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+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Compare the mantissa to the halfway representation of the float.
+//!
+//! Compares the actual significant digits of the mantissa to the
+//! theoretical digits from `b+h`, scaled into the proper range.
+
+use super::bignum::*;
+use super::digit::*;
+use super::exponent::*;
+use super::float::*;
+use super::math::*;
+use super::num::*;
+use super::rounding::*;
+use core::{cmp, mem};
+
+// MANTISSA
+
+/// Parse the full mantissa into a big integer.
+///
+/// Max digits is the maximum number of digits plus one.
+fn parse_mantissa<F>(integer: &[u8], fraction: &[u8]) -> Bigint
+where
+ F: Float,
+{
+ // Main loop
+ let small_powers = POW10_LIMB;
+ let step = small_powers.len() - 2;
+ let max_digits = F::MAX_DIGITS - 1;
+ let mut counter = 0;
+ let mut value: Limb = 0;
+ let mut i: usize = 0;
+ let mut result = Bigint::default();
+
+ // Iteratively process all the data in the mantissa.
+ for &digit in integer.iter().chain(fraction) {
+ // We've parsed the max digits using small values, add to bignum
+ if counter == step {
+ result.imul_small(small_powers[counter]);
+ result.iadd_small(value);
+ counter = 0;
+ value = 0;
+ }
+
+ value *= 10;
+ value += as_limb(to_digit(digit).unwrap());
+
+ i += 1;
+ counter += 1;
+ if i == max_digits {
+ break;
+ }
+ }
+
+ // We will always have a remainder, as long as we entered the loop
+ // once, or counter % step is 0.
+ if counter != 0 {
+ result.imul_small(small_powers[counter]);
+ result.iadd_small(value);
+ }
+
+ // If we have any remaining digits after the last value, we need
+ // to add a 1 after the rest of the array, it doesn't matter where,
+ // just move it up. This is good for the worst-possible float
+ // representation. We also need to return an index.
+ // Since we already trimmed trailing zeros, we know there has
+ // to be a non-zero digit if there are any left.
+ if i < integer.len() + fraction.len() {
+ result.imul_small(10);
+ result.iadd_small(1);
+ }
+
+ result
+}
+
+// FLOAT OPS
+
+/// Calculate `b` from a a representation of `b` as a float.
+#[inline]
+pub(super) fn b_extended<F: Float>(f: F) -> ExtendedFloat {
+ ExtendedFloat::from_float(f)
+}
+
+/// Calculate `b+h` from a a representation of `b` as a float.
+#[inline]
+pub(super) fn bh_extended<F: Float>(f: F) -> ExtendedFloat {
+ // None of these can overflow.
+ let b = b_extended(f);
+ ExtendedFloat {
+ mant: (b.mant << 1) + 1,
+ exp: b.exp - 1,
+ }
+}
+
+// ROUNDING
+
+/// Custom round-nearest, tie-event algorithm for bhcomp.
+#[inline]
+fn round_nearest_tie_even(fp: &mut ExtendedFloat, shift: i32, is_truncated: bool) {
+ let (mut is_above, mut is_halfway) = round_nearest(fp, shift);
+ if is_halfway && is_truncated {
+ is_above = true;
+ is_halfway = false;
+ }
+ tie_even(fp, is_above, is_halfway);
+}
+
+// BHCOMP
+
+/// Calculate the mantissa for a big integer with a positive exponent.
+fn large_atof<F>(mantissa: Bigint, exponent: i32) -> F
+where
+ F: Float,
+{
+ let bits = mem::size_of::<u64>() * 8;
+
+ // 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.
+ let mut bigmant = mantissa;
+ bigmant.imul_pow10(exponent as u32);
+
+ // Get the exact representation of the float from the big integer.
+ let (mant, is_truncated) = bigmant.hi64();
+ let exp = bigmant.bit_length() as i32 - bits as i32;
+ let mut fp = ExtendedFloat { mant, exp };
+ fp.round_to_native::<F, _>(|fp, shift| round_nearest_tie_even(fp, shift, is_truncated));
+ into_float(fp)
+}
+
+/// Calculate the mantissa for a big integer with a negative exponent.
+///
+/// This invokes the comparison with `b+h`.
+fn small_atof<F>(mantissa: Bigint, exponent: i32, f: F) -> F
+where
+ F: Float,
+{
+ // Get the significant digits and radix exponent for the real digits.
+ let mut real_digits = mantissa;
+ let real_exp = exponent;
+ debug_assert!(real_exp < 0);
+
+ // Get the significant digits and the binary exponent for `b+h`.
+ let theor = bh_extended(f);
+ 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.
+
+ // Can remove a power-of-two, since the radix is 10.
+ // 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;
+ let radix_exp = 0;
+
+ // Carry out our multiplication.
+ if halfradix_exp != 0 {
+ theor_digits.imul_pow5(halfradix_exp as u32);
+ }
+ if radix_exp != 0 {
+ theor_digits.imul_pow10(radix_exp as u32);
+ }
+ if binary_exp > 0 {
+ theor_digits.imul_pow2(binary_exp as u32);
+ } else if binary_exp < 0 {
+ real_digits.imul_pow2(-binary_exp as u32);
+ }
+
+ // Compare real digits to theoretical digits and round the float.
+ match real_digits.compare(&theor_digits) {
+ cmp::Ordering::Greater => f.next_positive(),
+ cmp::Ordering::Less => f,
+ cmp::Ordering::Equal => f.round_positive_even(),
+ }
+}
+
+/// Calculate the exact value of the float.
+///
+/// Note: fraction must not have trailing zeros.
+pub(crate) fn bhcomp<F>(b: F, integer: &[u8], mut fraction: &[u8], exponent: i32) -> F
+where
+ F: Float,
+{
+ // Calculate the number of integer digits and use that to determine
+ // where the significant digits start in the fraction.
+ let integer_digits = integer.len();
+ let fraction_digits = fraction.len();
+ let digits_start = if integer_digits == 0 {
+ let start = fraction.iter().take_while(|&x| *x == b'0').count();
+ fraction = &fraction[start..];
+ start
+ } else {
+ 0
+ };
+ let sci_exp = scientific_exponent(exponent, integer_digits, digits_start);
+ let count = F::MAX_DIGITS.min(integer_digits + fraction_digits - digits_start);
+ let scaled_exponent = sci_exp + 1 - count as i32;
+
+ let mantissa = parse_mantissa::<F>(integer, fraction);
+ if scaled_exponent >= 0 {
+ large_atof(mantissa, scaled_exponent)
+ } else {
+ small_atof(mantissa, scaled_exponent, b)
+ }
+}