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// 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))
}
}