Adding upstream version 115.7.0esr.upstream/115.7.0esrupstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 403 insertions, 0 deletions

diff --git a/third_party/rust/minimal-lexical/src/slow.rs b/third_party/rust/minimal-lexical/src/slow.rs
new file mode 100644
index 0000000000..59d526ba42
--- /dev/null
+++ b/third_party/rust/minimal-lexical/src/slow.rs
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+//! Slow, fallback cases where we cannot unambiguously round a float.
+//!
+//! This occurs when we cannot determine the exact representation using
+//! both the fast path (native) cases nor the Lemire/Bellerophon algorithms,
+//! and therefore must fallback to a slow, arbitrary-precision representation.
+
+#![doc(hidden)]
+
+use crate::bigint::{Bigint, Limb, LIMB_BITS};
+use crate::extended_float::{extended_to_float, ExtendedFloat};
+use crate::num::Float;
+use crate::number::Number;
+use crate::rounding::{round, round_down, round_nearest_tie_even};
+use core::cmp;
+
+// ALGORITHM
+// ---------
+
+/// Parse the significant digits and biased, binary exponent of a float.
+///
+/// This is a fallback algorithm that uses a big-integer representation
+/// of the float, and therefore is considerably slower than faster
+/// approximations. However, it will always determine how to round
+/// the significant digits to the nearest machine float, allowing
+/// use to handle near half-way cases.
+///
+/// Near half-way cases are halfway between two consecutive machine floats.
+/// For example, the float `16777217.0` has a bitwise representation of
+/// `100000000000000000000000 1`. Rounding to a single-precision float,
+/// the trailing `1` is truncated. Using round-nearest, tie-even, any
+/// value above `16777217.0` must be rounded up to `16777218.0`, while
+/// any value before or equal to `16777217.0` must be rounded down
+/// to `16777216.0`. These near-halfway conversions therefore may require
+/// a large number of digits to unambiguously determine how to round.
+#[inline]
+pub fn slow<'a, F, Iter1, Iter2>(
+    num: Number,
+    fp: ExtendedFloat,
+    integer: Iter1,
+    fraction: Iter2,
+) -> ExtendedFloat
+where
+    F: Float,
+    Iter1: Iterator<Item = &'a u8> + Clone,
+    Iter2: Iterator<Item = &'a u8> + Clone,
+{
+    // Ensure our preconditions are valid:
+    //  1. The significant digits are not shifted into place.
+    debug_assert!(fp.mant & (1 << 63) != 0);
+
+    // This assumes the sign bit has already been parsed, and we're
+    // starting with the integer digits, and the float format has been
+    // correctly validated.
+    let sci_exp = scientific_exponent(&num);
+
+    // We have 2 major algorithms we use for this:
+    //  1. An algorithm with a finite number of digits and a positive exponent.
+    //  2. An algorithm with a finite number of digits and a negative exponent.
+    let (bigmant, digits) = parse_mantissa(integer, fraction, F::MAX_DIGITS);
+    let exponent = sci_exp + 1 - digits as i32;
+    if exponent >= 0 {
+        positive_digit_comp::<F>(bigmant, exponent)
+    } else {
+        negative_digit_comp::<F>(bigmant, fp, exponent)
+    }
+}
+
+/// Generate the significant digits with a positive exponent relative to mantissa.
+pub fn positive_digit_comp<F: Float>(mut bigmant: Bigint, exponent: i32) -> ExtendedFloat {
+    // Simple, we just need to multiply by the power of the radix.
+    // Now, we can calculate the mantissa and the exponent from this.
+    // The binary exponent is the binary exponent for the mantissa
+    // shifted to the hidden bit.
+    bigmant.pow(10, exponent as u32).unwrap();
+
+    // Get the exact representation of the float from the big integer.
+    // hi64 checks **all** the remaining bits after the mantissa,
+    // so it will check if **any** truncated digits exist.
+    let (mant, is_truncated) = bigmant.hi64();
+    let exp = bigmant.bit_length() as i32 - 64 + F::EXPONENT_BIAS;
+    let mut fp = ExtendedFloat {
+        mant,
+        exp,
+    };
+
+    // Shift the digits into position and determine if we need to round-up.
+    round::<F, _>(&mut fp, |f, s| {
+        round_nearest_tie_even(f, s, |is_odd, is_halfway, is_above| {
+            is_above || (is_halfway && is_truncated) || (is_odd && is_halfway)
+        });
+    });
+    fp
+}
+
+/// Generate the significant digits with a negative exponent relative to mantissa.
+///
+/// This algorithm is quite simple: we have the significant digits `m1 * b^N1`,
+/// where `m1` is the bigint mantissa, `b` is the radix, and `N1` is the radix
+/// exponent. We then calculate the theoretical representation of `b+h`, which
+/// is `m2 * 2^N2`, where `m2` is the bigint mantissa and `N2` is the binary
+/// exponent. If we had infinite, efficient floating precision, this would be
+/// equal to `m1 / b^-N1` and then compare it to `m2 * 2^N2`.
+///
+/// Since we cannot divide and keep precision, we must multiply the other:
+/// if we want to do `m1 / b^-N1 >= m2 * 2^N2`, we can do
+/// `m1 >= m2 * b^-N1 * 2^N2` Going to the decimal case, we can show and example
+/// and simplify this further: `m1 >= m2 * 2^N2 * 10^-N1`. Since we can remove
+/// a power-of-two, this is `m1 >= m2 * 2^(N2 - N1) * 5^-N1`. Therefore, if
+/// `N2 - N1 > 0`, we need have `m1 >= m2 * 2^(N2 - N1) * 5^-N1`, otherwise,
+/// we have `m1 * 2^(N1 - N2) >= m2 * 5^-N1`, where the resulting exponents
+/// are all positive.
+///
+/// This allows us to compare both floats using integers efficiently
+/// without any loss of precision.
+#[allow(clippy::comparison_chain)]
+pub fn negative_digit_comp<F: Float>(
+    bigmant: Bigint,
+    mut fp: ExtendedFloat,
+    exponent: i32,
+) -> ExtendedFloat {
+    // Ensure our preconditions are valid:
+    //  1. The significant digits are not shifted into place.
+    debug_assert!(fp.mant & (1 << 63) != 0);
+
+    // Get the significant digits and radix exponent for the real digits.
+    let mut real_digits = bigmant;
+    let real_exp = exponent;
+    debug_assert!(real_exp < 0);
+
+    // Round down our extended-precision float and calculate `b`.
+    let mut b = fp;
+    round::<F, _>(&mut b, round_down);
+    let b = extended_to_float::<F>(b);
+
+    // Get the significant digits and the binary exponent for `b+h`.
+    let theor = bh(b);
+    let mut theor_digits = Bigint::from_u64(theor.mant);
+    let theor_exp = theor.exp;
+
+    // We need to scale the real digits and `b+h` digits to be the same
+    // order. We currently have `real_exp`, in `radix`, that needs to be
+    // shifted to `theor_digits` (since it is negative), and `theor_exp`
+    // to either `theor_digits` or `real_digits` as a power of 2 (since it
+    // may be positive or negative). Try to remove as many powers of 2
+    // as possible. All values are relative to `theor_digits`, that is,
+    // reflect the power you need to multiply `theor_digits` by.
+    //
+    // Both are on opposite-sides of equation, can factor out a
+    // power of two.
+    //
+    // Example: 10^-10, 2^-10   -> ( 0, 10, 0)
+    // Example: 10^-10, 2^-15   -> (-5, 10, 0)
+    // Example: 10^-10, 2^-5    -> ( 5, 10, 0)
+    // Example: 10^-10, 2^5     -> (15, 10, 0)
+    let binary_exp = theor_exp - real_exp;
+    let halfradix_exp = -real_exp;
+    if halfradix_exp != 0 {
+        theor_digits.pow(5, halfradix_exp as u32).unwrap();
+    }
+    if binary_exp > 0 {
+        theor_digits.pow(2, binary_exp as u32).unwrap();
+    } else if binary_exp < 0 {
+        real_digits.pow(2, (-binary_exp) as u32).unwrap();
+    }
+
+    // Compare our theoretical and real digits and round nearest, tie even.
+    let ord = real_digits.data.cmp(&theor_digits.data);
+    round::<F, _>(&mut fp, |f, s| {
+        round_nearest_tie_even(f, s, |is_odd, _, _| {
+            // Can ignore `is_halfway` and `is_above`, since those were
+            // calculates using less significant digits.
+            match ord {
+                cmp::Ordering::Greater => true,
+                cmp::Ordering::Less => false,
+                cmp::Ordering::Equal if is_odd => true,
+                cmp::Ordering::Equal => false,
+            }
+        });
+    });
+    fp
+}
+
+/// Add a digit to the temporary value.
+macro_rules! add_digit {
+    ($c:ident, $value:ident, $counter:ident, $count:ident) => {{
+        let digit = $c - b'0';
+        $value *= 10 as Limb;
+        $value += digit as Limb;
+
+        // Increment our counters.
+        $counter += 1;
+        $count += 1;
+    }};
+}
+
+/// Add a temporary value to our mantissa.
+macro_rules! add_temporary {
+    // Multiply by the small power and add the native value.
+    (@mul $result:ident, $power:expr, $value:expr) => {
+        $result.data.mul_small($power).unwrap();
+        $result.data.add_small($value).unwrap();
+    };
+
+    // # Safety
+    //
+    // Safe is `counter <= step`, or smaller than the table size.
+    ($format:ident, $result:ident, $counter:ident, $value:ident) => {
+        if $counter != 0 {
+            // SAFETY: safe, since `counter <= step`, or smaller than the table size.
+            let small_power = unsafe { f64::int_pow_fast_path($counter, 10) };
+            add_temporary!(@mul $result, small_power as Limb, $value);
+            $counter = 0;
+            $value = 0;
+        }
+    };
+
+    // Add a temporary where we won't read the counter results internally.
+    //
+    // # Safety
+    //
+    // Safe is `counter <= step`, or smaller than the table size.
+    (@end $format:ident, $result:ident, $counter:ident, $value:ident) => {
+        if $counter != 0 {
+            // SAFETY: safe, since `counter <= step`, or smaller than the table size.
+            let small_power = unsafe { f64::int_pow_fast_path($counter, 10) };
+            add_temporary!(@mul $result, small_power as Limb, $value);
+        }
+    };
+
+    // Add the maximum native value.
+    (@max $format:ident, $result:ident, $counter:ident, $value:ident, $max:ident) => {
+        add_temporary!(@mul $result, $max, $value);
+        $counter = 0;
+        $value = 0;
+    };
+}
+
+/// Round-up a truncated value.
+macro_rules! round_up_truncated {
+    ($format:ident, $result:ident, $count:ident) => {{
+        // Need to round-up.
+        // Can't just add 1, since this can accidentally round-up
+        // values to a halfway point, which can cause invalid results.
+        add_temporary!(@mul $result, 10, 1);
+        $count += 1;
+    }};
+}
+
+/// Check and round-up the fraction if any non-zero digits exist.
+macro_rules! round_up_nonzero {
+    ($format:ident, $iter:expr, $result:ident, $count:ident) => {{
+        for &digit in $iter {
+            if digit != b'0' {
+                round_up_truncated!($format, $result, $count);
+                return ($result, $count);
+            }
+        }
+    }};
+}
+
+/// Parse the full mantissa into a big integer.
+///
+/// Returns the parsed mantissa and the number of digits in the mantissa.
+/// The max digits is the maximum number of digits plus one.
+pub fn parse_mantissa<'a, Iter1, Iter2>(
+    mut integer: Iter1,
+    mut fraction: Iter2,
+    max_digits: usize,
+) -> (Bigint, usize)
+where
+    Iter1: Iterator<Item = &'a u8> + Clone,
+    Iter2: Iterator<Item = &'a u8> + Clone,
+{
+    // Iteratively process all the data in the mantissa.
+    // We do this via small, intermediate values which once we reach
+    // the maximum number of digits we can process without overflow,
+    // we add the temporary to the big integer.
+    let mut counter: usize = 0;
+    let mut count: usize = 0;
+    let mut value: Limb = 0;
+    let mut result = Bigint::new();
+
+    // Now use our pre-computed small powers iteratively.
+    // This is calculated as `⌊log(2^BITS - 1, 10)⌋`.
+    let step: usize = if LIMB_BITS == 32 {
+        9
+    } else {
+        19
+    };
+    let max_native = (10 as Limb).pow(step as u32);
+
+    // Process the integer digits.
+    'integer: loop {
+        // Parse a digit at a time, until we reach step.
+        while counter < step && count < max_digits {
+            if let Some(&c) = integer.next() {
+                add_digit!(c, value, counter, count);
+            } else {
+                break 'integer;
+            }
+        }
+
+        // Check if we've exhausted our max digits.
+        if count == max_digits {
+            // Need to check if we're truncated, and round-up accordingly.
+            // SAFETY: safe since `counter <= step`.
+            add_temporary!(@end format, result, counter, value);
+            round_up_nonzero!(format, integer, result, count);
+            round_up_nonzero!(format, fraction, result, count);
+            return (result, count);
+        } else {
+            // Add our temporary from the loop.
+            // SAFETY: safe since `counter <= step`.
+            add_temporary!(@max format, result, counter, value, max_native);
+        }
+    }
+
+    // Skip leading fraction zeros.
+    // Required to get an accurate count.
+    if count == 0 {
+        for &c in &mut fraction {
+            if c != b'0' {
+                add_digit!(c, value, counter, count);
+                break;
+            }
+        }
+    }
+
+    // Process the fraction digits.
+    'fraction: loop {
+        // Parse a digit at a time, until we reach step.
+        while counter < step && count < max_digits {
+            if let Some(&c) = fraction.next() {
+                add_digit!(c, value, counter, count);
+            } else {
+                break 'fraction;
+            }
+        }
+
+        // Check if we've exhausted our max digits.
+        if count == max_digits {
+            // SAFETY: safe since `counter <= step`.
+            add_temporary!(@end format, result, counter, value);
+            round_up_nonzero!(format, fraction, result, count);
+            return (result, count);
+        } else {
+            // Add our temporary from the loop.
+            // SAFETY: safe since `counter <= step`.
+            add_temporary!(@max format, result, counter, value, max_native);
+        }
+    }
+
+    // We will always have a remainder, as long as we entered the loop
+    // once, or counter % step is 0.
+    // SAFETY: safe since `counter <= step`.
+    add_temporary!(@end format, result, counter, value);
+
+    (result, count)
+}
+
+// SCALING
+// -------
+
+/// Calculate the scientific exponent from a `Number` value.
+/// Any other attempts would require slowdowns for faster algorithms.
+#[inline]
+pub fn scientific_exponent(num: &Number) -> i32 {
+    // Use power reduction to make this faster.
+    let mut mantissa = num.mantissa;
+    let mut exponent = num.exponent;
+    while mantissa >= 10000 {
+        mantissa /= 10000;
+        exponent += 4;
+    }
+    while mantissa >= 100 {
+        mantissa /= 100;
+        exponent += 2;
+    }
+    while mantissa >= 10 {
+        mantissa /= 10;
+        exponent += 1;
+    }
+    exponent as i32
+}
+
+/// Calculate `b` from a a representation of `b` as a float.
+#[inline]
+pub fn b<F: Float>(float: F) -> ExtendedFloat {
+    ExtendedFloat {
+        mant: float.mantissa(),
+        exp: float.exponent(),
+    }
+}
+
+/// Calculate `b+h` from a a representation of `b` as a float.
+#[inline]
+pub fn bh<F: Float>(float: F) -> ExtendedFloat {
+    let fp = b(float);
+    ExtendedFloat {
+        mant: (fp.mant << 1) + 1,
+        exp: fp.exp - 1,
+    }
+}