Add float and integer traits from compiler-builtins

In preparation of adding generic algorithms to `libm`, add the traits
from `compiler-builtins`.

Eventually we should be able to unify the two crates so we don't have
duplicate implementations.

library/compiler-builtins/libm/src/math/mod.rs

@@ -105,6 +105,8 @@ use self::k_tanf::k_tanf;
 use self::rem_pio2::rem_pio2;
 use self::rem_pio2_large::rem_pio2_large;
 use self::rem_pio2f::rem_pio2f;
+#[allow(unused_imports)]
+use self::support::{CastFrom, CastInto, DInt, Float, HInt, Int, MinInt};
 
 // Public modules
 mod acos;

library/compiler-builtins/libm/src/math/support/float_traits.rs

@@ -0,0 +1,168 @@
+use core::ops;
+
+use super::int_traits::{Int, MinInt};
+
+/// 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, UnsignedInt = Self::Int>;
+
+    /// A int of the same width as the float
+    type SignedInt: Int + MinInt<OtherSign = Self::Int, UnsignedInt = 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 SIGNIFICAND_BITS: u32;
+
+    /// The bitwidth of the exponent
+    const EXPONENT_BITS: u32 = Self::BITS - Self::SIGNIFICAND_BITS - 1;
+
+    /// The saturated value of the exponent (infinite representation), in the rightmost postiion.
+    const EXPONENT_MAX: u32 = (1 << Self::EXPONENT_BITS) - 1;
+
+    /// The exponent bias value
+    const EXPONENT_BIAS: u32 = Self::EXPONENT_MAX >> 1;
+
+    /// A mask for the sign bit
+    const SIGN_MASK: Self::Int;
+
+    /// A mask for the significand
+    const SIGNIFICAND_MASK: Self::Int;
+
+    /// The implicit bit of the float format
+    const IMPLICIT_BIT: Self::Int;
+
+    /// A mask for the exponent
+    const EXPONENT_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 SIGNIFICAND_BITS: u32 = $significand_bits;
+
+            const SIGN_MASK: Self::Int = 1 << (Self::BITS - 1);
+            const SIGNIFICAND_MASK: Self::Int = (1 << Self::SIGNIFICAND_BITS) - 1;
+            const IMPLICIT_BIT: Self::Int = 1 << Self::SIGNIFICAND_BITS;
+            const EXPONENT_MASK: Self::Int = !(Self::SIGN_MASK | Self::SIGNIFICAND_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 {
+                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::EXPONENT_MASK == $ty::EXPONENT_MASK
+                        && x.to_bits() & $ty::SIGNIFICAND_MASK != 0
+                }
+                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::EXPONENT_MASK) >> Self::SIGNIFICAND_BITS) as Self::ExpInt
+            }
+            fn frac(self) -> Self::Int {
+                self.to_bits() & Self::SIGNIFICAND_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::SIGNIFICAND_BITS) & Self::EXPONENT_MASK)
+                        | (significand & Self::SIGNIFICAND_MASK),
+                )
+            }
+            fn normalize(significand: Self::Int) -> (i32, Self::Int) {
+                let shift = significand.leading_zeros().wrapping_sub(Self::EXPONENT_BITS);
+                (1i32.wrapping_sub(shift as i32), significand << shift as Self::Int)
+            }
+            fn is_subnormal(self) -> bool {
+                (self.to_bits() & Self::EXPONENT_MASK) == Self::Int::ZERO
+            }
+        }
+    };
+}
+
+float_impl!(f32, u32, i32, i16, 32, 23);
+float_impl!(f64, u64, i64, i16, 64, 52);

library/compiler-builtins/libm/src/math/support/int_traits.rs

@@ -0,0 +1,343 @@
+use core::{fmt, ops};
+
+/// Minimal integer implementations needed on all integer types, including wide integers.
+#[allow(dead_code)]
+pub trait MinInt:
+    Copy
+    + fmt::Debug
+    + ops::BitOr<Output = Self>
+    + ops::Not<Output = Self>
+    + ops::Shl<u32, Output = Self>
+{
+    /// Type with the same width but other signedness
+    type OtherSign: MinInt;
+    /// Unsigned version of Self
+    type UnsignedInt: MinInt;
+
+    /// If `Self` is a signed integer
+    const SIGNED: bool;
+
+    /// The bitwidth of the int type
+    const BITS: u32;
+
+    const ZERO: Self;
+    const ONE: Self;
+    const MIN: Self;
+    const MAX: Self;
+}
+
+/// Trait for some basic operations on integers
+#[allow(dead_code)]
+pub trait Int:
+    MinInt
+    + PartialEq
+    + PartialOrd
+    + ops::AddAssign
+    + ops::SubAssign
+    + ops::BitAndAssign
+    + ops::BitOrAssign
+    + ops::BitXorAssign
+    + ops::ShlAssign<i32>
+    + ops::ShrAssign<u32>
+    + ops::Add<Output = Self>
+    + ops::Sub<Output = Self>
+    + ops::Mul<Output = Self>
+    + ops::Div<Output = Self>
+    + ops::Shr<u32, Output = Self>
+    + ops::BitXor<Output = Self>
+    + ops::BitAnd<Output = Self>
+{
+    fn unsigned(self) -> Self::UnsignedInt;
+    fn from_unsigned(unsigned: Self::UnsignedInt) -> Self;
+
+    fn from_bool(b: bool) -> Self;
+
+    /// Prevents the need for excessive conversions between signed and unsigned
+    fn logical_shr(self, other: u32) -> Self;
+
+    /// Absolute difference between two integers.
+    fn abs_diff(self, other: Self) -> Self::UnsignedInt;
+
+    // copied from primitive integers, but put in a trait
+    fn is_zero(self) -> bool;
+    fn wrapping_neg(self) -> Self;
+    fn wrapping_add(self, other: Self) -> Self;
+    fn wrapping_mul(self, other: Self) -> Self;
+    fn wrapping_sub(self, other: Self) -> Self;
+    fn wrapping_shl(self, other: u32) -> Self;
+    fn wrapping_shr(self, other: u32) -> Self;
+    fn rotate_left(self, other: u32) -> Self;
+    fn overflowing_add(self, other: Self) -> (Self, bool);
+    fn leading_zeros(self) -> u32;
+    fn ilog2(self) -> u32;
+}
+
+macro_rules! int_impl_common {
+    ($ty:ty) => {
+        fn from_bool(b: bool) -> Self {
+            b as $ty
+        }
+
+        fn logical_shr(self, other: u32) -> Self {
+            Self::from_unsigned(self.unsigned().wrapping_shr(other))
+        }
+
+        fn is_zero(self) -> bool {
+            self == Self::ZERO
+        }
+
+        fn wrapping_neg(self) -> Self {
+            <Self>::wrapping_neg(self)
+        }
+
+        fn wrapping_add(self, other: Self) -> Self {
+            <Self>::wrapping_add(self, other)
+        }
+
+        fn wrapping_mul(self, other: Self) -> Self {
+            <Self>::wrapping_mul(self, other)
+        }
+
+        fn wrapping_sub(self, other: Self) -> Self {
+            <Self>::wrapping_sub(self, other)
+        }
+
+        fn wrapping_shl(self, other: u32) -> Self {
+            <Self>::wrapping_shl(self, other)
+        }
+
+        fn wrapping_shr(self, other: u32) -> Self {
+            <Self>::wrapping_shr(self, other)
+        }
+
+        fn rotate_left(self, other: u32) -> Self {
+            <Self>::rotate_left(self, other)
+        }
+
+        fn overflowing_add(self, other: Self) -> (Self, bool) {
+            <Self>::overflowing_add(self, other)
+        }
+
+        fn leading_zeros(self) -> u32 {
+            <Self>::leading_zeros(self)
+        }
+
+        fn ilog2(self) -> u32 {
+            <Self>::ilog2(self)
+        }
+    };
+}
+
+macro_rules! int_impl {
+    ($ity:ty, $uty:ty) => {
+        impl MinInt for $uty {
+            type OtherSign = $ity;
+            type UnsignedInt = $uty;
+
+            const BITS: u32 = <Self as MinInt>::ZERO.count_zeros();
+            const SIGNED: bool = Self::MIN != Self::ZERO;
+
+            const ZERO: Self = 0;
+            const ONE: Self = 1;
+            const MIN: Self = <Self>::MIN;
+            const MAX: Self = <Self>::MAX;
+        }
+
+        impl Int for $uty {
+            fn unsigned(self) -> $uty {
+                self
+            }
+
+            // It makes writing macros easier if this is implemented for both signed and unsigned
+            #[allow(clippy::wrong_self_convention)]
+            fn from_unsigned(me: $uty) -> Self {
+                me
+            }
+
+            fn abs_diff(self, other: Self) -> Self {
+                if self < other { other.wrapping_sub(self) } else { self.wrapping_sub(other) }
+            }
+
+            int_impl_common!($uty);
+        }
+
+        impl MinInt for $ity {
+            type OtherSign = $uty;
+            type UnsignedInt = $uty;
+
+            const BITS: u32 = <Self as MinInt>::ZERO.count_zeros();
+            const SIGNED: bool = Self::MIN != Self::ZERO;
+
+            const ZERO: Self = 0;
+            const ONE: Self = 1;
+            const MIN: Self = <Self>::MIN;
+            const MAX: Self = <Self>::MAX;
+        }
+
+        impl Int for $ity {
+            fn unsigned(self) -> $uty {
+                self as $uty
+            }
+
+            fn from_unsigned(me: $uty) -> Self {
+                me as $ity
+            }
+
+            fn abs_diff(self, other: Self) -> $uty {
+                self.wrapping_sub(other).wrapping_abs() as $uty
+            }
+
+            int_impl_common!($ity);
+        }
+    };
+}
+
+int_impl!(isize, usize);
+int_impl!(i8, u8);
+int_impl!(i16, u16);
+int_impl!(i32, u32);
+int_impl!(i64, u64);
+int_impl!(i128, u128);
+
+/// Trait for integers twice the bit width of another integer. This is implemented for all
+/// primitives except for `u8`, because there is not a smaller primitive.
+#[allow(unused)]
+pub trait DInt: MinInt {
+    /// Integer that is half the bit width of the integer this trait is implemented for
+    type H: HInt<D = Self>;
+
+    /// Returns the low half of `self`
+    fn lo(self) -> Self::H;
+    /// Returns the high half of `self`
+    fn hi(self) -> Self::H;
+    /// Returns the low and high halves of `self` as a tuple
+    fn lo_hi(self) -> (Self::H, Self::H) {
+        (self.lo(), self.hi())
+    }
+    /// Constructs an integer using lower and higher half parts
+    fn from_lo_hi(lo: Self::H, hi: Self::H) -> Self {
+        lo.zero_widen() | hi.widen_hi()
+    }
+}
+
+/// Trait for integers half the bit width of another integer. This is implemented for all
+/// primitives except for `u128`, because it there is not a larger primitive.
+#[allow(unused)]
+pub trait HInt: Int {
+    /// Integer that is double the bit width of the integer this trait is implemented for
+    type D: DInt<H = Self> + MinInt;
+
+    // NB: some of the below methods could have default implementations (e.g. `widen_hi`), but for
+    // unknown reasons this can cause infinite recursion when optimizations are disabled. See
+    // <https://github.com/rust-lang/compiler-builtins/pull/707> for context.
+
+    /// Widens (using default extension) the integer to have double bit width
+    fn widen(self) -> Self::D;
+    /// Widens (zero extension only) the integer to have double bit width. This is needed to get
+    /// around problems with associated type bounds (such as `Int<Othersign: DInt>`) being unstable
+    fn zero_widen(self) -> Self::D;
+    /// Widens the integer to have double bit width and shifts the integer into the higher bits
+    fn widen_hi(self) -> Self::D;
+    /// Widening multiplication with zero widening. This cannot overflow.
+    fn zero_widen_mul(self, rhs: Self) -> Self::D;
+    /// Widening multiplication. This cannot overflow.
+    fn widen_mul(self, rhs: Self) -> Self::D;
+}
+
+macro_rules! impl_d_int {
+    ($($X:ident $D:ident),*) => {
+        $(
+            impl DInt for $D {
+                type H = $X;
+
+                fn lo(self) -> Self::H {
+                    self as $X
+                }
+                fn hi(self) -> Self::H {
+                    (self >> <$X as MinInt>::BITS) as $X
+                }
+            }
+        )*
+    };
+}
+
+macro_rules! impl_h_int {
+    ($($H:ident $uH:ident $X:ident),*) => {
+        $(
+            impl HInt for $H {
+                type D = $X;
+
+                fn widen(self) -> Self::D {
+                    self as $X
+                }
+                fn zero_widen(self) -> Self::D {
+                    (self as $uH) as $X
+                }
+                fn zero_widen_mul(self, rhs: Self) -> Self::D {
+                    self.zero_widen().wrapping_mul(rhs.zero_widen())
+                }
+                fn widen_mul(self, rhs: Self) -> Self::D {
+                    self.widen().wrapping_mul(rhs.widen())
+                }
+                fn widen_hi(self) -> Self::D {
+                    (self as $X) << <Self as MinInt>::BITS
+                }
+            }
+        )*
+    };
+}
+
+impl_d_int!(u8 u16, u16 u32, u32 u64, u64 u128, i8 i16, i16 i32, i32 i64, i64 i128);
+impl_h_int!(
+    u8 u8 u16,
+    u16 u16 u32,
+    u32 u32 u64,
+    u64 u64 u128,
+    i8 u8 i16,
+    i16 u16 i32,
+    i32 u32 i64,
+    i64 u64 i128
+);
+
+/// Trait to express (possibly lossy) casting of integers
+#[allow(unused)]
+pub trait CastInto<T: Copy>: Copy {
+    fn cast(self) -> T;
+}
+
+#[allow(unused)]
+pub trait CastFrom<T: Copy>: Copy {
+    fn cast_from(value: T) -> Self;
+}
+
+impl<T: Copy, U: CastInto<T> + Copy> CastFrom<U> for T {
+    fn cast_from(value: U) -> Self {
+        value.cast()
+    }
+}
+
+macro_rules! cast_into {
+    ($ty:ty) => {
+        cast_into!($ty; usize, isize, u8, i8, u16, i16, u32, i32, u64, i64, u128, i128);
+    };
+    ($ty:ty; $($into:ty),*) => {$(
+        impl CastInto<$into> for $ty {
+            fn cast(self) -> $into {
+                self as $into
+            }
+        }
+    )*};
+}
+
+cast_into!(usize);
+cast_into!(isize);
+cast_into!(u8);
+cast_into!(i8);
+cast_into!(u16);
+cast_into!(i16);
+cast_into!(u32);
+cast_into!(i32);
+cast_into!(u64);
+cast_into!(i64);
+cast_into!(u128);
+cast_into!(i128);

library/compiler-builtins/libm/src/math/support/mod.rs

@@ -1,2 +1,7 @@
 #[macro_use]
 pub mod macros;
+mod float_traits;
+mod int_traits;
+
+pub use float_traits::Float;
+pub use int_traits::{CastFrom, CastInto, DInt, HInt, Int, MinInt};