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//! Representation of a float as the significant digits and exponent.
use crate::dec2flt::float::RawFloat;
use crate::dec2flt::fpu::set_precision;
const INT_POW10: [u64; 16] = [
1,
10,
100,
1000,
10000,
100000,
1000000,
10000000,
100000000,
1000000000,
10000000000,
100000000000,
1000000000000,
10000000000000,
100000000000000,
1000000000000000,
];
/// A floating point number with up to 64 bits of mantissa and an `i64` exponent.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
pub struct Decimal {
pub exponent: i64,
pub mantissa: u64,
pub negative: bool,
pub many_digits: bool,
}
impl Decimal {
/// Detect if the float can be accurately reconstructed from native floats.
#[inline]
fn can_use_fast_path<F: RawFloat>(&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
}
/// Try turning the decimal into an exact float representation, 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: RawFloat>(&self) -> Option<F> {
// Here we need to work around <https://github.com/rust-lang/rust/issues/114479>.
// 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).
let _cw = set_precision::<F>();
if !self.can_use_fast_path::<F>() {
return None;
}
let value = if self.exponent <= F::MAX_EXPONENT_FAST_PATH {
// normal fast path
let value = F::from_u64(self.mantissa);
if self.exponent < 0 {
value / F::pow10_fast_path((-self.exponent) as _)
} else {
value * F::pow10_fast_path(self.exponent as _)
}
} else {
// disguised fast path
let shift = self.exponent - F::MAX_EXPONENT_FAST_PATH;
let mantissa = self.mantissa.checked_mul(INT_POW10[shift as usize])?;
if mantissa > F::MAX_MANTISSA_FAST_PATH {
return None;
}
F::from_u64(mantissa) * F::pow10_fast_path(F::MAX_EXPONENT_FAST_PATH as _)
};
if self.negative {
Some(-value)
} else {
Some(value)
}
}
}