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//! Representation of a float as the significant digits and exponent.
//!
#![doc(hidden)]
#[cfg(feature = "nightly")]
use crate::fpu::set_precision;
use crate::num::Float;
/// Representation of a number as the significant digits and exponent.
///
/// This is only used if the exponent base and the significant digit
/// radix are the same, since we need to be able to move powers in and
/// out of the exponent.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
pub struct Number {
/// The exponent of the float, scaled to the mantissa.
pub exponent: i32,
/// The significant digits of the float.
pub mantissa: u64,
/// If the significant digits were truncated.
pub many_digits: bool,
}
impl Number {
/// Detect if the float can be accurately reconstructed from native floats.
#[inline]
pub fn is_fast_path<F: Float>(&self) -> bool {
F::MIN_EXPONENT_FAST_PATH <= self.exponent
&& self.exponent <= F::MAX_EXPONENT_DISGUISED_FAST_PATH
&& self.mantissa <= F::MAX_MANTISSA_FAST_PATH
&& !self.many_digits
}
/// The fast path algorithmn using machine-sized integers and floats.
///
/// This is extracted into a separate function so that it can be attempted before constructing
/// a Decimal. This only works if both the mantissa and the exponent
/// can be exactly represented as a machine float, since IEE-754 guarantees
/// no rounding will occur.
///
/// There is an exception: disguised fast-path cases, where we can shift
/// powers-of-10 from the exponent to the significant digits.
pub fn try_fast_path<F: Float>(&self) -> Option<F> {
// The fast path crucially depends on arithmetic being rounded to the correct number of bits
// without any intermediate rounding. On x86 (without SSE or SSE2) this requires the precision
// of the x87 FPU stack to be changed so that it directly rounds to 64/32 bit.
// The `set_precision` function takes care of setting the precision on architectures which
// require setting it by changing the global state (like the control word of the x87 FPU).
#[cfg(feature = "nightly")]
let _cw = set_precision::<F>();
if self.is_fast_path::<F>() {
let max_exponent = F::MAX_EXPONENT_FAST_PATH;
Some(if self.exponent <= max_exponent {
// normal fast path
let value = F::from_u64(self.mantissa);
if self.exponent < 0 {
// SAFETY: safe, since the `exponent <= max_exponent`.
value / unsafe { F::pow_fast_path((-self.exponent) as _) }
} else {
// SAFETY: safe, since the `exponent <= max_exponent`.
value * unsafe { F::pow_fast_path(self.exponent as _) }
}
} else {
// disguised fast path
let shift = self.exponent - max_exponent;
// SAFETY: safe, since `shift <= (max_disguised - max_exponent)`.
let int_power = unsafe { F::int_pow_fast_path(shift as usize, 10) };
let mantissa = self.mantissa.checked_mul(int_power)?;
if mantissa > F::MAX_MANTISSA_FAST_PATH {
return None;
}
// SAFETY: safe, since the `table.len() - 1 == max_exponent`.
F::from_u64(mantissa) * unsafe { F::pow_fast_path(max_exponent as _) }
})
} else {
None
}
}
}