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bigint.rs
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bigint.rs
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// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements. See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership. The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License. You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied. See the License for the
// specific language governing permissions and limitations
// under the License.
use num::cast::AsPrimitive;
use num::BigInt;
use std::cmp::Ordering;
/// A signed 256-bit integer
#[allow(non_camel_case_types)]
#[derive(Copy, Clone, Default, Eq, PartialEq, Hash)]
pub struct i256 {
low: u128,
high: i128,
}
impl std::fmt::Debug for i256 {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self)
}
}
impl std::fmt::Display for i256 {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", BigInt::from_signed_bytes_le(&self.to_le_bytes()))
}
}
impl PartialOrd for i256 {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for i256 {
fn cmp(&self, other: &Self) -> Ordering {
// This is 25x faster than using a variable length encoding such
// as BigInt as it avoids allocation and branching
self.high.cmp(&other.high).then(self.low.cmp(&other.low))
}
}
impl i256 {
/// The additive identity for this integer type, i.e. `0`.
pub const ZERO: Self = i256 { low: 0, high: 0 };
/// The multiplicative identity for this integer type, i.e. `1`.
pub const ONE: Self = i256 { low: 1, high: 0 };
/// The multiplicative inverse for this integer type, i.e. `-1`.
pub const MINUS_ONE: Self = i256 {
low: u128::MAX,
high: -1,
};
/// The maximum value that can be represented by this integer type
pub const MAX: Self = i256 {
low: u128::MAX,
high: i128::MAX,
};
/// The minimum value that can be represented by this integer type
pub const MIN: Self = i256 {
low: u128::MIN,
high: i128::MIN,
};
/// Create an integer value from its representation as a byte array in little-endian.
#[inline]
pub fn from_le_bytes(b: [u8; 32]) -> Self {
Self {
high: i128::from_le_bytes(b[16..32].try_into().unwrap()),
low: u128::from_le_bytes(b[0..16].try_into().unwrap()),
}
}
/// Create an integer value from its representation as a byte array in little-endian.
#[inline]
pub fn from_be_bytes(b: [u8; 32]) -> Self {
Self {
high: i128::from_be_bytes(b[0..16].try_into().unwrap()),
low: u128::from_be_bytes(b[16..32].try_into().unwrap()),
}
}
pub fn from_i128(v: i128) -> Self {
let mut bytes = if num::Signed::is_negative(&v) {
[255_u8; 32]
} else {
[0; 32]
};
bytes[0..16].copy_from_slice(&v.to_le_bytes());
Self::from_le_bytes(bytes)
}
/// Create an i256 from the provided low u128 and high i128
#[inline]
pub fn from_parts(low: u128, high: i128) -> Self {
Self { low, high }
}
/// Returns this `i256` as a low u128 and high i128
pub fn to_parts(self) -> (u128, i128) {
(self.low, self.high)
}
/// Converts this `i256` into an `i128` returning `None` if this would result
/// in truncation/overflow
pub fn to_i128(self) -> Option<i128> {
let as_i128 = self.low as i128;
let high_negative = self.high < 0;
let low_negative = as_i128 < 0;
let high_valid = self.high == -1 || self.high == 0;
(high_negative == low_negative && high_valid).then_some(self.low as i128)
}
/// Return the memory representation of this integer as a byte array in little-endian byte order.
#[inline]
pub fn to_le_bytes(self) -> [u8; 32] {
let mut t = [0; 32];
let t_low: &mut [u8; 16] = (&mut t[0..16]).try_into().unwrap();
*t_low = self.low.to_le_bytes();
let t_high: &mut [u8; 16] = (&mut t[16..32]).try_into().unwrap();
*t_high = self.high.to_le_bytes();
t
}
/// Return the memory representation of this integer as a byte array in big-endian byte order.
#[inline]
pub fn to_be_bytes(self) -> [u8; 32] {
let mut t = [0; 32];
let t_low: &mut [u8; 16] = (&mut t[0..16]).try_into().unwrap();
*t_low = self.high.to_be_bytes();
let t_high: &mut [u8; 16] = (&mut t[16..32]).try_into().unwrap();
*t_high = self.low.to_be_bytes();
t
}
/// Create an i256 from the provided [`BigInt`] returning a bool indicating
/// if overflow occurred
fn from_bigint_with_overflow(v: BigInt) -> (Self, bool) {
let v_bytes = v.to_signed_bytes_le();
match v_bytes.len().cmp(&32) {
Ordering::Less => {
let mut bytes = if num::Signed::is_negative(&v) {
[255_u8; 32]
} else {
[0; 32]
};
bytes[0..v_bytes.len()].copy_from_slice(&v_bytes[..v_bytes.len()]);
(Self::from_le_bytes(bytes), false)
}
Ordering::Equal => (Self::from_le_bytes(v_bytes.try_into().unwrap()), false),
Ordering::Greater => {
(Self::from_le_bytes(v_bytes[..32].try_into().unwrap()), true)
}
}
}
/// Computes the absolute value of this i256
#[inline]
pub fn wrapping_abs(self) -> Self {
// -1 if negative, otherwise 0
let sa = self.high >> 127;
let sa = Self::from_parts(sa as u128, sa);
// Inverted if negative
Self::from_parts(self.low ^ sa.low, self.high ^ sa.high).wrapping_sub(sa)
}
/// Computes the absolute value of this i256 returning `None` if `Self == Self::MIN`
#[inline]
pub fn checked_abs(self) -> Option<Self> {
(self != Self::MIN).then(|| self.wrapping_abs())
}
/// Performs wrapping addition
#[inline]
pub fn wrapping_add(self, other: Self) -> Self {
let (low, carry) = self.low.overflowing_add(other.low);
let high = self.high.wrapping_add(other.high).wrapping_add(carry as _);
Self { low, high }
}
/// Performs checked addition
#[inline]
pub fn checked_add(self, other: Self) -> Option<Self> {
let (low, carry) = self.low.overflowing_add(other.low);
let high = self.high.checked_add(other.high)?.checked_add(carry as _)?;
Some(Self { low, high })
}
/// Performs wrapping subtraction
#[inline]
pub fn wrapping_sub(self, other: Self) -> Self {
let (low, carry) = self.low.overflowing_sub(other.low);
let high = self.high.wrapping_sub(other.high).wrapping_sub(carry as _);
Self { low, high }
}
/// Performs checked subtraction
#[inline]
pub fn checked_sub(self, other: Self) -> Option<Self> {
let (low, carry) = self.low.overflowing_sub(other.low);
let high = self.high.checked_sub(other.high)?.checked_sub(carry as _)?;
Some(Self { low, high })
}
/// Performs wrapping multiplication
#[inline]
pub fn wrapping_mul(self, other: Self) -> Self {
let (low, high) = mulx(self.low, other.low);
// Compute the high multiples, only impacting the high 128-bits
let hl = self.high.wrapping_mul(other.low as i128);
let lh = (self.low as i128).wrapping_mul(other.high);
Self {
low,
high: (high as i128).wrapping_add(hl).wrapping_add(lh),
}
}
/// Performs checked multiplication
#[inline]
pub fn checked_mul(self, other: Self) -> Option<Self> {
// Shift sign bit down to construct mask of all set bits if negative
let l_sa = self.high >> 127;
let r_sa = other.high >> 127;
let out_sa = l_sa ^ r_sa;
// Compute absolute values
let l_abs = self.wrapping_abs();
let r_abs = other.wrapping_abs();
// Overflow if both high parts are non-zero
if l_abs.high != 0 && r_abs.high != 0 {
return None;
}
// Perform checked multiplication on absolute values
let (low, high) = mulx(l_abs.low, r_abs.low);
// Compute the high multiples, only impacting the high 128-bits
let hl = (l_abs.high as u128).checked_mul(r_abs.low)?;
let lh = l_abs.low.checked_mul(r_abs.high as u128)?;
let high: i128 = high.checked_add(hl)?.checked_add(lh)?.try_into().ok()?;
// Reverse absolute value, if necessary
let (low, c) = (low ^ out_sa as u128).overflowing_sub(out_sa as u128);
let high = (high ^ out_sa).wrapping_sub(out_sa).wrapping_sub(c as i128);
Some(Self { low, high })
}
/// Performs wrapping division
#[inline]
pub fn wrapping_div(self, other: Self) -> Self {
let l = BigInt::from_signed_bytes_le(&self.to_le_bytes());
let r = BigInt::from_signed_bytes_le(&other.to_le_bytes());
Self::from_bigint_with_overflow(l / r).0
}
/// Performs checked division
#[inline]
pub fn checked_div(self, other: Self) -> Option<Self> {
let l = BigInt::from_signed_bytes_le(&self.to_le_bytes());
let r = BigInt::from_signed_bytes_le(&other.to_le_bytes());
let (val, overflow) = Self::from_bigint_with_overflow(l / r);
(!overflow).then_some(val)
}
/// Performs wrapping remainder
#[inline]
pub fn wrapping_rem(self, other: Self) -> Self {
let l = BigInt::from_signed_bytes_le(&self.to_le_bytes());
let r = BigInt::from_signed_bytes_le(&other.to_le_bytes());
Self::from_bigint_with_overflow(l % r).0
}
/// Performs checked remainder
#[inline]
pub fn checked_rem(self, other: Self) -> Option<Self> {
if other == Self::ZERO {
return None;
}
let l = BigInt::from_signed_bytes_le(&self.to_le_bytes());
let r = BigInt::from_signed_bytes_le(&other.to_le_bytes());
let (val, overflow) = Self::from_bigint_with_overflow(l % r);
(!overflow).then_some(val)
}
}
/// Performs an unsigned multiplication of `a * b` returning a tuple of
/// `(low, high)` where `low` contains the lower 128-bits of the result
/// and `high` the higher 128-bits
///
/// This mirrors the x86 mulx instruction but for 128-bit types
#[inline]
fn mulx(a: u128, b: u128) -> (u128, u128) {
let split = |a: u128| (a & (u64::MAX as u128), a >> 64);
const MASK: u128 = u64::MAX as _;
let (a_low, a_high) = split(a);
let (b_low, b_high) = split(b);
// Carry stores the upper 64-bits of low and lower 64-bits of high
let (mut low, mut carry) = split(a_low * b_low);
carry += a_high * b_low;
// Update low and high with corresponding parts of carry
low += carry << 64;
let mut high = carry >> 64;
// Update carry with overflow from low
carry = low >> 64;
low &= MASK;
// Perform multiply including overflow from low
carry += b_high * a_low;
// Update low and high with values from carry
low += carry << 64;
high += carry >> 64;
// Perform 4th multiplication
high += a_high * b_high;
(low, high)
}
macro_rules! define_as_primitive {
($native_ty:ty) => {
impl AsPrimitive<i256> for $native_ty {
fn as_(self) -> i256 {
i256::from_i128(self as i128)
}
}
};
}
define_as_primitive!(i8);
define_as_primitive!(i16);
define_as_primitive!(i32);
define_as_primitive!(i64);
#[cfg(test)]
mod tests {
use super::*;
use num::{BigInt, FromPrimitive, Signed, ToPrimitive};
use rand::{thread_rng, Rng};
#[test]
fn test_signed_cmp() {
let a = i256::from_parts(i128::MAX as u128, 12);
let b = i256::from_parts(i128::MIN as u128, 12);
assert!(a < b);
let a = i256::from_parts(i128::MAX as u128, 12);
let b = i256::from_parts(i128::MIN as u128, -12);
assert!(a > b);
}
#[test]
fn test_to_i128() {
let vals = [
BigInt::from_i128(-1).unwrap(),
BigInt::from_i128(i128::MAX).unwrap(),
BigInt::from_i128(i128::MIN).unwrap(),
BigInt::from_u128(u128::MIN).unwrap(),
BigInt::from_u128(u128::MAX).unwrap(),
];
for v in vals {
let (t, overflow) = i256::from_bigint_with_overflow(v.clone());
assert!(!overflow);
assert_eq!(t.to_i128(), v.to_i128(), "{} vs {}", v, t);
}
}
/// Tests operations against the two provided [`i256`]
fn test_ops(il: i256, ir: i256) {
let bl = BigInt::from_signed_bytes_le(&il.to_le_bytes());
let br = BigInt::from_signed_bytes_le(&ir.to_le_bytes());
// Comparison
assert_eq!(il.cmp(&ir), bl.cmp(&br), "{} cmp {}", bl, br);
// To i128
assert_eq!(il.to_i128(), bl.to_i128(), "{}", bl);
assert_eq!(ir.to_i128(), br.to_i128(), "{}", br);
// Absolute value
let (abs, overflow) = i256::from_bigint_with_overflow(bl.abs());
assert_eq!(il.wrapping_abs(), abs);
assert_eq!(il.checked_abs().is_none(), overflow);
let (abs, overflow) = i256::from_bigint_with_overflow(br.abs());
assert_eq!(ir.wrapping_abs(), abs);
assert_eq!(ir.checked_abs().is_none(), overflow);
// Addition
let actual = il.wrapping_add(ir);
let (expected, overflow) =
i256::from_bigint_with_overflow(bl.clone() + br.clone());
assert_eq!(actual, expected);
let checked = il.checked_add(ir);
match overflow {
true => assert!(checked.is_none()),
false => assert_eq!(checked.unwrap(), actual),
}
// Subtraction
let actual = il.wrapping_sub(ir);
let (expected, overflow) =
i256::from_bigint_with_overflow(bl.clone() - br.clone());
assert_eq!(actual.to_string(), expected.to_string());
let checked = il.checked_sub(ir);
match overflow {
true => assert!(checked.is_none()),
false => assert_eq!(checked.unwrap(), actual),
}
// Multiplication
let actual = il.wrapping_mul(ir);
let (expected, overflow) =
i256::from_bigint_with_overflow(bl.clone() * br.clone());
assert_eq!(actual.to_string(), expected.to_string());
let checked = il.checked_mul(ir);
match overflow {
true => assert!(
checked.is_none(),
"{} * {} = {} vs {} * {} = {}",
il,
ir,
actual,
bl,
br,
expected
),
false => assert_eq!(
checked.unwrap(),
actual,
"{} * {} = {} vs {} * {} = {}",
il,
ir,
actual,
bl,
br,
expected
),
}
}
#[test]
fn test_i256() {
let candidates = [
i256::from_parts(0, 0),
i256::from_parts(0, 1),
i256::from_parts(0, -1),
i256::from_parts(u128::MAX, 1),
i256::from_parts(u128::MAX, -1),
i256::from_parts(0, 1),
i256::from_parts(0, -1),
i256::from_parts(100, 32),
];
for il in candidates {
for ir in candidates {
test_ops(il, ir)
}
}
}
#[test]
#[cfg_attr(miri, ignore)]
fn test_i256_fuzz() {
let mut rng = thread_rng();
for _ in 0..1000 {
let mut l = [0_u8; 32];
let len = rng.gen_range(0..32);
l.iter_mut().take(len).for_each(|x| *x = rng.gen());
let mut r = [0_u8; 32];
let len = rng.gen_range(0..32);
r.iter_mut().take(len).for_each(|x| *x = rng.gen());
test_ops(i256::from_le_bytes(l), i256::from_le_bytes(r))
}
}
}