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use core::ops;
use crate::int::{DInt, Int, MinInt};
/// Wrapper to extract the integer type half of the float's size
pub type HalfRep<F> = <<F as Float>::Int as DInt>::H;
/// Trait for some basic operations on floats
#[allow(dead_code)]
pub trait Float:
Copy
+ core::fmt::Debug
+ PartialEq
+ PartialOrd
+ ops::AddAssign
+ ops::MulAssign
+ ops::Add<Output = Self>
+ ops::Sub<Output = Self>
+ ops::Div<Output = Self>
+ ops::Rem<Output = Self>
{
/// A uint of the same width as the float
type Int: Int<OtherSign = Self::SignedInt, Unsigned = Self::Int>;
/// A int of the same width as the float
type SignedInt: Int + MinInt<OtherSign = Self::Int, Unsigned = Self::Int>;
/// An int capable of containing the exponent bits plus a sign bit. This is signed.
type ExpInt: Int;
const ZERO: Self;
const ONE: Self;
/// The bitwidth of the float type.
const BITS: u32;
/// The bitwidth of the significand.
const SIG_BITS: u32;
/// The bitwidth of the exponent.
const EXP_BITS: u32 = Self::BITS - Self::SIG_BITS - 1;
/// The saturated (maximum bitpattern) value of the exponent, i.e. the infinite
/// representation.
///
/// This is in the rightmost position, use `EXP_MASK` for the shifted value.
const EXP_SAT: u32 = (1 << Self::EXP_BITS) - 1;
/// The exponent bias value.
const EXP_BIAS: u32 = Self::EXP_SAT >> 1;
/// A mask for the sign bit.
const SIGN_MASK: Self::Int;
/// A mask for the significand.
const SIG_MASK: Self::Int;
/// The implicit bit of the float format.
const IMPLICIT_BIT: Self::Int;
/// A mask for the exponent.
const EXP_MASK: Self::Int;
/// Returns `self` transmuted to `Self::Int`
fn to_bits(self) -> Self::Int;
/// Returns `self` transmuted to `Self::SignedInt`
fn to_bits_signed(self) -> Self::SignedInt;
/// Checks if two floats have the same bit representation. *Except* for NaNs! NaN can be
/// represented in multiple different ways. This method returns `true` if two NaNs are
/// compared.
fn eq_repr(self, rhs: Self) -> bool;
/// Returns true if the sign is negative
fn is_sign_negative(self) -> bool;
/// Returns the exponent, not adjusting for bias.
fn exp(self) -> Self::ExpInt;
/// Returns the significand with no implicit bit (or the "fractional" part)
fn frac(self) -> Self::Int;
/// Returns the significand with implicit bit
fn imp_frac(self) -> Self::Int;
/// Returns a `Self::Int` transmuted back to `Self`
fn from_bits(a: Self::Int) -> Self;
/// Constructs a `Self` from its parts. Inputs are treated as bits and shifted into position.
fn from_parts(negative: bool, exponent: Self::Int, significand: Self::Int) -> Self;
fn abs(self) -> Self {
let abs_mask = !Self::SIGN_MASK;
Self::from_bits(self.to_bits() & abs_mask)
}
/// Returns (normalized exponent, normalized significand)
fn normalize(significand: Self::Int) -> (i32, Self::Int);
/// Returns if `self` is subnormal
fn is_subnormal(self) -> bool;
}
macro_rules! float_impl {
($ty:ident, $ity:ident, $sity:ident, $expty:ident, $bits:expr, $significand_bits:expr) => {
impl Float for $ty {
type Int = $ity;
type SignedInt = $sity;
type ExpInt = $expty;
const ZERO: Self = 0.0;
const ONE: Self = 1.0;
const BITS: u32 = $bits;
const SIG_BITS: u32 = $significand_bits;
const SIGN_MASK: Self::Int = 1 << (Self::BITS - 1);
const SIG_MASK: Self::Int = (1 << Self::SIG_BITS) - 1;
const IMPLICIT_BIT: Self::Int = 1 << Self::SIG_BITS;
const EXP_MASK: Self::Int = !(Self::SIGN_MASK | Self::SIG_MASK);
fn to_bits(self) -> Self::Int {
self.to_bits()
}
fn to_bits_signed(self) -> Self::SignedInt {
self.to_bits() as Self::SignedInt
}
fn eq_repr(self, rhs: Self) -> bool {
#[cfg(feature = "mangled-names")]
fn is_nan(x: $ty) -> bool {
// When using mangled-names, the "real" compiler-builtins might not have the
// necessary builtin (__unordtf2) to test whether `f128` is NaN.
// FIXME(f16_f128): Remove once the nightly toolchain has the __unordtf2 builtin
// x is NaN if all the bits of the exponent are set and the significand is non-0
x.to_bits() & $ty::EXP_MASK == $ty::EXP_MASK && x.to_bits() & $ty::SIG_MASK != 0
}
#[cfg(not(feature = "mangled-names"))]
fn is_nan(x: $ty) -> bool {
x.is_nan()
}
if is_nan(self) && is_nan(rhs) {
true
} else {
self.to_bits() == rhs.to_bits()
}
}
fn is_sign_negative(self) -> bool {
self.is_sign_negative()
}
fn exp(self) -> Self::ExpInt {
((self.to_bits() & Self::EXP_MASK) >> Self::SIG_BITS) as Self::ExpInt
}
fn frac(self) -> Self::Int {
self.to_bits() & Self::SIG_MASK
}
fn imp_frac(self) -> Self::Int {
self.frac() | Self::IMPLICIT_BIT
}
fn from_bits(a: Self::Int) -> Self {
Self::from_bits(a)
}
fn from_parts(negative: bool, exponent: Self::Int, significand: Self::Int) -> Self {
Self::from_bits(
((negative as Self::Int) << (Self::BITS - 1))
| ((exponent << Self::SIG_BITS) & Self::EXP_MASK)
| (significand & Self::SIG_MASK),
)
}
fn normalize(significand: Self::Int) -> (i32, Self::Int) {
let shift = significand.leading_zeros().wrapping_sub(Self::EXP_BITS);
(
1i32.wrapping_sub(shift as i32),
significand << shift as Self::Int,
)
}
fn is_subnormal(self) -> bool {
(self.to_bits() & Self::EXP_MASK) == Self::Int::ZERO
}
}
};
}
#[cfg(f16_enabled)]
float_impl!(f16, u16, i16, i8, 16, 10);
float_impl!(f32, u32, i32, i16, 32, 23);
float_impl!(f64, u64, i64, i16, 64, 52);
#[cfg(f128_enabled)]
float_impl!(f128, u128, i128, i16, 128, 112);