val;
                }
            }
        }

        // probe not prime
        let mut probe_np = false;
        if accel_cnt[0] == 3 {
            accel_cnt[0] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[0] += 1;
            }
        }

        if probe[0] == 5 {
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[1] += 1;
            }
        }

        if accel_cnt[1] == 7 {
            accel_cnt[1] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[2] += 1;
            }
        }

        if accel_cnt[2] == 11 {
            accel_cnt[2] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[3] += 1;
            }
        }

        if accel_cnt[3] == 13 {
            accel_cnt[3] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[4] += 1;
            }
        }

        if accel_cnt[4] == 17 {
            accel_cnt[4] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[5] += 1;
            }
        }

        if accel_cnt[5] == 19 {
            accel_cnt[5] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[6] += 1;
            }
        }

        if accel_cnt[6] == 23 {
            accel_cnt[6] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[7] += 1;
            }
        }

        if accel_cnt[7] == 29 {
            accel_cnt[7] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[8] += 1;
            }
        }

        if accel_cnt[8] == 31 {
            accel_cnt[8] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[9] += 1;
            }
        }

        if accel_cnt[9] == 37 {
            accel_cnt[9] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[10] += 1;
            }
        }

        if accel_cnt[10] == 41 {
            accel_cnt[10] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[11] += 1;
            }
        }

        if accel_cnt[11] == 43 {
            accel_cnt[11] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[12] += 1;
            }
        }

        if accel_cnt[12] == 47 {
            accel_cnt[12] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[13] += 1;
            }
        }

        if accel_cnt[13] == 53 {
            accel_cnt[13] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[14] += 1;
            }
        }

        if accel_cnt[14] == 59 {
            accel_cnt[14] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[15] += 1;
            }
        }

        if accel_cnt[15] == 61 {
            accel_cnt[15] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[16] += 1;
            }
        }

        if accel_cnt[16] == 67 {
            accel_cnt[16] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[17] += 1;
            }
        }

        if accel_cnt[17] == 71 {
            accel_cnt[17] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[18] += 1;
            }
        }

        if accel_cnt[18] == 73 {
            accel_cnt[18] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[19] += 1;
            }
        }
        if accel_cnt[19] == 79 {
            accel_cnt[19] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[20] += 1;
            }
        }
        if accel_cnt[20] == 83 {
            accel_cnt[20] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[21] += 1;
            }
        }
        if accel_cnt[21] == 89 {
            accel_cnt[21] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[22] += 1;
            }
        }
        if accel_cnt[22] == 97 {
            accel_cnt[22] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[23] += 1;
            }
        }
        if accel_cnt[23] == 101 {
            accel_cnt[23] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[24] += 1;
            }
        }
        if accel_cnt[24] == 103 {
            accel_cnt[24] = 0;
            probe_np = true;

            #[cfg(test)]
            {
                tg.cntrs[25] += 1;
            }
        }

        if probe_np {
            continue;
        }

        let rem = division(
            row,
            &probe,
            #[cfg(test)]
            &mut vec![],
        )
        .0;

        if is_nought_raw(&rem) {
            #[cfg(test)]
            {
                if !tg.check_starts {
                    tg.esc = PrimeCkEscCode::Np;
                }
            }

            return Some(false);
        }
    }
}
/// Prime number generation result enumeration.
#[derive(Clone, PartialEq, Debug)]
pub enum PrimeGenRes<T> {
    /// All prime numbers generated variant.
    All(Vec<T>),
    /// Only maximal prime number generated variant.
    Max(T),
}

impl<T> PrimeGenRes<T> {
    /// Returns `Vec<T>` of `PrimeGenRes::All(Vec<T>)` or _panics_
    /// if not that variant.
    pub fn uproot_all(self) -> Vec<T> {
        if let PrimeGenRes::All(all) = self {
            return all;
        }

        panic!("Not `PrimeGenRes::All(_)` variant.");
    }

    /// Returns `T` of `PrimeGenRes::Max(T)` or _panics_
    /// if not that variant.
    pub fn uproot_max(self) -> T {
        if let PrimeGenRes::Max(max) = self {
            return max;
        }

        panic!("Not `PrimeGenRes::Max(_)` variant.");
    }
}

/// Helper trait for working with return type of [`pg`] and [`pg_sw`] which
/// is [`Result<PrimeGenRes, PrimeGenErr>`].
pub trait PrimeGenResAide<T> {
    /// Uproots `Vec<T>` of `PrimeGenRes::All(Vec<T>)`.
    fn uproot_all(self) -> Vec<T>;
    /// Uproots `T` of `PrimeGenRes::Max(T)`.
    fn uproot_max(self) -> T;
}

impl<T> PrimeGenResAide<T> for Result<PrimeGenRes<T>, PrimeGenErr> {
    /// Wraps call to [`PrimeGenRes::uproot_all()`].
    ///
    /// _Panics_ if not `Ok(_)` variant.
    fn uproot_all(self) -> Vec<T> {
        if let Ok(r) = self {
            return r.uproot_all();
        }

        panic!("Not `Ok(_)` variant.");
    }

    /// Wraps call to [`PrimeGenRes::uproot_max()`].
    ///
    /// _Panics_ if not `Ok(_)` variant.
    fn uproot_max(self) -> T {
        if let Ok(r) = self {
            return r.uproot_max();
        }

        panic!("Not `Ok(_)` variant.");
    }
}

/// Prime number generation error enumeration.
#[derive(Clone, PartialEq, Debug)]
pub enum PrimeGenErr {
    /// Input is greater than target type maximal size. Holds input provided.
    InputGreaterThanSizeMax(usize),
    /// Computed value cannot be cast to target type. Holds input provided, `0`, and value to be cast, `1`.
    ValueGreaterThanSizeMax(usize, usize),
    /// Aimless input for computation, like `1` for [`PrimeGenClass::Lim`].
    AimlessInput(usize),
    /// Time limit exhaustion.
    TimeframeExhaustion,
}

/// Prime number generation variants enumeration.
#[derive(Clone, PartialEq, Debug)]
pub enum PrimeGenClass {
    /// Nth prime number generation.
    Nth,
    /// Highest prime number lesser than input or equal to it generation.
    Lim,
}

/// Flexible prime number generator.
///
/// Beware, macro _returns_ [`Result<PrimeGenRes, PrimeGenErr>`]. Thus it can be directly unusable within `fn` body.
/// Check with [`PrimeGenRes`], [`PrimeGenErr`] for details.
///
/// Unity is not cosidered to be prime number.
///
/// 2 variants available:
/// - [`PrimeGenClass::Nth`] — generation runs up to nth prime number inclusively.
/// - [`PrimeGenClass::Lim`] — generation runs up to limit inclusively.
///
/// Both variants can return only number required or whole row of prime numbers.
///
/// ```
/// use big_num_math::{pg, PrimeGenClass, PrimeGenRes, PrimeGenErr, PrimeGenResAide};
/// use std::time::{Instant, Duration};
///
/// let all1 = || { pg!(11, PrimeGenClass::Nth, true, usize, None) };
/// let all2 = || { pg!(31, PrimeGenClass::Lim, true, usize, None) };
///
/// let proof: [usize; 11] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31];
///
/// let all1 = all1().uproot_all();
/// let all2 = all2().uproot_all();
///
/// assert_eq!(all1, all2);
/// assert_eq!(proof, all1.as_slice());
/// ```
///
/// In either case generation is limited by [`isize::MAX`] bytes. Expect memory reservation twice
/// amount of `$size` type byte size per one prime number. For [`PrimeGenClass::Lim`] variant expect more. Given
/// by formula `(lim ÷⌊max(1, ㏑(lim))⌋) ⋅1.15`.
///
/// Reason above implies that generating further large prime numbers can be impossible. Since direct generation of `PlaceRow`s
/// would be in-depth time demanding, this macro, sensibly, does use simpler numeric output.
///
/// Whole prime number row is generated and held, always. Since that, production
/// can require considerable amount of time and be optionally time-limited.
///
/// ```
/// use big_num_math::{pg, PrimeGenClass, PrimeGenRes, PrimeGenErr, PrimeGenResAide};
/// use std::time::{Instant, Duration};
///
/// let limit = Duration::from_secs(1);
/// let result = (|| { pg!(5_000, PrimeGenClass::Nth, false, u128, Some(limit)) })();
///
/// assert_eq!(48_611, result.uproot_max());
/// ```
///
/// When confident about outputs, type setting can speed up computation. Use `usize` or wider type in contrary case.
/// ```
/// use big_num_math::{pg, PrimeGenClass, PrimeGenRes, PrimeGenErr, PrimeGenResAide};
/// use std::time::{Instant, Duration};
///
/// let num = || { pg!(20_000, PrimeGenClass::Nth, false, u64, None) };
/// assert_eq!(224_737, num().uproot_max());
///
/// let num = || { pg!(20_000, PrimeGenClass::Nth, false, u32, None) };
/// assert_eq!(224_737, num().uproot_max());
/// ```
/// `u32` version of sample above will perform better. The gain stems from reduced data set size.
#[macro_export]
macro_rules! pg {
    ($input: expr, $pgc: expr, $all: expr, $size:tt, $lim: expr) => {{
        if 0 == $input {
            return Err(PrimeGenErr::AimlessInput(0));
        }

        #[allow(unused_comparisons)]
        if $input > $size::MAX as usize {
            return Err(PrimeGenErr::InputGreaterThanSizeMax($input));
        }

        let nth = $pgc == PrimeGenClass::Nth;

        let cap = if nth {
            $input
        } else {
            if $input == 1 {
                return Err(PrimeGenErr::AimlessInput(1));
            }

            let ln = ($input as f64).log(std::f64::consts::E);
            let divisor = ln.max(1.0).floor();
            let ratio = $input as f64 / divisor;

            (ratio * 1.15) as usize
        };

        let mut aperture = Vec::<($size, $size)>::new();
        aperture.reserve_exact(cap);

        aperture.push((2, 0));

        let then = Instant::now();
        let (limited, limit) = if let Some(d) = $lim {
            (true, d)
        } else {
            (false, Duration::ZERO)
        };

        let buff = aperture.as_mut_ptr();

        let mut len = 1;
        let mut attempt = 1;
        loop {
            attempt += 2;
            if nth {
                if len == $input {
                    break;
                }
            } else {
                if attempt > $input {
                    break;
                }
            }

            if limited && then.elapsed() >= limit {
                return Err(PrimeGenErr::TimeframeExhaustion);
            }

            let mut prime = true;

            let mut offset = 1;
            while offset < len {
                let scene = unsafe { buff.add(offset).as_mut().unwrap_unchecked() };

                offset += 1;

                let mut count = scene.1;
                count += 1;

                scene.1 = if count == scene.0 {
                    prime = false;
                    0
                } else {
                    count
                }
            }

            if prime {
                #[allow(irrefutable_let_patterns)]
                if let Ok(prime) = TryInto::<$size>::try_into(attempt) {
                    unsafe { buff.add(len).write((prime, 0)) };
                    len += 1;
                } else {
                    unsafe { aperture.set_len(len) }
                    return Err(PrimeGenErr::ValueGreaterThanSizeMax($input, attempt));
                }
            }
        }

        unsafe { aperture.set_len(len) }

        if $all {
            let mut all = Vec::<$size>::new();
            all.reserve_exact(len);

            let all_buff = all.as_mut_ptr();
            let mut ix = 0;
            while ix < len {
                unsafe {
                    let scene = buff.add(ix).as_ref().unwrap_unchecked();
                    all_buff.add(ix).write(scene.0)
                }
                ix += 1;
            }

            unsafe { all.set_len(len) }

            Ok(PrimeGenRes::All(all))
        } else {
            Ok(PrimeGenRes::Max(aperture[len - 1].0))
        }
    }};
}

/// Memory economic version of [`pg`] macro.
///
/// Since `pg_sw`, space wise prime generator, uses less space, it allows
/// to generate larger prime numbers compared to [`pg`].
///
/// Memory demands are reduced by one half. [`pg`] is considered to be time wise implementation.
///
/// In contrary to [`pg`], this macro cannot significantly gain from proper target type choice.
///
/// Check with [`pg`] for guidelines.
#[macro_export]
macro_rules! pg_sw {
    ($input: expr, $pgc: expr, $all: expr, $size:tt, $lim: expr) => {{
        if 0 == $input {
            return Err(PrimeGenErr::AimlessInput(0));
        }

        #[allow(unused_comparisons)]
        if $input > ($size::MAX as usize) {
            return Err(PrimeGenErr::InputGreaterThanSizeMax($input));
        }

        let nth = $pgc == PrimeGenClass::Nth;

        let cap = if nth {
            $input
        } else {
            if $input == 1 {
                return Err(PrimeGenErr::AimlessInput(1));
            }

            let ln = ($input as f64).log(std::f64::consts::E);
            let divisor = ln.max(1.0).floor();
            let ratio = $input as f64 / divisor;

            (ratio * 1.15) as usize
        };

        let mut aperture = Vec::<$size>::new();
        aperture.reserve_exact(cap);

        aperture.push(2);

        let then = Instant::now();
        let (limited, limit) = if let Some(d) = $lim {
            (true, d)
        } else {
            (false, Duration::ZERO)
        };

        let buff = aperture.as_mut_ptr();

        let mut len = 1;
        let mut attempt = 1;
        'gen: loop {
            attempt += 2;
            if nth {
                if len == $input {
                    break;
                }
            } else {
                if attempt > $input {
                    break;
                }
            }

            if limited && then.elapsed() >= limit {
                return Err(PrimeGenErr::TimeframeExhaustion);
            }

            let mut rix = 1;
            #[allow(unused_labels)]
            'ver: while rix < len {
                let scene = unsafe { buff.add(rix).read() };
                rix += 1;

                if attempt % scene as usize == 0 {
                    continue 'gen;
                }
            }

            #[allow(irrefutable_let_patterns)]
            if let Ok(prime) = TryInto::<$size>::try_into(attempt) {
                unsafe { buff.add(len).write(prime) };
                len += 1;
            } else {
                unsafe { aperture.set_len(len) };
                return Err(PrimeGenErr::ValueGreaterThanSizeMax($input, attempt));
            }
        }

        unsafe { aperture.set_len(len) }

        if $all {
            Ok(PrimeGenRes::All(aperture))
        } else {
            Ok(PrimeGenRes::Max(aperture[len - 1]))
        }
    }};
}

/// Computes integer square root of `num`.
///
/// Returns `PlacesRow` with result.
///
/// Uses Heron's method.
pub fn heron_sqrt(num: &PlacesRow) -> PlacesRow {
    let row = heron_sqrt_raw(&num.row);
    PlacesRow { row }
}

fn heron_sqrt_raw(row: &[u8]) -> RawRow {
    if is_unity_raw(&row) || is_nought_raw(&row) {
        return row.to_vec();
    }

    let two = &vec![2];
    let mut cur = division(
        row,
        two,
        #[cfg(test)]
        &mut vec![],
    )
    .1;

    loop {
        let mut rat = division(
            &row,
            &cur,
            #[cfg(test)]
            &mut vec![],
        )
        .1;

        addition_sum(&cur, &mut rat, 0);
        let nex = division_dynamo(
            rat,
            &two,
            #[cfg(test)]
            &mut vec![],
        )
        .1;

        if let Rel::Lesser(_) = rel_raw(&nex, &cur) {
            cur = nex;
        } else {
            break;
        }
    }

    cur
}

#[cfg(test)]
use tests_of_units::division::DivRemGrade;

fn division(
    dividend: &[u8],
    divisor: &[u8],
    #[cfg(test)] codes: &mut Vec<DivRemGrade>,
) -> (RawRow, RawRow) {
    let dividend = dividend.to_vec();
    division_dynamo(
        dividend,
        divisor,
        #[cfg(test)]
        codes,
    )
}

fn division_dynamo(
    mut end: Vec<u8>,
    sor: &[u8],
    #[cfg(test)] codes: &mut Vec<DivRemGrade>,
) -> (RawRow, RawRow) {
    let mut end_len = end.len();
    let sor_len = sor.len();

    #[cfg(test)]
    assert_eq!(false, is_nought_raw(sor));

    if end_len < sor_len {
        #[cfg(test)]
        codes.push(DivRemGrade::DLBPI);
        return (end, nought_raw());
    }

    let mut ratio = Vec::with_capacity(50);
    let mut start_ix = dividend_start(&end, sor);

    'div: loop {
        let (rat, rem_len) = subtraction_divisional(&mut end[start_ix..end_len], sor);

        #[cfg(test)]
        assert_eq!(true, rat.len() == 1);

        ratio.insert(0, rat[0]);

        end_len = start_ix + rem_len;

        if rem_len == 0 && end_len > 0 {
            // place index
            let mut pix = end_len;

            while pix > 0 {
                pix -= 1;
                if end[pix] != 0 {
                    pix += 1;
                    break;
                }
            }

            let places = end_len - pix;
            if places > 0 {
                add_places(&mut ratio, places);
                end_len -= places;
            }

            #[cfg(test)]
            {
                let c = if end_len == 0 {
                    DivRemGrade::DFVD
                } else if places > 0 {
                    DivRemGrade::DPVD
                } else {
                    DivRemGrade::NDVD
                };

                codes.push(c);
            }
        }

        if end_len == 0 {
            #[cfg(test)]
            codes.push(DivRemGrade::DEXH);

            break 'div;
        }

        let undivided_places = end_len - rem_len;
        if end_len < sor_len {
            if start_ix > 0 {
                #[cfg(test)]
                codes.push(DivRemGrade::RVD);

                add_places(&mut ratio, undivided_places);
            }

            #[cfg(test)]
            codes.push(DivRemGrade::DLBP);
            break 'div;
        }

        if start_ix == 0 {
            #[cfg(test)]
            codes.push(DivRemGrade::DLBV);

            break 'div;
        }

        start_ix = dividend_start(&end[..end_len], sor);
        let places = undivided_places - start_ix - 1;

        if places > 0 {
            #[cfg(test)]
            codes.push(DivRemGrade::DEVD);

            add_places(&mut ratio, places);
        }
    }

    #[cfg(test)]
    assert_eq!(true, (end_len == 0 && end[0] == 0) || end_len > 0);

    end.truncate(max(end_len, 1));

    return (end, ratio);

    fn add_places(ratio: &mut RawRow, mut p: usize) {
        while p > 0 {
            p -= 1;
            ratio.insert(0, 0);
        }
    }
}

// devnote: seemingly can be leveraged for examination of dividend and divisor equality
// and also has potential to determine remainder; involving extra complexity
fn dividend_start(end: &[u8], sor: &[u8]) -> usize {
    #[cfg(test)]
    assert_eq!(true, end.len() >= sor.len(), "Dividend has less places.");

    let mut end_ix = end.len();
    let mut sor_ix = sor.len();

    let mut start_ix = end_ix - sor_ix;

    if start_ix > 0 {
        while sor_ix > 0 {
            end_ix -= 1;
            sor_ix -= 1;

            let end_num = end[end_ix];
            let sor_num = sor[sor_ix];

            if end_num > sor_num {
                break;
            }

            if end_num < sor_num {
                start_ix -= 1;
                break;
            }
        }
    }

    start_ix
}

const MUL_DYNAMO_CAP: usize = 1000;
fn multiplication(mpler: &[u8], mcand: &[u8]) -> RawRow {
    let mpler_len = mpler.len();

    let mut sum = Vec::with_capacity(MUL_DYNAMO_CAP);

    let mut offset = 0;
    while offset < mpler_len {
        muladd(mpler[offset], &mcand, &mut sum, offset);
        offset += 1;
    }

    sum
}

fn power_steps(mut step: u16) -> Vec<u16> {
    #[cfg(test)]
    {
        if step < 2 {
            panic!("Pow steps for powers > 1 only.");
        }
    }

    let mut steps = Vec::with_capacity(15);
    loop {
        steps.push(step);

        step >>= 1;
        if step == 1 {
            break;
        }
    }

    steps
}

const POWER_CAP: usize = 2500;
fn power(base: &[u8], pow: u16) -> RawRow {
    let mut sum = Vec::with_capacity(POWER_CAP);
    let mut mcand = Vec::with_capacity(POWER_CAP);

    mcand.extend_from_slice(base);

    let steps = power_steps(pow);
    let mut s_iter = steps.iter();
    let mut curr_s = unsafe { s_iter.next_back().unwrap_unchecked() };

    let base_len = base.len();
    let mut offset;
    loop {
        let mcand_len = mcand.len();
        offset = 0;
        while offset < mcand_len {
            muladd(mcand[offset], &mcand, &mut sum, offset);
            offset += 1;
        }

        if curr_s & 1 == 1 {
            clear_swap(&mut mcand, &mut sum);

            offset = 0;
            while offset < base_len {
                muladd(base[offset], &mcand, &mut sum, offset);
                offset += 1;
            }
        }

        if let Some(s) = s_iter.next_back() {
            curr_s = s
        } else {
            break;
        }

        clear_swap(&mut mcand, &mut sum);
    }

    sum
}

fn clear_swap<'a>(mcand: *mut RawRow, i_sum: *mut RawRow) {
    unsafe {
        let mut swap = mcand.read();
        swap.clear();

        mcand.write(i_sum.read());
        i_sum.write(swap);
    }
}

/// Adding intermediate product directly to sums allows to avoid
/// temporal storaging of intermediate products on place.
///
/// For instance,
///  987
/// ⋅ 55
/// -----
///  4935
/// 49350
/// -----
/// 54285
/// = 5 +30 +900 +4000 +0 +50 +300 +9000 +40000
/// = 35 +400 +4500 +350 +4000 +45000
fn muladd(mpler: u8, mcand: &[u8], sum: &mut Vec<u8>, place_off: usize) {
    let mut ix = 0;
    let mcand_len = mcand.len();

    loop {
        let prod = mpler * mcand[ix];

        sumadd(prod, sum, place_off + ix);

        ix += 1;
        if ix == mcand_len {
            break;
        }
    }
}

fn sumadd(mut addend: u8, sum: &mut RawRow, mut off: usize) {
    let mut takeover = 0;
    let sum_len = sum.len();

    loop {
        if off < sum_len {
            sum[off] = ones(sum[off] + addend, &mut takeover);
            off += 1;
        } else {
            let num = ones(addend, &mut takeover);
            sum.push(num);
        };

        if takeover == 0 {
            break;
        } else {
            addend = 0;
        }
    }
}

fn addition_sum(addend: &[u8], sum: &mut RawRow, offset: usize) {
    let a_len = addend.len();
    let s_len = sum.len();

    let mut takeover = 0;
    let mut a_inx = 0;
    let mut s_inx = offset;

    loop {
        let a_available = a_inx < a_len;
        if !a_available && takeover == 0 {
            break;
        }

        let a_num = if a_available { addend[a_inx] } else { 0 };

        let s_available = s_inx < s_len;
        let s_num = if s_available { sum[s_inx] } else { 0 };

        let add = ones(s_num + a_num, &mut takeover);

        if s_available {
            sum[s_inx] = add;
        } else {
            sum.push(add);
        }

        a_inx += 1;
        s_inx += 1;
    }
}

fn addition_two(lh_addend: &[u8], rh_addend: &[u8], sum: &mut RawRow) {
    let lha_len = lh_addend.len();
    let rha_len = rh_addend.len();

    let mut takeover = 0;
    let mut a_inx = 0;

    loop {
        let lha_available = a_inx < lha_len;
        let rha_available = a_inx < rha_len;

        if !(lha_available || rha_available) && takeover == 0 {
            break;
        }

        let lha_num = if lha_available { lh_addend[a_inx] } else { 0 };
        let rha_num = if rha_available { rh_addend[a_inx] } else { 0 };

        let add = ones(lha_num + rha_num, &mut takeover);
        sum.push(add);

        a_inx += 1;
    }
}

fn subtraction_arithmetical(minuend: &mut RawRow, subtrahend: &[u8]) -> RawRow {
    let ratio = subtraction(
        minuend,
        subtrahend,
        false,
        #[cfg(test)]
        &mut 0,
    );

    truncate_leading_raw(minuend, 0, 1);
    ratio
}

fn subtraction_divisional(mut minuend: &mut [u8], subtrahend: &[u8]) -> (RawRow, usize) {
    let ratio = subtraction(
        minuend,
        subtrahend,
        true,
        #[cfg(test)]
        &mut 0,
    );

    let mut len = len_without_leading_raw(minuend, 9, subtrahend.len());
    minuend = &mut minuend[..len];

    len = len_without_leading_raw(minuend, 0, 0);

    (ratio, len)
}

/// For difference computation applies precondition minuend ≥ subtrahend.
/// Returns difference/remainder and ratio in order.
//
// NOTE: Support for longer subtrahend implies extended guard condition on
// correction `inx < subtrahend_len && inx < minuend_len`. See feature 'shorter-dividend-support'.
fn subtraction(
    minuend: &mut [u8],
    subtrahend: &[u8],
    remainder: bool,
    #[cfg(test)] ctr: &mut usize,
) -> RawRow {
    let minuend_len = minuend.len();
    let subtrahend_len = subtrahend.len();

    let mut ratio = nought_raw();
    let unity = unity_raw();

    let mut takeover;
    let mut inx;
    loop {
        #[cfg(test)]
        {
            *ctr += 1;
        }

        takeover = 0;
        inx = 0;

        while inx < minuend_len {
            let s_num = if inx < subtrahend_len {
                subtrahend[inx]
            } else if takeover == 0 {
                break;
            } else {
                0
            };

            let mut m_num = minuend[inx];

            let total_s = s_num + takeover;
            takeover = if m_num < total_s {
                m_num += 10;
                1
            } else {
                0
            };

            minuend[inx] = m_num - total_s;
            inx += 1;
        }

        // existing remainder implies _minuend_ exhaustion
        // thus remainder is one turn more than is correct
        if takeover == 1 {
            inx = 0;
            takeover = 0;

            while inx < subtrahend_len {
                let correction = minuend[inx] + subtrahend[inx];
                minuend[inx] = ones(correction, &mut takeover);
                inx += 1;
            }

            break;
        }

        addition_sum(&unity, &mut ratio, 0);

        if remainder {
            continue;
        }

        break;
    }

    ratio
}

/// Supports algorithimical decimal row computations.
/// Solve problem as ones to ones addition.
/// Takes current size of place `num`, adds takeover
/// `takeover_ref` to it, returns ones of summation
/// and sets up `takeover_ref` with tens of summation.
const fn ones(num: u8, takeover_ref: &mut u8) -> u8 {
    let mut takeover_val = *takeover_ref;
    let total = num + takeover_val;

    takeover_val = total / 10;
    *takeover_ref = takeover_val;

    total - takeover_val * 10
}

#[cfg(test)]
mod tests_of_units {

    use crate::RawRow;

    fn unity() -> RawRow {
        [1].to_vec()
    }

    fn nought() -> RawRow {
        [0].to_vec()
    }

    mod placesrow {
        use crate::Row;

        mod new_from_vec {
            use crate::Row;

            #[test]
            fn basic_test() {
                let row = vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
                let proof = row.clone();
                let row = Row::new_from_vec(row);

                assert!(row.is_ok());
                assert_eq!(proof, row.unwrap().row);
            }

            #[test]
            fn zero_len_test() {
                let row = Row::new_from_vec(vec![0; 0]);
                assert!(row.is_err());
                assert_eq!(None, row.err().unwrap());
            }

            #[test]
            fn unsupported_num_len_index_test() {
                let row = vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
                let row = Row::new_from_vec(row);

                assert!(row.is_err());
                assert_eq!(Some(10), row.err().unwrap());
            }

            #[test]
            fn unsupported_num_0_index_test() {
                let row = vec![10, 0, 0, 0];
                let row = Row::new_from_vec(row);

                assert!(row.is_err());
                assert_eq!(Some(0), row.err().unwrap());
            }

            #[test]
            fn leading_zeros_trim_test() {
                let row = Row::new_from_vec(vec![1, 2, 0, 0]);
                assert_eq!(&[1, 2], &*row.unwrap().row);
            }

            #[test]
            fn zero_reduction_test() {
                let row = Row::new_from_vec(vec![0, 0, 0, 0]);
                assert_eq!(&[0], &*row.unwrap().row);
            }
        }

        mod new_from {
            use crate::Row;

            #[test]
            fn zero_test() {
                let row = Row::new_from_usize(0);
                assert_eq!(&[0], &*row);
            }

            #[test]
            fn new_from_u8_test() {
                let row = Row::new_from_u8(000_123u8);
                assert_eq!(&[3, 2, 1], &*row);
            }

            #[test]
            fn new_from_u16_test() {
                let row = Row::new_from_u16(000_12345u16);
                assert_eq!(&[5, 4, 3, 2, 1], &*row);
            }

            #[test]
            fn new_from_u32_test() {
                let row = Row::new_from_u32(000_1234567890u32);
                assert_eq!(&[0, 9, 8, 7, 6, 5, 4, 3, 2, 1], &*row);
            }

            #[test]
            fn new_from_u64_test() {
                let row = Row::new_from_u64(000_1234567890u64);
                assert_eq!(&[0, 9, 8, 7, 6, 5, 4, 3, 2, 1], &*row);
            }

            #[test]
            fn new_from_u128_test() {
                let row = Row::new_from_u128(000_12345678900u128);
                assert_eq!(&[0, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1], &*row);
            }

            #[test]
            fn new_from_usize_test() {
                let row = Row::new_from_usize(000_1234567890usize);
                assert_eq!(&[0, 9, 8, 7, 6, 5, 4, 3, 2, 1], &*row);
            }
        }

        mod try_into {
            use crate::Row;

            #[test]
            fn try_into_u8_test() {
                let num = u8::MAX;
                let row = new_from_num!(num);
                let test = row.try_into_u8();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_u16_test() {
                let num = u16::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_u16();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_u32_test() {
                let num = u32::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_u32();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_u64_test() {
                let num = u64::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_u64();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_u128_test() {
                let num = u128::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_u128();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_usize_test() {
                let num = usize::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_usize();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_i8_test() {
                let num = i8::MAX;
                let row = new_from_num!(num);
                let test = row.try_into_i8();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_i16_test() {
                let num = i16::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_i16();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_i32_test() {
                let num = i32::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_i32();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_i64_test() {
                let num = i64::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_i64();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_i128_test() {
                let num = i128::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_i128();
                assert_eq!(Some(num), test);
            }

            #[test]
            fn try_into_isize_test() {
                let num = isize::MAX;
                let row = new_from_num!(num);

                let test = row.try_into_isize();
                assert_eq!(Some(num), test);
            }
        }

        mod new_from_str {

            use crate::Row;

            #[test]
            fn ok_test() {
                let row = Row::new_from_str("1234567890");
                assert_eq!(vec![0, 9, 8, 7, 6, 5, 4, 3, 2, 1], row.unwrap().row);
            }

            #[test]
            fn err_test() {
                let row = Row::new_from_str("");
                assert_eq!(Err(None), row);
            }
        }

        mod to_number {
            use crate::Row;

            #[test]
            fn basic_test() {
                let row = Row::new_from_vec(vec![0, 9, 8, 7, 6, 5, 4, 3, 2, 1]).unwrap();
                assert_eq!("1234567890", row.to_number().as_str());
            }
        }

        use super::{nought, unity};
        #[test]
        fn is_unity_test() {
            let test = Row { row: unity() };
            assert_eq!(true, test.is_unity());
        }

        #[test]
        fn is_nought_test() {
            let test = Row { row: nought() };
            assert_eq!(true, test.is_nought());
        }

        #[test]
        fn unity_test() {
            let proof = Row { row: unity() };
            assert_eq!(proof, Row::unity());
        }

        #[test]
        fn nought_test() {
            let proof = Row { row: nought() };
            assert_eq!(proof, Row::nought());
        }

        #[test]
        #[allow(deprecated)]
        fn zero_test() {
            assert_eq!(&[0], &*Row::zero());
        }

        #[test]
        fn places_test() {
            let unity = Row::unity();
            assert_eq!(1, unity.places());
        }

        #[test]
        fn to_string_test() {
            let row = Row::new_from_usize(1);
            assert_eq!("1", row.to_string());
        }

        #[test]
        fn from_u8_test() {
            let row: Row = From::<u8>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }

        #[test]
        fn from_u16_test() {
            let row: Row = From::<u16>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }

        #[test]
        fn from_u32_test() {
            let row: Row = From::<u32>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }

        #[test]
        fn from_u64_test() {
            let row: Row = From::<u64>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }

        #[test]
        fn from_u128_test() {
            let row: Row = From::<u128>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }

        #[test]
        fn from_usize_test() {
            let row: Row = From::<usize>::from(123);
            assert_eq!(&[3, 2, 1], &*row);
        }
    }

    mod new_from_str_raw {
        use crate::new_from_str_raw;

        #[test]
        fn zero_len_test() {
            let row = new_from_str_raw("");
            assert!(row.is_err());
            assert_eq!(None, row.err().unwrap());
        }

        #[test]
        fn leading_zeros_trim_test() {
            let row = new_from_str_raw("0021");
            assert!(row.is_ok());
            assert_eq!(&[1, 2], &*row.unwrap());
        }

        #[test]
        fn zeros_reduction_test() {
            let row = new_from_str_raw("0000");
            assert!(row.is_ok());
            assert_eq!(&[0], &*row.unwrap());
        }

        #[test]
        fn nondigit_str_test() {
            let row = new_from_str_raw("0012w123");
            assert!(row.is_err());
            let inx = row.err().unwrap();
            assert!(inx.is_some());
            assert_eq!(4, inx.unwrap());
        }

        #[test]
        fn basic_test() {
            let row = new_from_str_raw("1234567890");
            assert!(row.is_ok());
            assert_eq!(&[0, 9, 8, 7, 6, 5, 4, 3, 2, 1], &*row.unwrap());
        }
    }

    mod truncate_leading_raw {
        use crate::truncate_leading_raw;

        #[test]
        fn basic_test() {
            let mut row = vec![7, 7, 7, 7, 7];
            truncate_leading_raw(&mut row, 7, 3);
            assert_eq!(vec![7, 7, 7,], row);
        }
    }

    mod len_without_leading_raw {
        use crate::len_without_leading_raw;

        #[test]
        fn counting_test() {
            let count = len_without_leading_raw(&vec![1, 2, 5, 5, 5], 5, 0);
            assert_eq!(2, count);
        }

        #[test]
        fn preservation_test() {
            let count = len_without_leading_raw(&vec![5, 5, 5, 5], 5, 1);
            assert_eq!(1, count);
        }

        #[test]
        fn no_leading_test() {
            let count = len_without_leading_raw(&vec![5, 5, 5, 0], 5, 0);
            assert_eq!(4, count);
        }

        #[test]
        fn exto_equal_len_test() {
            let count = len_without_leading_raw(&vec![5, 5, 5], 5, 3);
            assert_eq!(3, count);
        }
    }

    use crate::{is_nought_raw, is_unity_raw, nought_raw, unity_raw};
    #[test]
    fn unity_raw_test() {
        assert_eq!(unity(), unity_raw());
    }

    #[test]
    fn nought_raw_test() {
        assert_eq!(nought(), nought_raw());
    }

    #[test]
    fn is_unity_raw_test() {
        assert_eq!(true, is_unity_raw(&unity()));
    }

    #[test]
    fn is_nought_raw_test() {
        assert_eq!(true, is_nought_raw(&nought()));
    }

    mod is_one_raw {
        use crate::is_one_raw;

        #[test]
        fn is_test() {
            let test = [3].to_vec();
            assert_eq!(true, is_one_raw(&test, 3));
        }

        #[test]
        fn different_test() {
            let test = [3].to_vec();
            assert_eq!(false, is_one_raw(&test, 4));
        }

        #[test]
        fn longer_test() {
            let test = [3, 3].to_vec();
            assert_eq!(false, is_one_raw(&test, 3));
        }
    }

    mod from_digit {

        use crate::from_digit;
        use std::panic::catch_unwind;

        #[test]
        fn basic_test() {
            for proof in 0..=9 {
                let test = from_digit(proof.to_string().chars().next().unwrap());
                assert_eq!(proof, test);
            }
        }

        #[test]
        fn unsupported_char_test() {
            let uc = ['0' as u8 - 1, '9' as u8 + 1];

            for c in uc {
                let c = c as char;

                let proof = format!("Unsupported char `{c}` conversion.");
                let catch = catch_unwind(|| from_digit(c));

                assert!(catch.is_err());
                let err = catch.unwrap_err().downcast::<String>().unwrap();
                assert_eq!(proof, *err);
            }
        }
    }

    mod to_digit {
        use crate::to_digit;

        #[test]
        fn basic_test() {
            for n in 0..=9 {
                let test = to_digit(n);
                let proof = n.to_string().chars().next().unwrap();
                assert_eq!(proof, test);
            }
        }

        #[test]
        #[should_panic(expected = "Only number < 10 supported.")]
        fn less_than_10_support_only_test() {
            to_digit(10);
        }
    }

    mod ord_of_mag {

        use crate::{ord_of_mag, Oom, OomClass, PlacesRow, Row};

        const PROOF: &str = "3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880014690519596700153903344921657179259940659150153474113339484124085316929577090471576461044369257879062037808609941828371711548406328552999118596824564203326961604691314336128949791890266529543612676178781350061388186278580463683134952478031143769334671973819513185678403231241795402218308045872844614600253577579702828644029024407977896034543989163349222652612067792651676031048436697793756926155720500369894909469421850007358348844643882731109289109042348054235653403907274019786543725939641726001306990000955784463109626790694418336130181302894541703315807731626386395193793704654765220632063686587197822049312426053454111609356979828132452297000798883523759585328579251362964686511497675217123459559238039375625125369855194955325099947038843990336466165470647234999796132343403021857052187836676345789510732982875157945215771652139626324438399018484560935762602";

        #[test]
        fn consts_test() {
            use crate::SQUARE_ROOT_TEN_COMPARATOR;

            assert_eq!(1000, SQUARE_ROOT_TEN_COMPARATOR.len());
            assert_eq!(PROOF, SQUARE_ROOT_TEN_COMPARATOR);
        }

        #[test]
        fn nought_test() {
            let r = Row::nought();
            let oom = unsafe { core::mem::transmute::<u8, OomClass>(u8::MAX) };

            assert_eq!(Oom::Undefined, ord_of_mag(&r, oom));
        }

        #[test]
        fn readme_sample_test() {
            let number_1 = PlacesRow::new_from_u128(3162277660168379331998893544432);
            let number_2 = PlacesRow::new_from_u128(3162277660168379331998893544433);

            assert_eq!(Oom::Precise(30), ord_of_mag(&number_1, OomClass::Strict));
            assert_eq!(Oom::Precise(31), ord_of_mag(&number_2, OomClass::Strict));
            assert_eq!(Oom::Precise(30), ord_of_mag(&number_2, OomClass::Loose));
        }

        mod strict {

            use super::PROOF;
            use crate::{ord_of_mag, Oom, OomClass::Strict, Row};

            #[test]
            fn universal_test() {
                #[rustfmt::skip]
                // lesser-shorter-greater triplets
                let values = [
                    (2,0), (3, 0), (4, 1),
                    (30, 1), (31, 1), (32, 2),
                    (315, 2), (316, 2), (317, 3),
                    (3161, 3), (3162, 3), (3163, 4),
                    (316_227_765, 8), (316_227_766, 8), (316_227_767, 9),
                ];

                for v in values {
                    let r = Row::new_from_usize(v.0);
                    let o = ord_of_mag(&r, Strict);

                    assert_eq!(Oom::Precise(v.1), o, "{:?}", v);
                }
            }

            #[test]
            fn full_precision_test() {
                let r = Row::new_from_str(PROOF).unwrap();
                let o = ord_of_mag(&r, Strict);

                assert_eq!(Oom::Precise(PROOF.len()), o);
            }

            #[test]
            fn behind_precision_test() {
                let mut proof = String::from(PROOF);
                proof.push('0');

                let r = Row::new_from_str(proof.as_str()).unwrap();
                let o = ord_of_mag(&r, Strict);

                let proof_len = proof.len();
                assert_eq!(1001, proof_len);
                assert_eq!(Oom::Approx(proof_len), o);
            }
        }

        mod loose {
            use crate::{ord_of_mag, Oom, OomClass::Loose, Row};

            #[test]
            fn universal_test() {
                #[rustfmt::skip]
                let values = [
                    // lesser-equal-greater triplet
                    (4, 0)    , (5, 1)     , (6, 1),
                    // lesser-longer-greater triplets
                    (40, 1)   , (50, 2)    , (60, 2),
                    (4000, 3) , (5000, 4)  , (6000, 4)
                ];

                for v in values {
                    let r = Row::new_from_usize(v.0);
                    let o = ord_of_mag(&r, Loose);

                    assert_eq!(Oom::Precise(v.1), o, "{:?}", v);
                }
            }
        }
    }

    // Relational comparison.
    mod rel {
        use crate::{rel, Rel, Row};

        #[test]
        fn basic_test() {
            let num = Row::new_from_usize(155);
            assert_eq!(Rel::Equal, rel(&num, &num));
        }
    }

    mod rel_raw {

        use crate::{rel_raw, Rel};

        #[test]
        fn longer_test() {
            let num = new_from_num_raw!(11);
            let comparand = new_from_num_raw!(9);

            let proof = Rel::Greater(Some((2, 1, 1)));
            assert_eq!(proof, rel_raw(&num, &comparand));
        }

        #[test]
        fn shorter_test() {
            let num = new_from_num_raw!(9);
            let comparand = new_from_num_raw!(10);

            let proof = Rel::Lesser(Some((1, 2, 1)));
            assert_eq!(proof, rel_raw(&num, &comparand));
        }

        #[test]
        fn greater_test() {
            let num_num = 1234567899;
            let cpd_num = 1234567890;

            let num = new_from_num_raw!(num_num);
            let comparand = new_from_num_raw!(cpd_num);

            assert_eq!(Rel::Greater(None), rel_raw(&num, &comparand));
        }

        #[test]
        fn equal_test() {
            let num = new_from_num_raw!(1234567890);
            assert_eq!(Rel::Equal, rel_raw(&num, &num));
        }

        #[test]
        fn lesser_test() {
            let num_num = 1234567890;
            let cpd_num = 1234567899;

            let num = new_from_num_raw!(num_num);
            let comparand = new_from_num_raw!(cpd_num);

            assert_eq!(Rel::Lesser(None), rel_raw(&num, &comparand));
        }

        #[test]
        fn both_nought_test() {
            let num = new_from_num_raw!(0);

            assert_eq!(Rel::Equal, rel_raw(&num, &num));
        }
    }

    mod rel_dec {
        use crate::{rel_dec, RelDec, Row};

        #[test]
        fn basic_test() {
            let num = Row::new_from_usize(9876543210);

            assert_eq!(RelDec::Equal(10), rel_dec(&num, &num));
        }

        #[test]
        #[rustfmt::skip]
        fn readme_sample_test() {
            let number    = Row::new_from_str("1489754132134687989463132131").unwrap();
            let comparand = Row::new_from_str(        "48645698946456531371").unwrap();
            let decrel = rel_dec(&number, &comparand);

            assert_eq!(RelDec::Greater((28, 20, 8)), decrel);
        }
    }

    mod rel_dec_raw {
        use crate::{rel_dec_raw, RelDec};

        #[test]
        fn equal_test() {
            let num = new_from_num_raw!(9876543210u64);

            assert_eq!(RelDec::Equal(10), rel_dec_raw(&num, &num));
        }

        #[test]
        fn lesser_test() {
            let num = new_from_num_raw!(10);
            let comparand = new_from_num_raw!(9876543210u64);

            let proof = RelDec::Lesser((2, 10, 8));
            assert_eq!(proof, rel_dec_raw(&num, &comparand));
        }

        #[test]
        fn greater_test() {
            let num = new_from_num_raw!(9876543210u64);
            let comparand = new_from_num_raw!(10);

            let proof = RelDec::Greater((10, 2, 8));
            assert_eq!(proof, rel_dec_raw(&num, &comparand));
        }

        #[test]
        fn nought_test() {
            let num = new_from_num_raw!(0);

            assert_eq!(RelDec::Equal(0), rel_dec_raw(&num, &num));
        }
    }

    mod dec_pla_cnt_raw {

        use crate::dec_pla_cnt_raw;

        #[test]
        fn nought_test() {
            let nought = vec![0; 1];
            assert_eq!(0, dec_pla_cnt_raw(&nought));
        }

        #[test]
        fn basic_test() {
            for test in [vec![1; 1], vec![1; 100]] {
                assert_eq!(test.len(), dec_pla_cnt_raw(&test));
            }
        }

        #[test]
        // function falsely reports zero len as nought
        // zero len happens nowhere, yet noted
        fn zero_len_pseudo_test() {
            let zero_len = vec![9; 0];
            assert_eq!(0, dec_pla_cnt_raw(&zero_len));
        }
    }

    // Addition.
    mod add {
        use crate::{add, Row};

        #[test]
        fn basic_test() {
            let row1 = Row::new_from_usize(4);
            let row2 = Row::new_from_usize(5);

            let sum = add(&row1, &row2);
            assert_eq!(&[9], &*sum.row);
        }

        #[test]
        fn left_num_longer_test() {
            let row1 = Row::new_from_usize(10_000);
            let row2 = Row::new_from_usize(5);

            let sum = add(&row1, &row2);
            assert_eq!(Row::new_from_usize(10_005), sum);
        }

        #[test]
        fn right_num_longer_test2() {
            let row1 = Row::new_from_usize(5);
            let row2 = Row::new_from_usize(10_000);

            let sum = add(&row1, &row2);
            assert_eq!(Row::new_from_usize(10_005), sum);
        }

        #[test]
        fn advanced_test() {
            let row = Row::new_from_str("680564733841876926926749214863536422910").unwrap();

            let sum = add(&row, &row);
            assert_eq!("1361129467683753853853498429727072845820", sum.to_number());
        }

        #[test]
        fn addend1_nought_test() {
            let addend1 = Row::nought();
            let addend2 = Row::new_from_usize(4321);
            let sum = add(&addend1, &addend2);
            assert_eq!(addend2, sum);
        }

        #[test]
        fn addend2_nought_test() {
            let addend1 = Row::new_from_usize(4321);
            let addend2 = Row::nought();
            let sum = add(&addend1, &addend2);
            assert_eq!(addend1, sum);
        }

        #[test]
        fn both_addends_nought_test() {
            let addend1 = Row::nought();
            let addend2 = Row::nought();
            let sum = add(&addend1, &addend2);
            assert_eq!(Row::nought(), sum);
        }
    }

    /// Subtraction.
    mod sub {
        use crate::{sub, Row};

        #[test]
        fn universal_test() {
            for triplet in [(99, 11, 88), (133, 133, 0), (90, 19, 71), (700, 699, 1)] {
                let minuend = new_from_num!(triplet.0);
                let subtrahend = new_from_num!(triplet.1);

                let proof = new_from_num!(triplet.2);
                let diff = sub(&minuend, &subtrahend);
                assert!(diff.is_some());

                assert_eq!(proof, diff.unwrap());
            }
        }

        #[test]
        fn nought_subtrahend_test() {
            let minuend = new_from_num!(40);
            let subtrahend = Row::nought();

            let proof = minuend.clone();
            let test = sub(&minuend, &subtrahend);
            assert_eq!(Some(proof), test);
        }

        #[test]
        fn lesser_minuend_test() {
            let minuend = new_from_num!(4);
            let subtrahend = new_from_num!(5);

            assert!(sub(&minuend, &subtrahend).is_none());
        }

        #[test]
        fn equal_operands_test() {
            let minuend = new_from_num!(1364);
            let subtrahend = minuend.clone();

            let proof = Row::nought();
            let test = sub(&minuend, &subtrahend);
            assert_eq!(Some(proof), test);
        }

        #[test]
        fn greater_minuend_test() {
            let minuend = new_from_num!(2);
            let subtrahend = new_from_num!(1);

            let res = sub(&minuend, &subtrahend);
            assert_eq!(Some(new_from_num!(1)), res);
        }

        #[test]
        fn boht_nought_test() {
            let minuend = Row::nought();
            let subtrahend = Row::nought();

            let proof = Row::nought();
            let test = sub(&minuend, &subtrahend);
            assert_eq!(Some(proof), test);
        }

        #[test]
        fn shrinking_test() {
            let minuend = new_from_num!(1234567890_1234567890usize);
            let subtrahend = new_from_num!(1234567890_1234567889usize);

            let proof = Row::unity();
            let test = sub(&minuend, &subtrahend);
            assert_eq!(Some(proof), test);
            assert_eq!(true, test.unwrap().row.capacity() < minuend.row.len());
        }
    }

    /// Multiplication.
    mod mul {
        use crate::{mul, Row, MUL_DYNAMO_CAP};

        #[test]
        fn basic_test() {
            let row1 = Row::new_from_usize(2);
            let row2 = Row::new_from_usize(3);
            let prod = mul(&row1, &row2);

            assert_eq!(true, prod.row.capacity() < MUL_DYNAMO_CAP);

            assert_eq!(&[6], &*prod);
        }

        #[test]
        fn row1_nought_test() {
            let row1 = Row::nought();
            let row2 = Row::new_from_usize(123456789_10111213);
            let prod = mul(&row1, &row2);
            let row = &prod.row;
            assert_eq!(&[0], row.as_slice());
            assert!(row.capacity() < row2.len());
        }

        #[test]
        fn row2_nought_test() {
            let row1 = Row::new_from_usize(123456789_10111213);
            let row2 = Row::nought();
            let prod = mul(&row1, &row2);
            let row = &prod.row;
            assert_eq!(&[0], row.as_slice());
            assert!(row.capacity() < row1.len());
        }

        #[test]
        fn both_nought_test() {
            let row1 = Row::nought();
            let row2 = Row::nought();
            let prod = mul(&row1, &row2);
            assert_eq!(&[0], &*prod);
        }

        #[test]
        fn advanced_test() {
            let row = Row::new_from_u128(u128::MAX);
            let prod = mul(&row, &row);
            let proof =
                "115792089237316195423570985008687907852589419931798687112530834793049593217025";
            assert_eq!(proof, prod.to_number());
        }

        #[test]
        fn decadic_test() {
            let row1 = Row::new_from_u128(100);
            let row2 = Row::new_from_u128(10_000);

            let proof = new_from_num!(1_000_000);
            let prod = mul(&row1, &row2);

            assert_eq!(proof, prod);
        }

        #[test]
        fn decadic_test2() {
            let row1 = Row::new_from_u128(100_000);
            let row2 = Row::new_from_u128(100_000);

            let proof = new_from_num!(10_000_000_000usize);
            let prod = mul(&row1, &row2);

            assert_eq!(proof, prod);
        }
    }

    mod mul_raw {

        use crate::{mul_raw, MUL_DYNAMO_CAP};
        #[test]
        fn shrinking_test() {
            let prod = mul_raw(&vec![2], &vec![3], false);
            assert_eq!(true, prod.capacity() == MUL_DYNAMO_CAP);

            let prod = mul_raw(&vec![2], &vec![3], true);
            assert_eq!(true, prod.capacity() < MUL_DYNAMO_CAP);
        }
    }

    mod mul_shortcut {
        use crate::{mul_shortcut, nought_raw, unity_raw};

        #[test]
        fn factor1_nought_test() {
            let row1 = nought_raw();
            let row2 = new_from_num_raw!(333_990);

            let res = mul_shortcut(&row1, &row2);
            assert_eq!(Some(row1), res);
        }

        #[test]
        fn factor2_nought_test() {
            let row1 = new_from_num_raw!(333_990);
            let row2 = nought_raw();

            let res = mul_shortcut(&row1, &row2);
            assert_eq!(Some(row2), res);
        }

        #[test]
        fn factor1_unity_test() {
            let row1 = unity_raw();
            let row2 = new_from_num_raw!(333_990);

            let res = mul_shortcut(&row1, &row2);
            assert_eq!(Some(row2), res);
        }

        #[test]
        fn factor2_unity_test() {
            let row1 = new_from_num_raw!(333_990);
            let row2 = unity_raw();

            let res = mul_shortcut(&row1, &row2);
            assert_eq!(Some(row1), res);
        }

        #[test]
        fn neither_unity_nor_nought_test() {
            let row = new_from_num_raw!(2);

            let res = mul_shortcut(&row, &row);
            assert_eq!(None, res);
        }
    }

    /// For base ≥ 0 and exponent ≥ 0 power can be viewed as nothing more
    /// than repetitive multiplication with number in question.
    /// 0º=1, 0¹=1×0, 0²=1×0×0, 0³=1×0×0×0, …
    /// 1º=1, 1¹=1×1, 1²=1×1×1, 1³=1×1×1×1, …
    /// 2º=1, 2¹=1×2, 2²=1×2×2, 2³=1×2×2×2, …
    ///                   ⋮
    mod pow {
        use crate::{pow, Row, POWER_CAP};

        #[test]
        fn basic_test() {
            let row = Row::new_from_usize(2);
            assert_eq!(&[4], &*pow(&row, 2));

            assert_eq!(true, row.row.capacity() < POWER_CAP);
        }

        #[test]
        fn advanced_test2() {
            let proof = Row::new_from_str("88817841970012523233890533447265625").unwrap();
            let row = Row::new_from_usize(25);
            assert_eq!(proof, pow(&row, 25));
        }

        #[test]
        fn advanced_test3() {
            let proof = Row::new_from_str(
                "949279437109690919948053832937215463733689853138782229364504479870922851876864",
            )
            .unwrap();

            let row = Row::new_from_usize(998);
            assert_eq!(proof, pow(&row, 26));
        }

        #[test]
        fn advanced_test4() {
            let proof = Row::new_from_str(
                "926336713898529563388567880069503262826159877325124512315660672063305037119488",
            )
            .unwrap();

            let row = Row::new_from_usize(2);
            assert_eq!(proof, pow(&row, 259));
        }

        #[test]
        // readme sample
        fn advanced_test5() {
            let row = Row::new_from_u128(u128::MAX);
            let pow = pow(&row, 500);
            let number = pow.to_number();

            assert!(number.starts_with("8312324609993336522"));
            assert_eq!(19266, number.len());
        }

        #[test]
        fn decadic_test() {
            let row = Row::new_from_u128(100);
            let pow = pow(&row, 4);
            let proof = new_from_num!(1_00_00_00_00);

            assert_eq!(proof, pow);
        }

        #[test]
        fn decadic_test2() {
            let row = Row::new_from_u128(100);
            let pow = pow(&row, 10);
            let proof = "1_00_00_00_00_00_00_00_00_00_00";
            let proof = Row::new_from_str(proof.replace("_", "").as_str()).unwrap();

            assert_eq!(proof, pow);
        }

        #[test]
        fn zero_power_test() {
            let row = Row::new_from_usize(0);
            let pow = pow(&row, 0);
            assert_eq!(&[1], &*pow);
        }

        #[test]
        fn one_power_test() {
            let row = Row::new_from_usize(3030);
            let pow = pow(&row, 1);
            assert_eq!(&[0, 3, 0, 3], &*pow);
        }

        #[test]
        fn power_of_nought_test() {
            let row = Row::new_from_usize(0);
            let pow = pow(&row, 1000);
            assert_eq!(&[0], &*pow);
        }

        #[test]
        fn power_of_one_test() {
            let row = Row::new_from_usize(1);
            let pow = pow(&row, u16::MAX);
            assert_eq!(&[1], &*pow);
        }
    }

    mod pow_raw {

        use crate::{pow_raw, POWER_CAP};
        #[test]
        fn shrinking_test() {
            let prod = pow_raw(&vec![2], 3, false);
            assert_eq!(true, prod.capacity() == POWER_CAP);

            let prod = pow_raw(&vec![2], 3, true);
            assert_eq!(true, prod.capacity() < POWER_CAP);
        }
    }

    mod pow_shortcut {
        use super::nought;
        use crate::{nought_raw, pow_shortcut, unity_raw};

        #[test]
        fn zero_power_test() {
            let row = nought();
            let pow = pow_shortcut(&row, 0);
            assert_eq!(Some(unity_raw()), pow);
        }

        #[test]
        fn power_of_nought_test() {
            let row = nought_raw();
            let pow = pow_shortcut(&row, 1000);
            assert_eq!(Some(row), pow);
        }

        #[test]
        fn one_power_test() {
            let row = new_from_num_raw!(3030);
            let pow = pow_shortcut(&row, 1);
            assert_eq!(Some(row), pow);
        }

        #[test]
        fn power_of_one_test() {
            let row = unity_raw();
            let pow = pow_shortcut(&row, u16::MAX);
            assert_eq!(Some(row), pow);
        }
    }

    /// Division with remainder.
    mod divrem {
        use crate::{divrem, Row};

        #[test]
        fn nought_divisor_test() {
            let dividend = Row::new_from_usize(1);
            let divisor = Row::new_from_usize(0);

            let ratrem = divrem(&dividend, &divisor);
            assert!(ratrem.is_none());
        }

        #[test]
        fn shorter_dividend_test() {
            let dividend = Row::new_from_usize(99);
            let divisor = Row::new_from_usize(999);

            let ratrem = divrem(&dividend, &divisor);
            assert!(ratrem.is_some());

            let ratrem = ratrem.unwrap();

            assert_eq!(Row::nought(), ratrem.0);
            assert_eq!(dividend, ratrem.1);
        }

        #[test]
        fn universal_test() {
            for quadruplet in [
                (0, 100, 0, 0),
                (99, 11, 9, 0),
                (133, 133, 1, 0),
                (90, 19, 4, 14),
                (700, 699, 1, 1),
                (700, 70, 10, 0),
            ] {
                let dividend = Row::new_from_usize(quadruplet.0);
                let divisor = Row::new_from_usize(quadruplet.1);

                let ratio = Row::new_from_usize(quadruplet.2);
                let remainder = Row::new_from_usize(quadruplet.3);
                let ratrem = divrem(&dividend, &divisor);

                assert!(ratrem.is_some());
                let ratrem = ratrem.unwrap();

                assert_eq!(ratio, ratrem.0);
                assert_eq!(remainder, ratrem.1);
            }
        }

        // readme sample
        #[test]
        fn load_test() {
            let dividend =
                Row::new_from_str("99999340282366920938463463374607431768211455").unwrap();
            let divisor = Row::new_from_usize(249);

            let ratio = Row::new_from_str("401603776234405304973748848894005750073138").unwrap();
            let remainder = Row::new_from_usize(93);

            let ratrem = divrem(&dividend, &divisor).unwrap();
            assert_eq!(ratio, ratrem.0);
            assert_eq!(remainder, ratrem.1);
        }

        #[test]
        fn readme_sample_test() {
            let dividend =
                Row::new_from_str("3402823669209384634633746074317682114565556668744123").unwrap();
            let divisor =
                Row::new_from_str("14034568236692093846346337460345176821145655563453").unwrap();
            let ratio = "242";
            let remainder = "6458155929897923817932408914149323848308022388497";

            let ratrem = divrem(&dividend, &divisor).unwrap();

            assert_eq!(ratio, ratrem.0.to_number());
            assert_eq!(remainder, ratrem.1.to_number());
        }

        #[test]
        fn shrinking_test() {
            let dividend =
                Row::new_from_str("1000000000000000000000000000000000000000000000").unwrap();
            let divisor = Row::unity();

            let ratrem = divrem(&dividend, &divisor).unwrap();

            assert_eq!(dividend, ratrem.0);

            let rem = ratrem.1;
            assert_eq!(Row::nought(), rem);

            assert_eq!(true, rem.row.capacity() < dividend.len());
        }
    }

    mod divrem_shortcut {
        use crate::{divrem_shortcut, nought_raw, unity_raw, Row};

        #[test]
        fn nought_divisor_test() {
            let dividend = nought_raw();
            let divisor = nought_raw();

            let ratrem = divrem_shortcut(&dividend, &divisor);
            assert_eq!(Some(None), ratrem);
        }

        #[test]
        fn nought_dividend_test() {
            let dividend = nought_raw();
            let divisor = new_from_num_raw!(4);

            let proof = (Row::nought(), Row::nought());
            let ratrem = divrem_shortcut(&dividend, &divisor);
            assert_eq!(Some(Some(proof)), ratrem);
        }

        #[test]
        fn unity_divisor_test() {
            let dividend = nought_raw();
            let divisor = unity_raw();

            let proof = (Row::nought(), Row::nought());
            let ratrem = divrem_shortcut(&dividend, &divisor);
            assert_eq!(Some(Some(proof)), ratrem);
        }

        #[test]
        fn unity_divisor_test2() {
            let dividend = new_from_num!(334_556);
            let divisor = unity_raw();

            let proof = (dividend.clone(), Row::nought());
            let ratrem = divrem_shortcut(&dividend.row, &divisor);
            assert_eq!(Some(Some(proof)), ratrem);
        }

        #[test]
        fn lesser_dividend_test() {
            let dividend = new_from_num!(0);
            let divisor = new_from_num_raw!(1);

            let proof = (Row::nought(), dividend.clone());
            let ratrem = divrem_shortcut(&dividend.row, &divisor);
            assert_eq!(Some(Some(proof)), ratrem);
        }
    }

    pub mod division {
        use crate::{division, new_from_str_raw, nought_raw, unity_raw};
        use DivRemGrade::*;

        #[derive(Debug, PartialEq)]
        pub enum DivRemGrade {
            /// dividend lesser by place initially
            DLBPI,
            /// dividend lesser by place
            DLBP,
            /// dividend lesser by value
            DLBV,
            /// dividend full virtual division
            DFVD,
            /// dividend partial virtual division
            DPVD,
            /// no dividend virtual division
            NDVD,
            /// dividend exhaustion
            DEXH,
            /// remainder virtual division
            RVD,
            /// dividend extension virtual division
            DEVD,
        }

        #[test]
        fn basic_test() {
            let dividend = new_from_num_raw!(65006);
            let divisor = vec![5];

            let proof_ra = new_from_num_raw!(13001);
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![1], rem);
            assert_eq!(proof_ra, ratio);
        }

        #[test]
        fn zero_division_test_1() {
            let dividend = nought_raw();
            let divisor = unity_raw();

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn zero_division_test_2() {
            let dividend = nought_raw();
            let divisor = new_from_num_raw!(usize::MAX);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0], ratio);

            assert_eq!(vec![DLBPI], codes);
        }

        #[test]
        fn one_division_test1() {
            let dividend = unity_raw();
            let divisor = unity_raw();

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn one_division_test2() {
            let dividend = unity_raw();
            let divisor = new_from_num_raw!(usize::MAX);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![1], rem);
            assert_eq!(vec![0], ratio);

            assert_eq!(vec![DLBPI], codes);
        }

        #[test]
        fn dividend_lesser_by_place_test() {
            let dividend = new_from_num_raw!(100);
            let divisor = new_from_num_raw!(1000);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(dividend, rem);
            assert_eq!(vec![0], ratio);

            assert_eq!(vec![DLBPI], codes);
        }

        #[test]
        fn dividend_lesser_by_value_test_1() {
            let dividend = new_from_num_raw!(1);
            let divisor = new_from_num_raw!(2);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![1], rem);
            assert_eq!(vec![0], ratio);
            assert_eq!(vec![DLBV], codes);
        }

        #[test]
        fn dividend_lesser_by_value_test_2() {
            let dividend = new_from_num_raw!(0);
            let divisor = new_from_num_raw!(1);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0], ratio);
            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn dividend_lesser_by_value_test_3() {
            let dividend = new_from_num_raw!(6_010_990);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0, 9, 1], rem);
            assert_eq!(vec![8, 1, 0, 0, 1], ratio);

            assert_eq!(vec![DEVD, DLBV], codes);
        }

        #[test]
        fn dividend_full_virtual_division_test_1() {
            let dividend = new_from_num_raw!(65000);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0, 0, 0, 1], ratio);

            assert_eq!(vec![DFVD, DEXH], codes);
        }

        #[test]
        fn dividend_full_virtual_division_test_2() {
            let dividend = new_from_num_raw!(65_650);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0, 1, 0, 1], ratio);

            assert_eq!(vec![NDVD, DEVD, DFVD, DEXH], codes);
        }

        #[test]
        fn dividend_full_virtual_division_test_3() {
            let dividend = new_from_num_raw!(6_500_650);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0, 1, 0, 0, 0, 1], ratio);

            assert_eq!(vec![DPVD, DEVD, DFVD, DEXH], codes);
        }

        #[test]
        fn dividend_full_virtual_division_test_4() {
            let dividend = new_from_num_raw!(600_000_000);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![0, 0, 0, 0, 0, 0, 1], ratio);

            assert_eq!(vec![DFVD, DEXH], codes);
        }

        #[test]
        fn dividend_partial_virtual_division_test_1() {
            let dividend = new_from_num_raw!(65066);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![1], rem);
            assert_eq!(vec![1, 0, 0, 1], ratio);

            assert_eq!(vec![DPVD, DEVD, DLBP], codes);
        }

        #[test]
        fn dividend_partial_virtual_division_test_2() {
            let dividend = new_from_num_raw!(65_650_075);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0, 1], rem);
            assert_eq!(vec![1, 0, 0, 0, 1, 0, 1], ratio);

            assert_eq!(vec![NDVD, DEVD, DPVD, DEVD, DLBV], codes);
        }

        #[test]
        fn dividend_exhaustion_test_1() {
            let dividend = new_from_num_raw!(65065);
            let divisor = dividend.clone();

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn dividend_exhaustion_test_2() {
            let dividend = new_from_num_raw!(65065);
            let divisor = new_from_num_raw!(65);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1, 0, 0, 1], ratio);

            assert_eq!(vec![DPVD, DEVD, DEXH], codes);
        }

        #[test]
        fn non_zero_remainder_test_a_1() {
            let dividend = new_from_num_raw!(60_055);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![5, 5], rem);
            assert_eq!(vec![0, 0, 1], ratio);
            assert_eq!(vec![NDVD, RVD, DLBP], codes);
        }

        #[test]
        fn non_zero_remainder_test_a_2() {
            let dividend = new_from_num_raw!(600_600_055);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![5, 5], rem);
            assert_eq!(vec![0, 0, 0, 1, 0, 0, 1], ratio);
            assert_eq!(vec![NDVD, DEVD, DPVD, RVD, DLBP], codes);
        }

        #[test]
        fn non_zero_remainder_test_b_1() {
            let dividend = new_from_num_raw!(655);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![5, 5], rem);
            assert_eq!(vec![1], ratio);
            assert_eq!(vec![DLBP], codes);
        }

        #[test]
        fn non_zero_remainder_test_b_2() {
            let dividend = new_from_num_raw!(600_655);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![5, 5], rem);
            assert_eq!(vec![1, 0, 0, 1], ratio);
            assert_eq!(vec![NDVD, DEVD, DLBP], codes);
        }

        #[test]
        fn non_zero_remainder_test_c_1() {
            let dividend = new_from_num_raw!(599);
            let divisor = new_from_num_raw!(300);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![9, 9, 2], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DLBV], codes);
        }

        #[test]
        fn non_zero_remainder_test_c_2() {
            let dividend = new_from_num_raw!(600_599);
            let divisor = new_from_num_raw!(300);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![9, 9, 2], rem);
            assert_eq!(vec![1, 0, 0, 2], ratio);

            assert_eq!(vec![NDVD, DEVD, DLBV], codes);
        }

        #[test]
        fn zero_remainder_test_1() {
            let dividend = new_from_num_raw!(usize::MAX);
            let divisor = new_from_num_raw!(usize::MAX);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn zero_remainder_test_2() {
            let dividend = new_from_num_raw!(2);
            let divisor = new_from_num_raw!(2);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn dividend_portion_computation_a_1() {
            let dividend = new_from_num_raw!(600);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DEXH], codes);
        }

        #[test]
        fn dividend_portion_computation_a_2() {
            let dividend = new_from_num_raw!(600);
            let divisor = new_from_num_raw!(599);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![1], rem);
            assert_eq!(vec![1], ratio);

            assert_eq!(vec![DLBP], codes);
        }

        #[test]
        fn dividend_portion_computation_a_3() {
            let dividend = new_from_num_raw!(5990);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0, 9, 5], rem);
            assert_eq!(vec![9], ratio);

            assert_eq!(vec![DLBV], codes);
        }

        #[test]
        fn dividend_portion_computation_b_1() {
            let dividend = new_from_num_raw!(600_600);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0], rem);
            assert_eq!(vec![1, 0, 0, 1], ratio);

            assert_eq!(vec![NDVD, DEVD, DEXH], codes);
        }

        #[test]
        fn dividend_portion_computation_b_2() {
            let dividend = new_from_num_raw!(600_599);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![9, 9, 5], rem);
            assert_eq!(vec![0, 0, 0, 1], ratio);

            assert_eq!(vec![NDVD, DEVD, DLBV], codes);
        }

        #[test]
        fn dividend_portion_computation_b_3() {
            let dividend = new_from_num_raw!(6_005_990);
            let divisor = new_from_num_raw!(600);

            let mut codes = vec![];
            let (rem, ratio) = division(&dividend, &divisor, &mut codes);

            assert_eq!(vec![0, 9, 5], rem);
            assert_eq!(vec![9, 0, 0, 0, 1], ratio);

            assert_eq!(vec![NDVD, DEVD, DLBV], codes);
        }

        #[test]
        fn load_test_1() {
            let dividend = new_from_num_raw!(u128::MAX);
            let divisor = new_from_num_raw!(249);

            let proof_ra = new_from_num_raw!(1366595851088106278969375933460916511u128);
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![6, 1, 2], rem);
            assert_eq!(proof_ra, ratio);
        }

        #[test]
        fn load_test_2() {
            let dividend = new_from_num_raw!(u128::MAX);
            let divisor = new_from_num_raw!(2);

            let proof_ra = new_from_num_raw!(170141183460469231731687303715884105727u128);
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![1], rem);
            assert_eq!(proof_ra, ratio);
        }

        #[test]
        fn load_test_3() {
            let dividend = new_from_num_raw!(u128::MAX);
            let divisor = new_from_num_raw!(u128::MAX / 2);

            let proof_ra = new_from_num_raw!(2);
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![1], rem);
            assert_eq!(proof_ra, ratio);
        }

        #[test]
        fn load_test_4() {
            let dividend = new_from_str_raw(
                "340282366920938463463374607431768211455340282366920938463463374607431768211455",
            )
            .unwrap();
            let divisor = new_from_num_raw!(13);

            let proof_ra = new_from_str_raw(
                "26175566686226035651028815956289862419641560182070841420266413431340905247035",
            )
            .unwrap();
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![0], rem);
            assert_eq!(proof_ra, ratio);
        }

        #[test]
        fn load_test_5() {
            let dividend = new_from_str_raw(
                "340282366920938463463374607431768211455340282366920938463463374607431768211455",
            )
            .unwrap();
            let divisor = new_from_num_raw!(14);

            let proof_ra = new_from_str_raw(
                "24305883351495604533098186245126300818238591597637209890247383900530840586532",
            )
            .unwrap();
            let (rem, ratio) = division(&dividend, &divisor, &mut vec![]);

            assert_eq!(vec![7], rem);
            assert_eq!(proof_ra, ratio);
        }
    }

    pub mod dividend_start {
        use crate::dividend_start;

        #[test]
        fn basic_test() {
            let dividend = new_from_num_raw!(333_333_333);
            let divisor = new_from_num_raw!(333);

            let portion = dividend_start(&dividend, &divisor);
            assert_eq!(6, portion);
        }

        #[test]
        fn place_satisfaction_test_1() {
            let dividend = new_from_num_raw!(911_111);

            for duo in [(19, 4), (899, 3), (911_10, 1)] {
                let divisor = new_from_num_raw!(duo.0);
                let portion = dividend_start(&dividend, &divisor);
                assert_eq!(duo.1, portion);
            }
        }

        #[test]
        fn place_satisfaction_test_2() {
            let dividend = new_from_num_raw!(911_111);

            for duo in [(9, 5), (911, 3), (911_11, 1), (911_111, 0)] {
                let divisor = new_from_num_raw!(duo.0);
                let portion = dividend_start(&dividend, &divisor);
                assert_eq!(duo.1, portion);
            }
        }

        #[test]
        fn place_unsatisfaction_test() {
            let dividend = new_from_num_raw!(809_000);

            for duo in [(90, 3), (81, 3), (9, 4), (80_901, 0), (809_001, 0)] {
                let divisor = new_from_num_raw!(duo.0);
                let portion = dividend_start(&dividend, &divisor);
                assert_eq!(duo.1, portion, "{:?}", duo);
            }
        }

        #[test]
        fn equal_places_indifference_test() {
            let dividend = new_from_num_raw!(809_000);

            for duo in [(100_000, 0), (809_000, 0), (999_999, 0)] {
                let divisor = new_from_num_raw!(duo.0);
                let portion = dividend_start(&dividend, &divisor);
                assert_eq!(duo.1, portion, "{:?}", duo);
            }
        }

        #[test]
        #[should_panic(expected = "Dividend has less places.")]
        fn length_precondition_test() {
            let dividend = new_from_num_raw!(1);
            let divisor = new_from_num_raw!(11);

            _ = dividend_start(&dividend, &divisor);
        }
    }

    pub mod prime_ck {
        use std::time::Duration;

        use crate::{prime_ck, Row};

        #[derive(PartialEq, Debug)]
        #[allow(non_camel_case_types)]
        pub enum PrimeCkEscCode {
            Unset,
            // prime number
            Pn,
            // needed for arithmetical correctness of consequent verifications
            Ar,
            // obviously not prime
            Ob,
            // sum divisible by three
            Dt,
            // not prime
            Np,
            Hit_3_Start,
            Hit_5_Start,
            Hit_7_Start,
            Hit_11_Start,
            Hit_13_Start,
            Hit_17_Start,
            Hit_19_Start,
            Hit_23_Start,
            Hit_29_Start,
            Hit_31_Start,
            Hit_37_Start,
            Hit_41_Start,
            Hit_43_Start,
            Hit_47_Start,
            Hit_53_Start,
            Hit_59_Start,
            Hit_61_Start,
            Hit_67_Start,
            Hit_71_Start,
            Hit_73_Start,
            Hit_79_Start,
            Hit_83_Start,
            Hit_89_Start,
            Hit_97_Start,
            Hit_101_Start,
            Hit_103_Start,
        }

        pub struct PrimeCkTestGauges {
            pub esc: PrimeCkEscCode,
            pub check_starts: bool,
            pub cntrs: [usize; 26],
            pub peekhole: usize,
            pub sqrt: usize,
        }

        impl PrimeCkTestGauges {
            fn blank() -> Self {
                Self {
                    esc: PrimeCkEscCode::Unset,
                    check_starts: false,
                    cntrs: [0; 26],
                    peekhole: 0,
                    sqrt: 0,
                }
            }
        }

        #[test]
        fn basic_test() {
            let row = new_from_num!(4643);
            assert_eq!(
                Some(true),
                prime_ck(&row, None, &mut PrimeCkTestGauges::blank())
            );
        }

        #[test]
        fn basic_values_test() {
            let vals = [
                (0, PrimeCkEscCode::Ob),
                (1, PrimeCkEscCode::Ob),
                (2, PrimeCkEscCode::Ar),
                (3, PrimeCkEscCode::Ar),
                (4, PrimeCkEscCode::Ob),
                (5, PrimeCkEscCode::Ar),
                (6, PrimeCkEscCode::Ob),
                (7, PrimeCkEscCode::Ar),
                (8, PrimeCkEscCode::Ob),
                (9, PrimeCkEscCode::Dt),
                (10, PrimeCkEscCode::Ob),
            ];

            for v in vals {
                let mut tg = PrimeCkTestGauges::blank();
                let row = new_from_num!(v.0);

                let pn = v.1 == PrimeCkEscCode::Ar;
                assert_eq!(Some(pn), prime_ck(&row, None, &mut tg), "{}", v.0);
                assert_eq!(v.1, tg.esc, "{}", v.0);
            }
        }

        #[test]
        fn advaced_values_test() {
            let vals = [
                (11, PrimeCkEscCode::Pn),
                (13, PrimeCkEscCode::Pn),
                (15, PrimeCkEscCode::Ob),
                (17, PrimeCkEscCode::Pn),
                (19, PrimeCkEscCode::Pn),
                (21, PrimeCkEscCode::Dt),
                (23, PrimeCkEscCode::Pn),
                (25, PrimeCkEscCode::Ob),
                (27, PrimeCkEscCode::Dt),
                (29, PrimeCkEscCode::Pn),
                (31, PrimeCkEscCode::Pn),
                (33, PrimeCkEscCode::Dt),
                (35, PrimeCkEscCode::Ob),
                (37, PrimeCkEscCode::Pn),
            ];

            for v in vals {
                let mut tg = PrimeCkTestGauges::blank();
                let row = new_from_num!(v.0);

                let pn = v.1 == PrimeCkEscCode::Pn;
                assert_eq!(Some(pn), prime_ck(&row, None, &mut tg), "{}", v.0);
                assert_eq!(v.1, tg.esc, "{}", v.0);
            }
        }

        #[test]
        fn division_cache_test() {
            // probe starts at 7
            let vals = [
                // beware, 3 does not starts in negative thus
                // acts as if it was already hit, false hit
                // ⌊√83⌋ = 9
                (83, PrimeCkEscCode::Hit_3_Start, 9),
                // beware, shares repetition with 3
                // but is subsequent in setting block, false hit
                // ⌊√227⌋ = 15
                (227, PrimeCkEscCode::Hit_5_Start, 15),
                (49, PrimeCkEscCode::Hit_7_Start, 7),
                (121, PrimeCkEscCode::Hit_11_Start, 11),
                (169, PrimeCkEscCode::Hit_13_Start, 13),
                (289, PrimeCkEscCode::Hit_17_Start, 17),
                (361, PrimeCkEscCode::Hit_19_Start, 19),
                (529, PrimeCkEscCode::Hit_23_Start, 23),
                (841, PrimeCkEscCode::Hit_29_Start, 29),
                (961, PrimeCkEscCode::Hit_31_Start, 31),
                (1369, PrimeCkEscCode::Hit_37_Start, 37),
                (1681, PrimeCkEscCode::Hit_41_Start, 41),
                (1849, PrimeCkEscCode::Hit_43_Start, 43),
                (2209, PrimeCkEscCode::Hit_47_Start, 47),
                (2809, PrimeCkEscCode::Hit_53_Start, 53),
                (3481, PrimeCkEscCode::Hit_59_Start, 59),
                (3721, PrimeCkEscCode::Hit_61_Start, 61),
                (4489, PrimeCkEscCode::Hit_67_Start, 67),
                (5041, PrimeCkEscCode::Hit_71_Start, 71),
                (5329, PrimeCkEscCode::Hit_73_Start, 73),
                (6241, PrimeCkEscCode::Hit_79_Start, 79),
                (6889, PrimeCkEscCode::Hit_83_Start, 83),
                (7921, PrimeCkEscCode::Hit_89_Start, 89),
                (9409, PrimeCkEscCode::Hit_97_Start, 97),
                (10201, PrimeCkEscCode::Hit_101_Start, 101),
                (10609, PrimeCkEscCode::Hit_103_Start, 103),
            ];

            for v in vals {
                let mut tg = PrimeCkTestGauges::blank();
                tg.check_starts = true;
                let row = new_from_num!(v.0);

                _ = prime_ck(&row, None, &mut tg);
                assert_eq!(v.1, tg.esc, "{}", v.0);
                assert_eq!(v.2, tg.sqrt, "{}", v.0);
                assert_eq!(v.2, tg.peekhole, "{}", v.0);
            }
        }

        #[test]
        fn division_cache_test2() {
            let mut tg = PrimeCkTestGauges::blank();

            // √96,721 = 311
            let row = new_from_num!(96_721);

            assert_eq!(Some(false), prime_ck(&row, None, &mut tg));

            // .....................................................................................................
            // : 0 : 1 : 2 : 3 : 4 : 5  : 6  : 7  : 8  : 9  : 10 : 11 : 12 : 13 : 14 : 15 : 16 : 17 : 18 : 19 : 20 :
            // :...:...:...:...:...:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:
            // : 1 : 3 : 5 : 7 : 9 : 11 : 13 : 15 : 17 : 19 : 21 : 23 : 25 : 27 : 29 : 31 : 33 : 35 : 37 : 39 : 41 :
            // :...:...:...:...:...:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:
            // .....................................................................................................
            // : 21 : 22 : 23 : 24 : 25 : 26 : 27 : 28 : 29 : 30 : 31 : 32 : 33 : 34 : 35 : 36 : 37 : 38 : 39 : 40 :
            // :....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:
            // : 43 : 45 : 47 : 49 : 51 : 53 : 55 : 57 : 59 : 61 : 63 : 65 : 67 : 69 : 71 : 73 : 75 : 77 : 79 : 81 :
            // :....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:....:
            // ..........................................................
            // : 41 : 42 : 43 : 44 : 45 : 46 : 47 : 48 : 49 : 50  : 51  :
            // :....:....:....:....:....:....:....:....:....:.....:.....:
            // : 83 : 85 : 87 : 89 : 91 : 93 : 95 : 97 : 99 : 101 : 103 :
            // :....:....:....:....:....:....:....:....:....:.....:.....:

            assert_eq!(311, tg.sqrt);

            // probe starts at 7
            let proof = [
                51, //  3,  3…103,    9…309
                30, //  5,  3 …61,   15…305
                21, //  7,  3 …43,   21…301
                13, // 11,  3 …27,   33…297
                11, // 13,  3 …23,   39…299
                8,  // 17,  3 …17,   51…289
                7,  // 19,  3 …15,   57…285
                6,  // 23,  3 …13,   69…299
                4,  // 29,  3 … 9    87…261
                4,  // 31,  3 … 9    93…279
                3,  // 37,  3 … 7,  111…259
                3,  // 41,  3 … 7,  123…287
                3,  // 43,  3 … 7,  129…301
                2,  // 47,  3 … 5,  141…235
                2,  // 53,  3 … 5,  159…265
                2,  // 59,  3 … 5,  177…295
                2,  // 61,  3 … 5,  183…305
                1,  // 67,  3 … 3,  201…201
                1,  // 71,  3 … 3,  213…213
                1,  // 73,  3 … 3,  219…219
                1,  // 79,  3 … 3,  237…237
                1,  // 83,  3 … 3,  249…249
                1,  // 89,  3 … 3,  267…267
                1,  // 97,  3 … 3,  291…291
                1,  // 101, 3 … 3,  303…303
                1,  // 103, 3 … 3,  309…309
            ];

            for (ix, c) in tg.cntrs.iter().enumerate() {
                assert_eq!(proof[ix], *c, "ix {ix}");
            }
        }

        #[test]
        fn easy_discard_test() {
            let vals = [0, 1, 1000, 2222, 3008, 5005, 5025, 7275];

            for v in vals {
                let row = new_from_num!(v);
                let mut tg = PrimeCkTestGauges::blank();
                assert_eq!(Some(false), prime_ck(&row, None, &mut tg), "{}", v);
                assert_eq!(PrimeCkEscCode::Ob, tg.esc, "{}", v);
            }
        }

        #[test]
        fn timeframe_exhaustion_test() {
            let prime = Row::new_from_str(
                "5210644015679228794060694325390955853335898483908056458352183851018372555735221",
            )
            .unwrap();
            let duration = Duration::from_secs(2);

            assert_eq!(
                None,
                prime_ck(&prime, Some(duration), &mut PrimeCkTestGauges::blank())
            );
        }

        #[test]
        fn primes_test() {
            let primes = [
                "4003",
                "7919",
                "19373",
                "100005583",
                "100010717",
                "1000037299",
                "1000062023",
                "100000012561",
                "100000002199",
                "100000015333",
                "2932031007403",
            ];

            for p in primes {
                let mut tg = PrimeCkTestGauges::blank();
                let row = Row::new_from_str(p).unwrap();
                assert_eq!(
                    Some(true),
                    prime_ck(&row, None, &mut tg),
                    "{}",
                    row.to_number()
                );
                assert_eq!(PrimeCkEscCode::Pn, tg.esc, "{}", row.to_number());
            }
        }

        #[test]
        #[cfg(feature = "ext-tests2")]
        fn primes_ext_test() {
            let primes = [
                "9999999900000001",
                "909090909090909091",
                "768614336404564651",
            ];

            for p in primes {
                let mut tg = PrimeCkTestGauges::blank();
                let row = Row::new_from_str(p).unwrap();
                assert_eq!(
                    Some(true),
                    prime_ck(&row, None, &mut tg),
                    "{}",
                    row.to_number()
                );
                assert_eq!(PrimeCkEscCode::Pn, tg.esc, "{}", row.to_number());
            }
        }

        // finish unseen yet
        #[test]
        #[cfg(feature = "ext-tests3")]
        fn primes_ext2_test() {
            let primes = [
                "5210644015679228794060694325390955853335898483908056458352183851018372555735221",
                 "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
                  "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127"  
            ];

            for p in primes {
                let mut tg = PrimeCkTestGauges::blank();
                let row = Row::new_from_str(p).unwrap();
                assert_eq!(
                    Some(true),
                    prime_ck(&row, None, &mut tg),
                    "{}",
                    row.to_number()
                );
                assert_eq!(PrimeCkEscCode::Pn, tg.esc, "{}", row.to_number());
            }
        }

        #[test]
        fn not_primes_test() {
            let not_primes = [
                ("6", PrimeCkEscCode::Ob),
                ("4009", PrimeCkEscCode::Np),
                ("7917", PrimeCkEscCode::Dt),
                ("19371", PrimeCkEscCode::Dt),
                ("100005587", PrimeCkEscCode::Np),
                ("100010713", PrimeCkEscCode::Np),
                ("1000037291", PrimeCkEscCode::Np),
                ("1000062029", PrimeCkEscCode::Np),
                ("5210644015679228794060694325390955853335898483908056458352183851018372555735223",  PrimeCkEscCode::Dt),
                ("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057153", PrimeCkEscCode::Dt),
                ("531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728121", PrimeCkEscCode::Np)
            ];

            for np in not_primes {
                let mut tg = PrimeCkTestGauges::blank();
                let row = Row::new_from_str(np.0).unwrap();
                assert_eq!(
                    Some(false),
                    prime_ck(&row, None, &mut tg),
                    "{}",
                    row.to_number()
                );
                assert_eq!(np.1, tg.esc, "{}", row.to_number());
            }
        }

        #[test]
        fn readme_sample_test() {
            let num = Row::new_from_str("340282366920938463463374607431768211479").unwrap();
            let limit = Duration::from_secs(3);
            assert_eq!(
                Some(false),
                prime_ck(&num, Some(limit), &mut PrimeCkTestGauges::blank())
            );
        }
    }

    mod prime_gen_res {
        use crate::PrimeGenRes;

        #[test]
        fn uproot_all_test() {
            let test = PrimeGenRes::All(vec![1, 2, 3, 4]);
            assert_eq!(vec![1, 2, 3, 4], test.uproot_all());
        }

        #[test]
        #[should_panic(expected = "Not `PrimeGenRes::All(_)` variant.")]
        fn uproot_all_not_all_test() {
            _ = PrimeGenRes::Max(0).uproot_all();
        }

        #[test]
        fn max_all_test() {
            let test = PrimeGenRes::Max(99);
            assert_eq!(99, test.uproot_max());
        }

        #[test]
        #[should_panic(expected = "Not `PrimeGenRes::Max(_)` variant.")]
        fn uproot_max_not_max_test() {
            _ = PrimeGenRes::All(vec![0; 0]).uproot_max();
        }
    }

    mod prime_gen_res_aide {
        use crate::{PrimeGenErr, PrimeGenRes, PrimeGenResAide};

        #[test]
        fn uproot_all_ok() {
            let proof = vec![3, 2, 1];
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Ok(PrimeGenRes::All(proof.clone()));
            let test = res.uproot_all();

            assert_eq!(proof, test);
        }

        #[test]
        #[should_panic(expected = "Not `Ok(_)` variant.")]
        fn uproot_all_err() {
            let err = PrimeGenErr::TimeframeExhaustion;
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Err(err);
            _ = res.uproot_all();
        }

        #[test]
        #[should_panic(expected = "Not `PrimeGenRes::All(_)` variant.")]
        fn uproot_all_ok_max() {
            let max = 17;
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Ok(PrimeGenRes::Max(max));
            _ = res.uproot_all();
        }

        #[test]
        fn uproot_max_ok() {
            let proof = 17;
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Ok(PrimeGenRes::Max(proof));
            let test = res.uproot_max();

            assert_eq!(proof, test);
        }

        #[test]
        #[should_panic(expected = "Not `Ok(_)` variant.")]
        fn uproot_max_err() {
            let err = PrimeGenErr::TimeframeExhaustion;
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Err(err);
            _ = res.uproot_max();
        }

        #[test]
        #[should_panic(expected = "Not `PrimeGenRes::Max(_)` variant.")]
        fn uproot_max_ok_all() {
            let all = vec![3, 2, 1];
            let res: Result<PrimeGenRes<usize>, PrimeGenErr> = Ok(PrimeGenRes::All(all));
            _ = res.uproot_max();
        }
    }

    mod pg {
        use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
        use std::time::{Duration, Instant};

        #[test]
        fn basic_primes_test() {
            let vals: [u8; 15] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47];

            for rix in 0..15 {
                let p = || pg!(rix + 1, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(vals[rix], p().uproot_max());
            }
        }

        #[test]
        fn basic_primes_test2() {
            let vals: [u8; 13] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41];

            for v in vals {
                let p = || pg!(v as usize, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(v, p().uproot_max());
            }
        }

        #[test]
        fn advanced_primes_test() {
            #[rustfmt::skip]
            let vals: [u16; 20] = [
                6143, 6151, 6163, 6173, 6197,
                6199, 6203, 6211, 6217, 6221,
                6229, 6247, 6257, 6263, 6269,
                6271, 6277, 6287, 6299, 6301,
            ];

            for rix in 0..20 {
                let p = || pg!(rix + 801, PrimeGenClass::Nth, false, u16, None);
                assert_eq!(vals[rix], p().uproot_max());
            }
        }

        #[test]
        fn advanced_primes_test2() {
            #[rustfmt::skip]
            let vals: [u16; 20] = [
                6143, 6151, 6163, 6173, 6197,
                6199, 6203, 6211, 6217, 6221,
                6229, 6247, 6257, 6263, 6269,
                6271, 6277, 6287, 6299, 6301,
            ];

            for v in vals {
                let p = || pg!(v as usize, PrimeGenClass::Lim, false, u16, None);
                assert_eq!(v, p().uproot_max());
            }
        }

        #[test]
        fn lim_test() {
            let vals: [u16; 2] = [65413, 65418];

            for v in vals {
                let p = || pg!(v as usize, PrimeGenClass::Lim, false, u16, None);
                assert_eq!(65413, p().uproot_max());
            }
        }

        #[test]
        #[cfg(feature = "ext-tests")]
        // readme sample
        fn large_nth_test() {
            let limit = Duration::from_secs(60);
            let p = || pg!(200_000, PrimeGenClass::Nth, false, u32, Some(limit));
            assert_eq!(Ok(PrimeGenRes::Max(2_750_159)), p());
        }

        mod timeframe_exhaustion {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes};
            use std::time::{Duration, Instant};
            #[test]
            fn basic_test() {
                let lim = Duration::from_secs(1);
                let res = || pg!(10_000_000, PrimeGenClass::Nth, false, u128, Some(lim));
                assert_eq!(Err(PrimeGenErr::TimeframeExhaustion), res());
            }

            #[test]
            fn two_always_test() {
                let lim = Duration::ZERO;
                let res = || pg!(1, PrimeGenClass::Nth, false, u8, Some(lim));
                assert_eq!(Ok(PrimeGenRes::Max(2)), res());

                let lim = Duration::ZERO;
                let res = || pg!(2, PrimeGenClass::Lim, false, u8, Some(lim));
                assert_eq!(Ok(PrimeGenRes::Max(2)), res());
            }
        }

        mod invalid_input {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes};
            use std::time::{Duration, Instant};

            #[test]
            fn invalid_nth_test() {
                let test = || pg!(0, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Err(PrimeGenErr::AimlessInput(0)), test());
            }

            #[test]
            fn invalid_limit_test() {
                for lim in [0, 1] {
                    let test = || pg!(lim, PrimeGenClass::Lim, false, usize, None);
                    assert_eq!(Err(PrimeGenErr::AimlessInput(lim)), test());
                }
            }

            #[test]
            fn limit_outside_type_size_test() {
                let test = || pg!(255, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(Ok(PrimeGenRes::Max(251)), test());

                let test = || pg!(256, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(Err(PrimeGenErr::InputGreaterThanSizeMax(256)), test());
            }

            #[test]
            fn nth_outside_type_size_test() {
                let test = || pg!(54, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Ok(PrimeGenRes::Max(251)), test());

                let test = || pg!(55, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Err(PrimeGenErr::ValueGreaterThanSizeMax(55, 257)), test());
            }

            #[test]
            #[should_panic(expected = "capacity overflow")]
            fn impossible_to_unfit_type_size_test() {
                let test = || pg!(usize::MAX, PrimeGenClass::Lim, false, u128, None);
                _ = test();
            }
        }

        mod cap {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
            use std::time::{Duration, Instant};

            #[test]
            fn lim_test() {
                // 7919 ÷⌊㏑7919⌋ ⋅1.15 ≈ 1138
                // 7919 is 1000ᵗʰ prime
                let test = || pg!(7919, PrimeGenClass::Lim, true, usize, None);
                let test = test().uproot_all();
                assert_eq!(true, test.capacity() < 1138);
            }

            #[test]
            fn nth_test() {
                let test = || pg!(1000, PrimeGenClass::Nth, true, usize, None);
                let test = test().uproot_all();
                assert_eq!(1000, test.capacity());
            }
        }

        mod all {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
            use std::time::{Duration, Instant};

            #[test]
            fn basic_test() {
                let test1 = || pg!(11, PrimeGenClass::Nth, true, u8, None);
                let test2 = || pg!(31, PrimeGenClass::Lim, true, u8, None);

                let proof: [u8; 11] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31];

                let test1 = test1().uproot_all();
                let test2 = test2().uproot_all();

                assert_eq!(test1, test2);
                assert_eq!(proof, test1.as_slice());
            }

            #[test]
            fn advanced_test() {
                let test1 = || pg!(1000, PrimeGenClass::Nth, true, u16, None);
                let test2 = || pg!(7919, PrimeGenClass::Lim, true, u16, None);

                let test1 = test1().uproot_all();
                let test2 = test2().uproot_all();

                assert_eq!(1000, test1.len());
                assert_eq!(1000, test2.len());
                assert_eq!(test1, test2);

                assert_eq!(7919, test1[999]);
                assert_eq!(6997, test1[899]);
                assert_eq!(6133, test1[799]);
                assert_eq!(5279, test1[699]);
                assert_eq!(4409, test1[599]);
                assert_eq!(3571, test1[499]);
                assert_eq!(2741, test1[399]);
                assert_eq!(1987, test1[299]);
                assert_eq!(1223, test1[199]);
                assert_eq!(541, test1[99]);
                assert_eq!(2, test1[0]);
            }
        }

        mod examples {

            #[test]
            fn example_1() {
                use crate::{pg, PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
                use std::time::{Duration, Instant};

                let all1 = || pg!(11, PrimeGenClass::Nth, true, usize, None);
                let all2 = || pg!(31, PrimeGenClass::Lim, true, usize, None);

                let proof: [usize; 11] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31];

                let all1 = all1().uproot_all();
                let all2 = all2().uproot_all();

                assert_eq!(all1, all2);
                assert_eq!(proof, all1.as_slice());
            }

            #[test]
            fn example_2() {
                use crate::{pg, PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
                use std::time::{Duration, Instant};

                let limit = Duration::from_secs(1);
                let result = (|| pg!(5_000, PrimeGenClass::Nth, false, u128, Some(limit)))();

                assert_eq!(48_611, result.uproot_max());
            }

            #[test]
            fn example_3() {
                use crate::{pg, PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
                use std::time::{Duration, Instant};

                let num = || pg!(20_000, PrimeGenClass::Nth, false, u64, None);
                assert_eq!(224_737, num().uproot_max());

                let num = || pg!(20_000, PrimeGenClass::Nth, false, u32, None);
                assert_eq!(224_737, num().uproot_max());
            }
        }
    }

    mod pg_sw {
        use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
        use std::time::{Duration, Instant};

        #[test]
        fn basic_primes_test() {
            let vals: [u8; 15] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47];

            for rix in 0..15 {
                let p = || pg_sw!(rix + 1, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(vals[rix], p().uproot_max());
            }
        }

        #[test]
        fn basic_primes_test2() {
            let vals: [u8; 13] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41];

            for v in vals {
                let p = || pg_sw!(v as usize, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(v, p().uproot_max());
            }
        }

        #[test]
        fn advanced_primes_test() {
            #[rustfmt::skip]
            let vals: [u16; 20] = [
                6143, 6151, 6163, 6173, 6197,
                6199, 6203, 6211, 6217, 6221,
                6229, 6247, 6257, 6263, 6269,
                6271, 6277, 6287, 6299, 6301,
            ];

            for rix in 0..20 {
                let p = || pg_sw!(rix + 801, PrimeGenClass::Nth, false, u16, None);
                assert_eq!(vals[rix], p().uproot_max());
            }
        }

        #[test]
        fn advanced_primes_test2() {
            #[rustfmt::skip]
            let vals: [u16; 20] = [
                6143, 6151, 6163, 6173, 6197,
                6199, 6203, 6211, 6217, 6221,
                6229, 6247, 6257, 6263, 6269,
                6271, 6277, 6287, 6299, 6301,
            ];

            for v in vals {
                let p = || pg_sw!(v as usize, PrimeGenClass::Lim, false, u16, None);
                assert_eq!(v, p().uproot_max());
            }
        }

        #[test]
        fn lim_test() {
            let vals: [u16; 2] = [65413, 65418];

            for v in vals {
                let p = || pg_sw!(v as usize, PrimeGenClass::Lim, false, u16, None);
                assert_eq!(65413, p().uproot_max());
            }
        }

        #[test]
        #[cfg(feature = "ext-tests")]
        fn large_nth_test() {
            let limit = Duration::from_secs(80);
            let p = || pg_sw!(200_000, PrimeGenClass::Nth, false, u32, Some(limit));
            assert_eq!(Ok(PrimeGenRes::Max(2_750_159)), p());
        }

        mod timeframe_exhaustion {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes};
            use std::time::{Duration, Instant};
            #[test]
            fn basic_test() {
                let lim = Duration::from_secs(1);
                let res = || pg_sw!(10_000_000, PrimeGenClass::Nth, false, u128, Some(lim));
                assert_eq!(Err(PrimeGenErr::TimeframeExhaustion), res());
            }

            #[test]
            fn two_always_test() {
                let lim = Duration::ZERO;
                let res = || pg_sw!(1, PrimeGenClass::Nth, false, u8, Some(lim));
                assert_eq!(Ok(PrimeGenRes::Max(2)), res());

                let lim = Duration::ZERO;
                let res = || pg_sw!(2, PrimeGenClass::Lim, false, u8, Some(lim));
                assert_eq!(Ok(PrimeGenRes::Max(2)), res());
            }
        }

        mod invalid_input {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes};
            use std::time::{Duration, Instant};

            #[test]
            fn invalid_nth_test() {
                let test = || pg_sw!(0, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Err(PrimeGenErr::AimlessInput(0)), test());
            }

            #[test]
            fn invalid_limit_test() {
                for lim in [0, 1] {
                    let test = || pg_sw!(lim, PrimeGenClass::Lim, false, usize, None);
                    assert_eq!(Err(PrimeGenErr::AimlessInput(lim)), test());
                }
            }

            #[test]
            fn limit_outside_type_size_test() {
                let test = || pg_sw!(255, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(Ok(PrimeGenRes::Max(251)), test());

                let test = || pg_sw!(256, PrimeGenClass::Lim, false, u8, None);
                assert_eq!(Err(PrimeGenErr::InputGreaterThanSizeMax(256)), test());
            }

            #[test]
            fn nth_outside_type_size_test() {
                let test = || pg_sw!(54, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Ok(PrimeGenRes::Max(251)), test());

                let test = || pg_sw!(55, PrimeGenClass::Nth, false, u8, None);
                assert_eq!(Err(PrimeGenErr::ValueGreaterThanSizeMax(55, 257)), test());
            }

            #[test]
            fn impossible_to_unfit_type_size_test() {
                let test = || pg_sw!(u8::MAX as usize, PrimeGenClass::Lim, false, u16, None);
                assert_eq!(Ok(PrimeGenRes::Max(251)), test());
            }
        }

        mod cap {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
            use std::time::{Duration, Instant};

            #[test]
            fn lim_test() {
                // 7919 ÷⌊㏑7919⌋ ⋅1.15 ≈ 1138
                // 7919 is 1000ᵗʰ prime
                let test = || pg_sw!(7919, PrimeGenClass::Lim, true, usize, None);
                let test = test().uproot_all();
                assert_eq!(1138, test.capacity());
            }

            #[test]
            fn nth_test() {
                let test = || pg_sw!(1000, PrimeGenClass::Nth, true, usize, None);
                let test = test().uproot_all();
                assert_eq!(1000, test.capacity());
            }
        }

        mod all {
            use crate::{PrimeGenClass, PrimeGenErr, PrimeGenRes, PrimeGenResAide};
            use std::time::{Duration, Instant};

            #[test]
            fn basic_test() {
                let test1 = || pg_sw!(11, PrimeGenClass::Nth, true, u8, None);
                let test2 = || pg_sw!(31, PrimeGenClass::Lim, true, u8, None);

                let proof: [u8; 11] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31];

                let test1 = test1().uproot_all();
                let test2 = test2().uproot_all();

                assert_eq!(test1, test2);
                assert_eq!(proof, test1.as_slice());
            }

            #[test]
            fn advanced_test() {
                let test1 = || pg_sw!(1000, PrimeGenClass::Nth, true, u16, None);
                let test2 = || pg_sw!(7919, PrimeGenClass::Lim, true, u16, None);

                let test1 = test1().uproot_all();
                let test2 = test2().uproot_all();

                assert_eq!(1000, test1.len());
                assert_eq!(1000, test2.len());
                assert_eq!(test1, test2);

                assert_eq!(7919, test1[999]);
                assert_eq!(6997, test1[899]);
                assert_eq!(6133, test1[799]);
                assert_eq!(5279, test1[699]);
                assert_eq!(4409, test1[599]);
                assert_eq!(3571, test1[499]);
                assert_eq!(2741, test1[399]);
                assert_eq!(1987, test1[299]);
                assert_eq!(1223, test1[199]);
                assert_eq!(541, test1[99]);
                assert_eq!(2, test1[0]);
            }
        }

        #[test]
        fn faster_test() {
            let test = || pg_sw!(20_000 as usize, PrimeGenClass::Nth, false, u32, None);
            let test = test().uproot_max();
            assert_eq!(224_737, test);
        }

        #[test]
        fn slower_test() {
            let test = || pg_sw!(20_000, PrimeGenClass::Nth, false, u64, None);
            let test = test().uproot_max();
            assert_eq!(224_737, test);
        }
    }

    mod heron_sqrt {
        use crate::{heron_sqrt, Row};
        #[test]
        fn basic_test() {
            let row = Row::new_from_u8(16);
            assert_eq!([4], &*heron_sqrt(&row));
        }

        #[test]
        #[rustfmt::skip]
        fn readme_sample_test() {
            let radicand  = Row::new_from_str("9754610577924096936222542295378750190521").unwrap();
            let test = Row::new_from_u128(98_765_432_100_123_456_789);
            assert_eq!(test, heron_sqrt(&radicand));
        }
    }

    mod heron_sqrt_raw {
        use crate::{heron_sqrt_raw, new_from_str_raw, nought_raw, unity_raw};

        #[test]
        fn test_2() {
            assert_eq!(vec![1], heron_sqrt_raw(&vec![2]));
        }

        #[test]
        fn test_3() {
            assert_eq!(vec![1], heron_sqrt_raw(&vec![3]));
        }

        #[test]
        fn test_4() {
            assert_eq!(vec![2], heron_sqrt_raw(&vec![4]));
        }

        #[test]
        fn test_7() {
            assert_eq!(vec![2], heron_sqrt_raw(&vec![8]));
        }

        #[test]
        fn test_8() {
            assert_eq!(vec![3], heron_sqrt_raw(&vec![9]));
        }

        #[test]
        fn test_17() {
            let test = new_from_num_raw!(17);
            assert_eq!(vec![4], heron_sqrt_raw(&test));
        }

        #[test]
        fn test_24() {
            let test = new_from_num_raw!(24);
            assert_eq!(vec![4], heron_sqrt_raw(&test));
        }

        #[test]
        fn test_25() {
            let test = new_from_num_raw!(25);
            assert_eq!(vec![5], heron_sqrt_raw(&test));
        }

        #[test]
        fn load_test() {
            let test = new_from_str_raw(
                "999999999999999999999999999999999999998000000000000000000000000000000000000001",
            )
            .unwrap();
            let proof = new_from_str_raw("999999999999999999999999999999999999999").unwrap();
            assert_eq!(proof, heron_sqrt_raw(&test));
        }

        #[test]
        fn unity_test() {
            assert_eq!(unity_raw(), heron_sqrt_raw(&unity_raw()));
        }

        #[test]
        fn nought_test() {
            assert_eq!(nought_raw(), heron_sqrt_raw(&nought_raw()));
        }
    }

    mod multiplication {
        use crate::multiplication;

        #[test]
        fn basic_test() {
            let mpler = vec![2];
            let mcand = vec![3, 2];

            let prod = multiplication(&mpler, &mcand);
            assert_eq!(vec![6, 4], prod);
        }

        #[test]
        // does not support zero multiplication
        fn zero_multiplier_test() {
            let mpler = vec![0];
            let mcand = vec![3, 2, 1];

            let prod = multiplication(&mpler, &mcand);
            assert_eq!(vec![0, 0, 0], prod);
        }

        #[test]
        fn one_multiplier_test() {
            let mpler = vec![1];
            let mcand = vec![3, 2, 1];

            let prod = multiplication(&mpler, &mcand);
            assert_eq!(mcand, prod);
        }

        #[test]
        fn load_test() {
            let mpler = vec![1, 2, 3, 4, 5];
            let mcand = vec![5, 4, 3, 2, 1];
            let proof = new_from_num_raw!(670_592_745);

            let prod = multiplication(&mpler, &mcand);
            assert_eq!(proof, prod);
        }
    }

    mod power_steps {
        use crate::power_steps;

        #[test]
        fn basic_test() {
            let steps = power_steps(4);
            let proof = vec![4, 2];

            assert_eq!(proof, steps);
            assert_eq!(15, steps.capacity());
        }

        #[test]
        fn max_test() {
            let mut step = u16::MAX;
            let steps = power_steps(step);
            assert_eq!(15, steps.len());

            for s in steps {
                assert_eq!(step, s);
                step /= 2;
            }
        }

        #[test]
        fn odd_end_test() {
            let steps = power_steps(12);
            let proof = vec![12, 6, 3];

            assert_eq!(proof, steps);
        }

        #[test]
        fn even_end_test() {
            let steps = power_steps(16);
            let proof = vec![16, 8, 4, 2];

            assert_eq!(proof, steps);
        }
    }

    mod power {
        use crate::{new_from_str_raw, nought_raw, power, unity_raw};

        #[test]
        fn basic_test() {
            let pow = power(&[2], 16);
            assert_eq!(vec![6, 3, 5, 5, 6], pow);
        }

        #[test]
        #[should_panic(expected = "Pow steps for powers > 1 only.")]
        fn pow_zero_test() {
            _ = power(&[2], 0);
        }

        #[test]
        #[should_panic(expected = "Pow steps for powers > 1 only.")]
        fn pow_one_test() {
            _ = power(&[2], 1);
        }

        #[test]
        fn pow_of_zero_test() {
            let pows = [2, 3, 5, 11, 20];
            let zero = nought_raw();

            for p in pows {
                let pow = power(&zero, p);
                assert_eq!(zero, pow);
            }
        }

        #[test]
        fn pow_of_one_test() {
            let pows = [2, 3, 5, 11, 20];
            let one = unity_raw();

            for p in pows {
                let pow = power(&one, p);
                assert_eq!(one, pow);
            }
        }

        #[test]
        fn pow_two_test() {
            let pow = power(&[5, 5, 2], 2);
            assert_eq!(vec![5, 2, 0, 5, 6], pow);
        }

        #[test]
        fn odd_test() {
            let pow = power(&[5, 5, 2], 11);
            let proof = new_from_str_raw("296443535898840969287109375").unwrap();

            assert_eq!(proof, pow);
        }

        #[test]
        fn even_test() {
            let pow = power(&[5, 5, 2], 10);
            let proof = new_from_str_raw("1162523670191533212890625").unwrap();

            assert_eq!(proof, pow);
        }
    }

    use crate::clear_swap;
    #[test]
    fn clear_swap_test() {
        let mut mcand = vec![3, 2, 1];
        let mut i_sum = vec![6, 5, 4];

        let mcand_ptr = mcand.as_ptr() as usize;
        let i_sum_ptr = i_sum.as_ptr() as usize;

        clear_swap(&mut mcand, &mut i_sum);

        assert_eq!(mcand.as_ptr() as usize, i_sum_ptr);
        assert_eq!(i_sum.as_ptr() as usize, mcand_ptr);
        assert_eq!(vec![6, 5, 4], mcand);
        assert_eq!(0, i_sum.len());
    }

    mod muladd {
        use crate::muladd;

        #[test]
        fn basic_test() {
            let mpler = 2;
            let mcand = [2, 3, 4];
            let mut sum = Vec::new();

            muladd(mpler, &mcand, &mut sum, 0);
            assert_eq!(vec![4, 6, 8], sum);
        }

        #[test]
        fn multiplication_test() {
            let mpler = 9;
            let mcand = [9, 8, 7, 6];
            let mut sum = Vec::new();

            muladd(mpler, &mcand, &mut sum, 0);
            assert_eq!(vec![1, 0, 1, 1, 6], sum);
        }

        #[test]
        fn offset_test() {
            let mpler = 9;
            let mcand = [1, 0, 0, 9];
            let mut sum = Vec::new();

            muladd(mpler, &mcand, &mut sum, 1);
            assert_eq!(vec![9, 0, 0, 1, 8], sum);
        }

        #[test]
        fn sum_test() {
            let mpler = 9;
            let mcand = [9, 9, 9, 9];
            let mut sum = vec![9, 9, 9, 9, 9];

            muladd(mpler, &mcand, &mut sum, 0);
            assert_eq!(vec![0, 9, 9, 9, 8, 1], sum);
        }
    }

    mod sumadd {
        use crate::sumadd;

        #[test]
        fn basic_test() {
            let mut sum = vec![1];

            sumadd(1, &mut sum, 0);
            assert_eq!(vec![2], sum);
        }

        #[test]
        fn empty_sum_test() {
            let mut sum = vec![];

            sumadd(9, &mut sum, 0);
            assert_eq!(vec![9], sum);
        }

        #[test]
        fn offset_test() {
            let mut sum = vec![0, 1];

            sumadd(1, &mut sum, 1);
            assert_eq!(vec![0, 2], sum);
        }

        #[test]
        fn takeover_test() {
            let mut sum = vec![1];

            sumadd(9, &mut sum, 0);
            assert_eq!(vec![0, 1], sum);
        }

        #[test]
        fn extension_test() {
            let mut sum = vec![1];

            sumadd(9, &mut sum, 0);
            assert_eq!(vec![0, 1], sum);
        }

        #[test]
        fn max_product_test() {
            let mut sum = vec![9, 9, 9, 9, 9, 9];

            sumadd(81, &mut sum, 1);
            assert_eq!(vec![9, 0, 8, 0, 0, 0, 1], sum);
        }

        #[test]
        fn extreme_test() {
            let mut sum = vec![0];

            sumadd(255, &mut sum, 0);
            assert_eq!(vec![5, 5, 2], sum);
        }

        #[test]
        fn extreme_test2() {
            let mut sum = vec![9, 9, 9];

            sumadd(246, &mut sum, 0);
            assert_eq!(vec![5, 4, 2, 1], sum);
        }
    }

    /// Column addition fact notes:
    /// - When adding ones, maximum sum is 18=9+9.
    /// - Thus maximum tens sum is 1=⌊18÷10⌋.
    /// - Since 18+1=19 any value fits into 1=⌊19÷10⌋ ten.
    mod addition {

        mod addition_sum {
            use crate::addition_sum;

            #[test]
            fn basic_test() {
                let ad = vec![1, 2, 3];
                let mut sum = vec![4, 3, 2, 5, 5];

                addition_sum(&ad, &mut sum, 0);

                assert_eq!(vec![5, 5, 5, 5, 5], sum);
            }

            #[test]
            fn takover_test() {
                let ad = vec![9];
                let mut sum = vec![9, 9, 9, 9, 9];

                addition_sum(&ad, &mut sum, 0);

                assert_eq!(vec![8, 0, 0, 0, 0, 1], sum);
            }

            #[test]
            fn longer_addition_test() {
                let ad = vec![8, 8, 9, 9, 9];
                let mut sum = vec![1, 1];

                addition_sum(&ad, &mut sum, 0);

                assert_eq!(vec![9, 9, 9, 9, 9], sum);
            }

            #[test]
            fn offset_test() {
                let ad = vec![9, 9, 9, 9];
                let mut sum = vec![1, 1, 7, 8];

                addition_sum(&ad, &mut sum, 2);

                assert_eq!(vec![1, 1, 6, 8, 0, 0, 1], sum);
            }
        }

        mod addition_two {
            use crate::addition_two;

            #[test]
            fn basic_test() {
                let ad1 = vec![8, 8, 7, 5];
                let ad2 = vec![1, 1, 2, 4, 9, 9];
                let mut sum = Vec::new();

                addition_two(&ad1, &ad2, &mut sum);

                assert_eq!(vec![9, 9, 9, 9, 9, 9], sum);
            }

            #[test]
            fn takover_test1() {
                let ad1 = vec![99];
                let ad2 = vec![9];
                let mut sum = Vec::new();

                addition_two(&ad1, &ad2, &mut sum);

                assert_eq!(vec![8, 0, 1], sum);
            }

            #[test]
            fn takover_test2() {
                let ad1 = vec![9];
                let ad2 = vec![99];
                let mut sum = Vec::new();

                addition_two(&ad1, &ad2, &mut sum);

                assert_eq!(vec![8, 0, 1], sum);
            }

            #[test]
            fn longer_addition_test1() {
                let ad1 = vec![8, 8, 9, 9, 9];
                let ad2 = vec![1, 1];
                let mut sum = Vec::new();

                addition_two(&ad1, &ad2, &mut sum);

                assert_eq!(vec![9, 9, 9, 9, 9], sum);
            }

            #[test]
            fn longer_addition_test2() {
                let ad1 = vec![1, 1];
                let ad2 = vec![8, 8, 9, 9, 9];
                let mut sum = Vec::new();

                addition_two(&ad1, &ad2, &mut sum);

                assert_eq!(vec![9, 9, 9, 9, 9], sum);
            }
        }
    }

    /// Column subtraction fact notes:
    /// - Subtrahend always must be lower or equal to minuend.
    /// - Minimum difference is 0=a-a, maximum 9=9-0=(9+a)-a, a ∈ [0;9].
    /// - Maximum subtrahend is 10=9+1(takeover).
    mod subtraction {

        mod subtraction_arithmetical {
            use crate::{new_from_str_raw, subtraction_arithmetical};

            #[test]
            fn basic_test() {
                let mut mindiff = vec![9, 9];
                let ratio = subtraction_arithmetical(&mut mindiff, &vec![0, 1]);
                assert_eq!(&[9, 8], &*mindiff);
                assert_eq!(&[1], &*ratio);
            }

            #[test]
            fn advanced_test() {
                let mut mindiff =
                    new_from_str_raw("6577102745386680762814942322444851025767571854389858533375")
                        .unwrap();
                let subtrahend =
                    new_from_str_raw("6296101835386680762814942322444851025767571854389858533376")
                        .unwrap();
                let proof =
                    new_from_str_raw("281000909999999999999999999999999999999999999999999999999")
                        .unwrap();

                let ratio = subtraction_arithmetical(&mut mindiff, &subtrahend);
                assert_eq!(proof, mindiff);
                assert_eq!(&[1], &*ratio);
            }

            #[test]
            /// tests takeover ∈ [0,1] carry on
            fn takeover_test() {
                let mut mindiff = vec![8, 2, 2, 0, 1];
                let ratio = subtraction_arithmetical(&mut mindiff, &vec![9, 2, 1, 1]);
                assert_eq!(&[9, 9, 0, 9], &*mindiff);
                assert_eq!(&[1], &*ratio);
            }

            #[test]
            // after invalid subtraction on remainder, places hold numbers resulting
            // from borrowing and subtracting
            // e.g. [2,0,0,0,0]-[7,7,3]=[5,2,6,9,9]:
            // - after remainder restoration [2,0,0,9,9],
            // - after `9`s truncation [2,0,0],
            // - after `0`s truncation [2]
            fn overrun_clearing_test() {
                let mut mindiff = vec![2, 0, 0, 0, 0];
                let ratio = subtraction_arithmetical(&mut mindiff, &vec![7, 7, 3]);

                assert_eq!(&[2, 0, 0, 9, 9], &*mindiff);
                assert_eq!(&[0], &*ratio);
            }

            #[test]
            fn zero_truncation_test() {
                let mut mindiff = vec![9, 9, 9];
                let ratio = subtraction_arithmetical(&mut mindiff, &vec![8, 9, 9]);
                assert_eq!(&[1], &*mindiff);
                assert_eq!(&[1], &*ratio);
            }

            // because it can be
            // [1,0,9] - [2,0,9] = [9,9,9]
            // [9,9,9] + [2,0,9] = [1,0,9]
            // top place 9 must be preserved
            #[test]
            fn top_place_9_preservation_test() {
                let mindiff = vec![1, 0, 9];
                let mut proof = mindiff.clone();

                let ratio = subtraction_arithmetical(&mut proof, &vec![2, 0, 9]);
                assert_eq!(mindiff, proof);
                assert_eq!(&[0], &*ratio);
            }

            // [1,1,1] - [3,4,7] = [8,6,3]
            // [8,6,3] + [3,4,7] = [1,1,1]
            // not user scenario, only internal expectation
            #[test]
            fn lesser_minuend_test() {
                let mindiff = vec![1, 1, 1];
                let mut proof = mindiff.clone();
                let ratio = subtraction_arithmetical(&mut proof, &vec![3, 4, 7]);
                assert_eq!(mindiff, proof);
                assert_eq!(&[0], &*ratio);
            }

            #[test]
            fn equal_operands_test() {
                let mut mindiff = vec![1, 1, 1];
                let subtrahend = mindiff.clone();

                let ratio = subtraction_arithmetical(&mut mindiff, &subtrahend);
                assert_eq!(&[0], &*mindiff);
                assert_eq!(&[1], &*ratio);
            }
        }

        mod subtraction_divisional {
            use crate::subtraction_divisional;

            #[test]
            fn basic_test() {
                let mut minrem = vec![3, 3];
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &vec![1, 1]);
                assert_eq!(&[0, 0], &*minrem);
                assert_eq!(&[3], &*ratio);
                assert_eq!(0, rem_len);
            }

            #[test]
            fn remainder_test() {
                let mut minrem = vec![9];
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &vec![7]);
                assert_eq!(&[2], &*minrem);
                assert_eq!(&[1], &*ratio);
                assert_eq!(1, rem_len);
            }

            #[test]
            fn takeover_test() {
                let mut minrem = vec![9, 0, 9];
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &vec![9]);
                assert_eq!(&[0, 9, 9], &*minrem);
                assert_eq!(&[1, 0, 1], &*ratio);
                assert_eq!(0, rem_len);
            }

            #[test]
            // after invalid subtraction on remainder, places hold numbers resulting
            // from borrowing and subtracting
            // e.g. [2,0,0,7,7]-[7,7]=[5,2,9,9,9]:
            // - after remainder restoration [2,0,9,9,9],
            // - after `9`s truncation [2,0],
            // - after `0`s truncation [2]
            fn overrun_clearing_test() {
                let mut minrem = vec![2, 0, 0, 7, 7];
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &vec![7, 7]);

                assert_eq!(&[2, 0, 9, 9, 9], &*minrem);
                assert_eq!(&[0, 0, 0, 1], &*ratio);
                assert_eq!(1, rem_len);
            }

            #[test]
            fn advanced_test() {
                let mut minrem = new_from_num_raw!(627710173);
                let remainder = new_from_num_raw!(999999_130);
                let ratio = new_from_num_raw!(1955483);

                let (rat, rem_len) = subtraction_divisional(&mut minrem, &vec![1, 2, 3]);
                assert_eq!(remainder, minrem);
                assert_eq!(ratio, rat);
                assert_eq!(3, rem_len);
            }

            #[test]
            fn advanced_test2() {
                let mut minrem = new_from_num_raw!(627710173);
                let subtrahend = new_from_num_raw!(3552741);
                let remainder = new_from_num_raw!(99__2_427_757);
                let ratio = new_from_num_raw!(176);

                let (rat, rem_len) = subtraction_divisional(&mut minrem, &subtrahend);
                assert_eq!(remainder, minrem);
                assert_eq!(ratio, rat);
                assert_eq!(7, rem_len);
            }

            #[test]
            fn advanced_test3() {
                let mut minrem = new_from_num_raw!(242775712);
                let subtrahend = new_from_num_raw!(33333);
                let remainder = new_from_num_raw!(9999__11_473);
                let ratio = new_from_num_raw!(7283);

                let (rat, rem_len) = subtraction_divisional(&mut minrem, &subtrahend);
                assert_eq!(remainder, minrem);
                assert_eq!(ratio, rat);
                assert_eq!(5, rem_len);
            }

            // because it can be
            // [1,0,9] - [2,0,9] = [9,9,9]
            // [9,9,9] + [2,0,9] = [1,0,9]
            // top place 9 must be preserved
            // 5411 = 5 ·902 +901
            #[test]
            fn top_place_9_preservation_test() {
                let mut minrem = vec![1, 1, 4, 5];
                let subtrahend = vec![2, 0, 9];
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &subtrahend);
                assert_eq!(&[1, 0, 9, 9], &*minrem);
                assert_eq!(&[5], &*ratio);
                assert_eq!(3, rem_len);
            }

            // [1,1,1] - [3,4,7] = [8,6,3]
            // [8,6,3] + [3,4,7] = [1,1,1]
            // implied by means of overrun correction
            #[test]
            fn lesser_dividend_test() {
                let mut minrem = vec![1, 1, 1];
                let proof = minrem.clone();
                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &vec![3, 4, 7]);
                assert_eq!(proof, minrem);
                assert_eq!(&[0], &*ratio);
                assert_eq!(3, rem_len);
            }

            // implied by means of overrun correction
            #[test]
            fn equal_operands_test() {
                let mut minrem = vec![1, 1, 1];
                let subtrahend = vec![1, 1, 1];

                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &subtrahend);
                assert_eq!(&[0, 0, 0], &*minrem);
                assert_eq!(&[1], &*ratio);
                assert_eq!(0, rem_len);
            }

            #[test]
            #[cfg(feature = "shorter-dividend-support")]
            fn shorter_dividend_test() {
                let mut minrem = vec![1, 1, 1];
                let subtrahend = vec![0, 4, 6, 8, 9, 3, 4, 7];
                let proof = minrem.clone();

                let (ratio, rem_len) = subtraction_divisional(&mut minrem, &subtrahend);
                assert_eq!(proof, minrem);
                assert_eq!(&[0], &*ratio);
                assert_eq!(3, rem_len);
            }
        }

        mod subtraction {

            use crate::subtraction;

            #[test]
            // after invalid subtraction on remainder, places hold numbers resulting
            // from borrowing and subtracting
            // e.g. [2,0,0,7,7]-[7,7]=[5,2,9,9,9]:
            // - after remainder restoration [2,0,9,9,9],
            // - after `9`s truncation [2,0],
            // - after `0`s truncation [2]
            fn overrun_test_1() {
                let mut ctr = 0;
                let mut minrem = vec![2, 0, 0, 7, 7];
                let ratio = subtraction(&mut minrem, &vec![7, 7], true, &mut ctr);

                assert_eq!(&[2, 0, 9, 9, 9], &*minrem);
                assert_eq!(&[0, 0, 0, 1], &*ratio);
                assert_eq!(1001, ctr);
            }

            #[test]
            // after invalid subtraction on remainder, places hold numbers resulting
            // from borrowing and subtracting
            // e.g. [2,0,0,0,0]-[7,7,3]=[5,2,6,9,9]:
            // - after remainder restoration [2,0,0,9,9],
            // - after `9`s truncation [2,0,0],
            // - after `0`s truncation [2]
            fn overrun_test_2() {
                let mut ctr = 0;
                let mut minrem = vec![2, 0, 0, 0, 0];
                let ratio = subtraction(&mut minrem, &vec![7, 7, 3], false, &mut ctr);

                assert_eq!(&[2, 0, 0, 9, 9], &*minrem);
                assert_eq!(&[0], &*ratio);
                assert_eq!(1, ctr);
            }
        }
    }

    /// Supporting method. Desinged to split ones from tens. Supports any range of tens.
    mod ones {
        use crate::ones;

        #[test]
        fn basic_test() {
            let num = 9;
            let mut takeover = 0;

            assert_eq!(9, ones(num, &mut takeover));
            assert_eq!(0, takeover);
        }

        #[test]
        fn split_test() {
            let num = 9;
            let mut takeover = 3;

            assert_eq!(2, ones(num, &mut takeover));
            assert_eq!(1, takeover);
        }

        #[test]
        fn maximum_test() {
            let num = 246;
            let mut takeover = 9;

            assert_eq!(5, ones(num, &mut takeover));
            assert_eq!(25, takeover);
        }
    }
}

// cargo fmt & cargo test --features ext-tests --release
// cargo test --features ext-tests2 --release primes_ext_test
// cargo test --features ext-tests3 --release primes_ext2_test
// cargo test --features ext-tests,shorter-dividend-support --release
// cargo fmt && cargo test --release
// cargo bench --test bench