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//! Defines rounding schemes for floating-point numbers.
#![doc(hidden)]
use crate::extended_float::ExtendedFloat;
use crate::mask::{lower_n_halfway, lower_n_mask};
use crate::num::Float;
// ROUNDING
// --------
/// Round an extended-precision float to the nearest machine float.
///
/// Shifts the significant digits into place, adjusts the exponent,
/// so it can be easily converted to a native float.
#[cfg_attr(not(feature = "compact"), inline)]
pub fn round<F, Cb>(fp: &mut ExtendedFloat, cb: Cb)
where
F: Float,
Cb: Fn(&mut ExtendedFloat, i32),
{
let fp_inf = ExtendedFloat {
mant: 0,
exp: F::INFINITE_POWER,
};
// Calculate our shift in significant digits.
let mantissa_shift = 64 - F::MANTISSA_SIZE - 1;
// Check for a denormal float, if after the shift the exponent is negative.
if -fp.exp >= mantissa_shift {
// Have a denormal float that isn't a literal 0.
// The extra 1 is to adjust for the denormal float, which is
// `1 - F::EXPONENT_BIAS`. This works as before, because our
// old logic rounded to `F::DENORMAL_EXPONENT` (now 1), and then
// checked if `exp == F::DENORMAL_EXPONENT` and no hidden mask
// bit was set. Here, we handle that here, rather than later.
//
// This might round-down to 0, but shift will be at **max** 65,
// for halfway cases rounding towards 0.
let shift = -fp.exp + 1;
debug_assert!(shift <= 65);
cb(fp, shift.min(64));
// Check for round-up: if rounding-nearest carried us to the hidden bit.
fp.exp = (fp.mant >= F::HIDDEN_BIT_MASK) as i32;
return;
}
// The float is normal, round to the hidden bit.
cb(fp, mantissa_shift);
// Check if we carried, and if so, shift the bit to the hidden bit.
let carry_mask = F::CARRY_MASK;
if fp.mant & carry_mask == carry_mask {
fp.mant >>= 1;
fp.exp += 1;
}
// Handle if we carried and check for overflow again.
if fp.exp >= F::INFINITE_POWER {
// Exponent is above largest normal value, must be infinite.
*fp = fp_inf;
return;
}
// Remove the hidden bit.
fp.mant &= F::MANTISSA_MASK;
}
/// Shift right N-bytes and round towards a direction.
///
/// Callback should take the following parameters:
/// 1. is_odd
/// 1. is_halfway
/// 1. is_above
#[cfg_attr(not(feature = "compact"), inline)]
pub fn round_nearest_tie_even<Cb>(fp: &mut ExtendedFloat, shift: i32, cb: Cb)
where
// is_odd, is_halfway, is_above
Cb: Fn(bool, bool, bool) -> bool,
{
// Ensure we've already handled denormal values that underflow.
debug_assert!(shift <= 64);
// Extract the truncated bits using mask.
// Calculate if the value of the truncated bits are either above
// the mid-way point, or equal to it.
//
// For example, for 4 truncated bytes, the mask would be 0b1111
// and the midway point would be 0b1000.
let mask = lower_n_mask(shift as u64);
let halfway = lower_n_halfway(shift as u64);
let truncated_bits = fp.mant & mask;
let is_above = truncated_bits > halfway;
let is_halfway = truncated_bits == halfway;
// Bit shift so the leading bit is in the hidden bit.
// This optimixes pretty well:
// ```text
// mov ecx, esi
// shr rdi, cl
// xor eax, eax
// cmp esi, 64
// cmovne rax, rdi
// ret
// ```
fp.mant = match shift == 64 {
true => 0,
false => fp.mant >> shift,
};
fp.exp += shift;
// Extract the last bit after shifting (and determine if it is odd).
let is_odd = fp.mant & 1 == 1;
// Calculate if we need to roundup.
// We need to roundup if we are above halfway, or if we are odd
// and at half-way (need to tie-to-even). Avoid the branch here.
fp.mant += cb(is_odd, is_halfway, is_above) as u64;
}
/// Round our significant digits into place, truncating them.
#[cfg_attr(not(feature = "compact"), inline)]
pub fn round_down(fp: &mut ExtendedFloat, shift: i32) {
// Might have a shift greater than 64 if we have an error.
fp.mant = match shift == 64 {
true => 0,
false => fp.mant >> shift,
};
fp.exp += shift;
}