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+// Adapted from https://github.com/Alexhuszagh/rust-lexical.
+
+//! Utilities for Rust numbers.
+
+use core::ops;
+
+/// Precalculated values of radix**i for i in range [0, arr.len()-1].
+/// Each value can be **exactly** represented as that type.
+const F32_POW10: [f32; 11] = [
+ 1.0,
+ 10.0,
+ 100.0,
+ 1000.0,
+ 10000.0,
+ 100000.0,
+ 1000000.0,
+ 10000000.0,
+ 100000000.0,
+ 1000000000.0,
+ 10000000000.0,
+];
+
+/// Precalculated values of radix**i for i in range [0, arr.len()-1].
+/// Each value can be **exactly** represented as that type.
+const F64_POW10: [f64; 23] = [
+ 1.0,
+ 10.0,
+ 100.0,
+ 1000.0,
+ 10000.0,
+ 100000.0,
+ 1000000.0,
+ 10000000.0,
+ 100000000.0,
+ 1000000000.0,
+ 10000000000.0,
+ 100000000000.0,
+ 1000000000000.0,
+ 10000000000000.0,
+ 100000000000000.0,
+ 1000000000000000.0,
+ 10000000000000000.0,
+ 100000000000000000.0,
+ 1000000000000000000.0,
+ 10000000000000000000.0,
+ 100000000000000000000.0,
+ 1000000000000000000000.0,
+ 10000000000000000000000.0,
+];
+
+/// Type that can be converted to primitive with `as`.
+pub trait AsPrimitive: Sized + Copy + PartialOrd {
+ fn as_u32(self) -> u32;
+ fn as_u64(self) -> u64;
+ fn as_u128(self) -> u128;
+ fn as_usize(self) -> usize;
+ fn as_f32(self) -> f32;
+ fn as_f64(self) -> f64;
+}
+
+macro_rules! as_primitive_impl {
+ ($($ty:ident)*) => {
+ $(
+ impl AsPrimitive for $ty {
+ #[inline]
+ fn as_u32(self) -> u32 {
+ self as u32
+ }
+
+ #[inline]
+ fn as_u64(self) -> u64 {
+ self as u64
+ }
+
+ #[inline]
+ fn as_u128(self) -> u128 {
+ self as u128
+ }
+
+ #[inline]
+ fn as_usize(self) -> usize {
+ self as usize
+ }
+
+ #[inline]
+ fn as_f32(self) -> f32 {
+ self as f32
+ }
+
+ #[inline]
+ fn as_f64(self) -> f64 {
+ self as f64
+ }
+ }
+ )*
+ };
+}
+
+as_primitive_impl! { u32 u64 u128 usize f32 f64 }
+
+/// An interface for casting between machine scalars.
+pub trait AsCast: AsPrimitive {
+ /// Creates a number from another value that can be converted into
+ /// a primitive via the `AsPrimitive` trait.
+ fn as_cast<N: AsPrimitive>(n: N) -> Self;
+}
+
+macro_rules! as_cast_impl {
+ ($ty:ident, $method:ident) => {
+ impl AsCast for $ty {
+ #[inline]
+ fn as_cast<N: AsPrimitive>(n: N) -> Self {
+ n.$method()
+ }
+ }
+ };
+}
+
+as_cast_impl!(u32, as_u32);
+as_cast_impl!(u64, as_u64);
+as_cast_impl!(u128, as_u128);
+as_cast_impl!(usize, as_usize);
+as_cast_impl!(f32, as_f32);
+as_cast_impl!(f64, as_f64);
+
+/// Numerical type trait.
+pub trait Number: AsCast + ops::Add<Output = Self> {}
+
+macro_rules! number_impl {
+ ($($ty:ident)*) => {
+ $(
+ impl Number for $ty {}
+ )*
+ };
+}
+
+number_impl! { u32 u64 u128 usize f32 f64 }
+
+/// Defines a trait that supports integral operations.
+pub trait Integer: Number + ops::BitAnd<Output = Self> + ops::Shr<i32, Output = Self> {
+ const ZERO: Self;
+}
+
+macro_rules! integer_impl {
+ ($($ty:tt)*) => {
+ $(
+ impl Integer for $ty {
+ const ZERO: Self = 0;
+ }
+ )*
+ };
+}
+
+integer_impl! { u32 u64 u128 usize }
+
+/// Type trait for the mantissa type.
+pub trait Mantissa: Integer {
+ /// Mask to extract the high bits from the integer.
+ const HIMASK: Self;
+ /// Mask to extract the low bits from the integer.
+ const LOMASK: Self;
+ /// Full size of the integer, in bits.
+ const FULL: i32;
+ /// Half size of the integer, in bits.
+ const HALF: i32 = Self::FULL / 2;
+}
+
+impl Mantissa for u64 {
+ const HIMASK: u64 = 0xFFFFFFFF00000000;
+ const LOMASK: u64 = 0x00000000FFFFFFFF;
+ const FULL: i32 = 64;
+}
+
+/// Get exact exponent limit for radix.
+pub trait Float: Number {
+ /// Unsigned type of the same size.
+ type Unsigned: Integer;
+
+ /// Literal zero.
+ const ZERO: Self;
+ /// Maximum number of digits that can contribute in the mantissa.
+ ///
+ /// We can exactly represent a float in radix `b` from radix 2 if
+ /// `b` is divisible by 2. This function calculates the exact number of
+ /// digits required to exactly represent that float.
+ ///
+ /// According to the "Handbook of Floating Point Arithmetic",
+ /// for IEEE754, with emin being the min exponent, p2 being the
+ /// precision, and b being the radix, the number of digits follows as:
+ ///
+ /// `−emin + p2 + ⌊(emin + 1) log(2, b) − log(1 − 2^(−p2), b)⌋`
+ ///
+ /// For f32, this follows as:
+ /// emin = -126
+ /// p2 = 24
+ ///
+ /// For f64, this follows as:
+ /// emin = -1022
+ /// p2 = 53
+ ///
+ /// In Python:
+ /// `-emin + p2 + math.floor((emin+1)*math.log(2, b) - math.log(1-2**(-p2), b))`
+ ///
+ /// This was used to calculate the maximum number of digits for [2, 36].
+ const MAX_DIGITS: usize;
+
+ // MASKS
+
+ /// Bitmask for the sign bit.
+ const SIGN_MASK: Self::Unsigned;
+ /// Bitmask for the exponent, including the hidden bit.
+ const EXPONENT_MASK: Self::Unsigned;
+ /// Bitmask for the hidden bit in exponent, which is an implicit 1 in the fraction.
+ const HIDDEN_BIT_MASK: Self::Unsigned;
+ /// Bitmask for the mantissa (fraction), excluding the hidden bit.
+ const MANTISSA_MASK: Self::Unsigned;
+
+ // PROPERTIES
+
+ /// Positive infinity as bits.
+ const INFINITY_BITS: Self::Unsigned;
+ /// Positive infinity as bits.
+ const NEGATIVE_INFINITY_BITS: Self::Unsigned;
+ /// Size of the significand (mantissa) without hidden bit.
+ const MANTISSA_SIZE: i32;
+ /// Bias of the exponet
+ const EXPONENT_BIAS: i32;
+ /// Exponent portion of a denormal float.
+ const DENORMAL_EXPONENT: i32;
+ /// Maximum exponent value in float.
+ const MAX_EXPONENT: i32;
+
+ // ROUNDING
+
+ /// Default number of bits to shift (or 64 - mantissa size - 1).
+ const DEFAULT_SHIFT: i32;
+ /// Mask to determine if a full-carry occurred (1 in bit above hidden bit).
+ const CARRY_MASK: u64;
+
+ /// Get min and max exponent limits (exact) from radix.
+ fn exponent_limit() -> (i32, i32);
+
+ /// Get the number of digits that can be shifted from exponent to mantissa.
+ fn mantissa_limit() -> i32;
+
+ // Re-exported methods from std.
+ fn pow10(self, n: i32) -> Self;
+ fn from_bits(u: Self::Unsigned) -> Self;
+ fn to_bits(self) -> Self::Unsigned;
+ fn is_sign_positive(self) -> bool;
+ fn is_sign_negative(self) -> bool;
+
+ /// Returns true if the float is a denormal.
+ #[inline]
+ fn is_denormal(self) -> bool {
+ self.to_bits() & Self::EXPONENT_MASK == Self::Unsigned::ZERO
+ }
+
+ /// Returns true if the float is a NaN or Infinite.
+ #[inline]
+ fn is_special(self) -> bool {
+ self.to_bits() & Self::EXPONENT_MASK == Self::EXPONENT_MASK
+ }
+
+ /// Returns true if the float is infinite.
+ #[inline]
+ fn is_inf(self) -> bool {
+ self.is_special() && (self.to_bits() & Self::MANTISSA_MASK) == Self::Unsigned::ZERO
+ }
+
+ /// Get exponent component from the float.
+ #[inline]
+ fn exponent(self) -> i32 {
+ if self.is_denormal() {
+ return Self::DENORMAL_EXPONENT;
+ }
+
+ let bits = self.to_bits();
+ let biased_e = ((bits & Self::EXPONENT_MASK) >> Self::MANTISSA_SIZE).as_u32();
+ biased_e as i32 - Self::EXPONENT_BIAS
+ }
+
+ /// Get mantissa (significand) component from float.
+ #[inline]
+ fn mantissa(self) -> Self::Unsigned {
+ let bits = self.to_bits();
+ let s = bits & Self::MANTISSA_MASK;
+ if !self.is_denormal() {
+ s + Self::HIDDEN_BIT_MASK
+ } else {
+ s
+ }
+ }
+
+ /// Get next greater float for a positive float.
+ /// Value must be >= 0.0 and < INFINITY.
+ #[inline]
+ fn next_positive(self) -> Self {
+ debug_assert!(self.is_sign_positive() && !self.is_inf());
+ Self::from_bits(self.to_bits() + Self::Unsigned::as_cast(1u32))
+ }
+
+ /// Round a positive number to even.
+ #[inline]
+ fn round_positive_even(self) -> Self {
+ if self.mantissa() & Self::Unsigned::as_cast(1u32) == Self::Unsigned::as_cast(1u32) {
+ self.next_positive()
+ } else {
+ self
+ }
+ }
+}
+
+impl Float for f32 {
+ type Unsigned = u32;
+
+ const ZERO: f32 = 0.0;
+ const MAX_DIGITS: usize = 114;
+ const SIGN_MASK: u32 = 0x80000000;
+ const EXPONENT_MASK: u32 = 0x7F800000;
+ const HIDDEN_BIT_MASK: u32 = 0x00800000;
+ const MANTISSA_MASK: u32 = 0x007FFFFF;
+ const INFINITY_BITS: u32 = 0x7F800000;
+ const NEGATIVE_INFINITY_BITS: u32 = Self::INFINITY_BITS | Self::SIGN_MASK;
+ const MANTISSA_SIZE: i32 = 23;
+ const EXPONENT_BIAS: i32 = 127 + Self::MANTISSA_SIZE;
+ const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
+ const MAX_EXPONENT: i32 = 0xFF - Self::EXPONENT_BIAS;
+ const DEFAULT_SHIFT: i32 = u64::FULL - f32::MANTISSA_SIZE - 1;
+ const CARRY_MASK: u64 = 0x1000000;
+
+ #[inline]
+ fn exponent_limit() -> (i32, i32) {
+ (-10, 10)
+ }
+
+ #[inline]
+ fn mantissa_limit() -> i32 {
+ 7
+ }
+
+ #[inline]
+ fn pow10(self, n: i32) -> f32 {
+ // Check the exponent is within bounds in debug builds.
+ debug_assert!({
+ let (min, max) = Self::exponent_limit();
+ n >= min && n <= max
+ });
+
+ if n > 0 {
+ self * F32_POW10[n as usize]
+ } else {
+ self / F32_POW10[-n as usize]
+ }
+ }
+
+ #[inline]
+ fn from_bits(u: u32) -> f32 {
+ f32::from_bits(u)
+ }
+
+ #[inline]
+ fn to_bits(self) -> u32 {
+ f32::to_bits(self)
+ }
+
+ #[inline]
+ fn is_sign_positive(self) -> bool {
+ f32::is_sign_positive(self)
+ }
+
+ #[inline]
+ fn is_sign_negative(self) -> bool {
+ f32::is_sign_negative(self)
+ }
+}
+
+impl Float for f64 {
+ type Unsigned = u64;
+
+ const ZERO: f64 = 0.0;
+ const MAX_DIGITS: usize = 769;
+ const SIGN_MASK: u64 = 0x8000000000000000;
+ const EXPONENT_MASK: u64 = 0x7FF0000000000000;
+ const HIDDEN_BIT_MASK: u64 = 0x0010000000000000;
+ const MANTISSA_MASK: u64 = 0x000FFFFFFFFFFFFF;
+ const INFINITY_BITS: u64 = 0x7FF0000000000000;
+ const NEGATIVE_INFINITY_BITS: u64 = Self::INFINITY_BITS | Self::SIGN_MASK;
+ const MANTISSA_SIZE: i32 = 52;
+ const EXPONENT_BIAS: i32 = 1023 + Self::MANTISSA_SIZE;
+ const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
+ const MAX_EXPONENT: i32 = 0x7FF - Self::EXPONENT_BIAS;
+ const DEFAULT_SHIFT: i32 = u64::FULL - f64::MANTISSA_SIZE - 1;
+ const CARRY_MASK: u64 = 0x20000000000000;
+
+ #[inline]
+ fn exponent_limit() -> (i32, i32) {
+ (-22, 22)
+ }
+
+ #[inline]
+ fn mantissa_limit() -> i32 {
+ 15
+ }
+
+ #[inline]
+ fn pow10(self, n: i32) -> f64 {
+ // Check the exponent is within bounds in debug builds.
+ debug_assert!({
+ let (min, max) = Self::exponent_limit();
+ n >= min && n <= max
+ });
+
+ if n > 0 {
+ self * F64_POW10[n as usize]
+ } else {
+ self / F64_POW10[-n as usize]
+ }
+ }
+
+ #[inline]
+ fn from_bits(u: u64) -> f64 {
+ f64::from_bits(u)
+ }
+
+ #[inline]
+ fn to_bits(self) -> u64 {
+ f64::to_bits(self)
+ }
+
+ #[inline]
+ fn is_sign_positive(self) -> bool {
+ f64::is_sign_positive(self)
+ }
+
+ #[inline]
+ fn is_sign_negative(self) -> bool {
+ f64::is_sign_negative(self)
+ }
+}