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+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+// FLOAT TYPE
+
+use super::num::*;
+use super::rounding::*;
+use super::shift::*;
+
+/// Extended precision floating-point type.
+///
+/// Private implementation, exposed only for testing purposes.
+#[doc(hidden)]
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub(crate) struct ExtendedFloat {
+ /// Mantissa for the extended-precision float.
+ pub mant: u64,
+ /// Binary exponent for the extended-precision float.
+ pub exp: i32,
+}
+
+impl ExtendedFloat {
+ // PROPERTIES
+
+ // OPERATIONS
+
+ /// Multiply two normalized extended-precision floats, as if by `a*b`.
+ ///
+ /// The precision is maximal when the numbers are normalized, however,
+ /// decent precision will occur as long as both values have high bits
+ /// set. The result is not normalized.
+ ///
+ /// Algorithm:
+ /// 1. Non-signed multiplication of mantissas (requires 2x as many bits as input).
+ /// 2. Normalization of the result (not done here).
+ /// 3. Addition of exponents.
+ pub(crate) fn mul(&self, b: &ExtendedFloat) -> ExtendedFloat {
+ // Logic check, values must be decently normalized prior to multiplication.
+ debug_assert!((self.mant & u64::HIMASK != 0) && (b.mant & u64::HIMASK != 0));
+
+ // Extract high-and-low masks.
+ let ah = self.mant >> u64::HALF;
+ let al = self.mant & u64::LOMASK;
+ let bh = b.mant >> u64::HALF;
+ let bl = b.mant & u64::LOMASK;
+
+ // Get our products
+ let ah_bl = ah * bl;
+ let al_bh = al * bh;
+ let al_bl = al * bl;
+ let ah_bh = ah * bh;
+
+ let mut tmp = (ah_bl & u64::LOMASK) + (al_bh & u64::LOMASK) + (al_bl >> u64::HALF);
+ // round up
+ tmp += 1 << (u64::HALF - 1);
+
+ ExtendedFloat {
+ mant: ah_bh + (ah_bl >> u64::HALF) + (al_bh >> u64::HALF) + (tmp >> u64::HALF),
+ exp: self.exp + b.exp + u64::FULL,
+ }
+ }
+
+ /// Multiply in-place, as if by `a*b`.
+ ///
+ /// The result is not normalized.
+ #[inline]
+ pub(crate) fn imul(&mut self, b: &ExtendedFloat) {
+ *self = self.mul(b);
+ }
+
+ // NORMALIZE
+
+ /// Normalize float-point number.
+ ///
+ /// Shift the mantissa so the number of leading zeros is 0, or the value
+ /// itself is 0.
+ ///
+ /// Get the number of bytes shifted.
+ #[inline]
+ pub(crate) fn normalize(&mut self) -> u32 {
+ // Note:
+ // Using the cltz intrinsic via leading_zeros is way faster (~10x)
+ // than shifting 1-bit at a time, via while loop, and also way
+ // faster (~2x) than an unrolled loop that checks at 32, 16, 4,
+ // 2, and 1 bit.
+ //
+ // Using a modulus of pow2 (which will get optimized to a bitwise
+ // and with 0x3F or faster) is slightly slower than an if/then,
+ // however, removing the if/then will likely optimize more branched
+ // code as it removes conditional logic.
+
+ // Calculate the number of leading zeros, and then zero-out
+ // any overflowing bits, to avoid shl overflow when self.mant == 0.
+ let shift = if self.mant == 0 {
+ 0
+ } else {
+ self.mant.leading_zeros()
+ };
+ shl(self, shift as i32);
+ shift
+ }
+
+ // ROUND
+
+ /// Lossy round float-point number to native mantissa boundaries.
+ #[inline]
+ pub(crate) fn round_to_native<F, Algorithm>(&mut self, algorithm: Algorithm)
+ where
+ F: Float,
+ Algorithm: FnOnce(&mut ExtendedFloat, i32),
+ {
+ round_to_native::<F, _>(self, algorithm);
+ }
+
+ // FROM
+
+ /// Create extended float from native float.
+ #[inline]
+ pub fn from_float<F: Float>(f: F) -> ExtendedFloat {
+ from_float(f)
+ }
+
+ // INTO
+
+ /// Convert into default-rounded, lower-precision native float.
+ #[inline]
+ pub(crate) fn into_float<F: Float>(mut self) -> F {
+ self.round_to_native::<F, _>(round_nearest_tie_even);
+ into_float(self)
+ }
+
+ /// Convert into downward-rounded, lower-precision native float.
+ #[inline]
+ pub(crate) fn into_downward_float<F: Float>(mut self) -> F {
+ self.round_to_native::<F, _>(round_downward);
+ into_float(self)
+ }
+}
+
+// FROM FLOAT
+
+// Import ExtendedFloat from native float.
+#[inline]
+pub(crate) fn from_float<F>(f: F) -> ExtendedFloat
+where
+ F: Float,
+{
+ ExtendedFloat {
+ mant: u64::as_cast(f.mantissa()),
+ exp: f.exponent(),
+ }
+}
+
+// INTO FLOAT
+
+// Export extended-precision float to native float.
+//
+// The extended-precision float must be in native float representation,
+// with overflow/underflow appropriately handled.
+#[inline]
+pub(crate) fn into_float<F>(fp: ExtendedFloat) -> F
+where
+ F: Float,
+{
+ // Export floating-point number.
+ if fp.mant == 0 || fp.exp < F::DENORMAL_EXPONENT {
+ // sub-denormal, underflow
+ F::ZERO
+ } else if fp.exp >= F::MAX_EXPONENT {
+ // overflow
+ F::from_bits(F::INFINITY_BITS)
+ } else {
+ // calculate the exp and fraction bits, and return a float from bits.
+ let exp: u64;
+ if (fp.exp == F::DENORMAL_EXPONENT) && (fp.mant & F::HIDDEN_BIT_MASK.as_u64()) == 0 {
+ exp = 0;
+ } else {
+ exp = (fp.exp + F::EXPONENT_BIAS) as u64;
+ }
+ let exp = exp << F::MANTISSA_SIZE;
+ let mant = fp.mant & F::MANTISSA_MASK.as_u64();
+ F::from_bits(F::Unsigned::as_cast(mant | exp))
+ }
+}