1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315
//! `Arithmetic` trait and its implementations.
//!
//! # Traits
//!
//! An [`Arithmetic`] defines fallible arithmetic operations on primitive values
//! of an [`ExecutableModule`], namely, addition, subtraction, multiplication, division,
//! exponentiation (all binary ops), and negation (a unary op). Any module can be run
//! with any `Arithmetic` on its primitive values, although some modules are reasonably tied
//! to a particular arithmetic or a class of arithmetics (e.g., arithmetics on finite fields).
//!
//! [`OrdArithmetic`] extends [`Arithmetic`] with a partial comparison operation
//! (i.e., an analogue to [`PartialOrd`]). This is motivated by the fact that comparisons
//! may be switched off during parsing, and some `Arithmetic`s do not have well-defined comparisons.
//!
//! [`ArithmeticExt`] helps converting an [`Arithmetic`] into an [`OrdArithmetic`].
//!
//! # Implementations
//!
//! This module defines the following kinds of arithmetics:
//!
//! - [`StdArithmetic`] takes all implementations from the corresponding [`ops`](core::ops) traits.
//! This means that it's safe to use *provided* the ops are infallible. As a counter-example,
//! using [`StdArithmetic`] with built-in integer types (such as `u64`) is usually not a good
//! idea since the corresponding ops have failure modes (e.g., division by zero or integer
//! overflow).
//! - [`WrappingArithmetic`] is defined for integer types; it uses wrapping semantics for all ops.
//! - [`CheckedArithmetic`] is defined for integer types; it uses checked semantics for all ops.
//! - [`ModularArithmetic`] operates on integers modulo the specified number.
//!
//! All defined [`Arithmetic`]s strive to be as generic as possible.
//!
//! [`ExecutableModule`]: crate::ExecutableModule
use core::{cmp::Ordering, fmt};
pub use self::{
generic::{
Checked, CheckedArithmetic, CheckedArithmeticKind, NegateOnlyZero, StdArithmetic,
Unchecked, WrappingArithmetic,
},
modular::{DoubleWidth, ModularArithmetic},
};
use crate::{alloc::Box, error::ArithmeticError};
#[cfg(feature = "bigint")]
mod bigint;
mod generic;
mod modular;
/// Encapsulates arithmetic operations on a certain primitive type (or an enum of primitive types).
///
/// Unlike operations on built-in integer types, arithmetic operations may be fallible.
/// Additionally, the arithmetic can have a state. This is used, for example, in
/// [`ModularArithmetic`], which stores the modulus in the state.
pub trait Arithmetic<T> {
/// Adds two values.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., on integer overflow).
fn add(&self, x: T, y: T) -> Result<T, ArithmeticError>;
/// Subtracts two values.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., on integer underflow).
fn sub(&self, x: T, y: T) -> Result<T, ArithmeticError>;
/// Multiplies two values.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., on integer overflow).
fn mul(&self, x: T, y: T) -> Result<T, ArithmeticError>;
/// Divides two values.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., if `y` is zero or does
/// not have a multiplicative inverse in the case of modular arithmetic).
fn div(&self, x: T, y: T) -> Result<T, ArithmeticError>;
/// Raises `x` to the power of `y`.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., on integer overflow).
fn pow(&self, x: T, y: T) -> Result<T, ArithmeticError>;
/// Negates a value.
///
/// # Errors
///
/// Returns an error if the operation is unsuccessful (e.g., on integer overflow).
fn neg(&self, x: T) -> Result<T, ArithmeticError>;
/// Checks if two values are equal. Note that equality can be a non-trivial operation;
/// e.g., different numbers may be equal as per modular arithmetic.
fn eq(&self, x: &T, y: &T) -> bool;
}
/// Extends an [`Arithmetic`] with a comparison operation on values.
pub trait OrdArithmetic<T>: Arithmetic<T> {
/// Compares two values. Returns `None` if the numbers are not comparable, or the comparison
/// result otherwise.
fn partial_cmp(&self, x: &T, y: &T) -> Option<Ordering>;
}
impl<T> fmt::Debug for dyn OrdArithmetic<T> + '_ {
fn fmt(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
formatter.debug_tuple("OrdArithmetic").finish()
}
}
impl<T> Arithmetic<T> for Box<dyn OrdArithmetic<T>> {
#[inline]
fn add(&self, x: T, y: T) -> Result<T, ArithmeticError> {
(**self).add(x, y)
}
#[inline]
fn sub(&self, x: T, y: T) -> Result<T, ArithmeticError> {
(**self).sub(x, y)
}
#[inline]
fn mul(&self, x: T, y: T) -> Result<T, ArithmeticError> {
(**self).mul(x, y)
}
#[inline]
fn div(&self, x: T, y: T) -> Result<T, ArithmeticError> {
(**self).div(x, y)
}
#[inline]
fn pow(&self, x: T, y: T) -> Result<T, ArithmeticError> {
(**self).pow(x, y)
}
#[inline]
fn neg(&self, x: T) -> Result<T, ArithmeticError> {
(**self).neg(x)
}
#[inline]
fn eq(&self, x: &T, y: &T) -> bool {
(**self).eq(x, y)
}
}
impl<T> OrdArithmetic<T> for Box<dyn OrdArithmetic<T>> {
#[inline]
fn partial_cmp(&self, x: &T, y: &T) -> Option<Ordering> {
(**self).partial_cmp(x, y)
}
}
/// Wrapper type allowing to extend an [`Arithmetic`] to an [`OrdArithmetic`] implementation.
///
/// # Examples
///
/// This type can only be constructed via [`ArithmeticExt`] trait. See it for the examples
/// of usage.
pub struct FullArithmetic<T, A> {
base: A,
comparison: fn(&T, &T) -> Option<Ordering>,
}
impl<T, A: Clone> Clone for FullArithmetic<T, A> {
fn clone(&self) -> Self {
Self {
base: self.base.clone(),
comparison: self.comparison,
}
}
}
impl<T, A: Copy> Copy for FullArithmetic<T, A> {}
impl<T, A: fmt::Debug> fmt::Debug for FullArithmetic<T, A> {
fn fmt(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
formatter
.debug_struct("FullArithmetic")
.field("base", &self.base)
.finish_non_exhaustive()
}
}
impl<T, A> Arithmetic<T> for FullArithmetic<T, A>
where
A: Arithmetic<T>,
{
#[inline]
fn add(&self, x: T, y: T) -> Result<T, ArithmeticError> {
self.base.add(x, y)
}
#[inline]
fn sub(&self, x: T, y: T) -> Result<T, ArithmeticError> {
self.base.sub(x, y)
}
#[inline]
fn mul(&self, x: T, y: T) -> Result<T, ArithmeticError> {
self.base.mul(x, y)
}
#[inline]
fn div(&self, x: T, y: T) -> Result<T, ArithmeticError> {
self.base.div(x, y)
}
#[inline]
fn pow(&self, x: T, y: T) -> Result<T, ArithmeticError> {
self.base.pow(x, y)
}
#[inline]
fn neg(&self, x: T) -> Result<T, ArithmeticError> {
self.base.neg(x)
}
#[inline]
fn eq(&self, x: &T, y: &T) -> bool {
self.base.eq(x, y)
}
}
impl<T, A> OrdArithmetic<T> for FullArithmetic<T, A>
where
A: Arithmetic<T>,
{
fn partial_cmp(&self, x: &T, y: &T) -> Option<Ordering> {
(self.comparison)(x, y)
}
}
/// Extension trait for [`Arithmetic`] allowing to combine the arithmetic with comparisons.
///
/// # Examples
///
/// ```
/// use arithmetic_eval::arith::{ArithmeticExt, ModularArithmetic};
/// # use arithmetic_eval::{Environment, ExecutableModule, Value};
/// # use arithmetic_parser::grammars::{NumGrammar, Untyped, Parse};
///
/// # fn main() -> anyhow::Result<()> {
/// let base = ModularArithmetic::new(11);
///
/// // `ModularArithmetic` requires to define how numbers will be compared -
/// // and the simplest solution is to not compare them at all.
/// let program = Untyped::<NumGrammar<u32>>::parse_statements("1 < 3 || 1 >= 3")?;
/// let module = ExecutableModule::new("test", &program)?;
/// let env = Environment::with_arithmetic(base.without_comparisons());
/// assert_eq!(module.with_env(&env)?.run()?, Value::Bool(false));
///
/// // We can compare numbers by their integer value. This can lead
/// // to pretty confusing results, though.
/// let bogus_arithmetic = base.with_natural_comparison();
/// let program = Untyped::<NumGrammar<u32>>::parse_statements("
/// (x, y, z) = (1, 12, 5);
/// x == y && x < z && y > z
/// ")?;
/// let module = ExecutableModule::new("test", &program)?;
/// let env = Environment::with_arithmetic(bogus_arithmetic);
/// assert_eq!(module.with_env(&env)?.run()?, Value::Bool(true));
///
/// // It's possible to fix the situation using a custom comparison function,
/// // which will compare numbers by their residual class.
/// let less_bogus_arithmetic = base.with_comparison(|&x: &u32, &y: &u32| {
/// (x % 11).partial_cmp(&(y % 11))
/// });
/// let env = Environment::with_arithmetic(less_bogus_arithmetic);
/// assert_eq!(module.with_env(&env)?.run()?, Value::Bool(false));
/// # Ok(())
/// # }
/// ```
pub trait ArithmeticExt<T>: Arithmetic<T> + Sized {
/// Combines this arithmetic with a comparison function that assumes any two values are
/// incomparable.
fn without_comparisons(self) -> FullArithmetic<T, Self> {
FullArithmetic {
base: self,
comparison: |_, _| None,
}
}
/// Combines this arithmetic with a comparison function specified by the [`PartialOrd`]
/// implementation for `T`.
fn with_natural_comparison(self) -> FullArithmetic<T, Self>
where
T: PartialOrd,
{
FullArithmetic {
base: self,
comparison: T::partial_cmp,
}
}
/// Combines this arithmetic with the specified comparison function.
fn with_comparison(
self,
comparison: fn(&T, &T) -> Option<Ordering>,
) -> FullArithmetic<T, Self> {
FullArithmetic {
base: self,
comparison,
}
}
}
impl<T, A> ArithmeticExt<T> for A where A: Arithmetic<T> {}