library/core/src/num/imp/traits.rs - rust - Git at Google

 //! Numeric traits used for internal implementations.

 #![doc(hidden)]
 #![unstable(
     feature = "num_internals",
     reason = "internal routines only exposed for testing",
     issue = "none"
 )]

 use crate::num::FpCategory;
 use crate::{f64, fmt, ops};

 /// Lossy `as` casting between two types.
 pub trait CastInto<T: Copy>: Copy {
     fn cast(self) -> T;
 }

 /// Collection of traits that allow us to be generic over integer size.
 pub trait Int:
     Sized
     + Clone
     + Copy
     + fmt::Debug
     + ops::Shr<u32, Output = Self>
     + ops::Shl<u32, Output = Self>
     + ops::BitAnd<Output = Self>
     + ops::BitOr<Output = Self>
     + PartialEq
     + CastInto<i16>
 {
     const ZERO: Self;
     const ONE: Self;
 }

 macro_rules! int {
     ($($ty:ty),+) => {
         $(
             impl CastInto<i16> for $ty {
                 fn cast(self) -> i16 {
                     self as i16
                 }
             }

             impl Int for $ty {
                 const ZERO: Self = 0;
                 const ONE: Self = 1;
             }
         )+
     }
 }

 int!(u16, u32, u64);

 /// A helper trait to avoid duplicating basically all the conversion code for IEEE floats.
 #[doc(hidden)]
 pub trait Float:
     Sized
     + ops::Div<Output = Self>
     + ops::Neg<Output = Self>
     + ops::Mul<Output = Self>
     + ops::Add<Output = Self>
     + fmt::Debug
     + PartialEq
     + PartialOrd
     + Default
     + Clone
     + Copy
 {
     /// The unsigned integer with the same size as the float
     type Int: Int + Into<u64>;

     /* general constants */

     const INFINITY: Self;
     const NEG_INFINITY: Self;
     const NAN: Self;
     const NEG_NAN: Self;

     /// Bit width of the float
     const BITS: u32;

     /// The number of bits in the significand, *including* the hidden bit.
     const SIG_TOTAL_BITS: u32;

     const EXP_MASK: Self::Int;
     const SIG_MASK: Self::Int;

     /// The number of bits in the significand, *excluding* the hidden bit.
     const SIG_BITS: u32 = Self::SIG_TOTAL_BITS - 1;

     /// Number of bits in 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 shifted fully right, use `EXP_MASK` for the shifted value.
     const EXP_SAT: u32 = (1 << Self::EXP_BITS) - 1;

     /// Signed version of `EXP_SAT` since we convert a lot.
     const INFINITE_POWER: i32 = Self::EXP_SAT as i32;

     /// The exponent bias value. This is also the maximum value of the exponent.
     const EXP_BIAS: u32 = Self::EXP_SAT >> 1;

     /// Minimum exponent value of normal values.
     const EXP_MIN: i32 = -(Self::EXP_BIAS as i32 - 1);

     /// Round-to-even only happens for negative values of q
     /// when q ≥ −4 in the 64-bit case and when q ≥ −17 in
     /// the 32-bit case.
     ///
     /// When q ≥ 0,we have that 5^q ≤ 2m+1. In the 64-bit case,we
     /// have 5^q ≤ 2m+1 ≤ 2^54 or q ≤ 23. In the 32-bit case,we have
     /// 5^q ≤ 2m+1 ≤ 2^25 or q ≤ 10.
     ///
     /// When q < 0, we have w ≥ (2m+1)×5^−q. We must have that w < 2^64
     /// so (2m+1)×5^−q < 2^64. We have that 2m+1 > 2^53 (64-bit case)
     /// or 2m+1 > 2^24 (32-bit case). Hence,we must have 2^53×5^−q < 2^64
     /// (64-bit) and 2^24×5^−q < 2^64 (32-bit). Hence we have 5^−q < 2^11
     /// or q ≥ −4 (64-bit case) and 5^−q < 2^40 or q ≥ −17 (32-bit case).
     ///
     /// Thus we have that we only need to round ties to even when
     /// we have that q ∈ [−4,23](in the 64-bit case) or q∈[−17,10]
     /// (in the 32-bit case). In both cases,the power of five(5^|q|)
     /// fits in a 64-bit word.
     const MIN_EXPONENT_ROUND_TO_EVEN: i32;
     const MAX_EXPONENT_ROUND_TO_EVEN: i32;

     /// Largest decimal exponent for a non-infinite value.
     ///
     /// This is the max exponent in binary converted to the max exponent in decimal. Allows fast
     /// pathing anything larger than `10^LARGEST_POWER_OF_TEN`, which will round to infinity.
     const LARGEST_POWER_OF_TEN: i32 = {
         let largest_pow2 = Self::EXP_BIAS + 1;
         pow2_to_pow10(largest_pow2 as i64) as i32
     };

     /// Smallest decimal exponent for a non-zero value. This allows for fast pathing anything
     /// smaller than `10^SMALLEST_POWER_OF_TEN`, which will round to zero.
     ///
     /// The smallest power of ten is represented by `⌊log10(2^-n / (2^64 - 1))⌋`, where `n` is
     /// the smallest power of two. The `2^64 - 1)` denominator comes from the number of values
     /// that are representable by the intermediate storage format. I don't actually know _why_
     /// the storage format is relevant here.
     ///
     /// The values may be calculated using the formula. Unfortunately we cannot calculate them at
     /// compile time since intermediates exceed the range of an `f64`.
     const SMALLEST_POWER_OF_TEN: i32;

     /// Returns the category that this number falls into.
     fn classify(self) -> FpCategory;

     /// Transmute to the integer representation
     fn to_bits(self) -> Self::Int;
 }

 /// Items that ideally would be on `Float`, but don't apply to all float types because they
 /// rely on the mantissa fitting into a `u64` (which isn't true for `f128`).
 #[doc(hidden)]
 pub trait FloatExt: Float {
     /// Performs a raw transmutation from an integer.
     fn from_u64_bits(v: u64) -> Self;

     /// Returns the mantissa, exponent and sign as integers.
     ///
     /// This returns `(m, p, s)` such that `s * m * 2^p` represents the original float. For 0, the
     /// exponent will be `-(EXP_BIAS + SIG_BITS)`, which is the minimum subnormal power. For
     /// infinity or NaN, the exponent will be `EXP_SAT - EXP_BIAS - SIG_BITS`.
     ///
     /// If subnormal, the mantissa will be shifted one bit to the left. Otherwise, it is returned
     /// with the explicit bit set but otherwise unshifted
     ///
     /// `s` is only ever +/-1.
     fn integer_decode(self) -> (u64, i16, i8) {
         let bits = self.to_bits();
         let sign: i8 = if bits >> (Self::BITS - 1) == Self::Int::ZERO { 1 } else { -1 };
         let mut exponent: i16 = ((bits & Self::EXP_MASK) >> Self::SIG_BITS).cast();
         let mantissa = if exponent == 0 {
             (bits & Self::SIG_MASK) << 1
         } else {
             (bits & Self::SIG_MASK) | (Self::Int::ONE << Self::SIG_BITS)
         };
         // Exponent bias + mantissa shift
         exponent -= (Self::EXP_BIAS + Self::SIG_BITS) as i16;
         (mantissa.into(), exponent, sign)
     }
 }

 /// Solve for `b` in `10^b = 2^a`
 const fn pow2_to_pow10(a: i64) -> i64 {
     let res = (a as f64) / f64::consts::LOG2_10;
     res as i64
 }

 #[cfg(target_has_reliable_f16)]
 impl Float for f16 {
     type Int = u16;

     const INFINITY: Self = Self::INFINITY;
     const NEG_INFINITY: Self = Self::NEG_INFINITY;
     const NAN: Self = Self::NAN;
     const NEG_NAN: Self = -Self::NAN;

     const BITS: u32 = 16;
     const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
     const EXP_MASK: Self::Int = Self::EXP_MASK;
     const SIG_MASK: Self::Int = Self::MAN_MASK;

     const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -22;
     const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 5;
     const SMALLEST_POWER_OF_TEN: i32 = -27;

     fn to_bits(self) -> Self::Int {
         self.to_bits()
     }

     fn classify(self) -> FpCategory {
         self.classify()
     }
 }

 #[cfg(target_has_reliable_f16)]
 impl FloatExt for f16 {
     #[inline]
     fn from_u64_bits(v: u64) -> Self {
         Self::from_bits((v & 0xFFFF) as u16)
     }
 }

 impl Float for f32 {
     type Int = u32;

     const INFINITY: Self = f32::INFINITY;
     const NEG_INFINITY: Self = f32::NEG_INFINITY;
     const NAN: Self = f32::NAN;
     const NEG_NAN: Self = -f32::NAN;

     const BITS: u32 = 32;
     const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
     const EXP_MASK: Self::Int = Self::EXP_MASK;
     const SIG_MASK: Self::Int = Self::MAN_MASK;

     const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -17;
     const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 10;
     const SMALLEST_POWER_OF_TEN: i32 = -65;

     fn to_bits(self) -> Self::Int {
         self.to_bits()
     }

     fn classify(self) -> FpCategory {
         self.classify()
     }
 }

 impl FloatExt for f32 {
     #[inline]
     fn from_u64_bits(v: u64) -> Self {
         f32::from_bits((v & 0xFFFFFFFF) as u32)
     }
 }

 impl Float for f64 {
     type Int = u64;

     const INFINITY: Self = Self::INFINITY;
     const NEG_INFINITY: Self = Self::NEG_INFINITY;
     const NAN: Self = Self::NAN;
     const NEG_NAN: Self = -Self::NAN;

     const BITS: u32 = 64;
     const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
     const EXP_MASK: Self::Int = Self::EXP_MASK;
     const SIG_MASK: Self::Int = Self::MAN_MASK;

     const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -4;
     const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 23;
     const SMALLEST_POWER_OF_TEN: i32 = -342;

     fn to_bits(self) -> Self::Int {
         self.to_bits()
     }

     fn classify(self) -> FpCategory {
         self.classify()
     }
 }

 impl FloatExt for f64 {
     #[inline]
     fn from_u64_bits(v: u64) -> Self {
         f64::from_bits(v)
     }
 }
	//! Numeric traits used for internal implementations.

	#![doc(hidden)]
	#![unstable(
	feature = "num_internals",
	reason = "internal routines only exposed for testing",
	issue = "none"
	)]

	use crate::num::FpCategory;
	use crate::{f64, fmt, ops};

	/// Lossy `as` casting between two types.
	pub trait CastInto<T: Copy>: Copy {
	fn cast(self) -> T;
	}

	/// Collection of traits that allow us to be generic over integer size.
	pub trait Int:
	Sized
	+ Clone
	+ Copy
	+ fmt::Debug
	+ ops::Shr<u32, Output = Self>
	+ ops::Shl<u32, Output = Self>
	+ ops::BitAnd<Output = Self>
	+ ops::BitOr<Output = Self>
	+ PartialEq
	+ CastInto<i16>
	{
	const ZERO: Self;
	const ONE: Self;
	}

	macro_rules! int {
	($($ty:ty),+) => {
	$(
	impl CastInto<i16> for $ty {
	fn cast(self) -> i16 {
	self as i16
	}
	}

	impl Int for $ty {
	const ZERO: Self = 0;
	const ONE: Self = 1;
	}
	)+
	}
	}

	int!(u16, u32, u64);

	/// A helper trait to avoid duplicating basically all the conversion code for IEEE floats.
	#[doc(hidden)]
	pub trait Float:
	Sized
	+ ops::Div<Output = Self>
	+ ops::Neg<Output = Self>
	+ ops::Mul<Output = Self>
	+ ops::Add<Output = Self>
	+ fmt::Debug
	+ PartialEq
	+ PartialOrd
	+ Default
	+ Clone
	+ Copy
	{
	/// The unsigned integer with the same size as the float
	type Int: Int + Into<u64>;

	/* general constants */

	const INFINITY: Self;
	const NEG_INFINITY: Self;
	const NAN: Self;
	const NEG_NAN: Self;

	/// Bit width of the float
	const BITS: u32;

	/// The number of bits in the significand, including the hidden bit.
	const SIG_TOTAL_BITS: u32;

	const EXP_MASK: Self::Int;
	const SIG_MASK: Self::Int;

	/// The number of bits in the significand, excluding the hidden bit.
	const SIG_BITS: u32 = Self::SIG_TOTAL_BITS - 1;

	/// Number of bits in 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 shifted fully right, use `EXP_MASK` for the shifted value.
	const EXP_SAT: u32 = (1 << Self::EXP_BITS) - 1;

	/// Signed version of `EXP_SAT` since we convert a lot.
	const INFINITE_POWER: i32 = Self::EXP_SAT as i32;

	/// The exponent bias value. This is also the maximum value of the exponent.
	const EXP_BIAS: u32 = Self::EXP_SAT >> 1;

	/// Minimum exponent value of normal values.
	const EXP_MIN: i32 = -(Self::EXP_BIAS as i32 - 1);

	/// Round-to-even only happens for negative values of q
	/// when q ≥ −4 in the 64-bit case and when q ≥ −17 in
	/// the 32-bit case.
	///
	/// When q ≥ 0,we have that 5^q ≤ 2m+1. In the 64-bit case,we
	/// have 5^q ≤ 2m+1 ≤ 2^54 or q ≤ 23. In the 32-bit case,we have
	/// 5^q ≤ 2m+1 ≤ 2^25 or q ≤ 10.
	///
	/// When q < 0, we have w ≥ (2m+1)×5^−q. We must have that w < 2^64
	/// so (2m+1)×5^−q < 2^64. We have that 2m+1 > 2^53 (64-bit case)
	/// or 2m+1 > 2^24 (32-bit case). Hence,we must have 2^53×5^−q < 2^64
	/// (64-bit) and 2^24×5^−q < 2^64 (32-bit). Hence we have 5^−q < 2^11
	/// or q ≥ −4 (64-bit case) and 5^−q < 2^40 or q ≥ −17 (32-bit case).
	///
	/// Thus we have that we only need to round ties to even when
	/// we have that q ∈ [−4,23](in the 64-bit case) or q∈[−17,10]
	/// (in the 32-bit case). In both cases,the power of five(5^\|q\|)
	/// fits in a 64-bit word.
	const MIN_EXPONENT_ROUND_TO_EVEN: i32;
	const MAX_EXPONENT_ROUND_TO_EVEN: i32;

	/// Largest decimal exponent for a non-infinite value.
	///
	/// This is the max exponent in binary converted to the max exponent in decimal. Allows fast
	/// pathing anything larger than `10^LARGEST_POWER_OF_TEN`, which will round to infinity.
	const LARGEST_POWER_OF_TEN: i32 = {
	let largest_pow2 = Self::EXP_BIAS + 1;
	pow2_to_pow10(largest_pow2 as i64) as i32
	};

	/// Smallest decimal exponent for a non-zero value. This allows for fast pathing anything
	/// smaller than `10^SMALLEST_POWER_OF_TEN`, which will round to zero.
	///
	/// The smallest power of ten is represented by `⌊log10(2^-n / (2^64 - 1))⌋`, where `n` is
	/// the smallest power of two. The `2^64 - 1)` denominator comes from the number of values
	/// that are representable by the intermediate storage format. I don't actually know _why_
	/// the storage format is relevant here.
	///
	/// The values may be calculated using the formula. Unfortunately we cannot calculate them at
	/// compile time since intermediates exceed the range of an `f64`.
	const SMALLEST_POWER_OF_TEN: i32;

	/// Returns the category that this number falls into.
	fn classify(self) -> FpCategory;

	/// Transmute to the integer representation
	fn to_bits(self) -> Self::Int;
	}

	/// Items that ideally would be on `Float`, but don't apply to all float types because they
	/// rely on the mantissa fitting into a `u64` (which isn't true for `f128`).
	#[doc(hidden)]
	pub trait FloatExt: Float {
	/// Performs a raw transmutation from an integer.
	fn from_u64_bits(v: u64) -> Self;

	/// Returns the mantissa, exponent and sign as integers.
	///
	/// This returns `(m, p, s)` such that `s * m * 2^p` represents the original float. For 0, the
	/// exponent will be `-(EXP_BIAS + SIG_BITS)`, which is the minimum subnormal power. For
	/// infinity or NaN, the exponent will be `EXP_SAT - EXP_BIAS - SIG_BITS`.
	///
	/// If subnormal, the mantissa will be shifted one bit to the left. Otherwise, it is returned
	/// with the explicit bit set but otherwise unshifted
	///
	/// `s` is only ever +/-1.
	fn integer_decode(self) -> (u64, i16, i8) {
	let bits = self.to_bits();
	let sign: i8 = if bits >> (Self::BITS - 1) == Self::Int::ZERO { 1 } else { -1 };
	let mut exponent: i16 = ((bits & Self::EXP_MASK) >> Self::SIG_BITS).cast();
	let mantissa = if exponent == 0 {
	(bits & Self::SIG_MASK) << 1
	} else {
	(bits & Self::SIG_MASK) \| (Self::Int::ONE << Self::SIG_BITS)
	};
	// Exponent bias + mantissa shift
	exponent -= (Self::EXP_BIAS + Self::SIG_BITS) as i16;
	(mantissa.into(), exponent, sign)
	}
	}

	/// Solve for `b` in `10^b = 2^a`
	const fn pow2_to_pow10(a: i64) -> i64 {
	let res = (a as f64) / f64::consts::LOG2_10;
	res as i64
	}

	#[cfg(target_has_reliable_f16)]
	impl Float for f16 {
	type Int = u16;

	const INFINITY: Self = Self::INFINITY;
	const NEG_INFINITY: Self = Self::NEG_INFINITY;
	const NAN: Self = Self::NAN;
	const NEG_NAN: Self = -Self::NAN;

	const BITS: u32 = 16;
	const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
	const EXP_MASK: Self::Int = Self::EXP_MASK;
	const SIG_MASK: Self::Int = Self::MAN_MASK;

	const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -22;
	const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 5;
	const SMALLEST_POWER_OF_TEN: i32 = -27;

	fn to_bits(self) -> Self::Int {
	self.to_bits()
	}

	fn classify(self) -> FpCategory {
	self.classify()
	}
	}

	#[cfg(target_has_reliable_f16)]
	impl FloatExt for f16 {
	#[inline]
	fn from_u64_bits(v: u64) -> Self {
	Self::from_bits((v & 0xFFFF) as u16)
	}
	}

	impl Float for f32 {
	type Int = u32;

	const INFINITY: Self = f32::INFINITY;
	const NEG_INFINITY: Self = f32::NEG_INFINITY;
	const NAN: Self = f32::NAN;
	const NEG_NAN: Self = -f32::NAN;

	const BITS: u32 = 32;
	const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
	const EXP_MASK: Self::Int = Self::EXP_MASK;
	const SIG_MASK: Self::Int = Self::MAN_MASK;

	const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -17;
	const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 10;
	const SMALLEST_POWER_OF_TEN: i32 = -65;

	fn to_bits(self) -> Self::Int {
	self.to_bits()
	}

	fn classify(self) -> FpCategory {
	self.classify()
	}
	}

	impl FloatExt for f32 {
	#[inline]
	fn from_u64_bits(v: u64) -> Self {
	f32::from_bits((v & 0xFFFFFFFF) as u32)
	}
	}

	impl Float for f64 {
	type Int = u64;

	const INFINITY: Self = Self::INFINITY;
	const NEG_INFINITY: Self = Self::NEG_INFINITY;
	const NAN: Self = Self::NAN;
	const NEG_NAN: Self = -Self::NAN;

	const BITS: u32 = 64;
	const SIG_TOTAL_BITS: u32 = Self::MANTISSA_DIGITS;
	const EXP_MASK: Self::Int = Self::EXP_MASK;
	const SIG_MASK: Self::Int = Self::MAN_MASK;

	const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -4;
	const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 23;
	const SMALLEST_POWER_OF_TEN: i32 = -342;

	fn to_bits(self) -> Self::Int {
	self.to_bits()
	}

	fn classify(self) -> FpCategory {
	self.classify()
	}
	}

	impl FloatExt for f64 {
	#[inline]
	fn from_u64_bits(v: u64) -> Self {
	f64::from_bits(v)
	}
	}