1 files changed, 1483 insertions, 0 deletions
diff --git a/vendor/half/src/num_traits.rs b/vendor/half/src/num_traits.rs
new file mode 100644
index 0000000..4318699
--- /dev/null
+++ b/vendor/half/src/num_traits.rs
@@ -0,0 +1,1483 @@
+use crate::{bf16, f16};
+use core::cmp::Ordering;
+use core::{num::FpCategory, ops::Div};
+use num_traits::{
+    AsPrimitive, Bounded, FloatConst, FromPrimitive, Num, NumCast, One, ToPrimitive, Zero,
+};
+
+impl ToPrimitive for f16 {
+    #[inline]
+    fn to_i64(&self) -> Option<i64> {
+        Self::to_f32(*self).to_i64()
+    }
+    #[inline]
+    fn to_u64(&self) -> Option<u64> {
+        Self::to_f32(*self).to_u64()
+    }
+    #[inline]
+    fn to_i8(&self) -> Option<i8> {
+        Self::to_f32(*self).to_i8()
+    }
+    #[inline]
+    fn to_u8(&self) -> Option<u8> {
+        Self::to_f32(*self).to_u8()
+    }
+    #[inline]
+    fn to_i16(&self) -> Option<i16> {
+        Self::to_f32(*self).to_i16()
+    }
+    #[inline]
+    fn to_u16(&self) -> Option<u16> {
+        Self::to_f32(*self).to_u16()
+    }
+    #[inline]
+    fn to_i32(&self) -> Option<i32> {
+        Self::to_f32(*self).to_i32()
+    }
+    #[inline]
+    fn to_u32(&self) -> Option<u32> {
+        Self::to_f32(*self).to_u32()
+    }
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        Some(Self::to_f32(*self))
+    }
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        Some(Self::to_f64(*self))
+    }
+}
+
+impl FromPrimitive for f16 {
+    #[inline]
+    fn from_i64(n: i64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u64(n: u64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i8(n: i8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u8(n: u8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i16(n: i16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u16(n: u16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i32(n: i32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u32(n: u32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f32(n: f32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f64(n: f64) -> Option<Self> {
+        n.to_f64().map(Self::from_f64)
+    }
+}
+
+impl Num for f16 {
+    type FromStrRadixErr = <f32 as Num>::FromStrRadixErr;
+
+    #[inline]
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
+        Ok(Self::from_f32(f32::from_str_radix(str, radix)?))
+    }
+}
+
+impl One for f16 {
+    #[inline]
+    fn one() -> Self {
+        Self::ONE
+    }
+}
+
+impl Zero for f16 {
+    #[inline]
+    fn zero() -> Self {
+        Self::ZERO
+    }
+
+    #[inline]
+    fn is_zero(&self) -> bool {
+        *self == Self::ZERO
+    }
+}
+
+impl NumCast for f16 {
+    #[inline]
+    fn from<T: ToPrimitive>(n: T) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+}
+
+impl num_traits::float::FloatCore for f16 {
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_bits(self.to_bits() & 0x7FFF)
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        self.signum()
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    fn min(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => other,
+            Some(Ordering::Less) => self,
+        }
+    }
+
+    fn max(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => self,
+            Some(Ordering::Less) => other,
+        }
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, exp: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(exp))
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::FloatCore::integer_decode(self.to_f32())
+    }
+}
+
+impl num_traits::float::Float for f16 {
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_f32(self.to_f32().abs())
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        Self::from_f32(self.to_f32().signum())
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    #[inline]
+    fn mul_add(self, a: Self, b: Self) -> Self {
+        Self::from_f32(self.to_f32().mul_add(a.to_f32(), b.to_f32()))
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, n: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(n))
+    }
+
+    #[inline]
+    fn powf(self, n: Self) -> Self {
+        Self::from_f32(self.to_f32().powf(n.to_f32()))
+    }
+
+    #[inline]
+    fn sqrt(self) -> Self {
+        Self::from_f32(self.to_f32().sqrt())
+    }
+
+    #[inline]
+    fn exp(self) -> Self {
+        Self::from_f32(self.to_f32().exp())
+    }
+
+    #[inline]
+    fn exp2(self) -> Self {
+        Self::from_f32(self.to_f32().exp2())
+    }
+
+    #[inline]
+    fn ln(self) -> Self {
+        Self::from_f32(self.to_f32().ln())
+    }
+
+    #[inline]
+    fn log(self, base: Self) -> Self {
+        Self::from_f32(self.to_f32().log(base.to_f32()))
+    }
+
+    #[inline]
+    fn log2(self) -> Self {
+        Self::from_f32(self.to_f32().log2())
+    }
+
+    #[inline]
+    fn log10(self) -> Self {
+        Self::from_f32(self.to_f32().log10())
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn max(self, other: Self) -> Self {
+        self.max(other)
+    }
+
+    #[inline]
+    fn min(self, other: Self) -> Self {
+        self.min(other)
+    }
+
+    #[inline]
+    fn abs_sub(self, other: Self) -> Self {
+        Self::from_f32((self.to_f32() - other.to_f32()).max(0.0))
+    }
+
+    #[inline]
+    fn cbrt(self) -> Self {
+        Self::from_f32(self.to_f32().cbrt())
+    }
+
+    #[inline]
+    fn hypot(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().hypot(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin(self) -> Self {
+        Self::from_f32(self.to_f32().sin())
+    }
+
+    #[inline]
+    fn cos(self) -> Self {
+        Self::from_f32(self.to_f32().cos())
+    }
+
+    #[inline]
+    fn tan(self) -> Self {
+        Self::from_f32(self.to_f32().tan())
+    }
+
+    #[inline]
+    fn asin(self) -> Self {
+        Self::from_f32(self.to_f32().asin())
+    }
+
+    #[inline]
+    fn acos(self) -> Self {
+        Self::from_f32(self.to_f32().acos())
+    }
+
+    #[inline]
+    fn atan(self) -> Self {
+        Self::from_f32(self.to_f32().atan())
+    }
+
+    #[inline]
+    fn atan2(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().atan2(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin_cos(self) -> (Self, Self) {
+        let (sin, cos) = self.to_f32().sin_cos();
+        (Self::from_f32(sin), Self::from_f32(cos))
+    }
+
+    #[inline]
+    fn exp_m1(self) -> Self {
+        Self::from_f32(self.to_f32().exp_m1())
+    }
+
+    #[inline]
+    fn ln_1p(self) -> Self {
+        Self::from_f32(self.to_f32().ln_1p())
+    }
+
+    #[inline]
+    fn sinh(self) -> Self {
+        Self::from_f32(self.to_f32().sinh())
+    }
+
+    #[inline]
+    fn cosh(self) -> Self {
+        Self::from_f32(self.to_f32().cosh())
+    }
+
+    #[inline]
+    fn tanh(self) -> Self {
+        Self::from_f32(self.to_f32().tanh())
+    }
+
+    #[inline]
+    fn asinh(self) -> Self {
+        Self::from_f32(self.to_f32().asinh())
+    }
+
+    #[inline]
+    fn acosh(self) -> Self {
+        Self::from_f32(self.to_f32().acosh())
+    }
+
+    #[inline]
+    fn atanh(self) -> Self {
+        Self::from_f32(self.to_f32().atanh())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::Float::integer_decode(self.to_f32())
+    }
+}
+
+impl FloatConst for f16 {
+    #[inline]
+    fn E() -> Self {
+        Self::E
+    }
+
+    #[inline]
+    fn FRAC_1_PI() -> Self {
+        Self::FRAC_1_PI
+    }
+
+    #[inline]
+    fn FRAC_1_SQRT_2() -> Self {
+        Self::FRAC_1_SQRT_2
+    }
+
+    #[inline]
+    fn FRAC_2_PI() -> Self {
+        Self::FRAC_2_PI
+    }
+
+    #[inline]
+    fn FRAC_2_SQRT_PI() -> Self {
+        Self::FRAC_2_SQRT_PI
+    }
+
+    #[inline]
+    fn FRAC_PI_2() -> Self {
+        Self::FRAC_PI_2
+    }
+
+    #[inline]
+    fn FRAC_PI_3() -> Self {
+        Self::FRAC_PI_3
+    }
+
+    #[inline]
+    fn FRAC_PI_4() -> Self {
+        Self::FRAC_PI_4
+    }
+
+    #[inline]
+    fn FRAC_PI_6() -> Self {
+        Self::FRAC_PI_6
+    }
+
+    #[inline]
+    fn FRAC_PI_8() -> Self {
+        Self::FRAC_PI_8
+    }
+
+    #[inline]
+    fn LN_10() -> Self {
+        Self::LN_10
+    }
+
+    #[inline]
+    fn LN_2() -> Self {
+        Self::LN_2
+    }
+
+    #[inline]
+    fn LOG10_E() -> Self {
+        Self::LOG10_E
+    }
+
+    #[inline]
+    fn LOG2_E() -> Self {
+        Self::LOG2_E
+    }
+
+    #[inline]
+    fn PI() -> Self {
+        Self::PI
+    }
+
+    fn SQRT_2() -> Self {
+        Self::SQRT_2
+    }
+
+    #[inline]
+    fn LOG10_2() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG10_2
+    }
+
+    #[inline]
+    fn LOG2_10() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG2_10
+    }
+}
+
+impl Bounded for f16 {
+    #[inline]
+    fn min_value() -> Self {
+        f16::MIN
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        f16::MAX
+    }
+}
+
+macro_rules! impl_as_primitive_to_f16 {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<$ty> for f16 {
+            #[inline]
+            fn as_(self) -> $ty {
+                self.$meth().as_()
+            }
+        }
+    };
+}
+
+impl AsPrimitive<f16> for f16 {
+    #[inline]
+    fn as_(self) -> f16 {
+        self
+    }
+}
+
+impl_as_primitive_to_f16!(i64, to_f32);
+impl_as_primitive_to_f16!(u64, to_f32);
+impl_as_primitive_to_f16!(i8, to_f32);
+impl_as_primitive_to_f16!(u8, to_f32);
+impl_as_primitive_to_f16!(i16, to_f32);
+impl_as_primitive_to_f16!(u16, to_f32);
+impl_as_primitive_to_f16!(i32, to_f32);
+impl_as_primitive_to_f16!(u32, to_f32);
+impl_as_primitive_to_f16!(isize, to_f32);
+impl_as_primitive_to_f16!(usize, to_f32);
+impl_as_primitive_to_f16!(f32, to_f32);
+impl_as_primitive_to_f16!(f64, to_f64);
+
+macro_rules! impl_as_primitive_f16_from {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<f16> for $ty {
+            #[inline]
+            fn as_(self) -> f16 {
+                f16::$meth(self.as_())
+            }
+        }
+    };
+}
+
+impl_as_primitive_f16_from!(i64, from_f32);
+impl_as_primitive_f16_from!(u64, from_f32);
+impl_as_primitive_f16_from!(i8, from_f32);
+impl_as_primitive_f16_from!(u8, from_f32);
+impl_as_primitive_f16_from!(i16, from_f32);
+impl_as_primitive_f16_from!(u16, from_f32);
+impl_as_primitive_f16_from!(i32, from_f32);
+impl_as_primitive_f16_from!(u32, from_f32);
+impl_as_primitive_f16_from!(isize, from_f32);
+impl_as_primitive_f16_from!(usize, from_f32);
+impl_as_primitive_f16_from!(f32, from_f32);
+impl_as_primitive_f16_from!(f64, from_f64);
+
+impl ToPrimitive for bf16 {
+    #[inline]
+    fn to_i64(&self) -> Option<i64> {
+        Self::to_f32(*self).to_i64()
+    }
+    #[inline]
+    fn to_u64(&self) -> Option<u64> {
+        Self::to_f32(*self).to_u64()
+    }
+    #[inline]
+    fn to_i8(&self) -> Option<i8> {
+        Self::to_f32(*self).to_i8()
+    }
+    #[inline]
+    fn to_u8(&self) -> Option<u8> {
+        Self::to_f32(*self).to_u8()
+    }
+    #[inline]
+    fn to_i16(&self) -> Option<i16> {
+        Self::to_f32(*self).to_i16()
+    }
+    #[inline]
+    fn to_u16(&self) -> Option<u16> {
+        Self::to_f32(*self).to_u16()
+    }
+    #[inline]
+    fn to_i32(&self) -> Option<i32> {
+        Self::to_f32(*self).to_i32()
+    }
+    #[inline]
+    fn to_u32(&self) -> Option<u32> {
+        Self::to_f32(*self).to_u32()
+    }
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        Some(Self::to_f32(*self))
+    }
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        Some(Self::to_f64(*self))
+    }
+}
+
+impl FromPrimitive for bf16 {
+    #[inline]
+    fn from_i64(n: i64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u64(n: u64) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i8(n: i8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u8(n: u8) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i16(n: i16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u16(n: u16) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_i32(n: i32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_u32(n: u32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f32(n: f32) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+    #[inline]
+    fn from_f64(n: f64) -> Option<Self> {
+        n.to_f64().map(Self::from_f64)
+    }
+}
+
+impl Num for bf16 {
+    type FromStrRadixErr = <f32 as Num>::FromStrRadixErr;
+
+    #[inline]
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
+        Ok(Self::from_f32(f32::from_str_radix(str, radix)?))
+    }
+}
+
+impl One for bf16 {
+    #[inline]
+    fn one() -> Self {
+        Self::ONE
+    }
+}
+
+impl Zero for bf16 {
+    #[inline]
+    fn zero() -> Self {
+        Self::ZERO
+    }
+
+    #[inline]
+    fn is_zero(&self) -> bool {
+        *self == Self::ZERO
+    }
+}
+
+impl NumCast for bf16 {
+    #[inline]
+    fn from<T: ToPrimitive>(n: T) -> Option<Self> {
+        n.to_f32().map(Self::from_f32)
+    }
+}
+
+impl num_traits::float::FloatCore for bf16 {
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_bits(self.to_bits() & 0x7FFF)
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        self.signum()
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    fn min(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => other,
+            Some(Ordering::Less) => self,
+        }
+    }
+
+    fn max(self, other: Self) -> Self {
+        match self.partial_cmp(&other) {
+            None => {
+                if self.is_nan() {
+                    other
+                } else {
+                    self
+                }
+            }
+            Some(Ordering::Greater) | Some(Ordering::Equal) => self,
+            Some(Ordering::Less) => other,
+        }
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, exp: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(exp))
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::FloatCore::integer_decode(self.to_f32())
+    }
+}
+
+impl num_traits::float::Float for bf16 {
+    #[inline]
+    fn nan() -> Self {
+        Self::NAN
+    }
+
+    #[inline]
+    fn infinity() -> Self {
+        Self::INFINITY
+    }
+
+    #[inline]
+    fn neg_infinity() -> Self {
+        Self::NEG_INFINITY
+    }
+
+    #[inline]
+    fn neg_zero() -> Self {
+        Self::NEG_ZERO
+    }
+
+    #[inline]
+    fn min_value() -> Self {
+        Self::MIN
+    }
+
+    #[inline]
+    fn min_positive_value() -> Self {
+        Self::MIN_POSITIVE
+    }
+
+    #[inline]
+    fn epsilon() -> Self {
+        Self::EPSILON
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        Self::MAX
+    }
+
+    #[inline]
+    fn is_nan(self) -> bool {
+        self.is_nan()
+    }
+
+    #[inline]
+    fn is_infinite(self) -> bool {
+        self.is_infinite()
+    }
+
+    #[inline]
+    fn is_finite(self) -> bool {
+        self.is_finite()
+    }
+
+    #[inline]
+    fn is_normal(self) -> bool {
+        self.is_normal()
+    }
+
+    #[inline]
+    fn classify(self) -> FpCategory {
+        self.classify()
+    }
+
+    #[inline]
+    fn floor(self) -> Self {
+        Self::from_f32(self.to_f32().floor())
+    }
+
+    #[inline]
+    fn ceil(self) -> Self {
+        Self::from_f32(self.to_f32().ceil())
+    }
+
+    #[inline]
+    fn round(self) -> Self {
+        Self::from_f32(self.to_f32().round())
+    }
+
+    #[inline]
+    fn trunc(self) -> Self {
+        Self::from_f32(self.to_f32().trunc())
+    }
+
+    #[inline]
+    fn fract(self) -> Self {
+        Self::from_f32(self.to_f32().fract())
+    }
+
+    #[inline]
+    fn abs(self) -> Self {
+        Self::from_f32(self.to_f32().abs())
+    }
+
+    #[inline]
+    fn signum(self) -> Self {
+        Self::from_f32(self.to_f32().signum())
+    }
+
+    #[inline]
+    fn is_sign_positive(self) -> bool {
+        self.is_sign_positive()
+    }
+
+    #[inline]
+    fn is_sign_negative(self) -> bool {
+        self.is_sign_negative()
+    }
+
+    #[inline]
+    fn mul_add(self, a: Self, b: Self) -> Self {
+        Self::from_f32(self.to_f32().mul_add(a.to_f32(), b.to_f32()))
+    }
+
+    #[inline]
+    fn recip(self) -> Self {
+        Self::from_f32(self.to_f32().recip())
+    }
+
+    #[inline]
+    fn powi(self, n: i32) -> Self {
+        Self::from_f32(self.to_f32().powi(n))
+    }
+
+    #[inline]
+    fn powf(self, n: Self) -> Self {
+        Self::from_f32(self.to_f32().powf(n.to_f32()))
+    }
+
+    #[inline]
+    fn sqrt(self) -> Self {
+        Self::from_f32(self.to_f32().sqrt())
+    }
+
+    #[inline]
+    fn exp(self) -> Self {
+        Self::from_f32(self.to_f32().exp())
+    }
+
+    #[inline]
+    fn exp2(self) -> Self {
+        Self::from_f32(self.to_f32().exp2())
+    }
+
+    #[inline]
+    fn ln(self) -> Self {
+        Self::from_f32(self.to_f32().ln())
+    }
+
+    #[inline]
+    fn log(self, base: Self) -> Self {
+        Self::from_f32(self.to_f32().log(base.to_f32()))
+    }
+
+    #[inline]
+    fn log2(self) -> Self {
+        Self::from_f32(self.to_f32().log2())
+    }
+
+    #[inline]
+    fn log10(self) -> Self {
+        Self::from_f32(self.to_f32().log10())
+    }
+
+    #[inline]
+    fn to_degrees(self) -> Self {
+        Self::from_f32(self.to_f32().to_degrees())
+    }
+
+    #[inline]
+    fn to_radians(self) -> Self {
+        Self::from_f32(self.to_f32().to_radians())
+    }
+
+    #[inline]
+    fn max(self, other: Self) -> Self {
+        self.max(other)
+    }
+
+    #[inline]
+    fn min(self, other: Self) -> Self {
+        self.min(other)
+    }
+
+    #[inline]
+    fn abs_sub(self, other: Self) -> Self {
+        Self::from_f32((self.to_f32() - other.to_f32()).max(0.0))
+    }
+
+    #[inline]
+    fn cbrt(self) -> Self {
+        Self::from_f32(self.to_f32().cbrt())
+    }
+
+    #[inline]
+    fn hypot(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().hypot(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin(self) -> Self {
+        Self::from_f32(self.to_f32().sin())
+    }
+
+    #[inline]
+    fn cos(self) -> Self {
+        Self::from_f32(self.to_f32().cos())
+    }
+
+    #[inline]
+    fn tan(self) -> Self {
+        Self::from_f32(self.to_f32().tan())
+    }
+
+    #[inline]
+    fn asin(self) -> Self {
+        Self::from_f32(self.to_f32().asin())
+    }
+
+    #[inline]
+    fn acos(self) -> Self {
+        Self::from_f32(self.to_f32().acos())
+    }
+
+    #[inline]
+    fn atan(self) -> Self {
+        Self::from_f32(self.to_f32().atan())
+    }
+
+    #[inline]
+    fn atan2(self, other: Self) -> Self {
+        Self::from_f32(self.to_f32().atan2(other.to_f32()))
+    }
+
+    #[inline]
+    fn sin_cos(self) -> (Self, Self) {
+        let (sin, cos) = self.to_f32().sin_cos();
+        (Self::from_f32(sin), Self::from_f32(cos))
+    }
+
+    #[inline]
+    fn exp_m1(self) -> Self {
+        Self::from_f32(self.to_f32().exp_m1())
+    }
+
+    #[inline]
+    fn ln_1p(self) -> Self {
+        Self::from_f32(self.to_f32().ln_1p())
+    }
+
+    #[inline]
+    fn sinh(self) -> Self {
+        Self::from_f32(self.to_f32().sinh())
+    }
+
+    #[inline]
+    fn cosh(self) -> Self {
+        Self::from_f32(self.to_f32().cosh())
+    }
+
+    #[inline]
+    fn tanh(self) -> Self {
+        Self::from_f32(self.to_f32().tanh())
+    }
+
+    #[inline]
+    fn asinh(self) -> Self {
+        Self::from_f32(self.to_f32().asinh())
+    }
+
+    #[inline]
+    fn acosh(self) -> Self {
+        Self::from_f32(self.to_f32().acosh())
+    }
+
+    #[inline]
+    fn atanh(self) -> Self {
+        Self::from_f32(self.to_f32().atanh())
+    }
+
+    #[inline]
+    fn integer_decode(self) -> (u64, i16, i8) {
+        num_traits::float::Float::integer_decode(self.to_f32())
+    }
+}
+
+impl FloatConst for bf16 {
+    #[inline]
+    fn E() -> Self {
+        Self::E
+    }
+
+    #[inline]
+    fn FRAC_1_PI() -> Self {
+        Self::FRAC_1_PI
+    }
+
+    #[inline]
+    fn FRAC_1_SQRT_2() -> Self {
+        Self::FRAC_1_SQRT_2
+    }
+
+    #[inline]
+    fn FRAC_2_PI() -> Self {
+        Self::FRAC_2_PI
+    }
+
+    #[inline]
+    fn FRAC_2_SQRT_PI() -> Self {
+        Self::FRAC_2_SQRT_PI
+    }
+
+    #[inline]
+    fn FRAC_PI_2() -> Self {
+        Self::FRAC_PI_2
+    }
+
+    #[inline]
+    fn FRAC_PI_3() -> Self {
+        Self::FRAC_PI_3
+    }
+
+    #[inline]
+    fn FRAC_PI_4() -> Self {
+        Self::FRAC_PI_4
+    }
+
+    #[inline]
+    fn FRAC_PI_6() -> Self {
+        Self::FRAC_PI_6
+    }
+
+    #[inline]
+    fn FRAC_PI_8() -> Self {
+        Self::FRAC_PI_8
+    }
+
+    #[inline]
+    fn LN_10() -> Self {
+        Self::LN_10
+    }
+
+    #[inline]
+    fn LN_2() -> Self {
+        Self::LN_2
+    }
+
+    #[inline]
+    fn LOG10_E() -> Self {
+        Self::LOG10_E
+    }
+
+    #[inline]
+    fn LOG2_E() -> Self {
+        Self::LOG2_E
+    }
+
+    #[inline]
+    fn PI() -> Self {
+        Self::PI
+    }
+
+    #[inline]
+    fn SQRT_2() -> Self {
+        Self::SQRT_2
+    }
+
+    #[inline]
+    fn LOG10_2() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG10_2
+    }
+
+    #[inline]
+    fn LOG2_10() -> Self
+    where
+        Self: Sized + Div<Self, Output = Self>,
+    {
+        Self::LOG2_10
+    }
+}
+
+impl Bounded for bf16 {
+    #[inline]
+    fn min_value() -> Self {
+        bf16::MIN
+    }
+
+    #[inline]
+    fn max_value() -> Self {
+        bf16::MAX
+    }
+}
+
+impl AsPrimitive<bf16> for bf16 {
+    #[inline]
+    fn as_(self) -> bf16 {
+        self
+    }
+}
+
+macro_rules! impl_as_primitive_to_bf16 {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<$ty> for bf16 {
+            #[inline]
+            fn as_(self) -> $ty {
+                self.$meth().as_()
+            }
+        }
+    };
+}
+
+impl_as_primitive_to_bf16!(i64, to_f32);
+impl_as_primitive_to_bf16!(u64, to_f32);
+impl_as_primitive_to_bf16!(i8, to_f32);
+impl_as_primitive_to_bf16!(u8, to_f32);
+impl_as_primitive_to_bf16!(i16, to_f32);
+impl_as_primitive_to_bf16!(u16, to_f32);
+impl_as_primitive_to_bf16!(i32, to_f32);
+impl_as_primitive_to_bf16!(u32, to_f32);
+impl_as_primitive_to_bf16!(isize, to_f32);
+impl_as_primitive_to_bf16!(usize, to_f32);
+impl_as_primitive_to_bf16!(f32, to_f32);
+impl_as_primitive_to_bf16!(f64, to_f64);
+
+macro_rules! impl_as_primitive_bf16_from {
+    ($ty:ty, $meth:ident) => {
+        impl AsPrimitive<bf16> for $ty {
+            #[inline]
+            fn as_(self) -> bf16 {
+                bf16::$meth(self.as_())
+            }
+        }
+    };
+}
+
+impl_as_primitive_bf16_from!(i64, from_f32);
+impl_as_primitive_bf16_from!(u64, from_f32);
+impl_as_primitive_bf16_from!(i8, from_f32);
+impl_as_primitive_bf16_from!(u8, from_f32);
+impl_as_primitive_bf16_from!(i16, from_f32);
+impl_as_primitive_bf16_from!(u16, from_f32);
+impl_as_primitive_bf16_from!(i32, from_f32);
+impl_as_primitive_bf16_from!(u32, from_f32);
+impl_as_primitive_bf16_from!(isize, from_f32);
+impl_as_primitive_bf16_from!(usize, from_f32);
+impl_as_primitive_bf16_from!(f32, from_f32);
+impl_as_primitive_bf16_from!(f64, from_f64);