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Add i256 (#2637) #2781
Add i256 (#2637) #2781
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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. | ||
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use num::BigInt; | ||
use std::cmp::Ordering; | ||
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/// A signed 256-bit integer | ||
#[allow(non_camel_case_types)] | ||
#[derive(Copy, Clone, Default, Eq, PartialEq, Hash)] | ||
pub struct i256 { | ||
low: u128, | ||
high: i128, | ||
} | ||
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impl std::fmt::Debug for i256 { | ||
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { | ||
write!(f, "{}", self) | ||
} | ||
} | ||
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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())) | ||
} | ||
} | ||
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impl PartialOrd for i256 { | ||
fn partial_cmp(&self, other: &Self) -> Option<Ordering> { | ||
Some(self.cmp(other)) | ||
} | ||
} | ||
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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)) | ||
} | ||
} | ||
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impl i256 { | ||
/// The additive identity for this integer type, i.e. `0`. | ||
pub const ZERO: Self = i256 { low: 0, high: 0 }; | ||
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/// The multiplicative identity for this integer type, i.e. `1`. | ||
pub const ONE: Self = i256 { low: 1, high: 0 }; | ||
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/// The multiplicative inverse for this integer type, i.e. `-1`. | ||
pub const MINUS_ONE: Self = i256 { | ||
low: u128::MAX, | ||
high: -1, | ||
}; | ||
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/// 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()), | ||
} | ||
} | ||
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/// Create an i256 from the provided low u128 and high i128 | ||
#[inline] | ||
pub fn from_parts(low: u128, high: i128) -> Self { | ||
Self { low, high } | ||
} | ||
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/// Returns this `i256` as a low u128 and high i128 | ||
pub fn to_parts(self) -> (u128, i128) { | ||
(self.low, self.high) | ||
} | ||
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/// 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; | ||
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let high_negative = self.high < 0; | ||
let low_negative = as_i128 < 0; | ||
let high_valid = self.high == -1 || self.high == 0; | ||
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(high_negative == low_negative && high_valid).then_some(self.low as i128) | ||
} | ||
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/// 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 | ||
} | ||
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/// 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) | ||
} | ||
} | ||
} | ||
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/// 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 } | ||
} | ||
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/// 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 }) | ||
} | ||
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/// 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 } | ||
} | ||
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/// 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 }) | ||
} | ||
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/// Performs wrapping multiplication | ||
#[inline] | ||
pub fn wrapping_mul(self, other: Self) -> Self { | ||
let (low, high) = mulx(self.low, other.low); | ||
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// 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); | ||
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Self { | ||
low, | ||
high: (high as i128).wrapping_add(hl).wrapping_add(lh), | ||
} | ||
} | ||
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/// Performs checked multiplication | ||
#[inline] | ||
pub fn checked_mul(self, other: Self) -> Option<Self> { | ||
let (low, high) = mulx(self.low, other.low); | ||
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// Compute the high multiples, only impacting the high 128-bits | ||
let hl = self.high.checked_mul(other.low as i128)?; | ||
let lh = (self.low as i128).checked_mul(other.high)?; | ||
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Some(Self { | ||
low, | ||
high: (high as i128).checked_add(hl)?.checked_add(lh)?, | ||
}) | ||
} | ||
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/// 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 | ||
} | ||
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/// 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) | ||
} | ||
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/// 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 | ||
} | ||
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/// Performs checked remainder | ||
#[inline] | ||
pub fn checked_rem(self, other: Self) -> Option<Self> { | ||
if other == Self::ZERO { | ||
return None; | ||
} | ||
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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) | ||
} | ||
} | ||
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/// 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) { | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. A simple doc might be nicer. |
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let split = |a: u128| (a & (u64::MAX as u128), a >> 64); | ||
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const MASK: u128 = u64::MAX as _; | ||
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let (a_low, a_high) = split(a); | ||
let (b_low, b_high) = split(b); | ||
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// 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; | ||
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// Update low and high with corresponding parts of carry | ||
low += carry << 64; | ||
let mut high = carry >> 64; | ||
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// Update carry with overflow from low | ||
carry = low >> 64; | ||
low &= MASK; | ||
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// Perform multiply including overflow from low | ||
carry += b_high * a_low; | ||
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// Update low and high with values from carry | ||
low += carry << 64; | ||
high += carry >> 64; | ||
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// Perform 4th multiplication | ||
high += a_high * b_high; | ||
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(low, high) | ||
} | ||
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#[cfg(test)] | ||
mod tests { | ||
use super::*; | ||
use num::{BigInt, FromPrimitive, ToPrimitive}; | ||
use rand::{thread_rng, Rng}; | ||
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#[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); | ||
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let a = i256::from_parts(i128::MAX as u128, 12); | ||
let b = i256::from_parts(i128::MIN as u128, -12); | ||
assert!(a > b); | ||
} | ||
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#[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(), | ||
]; | ||
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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); | ||
} | ||
} | ||
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#[test] | ||
fn test_i256() { | ||
let mut rng = thread_rng(); | ||
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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()); | ||
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let mut r = [0_u8; 32]; | ||
let len = rng.gen_range(0..32); | ||
r.iter_mut().take(len).for_each(|x| *x = rng.gen()); | ||
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let il = i256::from_le_bytes(l); | ||
let ir = i256::from_le_bytes(r); | ||
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let bl = BigInt::from_signed_bytes_le(&l); | ||
let br = BigInt::from_signed_bytes_le(&r); | ||
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// Comparison | ||
assert_eq!(il.cmp(&ir), bl.cmp(&br), "{} cmp {}", bl, br); | ||
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// To i128 | ||
assert_eq!(il.to_i128(), bl.to_i128(), "{}", bl); | ||
assert_eq!(ir.to_i128(), br.to_i128(), "{}", br); | ||
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// Addition | ||
let actual = il.wrapping_add(ir); | ||
let (expected, overflow) = | ||
i256::from_bigint_with_overflow(bl.clone() + br.clone()); | ||
assert_eq!(actual, expected); | ||
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let checked = il.checked_add(ir); | ||
match overflow { | ||
true => assert!(checked.is_none()), | ||
false => assert_eq!(checked.unwrap(), actual), | ||
} | ||
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// 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()); | ||
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let checked = il.checked_sub(ir); | ||
match overflow { | ||
true => assert!(checked.is_none()), | ||
false => assert_eq!(checked.unwrap(), actual), | ||
} | ||
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// 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()); | ||
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let checked = il.checked_mul(ir); | ||
match overflow { | ||
true => assert!(checked.is_none()), | ||
false => assert_eq!(checked.unwrap(), actual), | ||
} | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. This doesn't include tests for div, rem because they are implemented using BigInt? There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Yeah I figured that would be a bit circular |
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} | ||
} | ||
} |
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This is related to #2360, performing the comparison this way is significantly faster than using memcmp, which is itself significantly faster than using BigInt.
FYI @liukun4515
See https://rust.godbolt.org/z/h9fjEP1b4
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genius method.