lexical_write_integer/

algorithm.rs

//! Radix-generic, optimized, integer-to-string conversion routines.
//!
//! These routines are highly optimized: they unroll 4 loops at a time,
//! using pre-computed base^2 tables. This was popularized by Andrei
//! Alexandrescu, and uses 2 digits per division, which we further optimize in
//! up to 4 digits per division with a bit shift.
//!
//! See [Algorithm](/docs/Algorithm.md) for a more detailed description of
//! the algorithm choice here. See [Benchmarks](/docs/Benchmarks.md) for
//! recent benchmark data.

#![cfg(not(feature = "compact"))]
#![cfg(feature = "power-of-two")]
#![doc(hidden)]

use lexical_util::assert::debug_assert_radix;
use lexical_util::digit::digit_to_char;
use lexical_util::div128::u128_divrem;
use lexical_util::format::{radix_from_flags, NumberFormat};
use lexical_util::num::{AsCast, UnsignedInteger};
use lexical_util::step::u64_step;

use crate::digit_count::DigitCount;

/// Index a buffer and get a mutable reference, without bounds checking.
/// The `($x:ident[$i:expr] = $y:ident[$j:expr])` is not used with [`compact`].
/// The newer version of the lint is `unused_macro_rules`, but this isn't
/// supported until nightly-2022-05-12.
///
/// By default, writers tend to be safe, due to Miri, Valgrind,
/// and other tests and careful validation against a wide range
/// of randomized input. Parsers are much trickier to validate.
///
/// [`compact`]: crate#compact
#[allow(unknown_lints, unused_macro_rules)]
macro_rules! i {
    ($x:ident[$i:expr]) => {
        *$x.get_unchecked_mut($i)
    };

    ($x:ident[$i:expr] = $y:ident[$j:expr]) => {
        *$x.get_unchecked_mut($i) = *$y.get_unchecked($j)
    };
}

/// Write 2 digits to buffer.
///
/// # Safety
///
/// Safe if `bytes` is large enough to hold 2 characters, `index >= 2`,
/// and if the 2 * remainder, or `r`, has it so `r + 1 < table.len()`.
macro_rules! write_digits {
    ($bytes:ident, $index:ident, $table:ident, $r:ident) => {{
        debug_assert!($index >= 2);
        debug_assert!($bytes.len() >= 2);
        debug_assert!($r + 1 < $table.len());
        $index -= 1;
        unsafe { i!($bytes[$index] = $table[$r + 1]) };
        $index -= 1;
        unsafe { i!($bytes[$index] = $table[$r]) };
    }};
}

/// Write 1 digit to buffer.
///
/// # Safety
///
/// Safe if `bytes` is large enough to hold 1 characters, and `r < 36`.
/// Adding in direct safety checks here destroys performance, often by
/// 30%+ so it's up to the caller to beware.
macro_rules! write_digit {
    ($bytes:ident, $index:ident, $r:ident) => {{
        debug_assert!($index >= 1);
        debug_assert!($bytes.len() >= 1);
        debug_assert!($r < 36);
        $index -= 1;
        unsafe { i!($bytes[$index]) = digit_to_char($r) };
    }};
}

// NOTE: Don't use too many generics:
//  We don't need generics for most of the internal algorithms,
//  and doing so kills performance. Why? I don't know, but assuming
//  it messed with the compiler's code generation.

/// Write integral digits to buffer.
///
/// This algorithm first writes 4, then 2 digits at a time, finally
/// the last 1 or 2 digits, using power reduction to speed up the
/// algorithm a lot.
///
/// # Safety
///
/// This is safe as long as the buffer is large enough to hold `T::MAX`
/// digits in radix `N` and the index >= digit count. Note  that making
/// small changes here can destroy performance, so it's crucial we do this
/// correctly.
///
/// If `buffer.len() >= T::DIGITS` and `index >= T::DIGITS`, then this is
/// safe. We first carve off 4 digits off the end, similar to the algorithm
/// in compact, then 2 at a time, then 1, index will never wrap under 0.
/// Since we validate the table size and radix inside, this is the only
/// safety precondition that must be held up.
///
/// See [algorithm] and the [crate] documentation for more detailed
/// information on the safety considerations.
#[inline(always)]
unsafe fn write_digits<T: UnsignedInteger>(
    mut value: T,
    radix: u32,
    table: &[u8],
    buffer: &mut [u8],
    mut index: usize,
    count: usize,
) -> usize {
    debug_assert_radix(radix);
    debug_assert!(buffer.len() >= count, "buffer must at least be as the digit count");

    // Calculate if we can do multi-digit optimizations
    assert!((2..=36).contains(&radix), "radix must be >= 2 and <= 36");
    let radix2 = radix * radix;
    let radix4 = radix2 * radix2;

    // Pre-compute our powers of radix.
    let radix = T::from_u32(radix);

    // SAFETY: All of these are safe for the buffer writes as long as
    // the buffer is large enough to hold `T::MAX` digits in radix `N`.
    // We confirm (which will be compiled out) that the table cannot
    // overflow since it's the indexing is `0..radix^2 * 2`.
    assert!(table.len() >= radix2 as usize * 2, "table must be 2 * radix^2 long");

    // Decode 4 digits at a time.
    if T::BITS >= 32 || radix4 < T::MAX.as_u32() {
        let radix2 = T::from_u32(radix2);
        let radix4 = T::from_u32(radix4);
        while value >= radix4 {
            let r = value % radix4;
            value /= radix4;
            let r1 = usize::as_cast(T::TWO * (r / radix2));
            let r2 = usize::as_cast(T::TWO * (r % radix2));

            // SAFETY: This is always safe, since the table is `2*radix^2`, and
            // `r1` and `r2` must be in the range `[0, 2*radix^2-1)`, since the maximum
            // value of r is `radix4-1`, which must have a `div` and `r`
            // in the range `[0, radix^2-1)`.
            write_digits!(buffer, index, table, r2);
            write_digits!(buffer, index, table, r1);
        }
    }

    // Decode 2 digits at a time.
    if T::BITS >= 16 || radix2 < T::MAX.as_u32() {
        let radix2 = T::from_u32(radix2);
        while value >= radix2 {
            let r = usize::as_cast(T::TWO * (value % radix2));
            value /= radix2;

            // SAFETY: this is always safe, since the table is `2*radix^2`, and
            // `r` must be in the range `[0, 2*radix^2-1)`.
            write_digits!(buffer, index, table, r);
        }
    }

    // Decode last 2 digits.
    if value < radix {
        let r = u32::as_cast(value);
        // SAFETY: this is always safe, since `value < radix`, so it must be < 36.
        write_digit!(buffer, index, r);
    } else {
        // NOTE: If this is a `u8`, we need to first widen the type.
        let r = usize::as_cast(T::TWO) * usize::as_cast(value);
        // SAFETY: this is always safe, since the table is `2*radix^2`, and
        // the value must `<= radix^2`, so rem must be in the range
        // `[0, 2*radix^2-1)`.
        write_digits!(buffer, index, table, r);
    }

    index
}

/// Specialized digits writer for u128, since it writes at least step digits.
///
/// # Safety
///
/// This is safe as long as the buffer is large enough to hold `T::MAX`
/// digits in radix `N`. See [algorithm] for more safety considerations.
#[inline(always)]
unsafe fn write_step_digits<T: UnsignedInteger>(
    value: T,
    radix: u32,
    table: &[u8],
    buffer: &mut [u8],
    index: usize,
    step: usize,
    count: usize,
) -> usize {
    debug_assert_radix(radix);

    let start = index;
    // SAFETY: safe as long as the call to `write_step_digits` is safe.
    let index = unsafe { write_digits(value, radix, table, buffer, index, count) };
    // Write the remaining 0 bytes.
    let end = start.saturating_sub(step);
    // SAFETY: this is always safe since `end < index && index < start`.
    let zeros = unsafe { &mut i!(buffer[end..index]) };
    zeros.fill(b'0');

    end
}

/// Optimized implementation for radix-N numbers.
///
/// This uses an Alexandrescu algorithm, which prints 2 digits at a time
/// which is much faster than a naive approach. However, the jeaiii algorithm
/// can be faster still for decimal numbers:
///     <https://jk-jeon.github.io/posts/2022/02/jeaiii-algorithm/>
///
/// # Safety
///
/// Safe as long as [`digit_count`] returns the number of written digits.
/// For performance reasons, this is always calculated as the exact number
/// of digits. If the value is too small, then the buffer will underflow,
/// causing out-of-bounds read/writes. Care must be used that [`digit_count`]
/// is correctly implemented.
///
/// Since [`digit_count`] is implemented as an unsafe trait, these guarantees
/// must be held.
///
/// See the crate [`crate`] documentation for more security considerations.
///
/// [`digit_count`]: `crate::digit_count::DigitCount`
#[inline(always)]
#[allow(clippy::unnecessary_safety_comment)]
pub fn algorithm<T>(value: T, radix: u32, table: &[u8], buffer: &mut [u8]) -> usize
where
    T: UnsignedInteger + DigitCount,
{
    // NOTE: These checks should be resolved at compile time, so
    // they're unlikely to add any performance overhead.
    assert!((2..=36).contains(&radix), "radix must be >= 2 and <= 36");
    assert!(table.len() >= (radix * radix * 2) as usize, "table must be 2 * radix^2 long");

    // get our digit count and only write up until that range
    // the digit count should be the exact number of digits written by
    // the number. this is for performance reasons: using `memcpy` destroys
    // performance.
    let count = value.digit_count(radix);
    assert!(
        count <= buffer.len(),
        "The buffer must be large enough to contain the significant digits."
    );
    let buffer = &mut buffer[..count];

    // SAFETY: Both forms of unchecked indexing cannot overflow.
    // The table always has `2*radix^2` elements, so it must be a legal index.
    // The buffer is ensured to have at least `FORMATTED_SIZE` or
    // `FORMATTED_SIZE_DECIMAL` characters, which is the maximum number of
    // digits an integer of that size may write.
    _ = unsafe { write_digits(value, radix, table, buffer, buffer.len(), count) };

    count
}

/// Optimized implementation for radix-N 128-bit numbers.
///
/// # Safety
///
/// Safe as long as [`digit_count`] returns the number of written digits.
/// For performance reasons, this is always calculated as the exact number
/// of digits. If the value is too small, then the buffer will underflow,
/// causing out-of-bounds read/writes. Care must be used that [`digit_count`]
/// is correctly implemented.
///
/// Since [`digit_count`] is implemented as an unsafe trait, these guarantees
/// must be held.
///
/// See the crate [`crate`] documentation for more security considerations.
///
/// [`digit_count`]: `crate::digit_count::DigitCount`
#[inline(always)]
pub fn algorithm_u128<const FORMAT: u128, const MASK: u128, const SHIFT: i32>(
    value: u128,
    table: &[u8],
    buffer: &mut [u8],
) -> usize {
    // NOTE: Use the const version of radix for `u64_step` and
    // `u128_divrem` to ensure they're evaluated at compile time.
    assert!(NumberFormat::<{ FORMAT }> {}.is_valid());
    // NOTE: These checks should be resolved at compile time, so
    // they're unlikely to add any performance overhead.
    let radix = radix_from_flags(FORMAT, MASK, SHIFT);
    assert!((2..=36).contains(&radix), "radix must be >= 2 and <= 36");
    assert!(table.len() >= (radix * radix * 2) as usize, "table must be 2 * radix^2 long");

    // Quick approximations to make the algorithm **a lot** faster.
    // If the value can be represented in a 64-bit integer, we can
    // do this as a native integer.
    if value <= u64::MAX as u128 {
        return algorithm(value as u64, radix, table, buffer);
    }

    // get our digit count and only write up until that range
    // the digit count should be the exact number of digits written by
    // the number. this is for performance reasons: using `memcpy` destroys
    // performance.
    let count = value.digit_count(radix);
    assert!(
        count <= buffer.len(),
        "The buffer must be large enough to contain the significant digits."
    );
    let buffer = &mut buffer[..count];

    // LOGIC: Both forms of unchecked indexing cannot overflow.
    // The table always has `2*radix^2` elements, so it must be a legal index.
    // The buffer is ensured to have at least `FORMATTED_SIZE` or
    // `FORMATTED_SIZE_DECIMAL` characters, which is the maximum number of
    // digits an integer of that size may write.

    // We use a fast 128-bit division algorithm, described in depth
    // in lexical_util/div128.

    // Decode 4-digits at a time.
    // To deal with internal 0 values or values with internal 0 digits set,
    // we store the starting index, and if not all digits are written,
    // we just skip down `digits` digits for the next value.
    let step = u64_step(radix);
    let (value, low) = u128_divrem(value, radix);
    let mut index = count;
    index = unsafe { write_step_digits(low, radix, table, buffer, index, step, count) };
    if value <= u64::MAX as u128 {
        unsafe { write_digits(value as u64, radix, table, buffer, index, count) };
        return count;
    }

    // Value has to be greater than 1.8e38
    let (value, mid) = u128_divrem(value, radix);
    index = unsafe { write_step_digits(mid, radix, table, buffer, index, step, count) };
    if index != 0 {
        debug_assert!(value != 0, "Writing high digits, must have a non-zero value.");
        index = unsafe { write_digits(value as u64, radix, table, buffer, index, count) };
    } else {
        debug_assert!(value == 0, "No more digits left to write, remainder must be 0.");
    }
    debug_assert!(
        index == 0,
        "The index after writing all digits should be at the start of the buffer."
    );

    count
}