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//! The Head Byte format, capable of storing integers and decimal fractions up to ±1.34078079e+281. //! //! It's recommended to use this format instead of Extended Head Byte if you're accepting numbers from potentially untrusted locations, since Head Byte imposes a size limit (which is still extremely big, suiting most use cases) while Extended Head Byte does not. use crate::Sign; use alloc::vec::Vec; /// The Head Byte format, capable of storing integers and decimal fractions up to ±1.34078079e+281. /// /// See the [module-level documentation][modhb] for more. /// /// [modhb]: index.html "bigbit::headbyte — the Head Byte format, capable of storing integers and fractions up to ±1.34078079e+281" #[derive(Clone)] pub struct HBNum { hb: HeadByte, exponent: Option<Exponent>, coefficients: Vec<u8> } impl HBNum { pub fn from_raw_parts(hb: HeadByte, exponent: Option<Exponent>, coefficients: Vec<u8>) -> Self { Self {hb, exponent, coefficients} } /// Returns the head byte. /// /// The results of inspecting the head byte are reliable and always match the properties of the actual value of the entire number. For example, if `has_exponent` on the head byte always returns `true`, there always is an exponent byte to retreieve. #[inline(always)] #[must_use] pub fn headbyte(&self) -> HeadByte { self.hb } /// Returns the exponent, or `None` if it's not used (mainly the case for integers). #[inline(always)] #[must_use] pub fn exponent(&self) -> Option<Exponent> { self.exponent } /// Returns an iterator over the coefficients in little endian byte order. #[inline(always)] pub fn coefficient_le_iter(&self) -> impl Iterator<Item = u8> + DoubleEndedIterator + '_ { self.coefficients.iter().copied() } /// Returns an iterator over the coefficients in big endian byte order. #[inline(always)] pub fn coefficient_be_iter(&self) -> impl Iterator<Item = u8> + DoubleEndedIterator + '_ { self.coefficient_le_iter().rev() } } /// The Head Byte itself, containing information about the sign, presence of the exponent and the number of coefficients. /// /// Follows the newtype pattern, meaning that it can be unwrapped into the inner byte. #[repr(transparent)] #[derive(Copy, Clone, PartialEq, Eq)] pub struct HeadByte(u8); impl HeadByte { /// The sign bit mask. /// /// Use [`sign`][0] to easily retreive the sign. /// /// [0]: #method.sign "sign — retreives the sign from a Head Byte" pub const SIGN_MASK: u8 = 0b10_000000; /// The mask used for retreiving the absolute value of the number. /// /// Use [`abs`][0] or bitwise-`AND` (`&`) this with the Head Byte to retreive the absolute value. /// /// [0]: #method.abs "abs — retreives the absolute value from the number whose Head Byte is self" pub const ABS_MASK: u8 = !Self::SIGN_MASK; /// The exponent presence bit mask. /// /// Use [`has_exponent`][0] to easily retreive this. /// /// [0]: #method.has_exponent "has_exponent — checks whether the Head Byte is supposed to be followed by an exponent byte" pub const HAS_EXPONENT_MASK: u8 = 0b01_000000; /// Mask for the number of coefficients. /// /// Use [`num_coefficients`][0] to easily retreive this. /// /// [0]: #method.num_coefficients "num_coefficients — retreives the number of following coefficients from a Head Byte" pub const NUM_COEFFICIENTS_MASK: u8 = 0b00_111111; /// The **∞** (positive infinity) value for the Head Byte. /// /// No following exponent or coefficients are allowed in this case, despite the exponent bit being set. pub const INFINITY: Self = Self(0b01_000000); /// The **-∞** (negative infinity) value for the Head Byte. /// /// No following exponent or coefficients are allowed in this case, despite the exponent bit being set. pub const NEG_INFINITY: Self = Self(0b11_000000); /// The zero value. There's no distinction between positive and negative zero. /// /// No following exponent or coefficients are allowed. pub const ZERO: Self = Self(0); /// The NaN (Not-a-Number) value. There's no distinction between negative/positive NaN or signalling/quiet NaN. (This implementation always generates quiet NaN.) /// /// NaN values aren't equal to themselves, just like in IEEE 754. To check for NaN values, use either `is_nan` or, if you're using the `try_nan` feature (which currently only works on Nightly), the `Try` trait, which returns an error if the value is NaN. /// /// No following exponent or coefficients are allowed. pub const NAN: Self = Self(0b10_000000); /// Retreives the sign from a Head Byte. #[inline(always)] #[must_use] pub fn sign(self) -> Sign { Sign::from((self.into_inner() & Self::SIGN_MASK) != 0) } /// Retreives the absolute value from the number whose Head Byte is `self`. /// /// Since the Head Byte stores the sign of the entire number, it's enough to just perform bitwise `AND` with the `ABS_MASK`, which in turn is the bitwise `NOT` of the sign mask. #[inline(always)] #[must_use] pub fn abs(self) -> Self { Self(self.0 & Self::ABS_MASK) } /// Checks whether the `HAS_EXPONENT` bit of the Head Byte is set, meaning either infinity or the presence of an actual exponent. /// /// For a version which also checks for the infinity special case, see [`has_exponent`][0]. /// /// [0]: #method.has_exponent "has_exponent — checks whether the Head Byte is supposed to be followed by an exponent byte" #[inline(always)] #[must_use] pub fn exponent_bit_set(self) -> bool { (self.0 & Self::HAS_EXPONENT_MASK) != 0 } /// Checks whether the Head Byte describes either positive or negative infinity. /// /// This is mostly uesd in [`has_exponent`][0] to check for the infinity special case. /// /// [0]: #method.has_exponent "has_exponent — checks whether the Head Byte is supposed to be followed by an exponent byte" #[inline(always)] #[must_use] pub fn is_infinite(self) -> bool { self.abs() == Self::INFINITY } /// Checks whether the Head Byte describes a NaN value. #[inline(always)] #[must_use] pub fn is_nan(self) -> bool { (self.0 & Self::SIGN_MASK) != 0 && (self.0 & Self::ABS_MASK) == 0 } /// Checks whether the Head Byte is supposed to be followed by an exponent byte. /// /// This includes the check for the special infinity value. For a version which does not check for infinity and thus plays more nicely with branch prediction, see [`exponent_bit_set`][0]. /// /// [0]: #method.exponent_bit_set "exponent_bit_set — checks whether the HAS_EXPONENT bit of the Head Byte is set, meaning either infinity or the presence of an actual exponent" #[inline(always)] #[must_use] pub fn has_exponent(self) -> bool { ( (self.0 & Self::HAS_EXPONENT_MASK) != 0 ) && ( !self.is_infinite() ) } /// Retreives the number of following coefficients from a Head Byte. #[inline(always)] #[must_use] pub fn num_coefficients(self) -> u8 { self.0 & Self::NUM_COEFFICIENTS_MASK } /// Consumes the value and returns the inner byte. #[inline(always)] #[must_use] pub fn into_inner(self) -> u8 { self.0 } } impl From<u8> for HeadByte { /// Wraps a byte into a Head Byte. #[inline(always)] #[must_use] fn from(op: u8) -> Self { Self(op) } } impl From<HeadByte> for u8 { /// Consumes the Head Byte and returns the underlying inner byte. #[inline(always)] #[must_use] fn from(op: HeadByte) -> Self { op.0 } } impl core::ops::Neg for HeadByte { type Output = Self; #[inline(always)] #[must_use] fn neg(self) -> Self::Output { if self.is_nan() || self == Self::ZERO { self } else { Self(!(self.0 & Self::SIGN_MASK) | self.abs().0) } } } impl core::fmt::Debug for HeadByte { fn fmt(&self, fmt: &mut core::fmt::Formatter) -> Result<(), core::fmt::Error> { if self.is_nan() { let mut ds = fmt.debug_tuple("HeadByte"); ds.field(&"NaN"); ds.finish() } else if self.is_infinite() { let mut ds = fmt.debug_tuple("HeadByte"); ds.field(&match self.sign() { Sign::Positive => "Infinity", Sign::Negative => "-Infinity" }); ds.finish() } else if *self == Self::ZERO { let mut ds = fmt.debug_tuple("HeadByte"); ds.field(&"0"); ds.finish() } else { let mut ds = fmt.debug_struct("HeadByte"); ds.field("sign", &crate::SignDisplayAsDebug(self.sign())); ds.field("has_exponent", &self.has_exponent()); ds.field("num_coefficients", &self.num_coefficients()); ds.finish() } } } /// An exponent for the Head Byte and Extended Head Byte formats. /// /// To retreive the real value of an \[E\]HB number, its stored value is multiplied by 10 raised to the power of this value as retreived using [`into_inner`][ii]. /// /// [ii]: #method.into_inner "into_inner — consumes the value and returns the inner byte" /// /// This is **not** a 2's complement signed number: it ranges from -127 to +127, having one bit as the sign and the rest as a normal 7-bit unsigned integer. As a consequence, it's possible to store `0b1_0000000` as the exponent, meaning a resulting exponent of 10⁻⁰, which is undefined. In most cases, this transformation is unwanted (that is, accidential, most likely happening because of a serious mistake during bitwise operations), and as such is not allowed, producing a `TryFrom` error. /// /// In other words, **protection against `-0` is a safety guarantee**, and actually creating an exponent with this value **requires unsafe code**. #[derive(Copy, Clone, Debug, PartialEq, Eq)] pub struct Exponent(u8); impl Exponent { /// The sign bit mask. /// /// Use [`sign`][0] to easily retreive the sign. /// /// [0]: #method.sign "sign — retreives the sign of the exponent" pub const SIGN_MASK: u8 = 0b1000_0000; pub const ABS_MASK: u8 = !Self::SIGN_MASK; /// Wraps a byte into an exponent, ignoring the invalid `0b1_0000000` case. /// /// This is the unsafe unchecked version of the `TryFrom` implementation. /// /// # Safety /// The value must never be `0b1_0000000` (`-0`), since avoiding that case is a safety guaranteee of the `Exponent` type. #[inline(always)] pub unsafe fn from_u8_unchecked(op: u8) -> Self { Self(op) } /// Retreives the sign from the exponent. `Negative` means that the coefficient is multiplied by 10 raised to the power of `-n`, where `n` is the rest of the exponent byte, and `Positive` simply means `10^n`. #[inline(always)] pub fn sign(self) -> Sign { Sign::from((self.0 & Self::SIGN_MASK) != 0) } /// Retreives the absolute value of the exponent, i.e. removes the minus in `10^-n` if it exists. #[inline(always)] #[must_use = "this is not an in-place operation"] pub fn abs(self) -> Self { Self(self.0 & Self::ABS_MASK) } /// Inverts the sign bit of the exponent. `10^2` (`0b0000_0010`) becomes `10^-2` (`0b1000_0010`), `10^127` → `10^-127` and so on. #[inline(always)] #[must_use = "this is not an in-place operation"] pub fn invert(self) -> Self { let sign = !(self.0 & Self::SIGN_MASK); Self((self.0 & Self::ABS_MASK) | sign) } #[inline(always)] #[must_use = "this is not an in-place operation"] pub fn checked_mul(self, rhs: Self) -> Option<Self> { if rhs.sign() == self.sign() { let sign = self.0 & Self::SIGN_MASK; if let Some(result) = self.abs().0.checked_add(rhs.abs().0) { Some(Self(sign | result)) } else {None} } else { self.checked_div(rhs) } } #[inline(always)] #[must_use = "this is not an in-place operation"] fn checked_div(self, rhs: Self) -> Option<Self> { if rhs.sign() == self.sign() { let sign = self.0 & Self::SIGN_MASK; if let Some(result) = self.abs().0.checked_sub(rhs.abs().0) { Some(Self(sign | result)) } else {None} } else { self.checked_mul(rhs) } } /// Consumes the value and returns the inner byte. /// /// See the struct-level documentation for the meaning of this value. #[inline(always)] #[must_use] pub fn into_inner(self) -> u8 { self.0 } } impl core::convert::TryFrom<u8> for Exponent { type Error = InvalidExponentError; /// Wraps a byte into an exponent. /// /// # Errors /// If the supplied value is `0b1_0000000` (`-0`), `Err(InvalidExponentError)` is returned, where [`InvalidExponentError`][0] is a marker error type. /// /// [0]: struct.InvalidExponentError.html "InvalidExponentError — the error marker for when 0b10000000 is encountered in the TryFrom implementation of Exponent" #[inline(always)] fn try_from(op: u8) -> Result<Self, InvalidExponentError> { if op == 0b1_0000000 {return Err(InvalidExponentError);} Ok(Self(op)) } } impl From<Exponent> for u8 { /// Consumes the exponent and returns the underlying inner byte. #[inline(always)] #[must_use] fn from(op: Exponent) -> Self { op.0 } } /// The error marker for when `0b10000000` is encountered in the `TryFrom` implementation of [`Exponent`][1]. /// /// [1]: struct.Exponent.html "Exponent — an exponent for the Head Byte format" #[derive(Copy, Clone, Debug, Default, PartialEq, Eq)] pub struct InvalidExponentError;