binius_core/

word.rs

// Copyright 2025 Irreducible Inc.
//! [`Word`] related definitions.

use std::{
	fmt,
	ops::{BitAnd, BitOr, BitXor, Not, Shl, Shr},
};

use binius_utils::{
	checked_arithmetics::checked_log_2,
	serialization::{DeserializeBytes, SerializationError, SerializeBytes},
};
use bytemuck::{Pod, Zeroable};
use bytes::{Buf, BufMut};

/// [`Word`] is 64-bit value and is a fundamental unit of data in Binius64. All computation and
/// constraints operate on it.
///
/// The transparent layout matches the inner 64-bit integer exactly.
/// That lets slices of words be reinterpreted as raw bytes, and back, for zero-copy bulk copies.
#[derive(Clone, Copy, PartialEq, Eq, Hash, PartialOrd, Ord, Pod, Zeroable)]
#[repr(transparent)]
pub struct Word(pub u64);

impl Word {
	/// The size of a [`Word`] in bytes; the protocol proves constraint systems over 64-bit words.
	pub const BYTES: usize = size_of::<Word>();
	/// log2 of [`Word::BYTES`].
	pub const LOG_BYTES: usize = checked_log_2(Self::BYTES);
	/// The size of a [`Word`] in bits (mirrors [`u64::BITS`]).
	pub const BITS: usize = Self::BYTES * 8;
	/// log2 of [`Word::BITS`].
	pub const LOG_BITS: usize = checked_log_2(Self::BITS);

	/// All zero bit pattern, zero, nil, null.
	pub const ZERO: Word = Word(0);
	/// 1.
	pub const ONE: Word = Word(1);
	/// All bits set to one.
	pub const ALL_ONE: Word = Word(u64::MAX);
	/// 32 lower bits are set to one, all other bits are zero.
	pub const MASK_32: Word = Word(0x00000000FFFFFFFF);
	/// Most Significant Bit is set to one, all other bits are zero.
	///
	/// This is a canonical representation of true.
	pub const MSB_ONE: Word = Word(0x8000000000000000);

	/// Creates a new `Word` from a 64-bit unsigned integer.
	pub const fn from_u64(value: u64) -> Word {
		Word(value)
	}

	/// Returns the bit at position `i`, counting from the least significant bit.
	///
	/// `i` must be in `0..64`.
	pub const fn extract_bit(self, i: usize) -> bool {
		(self.0 >> i) & 1 == 1
	}

	/// Performs parallel 32-bit additions on the upper and lower halves with carry-in.
	///
	/// Each 32-bit half is added independently, like [`sll32`](Word::sll32) operates on
	/// independent halves. The carry-in for the lower half is taken from bit 31 of `cin`,
	/// and the carry-in for the upper half is taken from bit 63 of `cin`.
	///
	/// Returns (sum, carry_out) where the ith carry_out bit is set to one if there is a
	/// carry out at that bit position.
	pub const fn iadd32_cin_cout(self, rhs: Word, cin: Word) -> (Word, Word) {
		let Word(lhs) = self;
		let Word(rhs) = rhs;
		let Word(cin) = cin;

		// Extract carry-in bits from MSBs of each 32-bit half
		let cin_lo = (cin >> 31) & 1;
		let cin_hi = (cin >> 63) & 1;

		// Extract 32-bit halves
		let lo_l = lhs as u32;
		let hi_l = (lhs >> 32) as u32;
		let lo_r = rhs as u32;
		let hi_r = (rhs >> 32) as u32;

		// Add each half independently with carry-in
		let lo_sum = (lo_l as u64) + (lo_r as u64) + cin_lo;
		let hi_sum = (hi_l as u64) + (hi_r as u64) + cin_hi;
		let sum = (lo_sum as u32 as u64) | ((hi_sum as u32 as u64) << 32);

		let cout = (lhs & rhs) | ((lhs ^ rhs) & !sum);
		(Word(sum), Word(cout))
	}

	/// Performs parallel 32-bit additions on the upper and lower halves.
	///
	/// Equivalent to [`iadd32_cin_cout`](Word::iadd32_cin_cout) with zero carry-in.
	pub const fn iadd_cout_32(self, rhs: Word) -> (Word, Word) {
		self.iadd32_cin_cout(rhs, Word::ZERO)
	}

	/// Performs 64-bit addition with carry input bit.
	///
	/// cin is a carry-in from the previous addition. Since it can only affect the LSB only, the cin
	/// could be 1 if there is carry over, or 0 otherwise.
	///
	/// Returns (sum, carry_out) where ith carry_out bit is set to one if there is a carry out at
	/// that bit position.
	pub fn iadd_cin_cout(self, rhs: Word, cin: Word) -> (Word, Word) {
		debug_assert!(cin == Word::ZERO || cin == Word::ONE, "cin must be 0 or 1");
		let Word(lhs) = self;
		let Word(rhs) = rhs;
		let Word(cin) = cin;
		let sum = lhs.wrapping_add(rhs).wrapping_add(cin);
		let cout = (lhs & rhs) | ((lhs ^ rhs) & !sum);
		(Word(sum), Word(cout))
	}

	/// Performs 64-bit subtraction with borrow input bit.
	///
	/// bin is a borrow-in from the previous subtraction. Since it can only affect the LSB only, the
	/// bin could be 1 if there is borrow over, or 0 otherwise.
	///
	/// Returns (diff, borrow_out) where ith borrow_out bit is set to one if there is a borrow out
	/// at that bit position.
	pub fn isub_bin_bout(self, rhs: Word, bin: Word) -> (Word, Word) {
		debug_assert!(bin == Word::ZERO || bin == Word::ONE, "bin must be 0 or 1");
		let Word(lhs) = self;
		let Word(rhs) = rhs;
		let Word(bin) = bin;
		let diff = lhs.wrapping_sub(rhs).wrapping_sub(bin);
		let bout = (!lhs & rhs) | (!(lhs ^ rhs) & diff);
		(Word(diff), Word(bout))
	}

	/// Performs shift right by a given number of bits followed by masking with a 32-bit mask.
	pub const fn shr_32(self, n: u32) -> Word {
		let Word(value) = self;
		// Shift right logically by n bits and mask with 32-bit mask
		let result = (value >> n) & Self::MASK_32.0;
		Word(result)
	}

	/// Shift Arithmetic Right by a given number of bits.
	///
	/// This is similar to a logical shift right, but it shifts the sign bit to the right.
	pub const fn sar(self, n: u32) -> Word {
		let Word(value) = self;
		let value = value as i64;
		let result = value >> n;
		Word(result as u64)
	}

	/// Rotate Right by a given number of bits.
	pub const fn rotr(self, n: u32) -> Word {
		let Word(value) = self;
		Word(value.rotate_right(n))
	}

	/// Shift Left Logical on 32-bit halves.
	///
	/// Performs independent logical left shifts on the upper and lower 32-bit halves.
	/// Only uses the lower 5 bits of the shift amount (0-31).
	pub const fn sll32(self, n: u32) -> Word {
		let Word(value) = self;
		let n = n & 0x1F; // Only use lower 5 bits

		// Extract 32-bit halves
		let lo = value as u32;
		let hi = (value >> 32) as u32;

		// Shift each half independently
		let lo_shifted = (lo << n) as u64;
		let hi_shifted = ((hi << n) as u64) << 32;

		Word(lo_shifted | hi_shifted)
	}

	/// Shift Right Logical on 32-bit halves.
	///
	/// Performs independent logical right shifts on the upper and lower 32-bit halves.
	/// Only uses the lower 5 bits of the shift amount (0-31).
	pub const fn srl32(self, n: u32) -> Word {
		let Word(value) = self;
		let n = n & 0x1F; // Only use lower 5 bits

		// Extract 32-bit halves
		let lo = value as u32;
		let hi = (value >> 32) as u32;

		// Shift each half independently
		let lo_shifted = (lo >> n) as u64;
		let hi_shifted = ((hi >> n) as u64) << 32;

		Word(lo_shifted | hi_shifted)
	}

	/// Shift Right Arithmetic on 32-bit halves.
	///
	/// Performs independent arithmetic right shifts on the upper and lower 32-bit halves.
	/// Sign extends each 32-bit half independently. Only uses the lower 5 bits of the shift amount
	/// (0-31).
	pub const fn sra32(self, n: u32) -> Word {
		let Word(value) = self;
		let n = n & 0x1F; // Only use lower 5 bits

		// Extract 32-bit halves as signed integers
		let lo = value as u32 as i32;
		let hi = (value >> 32) as u32 as i32;

		// Arithmetic shift each half independently
		let lo_shifted = ((lo >> n) as u32) as u64;
		let hi_shifted = (((hi >> n) as u32) as u64) << 32;

		Word(lo_shifted | hi_shifted)
	}

	/// Rotate Right on 32-bit halves.
	///
	/// Performs independent rotate right operations on the upper and lower 32-bit halves.
	/// Bits shifted off the right end wrap around to the left within each 32-bit half.
	/// Only uses the lower 5 bits of the shift amount (0-31).
	pub const fn rotr32(self, n: u32) -> Word {
		let Word(value) = self;
		let n = n & 0x1F; // Only use lower 5 bits

		// Extract 32-bit halves
		let lo = value as u32;
		let hi = (value >> 32) as u32;

		// Rotate each half independently
		let lo_rotated = lo.rotate_right(n) as u64;
		let hi_rotated = (hi.rotate_right(n) as u64) << 32;

		Word(lo_rotated | hi_rotated)
	}

	/// Unsigned integer multiplication.
	///
	/// Multiplies two 64-bit unsigned integers and returns the 128-bit result split into high and
	/// low 64-bit words, respectively.
	pub const fn imul(self, rhs: Word) -> (Word, Word) {
		let Word(lhs) = self;
		let Word(rhs) = rhs;
		let result = (lhs as u128) * (rhs as u128);

		let hi = (result >> 64) as u64;
		let lo = result as u64;
		(Word(hi), Word(lo))
	}

	/// Signed integer multiplication.
	///
	/// Multiplies two 64-bit signed integers and returns the 128-bit result split into high and
	/// low 64-bit words, respectively.
	pub const fn smul(self, rhs: Word) -> (Word, Word) {
		let Word(lhs) = self;
		let Word(rhs) = rhs;
		// Interpret as signed 64-bit integers
		let a = lhs as i64;
		let b = rhs as i64;
		// Perform signed multiplication as 128-bit
		let result = (a as i128) * (b as i128);
		// Extract high and low 64-bit words
		let hi = (result >> 64) as u64;
		let lo = result as u64;
		(Word(hi), Word(lo))
	}

	/// Integer addition.
	///
	/// Wraps around on overflow.
	pub const fn wrapping_add(self, rhs: Word) -> Word {
		Word(self.0.wrapping_add(rhs.0))
	}

	/// Integer subtraction.
	///
	/// Wraps around on overflow.
	pub const fn wrapping_sub(self, rhs: Word) -> Word {
		Word(self.0.wrapping_sub(rhs.0))
	}

	/// Returns the integer value as a 64-bit unsigned integer.
	pub const fn as_u64(self) -> u64 {
		self.0
	}

	/// Tests if this Word represents true as an MSB-bool.
	///
	/// In MSB-bool representation, a value is true if its Most Significant Bit (bit 63) is set to
	/// 1. All other bits are ignored for the boolean value.
	///
	/// Returns true if the MSB is 1, false otherwise.
	pub const fn is_msb_true(self) -> bool {
		(self.0 & Self::MSB_ONE.0) != 0
	}

	/// Tests if this Word represents false as an MSB-bool.
	///
	/// In MSB-bool representation, a value is false if its Most Significant Bit (bit 63) is 0.
	/// All other bits are ignored for the boolean value.
	///
	/// Returns true if the MSB is 0, false otherwise.
	pub const fn is_msb_false(self) -> bool {
		!self.is_msb_true()
	}
}

impl fmt::Debug for Word {
	fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
		write!(f, "Word({:#018x})", self.0)
	}
}

impl BitAnd for Word {
	type Output = Self;

	fn bitand(self, rhs: Self) -> Self::Output {
		Word(self.0 & rhs.0)
	}
}

impl BitOr for Word {
	type Output = Self;

	fn bitor(self, rhs: Self) -> Self::Output {
		Word(self.0 | rhs.0)
	}
}

impl BitXor for Word {
	type Output = Self;

	fn bitxor(self, rhs: Self) -> Self::Output {
		Word(self.0 ^ rhs.0)
	}
}

impl Shl<u32> for Word {
	type Output = Self;

	fn shl(self, rhs: u32) -> Self::Output {
		Word(self.0 << rhs)
	}
}

impl Shr<u32> for Word {
	type Output = Self;

	fn shr(self, rhs: u32) -> Self::Output {
		Word(self.0 >> rhs)
	}
}

impl Not for Word {
	type Output = Self;

	fn not(self) -> Self::Output {
		Word(!self.0)
	}
}

impl SerializeBytes for Word {
	fn serialize(&self, write_buf: impl BufMut) -> Result<(), SerializationError> {
		self.0.serialize(write_buf)
	}
}

impl DeserializeBytes for Word {
	fn deserialize(read_buf: impl Buf) -> Result<Self, SerializationError>
	where
		Self: Sized,
	{
		Ok(Word(u64::deserialize(read_buf)?))
	}
}

#[cfg(test)]
mod tests {
	use proptest::prelude::*;
	use rand::{Rng, SeedableRng, rngs::StdRng};

	use super::*;

	#[test]
	fn test_constants() {
		assert_eq!(Word::ZERO, Word(0));
		assert_eq!(Word::ONE, Word(1));
		assert_eq!(Word::ALL_ONE, Word(0xFFFFFFFFFFFFFFFF));
		assert_eq!(Word::MASK_32, Word(0x00000000FFFFFFFF));
		assert_eq!(Word::MSB_ONE, Word(0x8000000000000000));
	}

	#[test]
	fn test_msb_bool() {
		// Test MSB_ONE is true
		assert!(Word::MSB_ONE.is_msb_true());
		assert!(!Word::MSB_ONE.is_msb_false());

		// Test ZERO is false
		assert!(!Word::ZERO.is_msb_true());
		assert!(Word::ZERO.is_msb_false());

		// Test various values with MSB set
		assert!(Word(0x8000000000000000).is_msb_true());
		assert!(Word(0x8000000000000001).is_msb_true());
		assert!(Word(0x80000000FFFFFFFF).is_msb_true());
		assert!(Word(0xFFFFFFFFFFFFFFFF).is_msb_true());

		// Test various values with MSB clear
		assert!(Word(0x7FFFFFFFFFFFFFFF).is_msb_false());
		assert!(Word(0x0000000000000001).is_msb_false());
		assert!(Word(0x00000000FFFFFFFF).is_msb_false());
		assert!(Word(0x7000000000000000).is_msb_false());

		// Verify complementary behavior
		let test_word = Word(0x8123456789ABCDEF);
		assert!(test_word.is_msb_true());
		assert!(!test_word.is_msb_false());

		let test_word2 = Word(0x7123456789ABCDEF);
		assert!(!test_word2.is_msb_true());
		assert!(test_word2.is_msb_false());
	}

	proptest! {
		#[test]
		fn prop_msb_bool(val in any::<u64>()) {
			let word = Word(val);

			// is_msb_true and is_msb_false should be complementary
			assert_eq!(word.is_msb_true(), !word.is_msb_false());
			assert_eq!(word.is_msb_false(), !word.is_msb_true());

			// Check against direct bit manipulation
			let msb_set = (val & 0x8000000000000000) != 0;
			assert_eq!(word.is_msb_true(), msb_set);
			assert_eq!(word.is_msb_false(), !msb_set);

			// MSB operations should ignore lower bits
			let word_with_msb = Word(val | 0x8000000000000000);
			let word_without_msb = Word(val & 0x7FFFFFFFFFFFFFFF);
			assert!(word_with_msb.is_msb_true());
			assert!(word_without_msb.is_msb_false());
		}

		#[test]
		fn prop_bitwise_and(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);

			// Basic AND properties
			assert_eq!((wa & wb).0, a & b);
			assert_eq!(wa & Word::ALL_ONE, wa);
			assert_eq!(wa & Word::ZERO, Word::ZERO);
			assert_eq!(wa & wa, wa); // Idempotent

			// Commutative
			assert_eq!(wa & wb, wb & wa);
		}

		#[test]
		fn prop_bitwise_or(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);

			// Basic OR properties
			assert_eq!((wa | wb).0, a | b);
			assert_eq!(wa | Word::ZERO, wa);
			assert_eq!(wa | Word::ALL_ONE, Word::ALL_ONE);
			assert_eq!(wa | wa, wa); // Idempotent

			// Commutative
			assert_eq!(wa | wb, wb | wa);
		}

		#[test]
		fn prop_bitwise_xor(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);

			// Basic XOR properties
			assert_eq!((wa ^ wb).0, a ^ b);
			assert_eq!(wa ^ Word::ZERO, wa);
			assert_eq!(wa ^ wa, Word::ZERO);
			assert_eq!(wa ^ Word::ALL_ONE, !wa);

			// Commutative
			assert_eq!(wa ^ wb, wb ^ wa);

			// Double XOR cancels
			assert_eq!(wa ^ wb ^ wb, wa);
		}

		#[test]
		fn prop_bitwise_not(a in any::<u64>()) {
			let wa = Word(a);

			// Basic NOT properties
			assert_eq!((!wa).0, !a);
			assert_eq!(!(!wa), wa); // Double negation
			assert_eq!(!Word::ZERO, Word::ALL_ONE);
			assert_eq!(!Word::ALL_ONE, Word::ZERO);

			// De Morgan's laws
			let wb = Word(a.wrapping_add(1));
			assert_eq!(!(wa & wb), !wa | !wb);
			assert_eq!(!(wa | wb), !wa & !wb);
		}

		#[test]
		fn prop_shift_left(val in any::<u64>(), shift in 0u32..64) {
			let w = Word(val);
			assert_eq!((w << shift).0, val << shift);

			// Shifting by 0 is identity
			assert_eq!(w << 0, w);

			// Shifting by 64 or more gives 0
			if shift >= 64 {
				assert_eq!((w << shift).0, 0);
			}
		}

		#[test]
		fn prop_shift_right(val in any::<u64>(), shift in 0u32..64) {
			let w = Word(val);
			assert_eq!((w >> shift).0, val >> shift);

			// Shifting by 0 is identity
			assert_eq!(w >> 0, w);

			// Shifting by 64 or more gives 0
			if shift >= 64 {
				assert_eq!((w >> shift).0, 0);
			}
		}

		#[test]
		fn prop_shift_inverse(val in any::<u64>(), shift in 1u32..64) {
			let w = Word(val);
			// Left then right shift loses high bits
			let mask = (1u64 << (64 - shift)) - 1;
			assert_eq!(((w << shift) >> shift).0, val & mask);

			// Right then left shift loses low bits
			let high_mask = !((1u64 << shift) - 1);
			assert_eq!(((w >> shift) << shift).0, val & high_mask);
		}

		#[test]
		fn prop_sar(val in any::<u64>(), shift in 0u32..64) {
			let w = Word(val);
			let expected = ((val as i64) >> shift) as u64;
			assert_eq!(w.sar(shift).0, expected);

			// SAR by 0 is identity
			assert_eq!(w.sar(0), w);

			// SAR by 63 gives all 0s or all 1s depending on sign
			let sign_extended = if (val as i64) < 0 {
				Word(0xFFFFFFFFFFFFFFFF)
			} else {
				Word(0)
			};
			assert_eq!(w.sar(63), sign_extended);
		}

		#[test]
		fn prop_sar_sign_extension(val in any::<u64>(), shift in 1u32..64) {
			let w = Word(val);
			let result = w.sar(shift);

			// Check sign bit is extended
			let is_negative = (val as i64) < 0;
			// The high bits are all 1 for a negative input and all 0 otherwise.
			let mask = !((1u64 << (64 - shift)) - 1);
			assert_eq!(result.0 & mask, if is_negative { mask } else { 0 });
		}

		#[test]
		fn prop_iadd32_cin_cout(
			a in any::<u64>(), b in any::<u64>(),
			cin_lo in proptest::bool::ANY, cin_hi in proptest::bool::ANY,
		) {
			// Build cin with carry bits at MSB of each 32-bit half
			let cin_word = ((cin_lo as u64) << 31) | ((cin_hi as u64) << 63);
			let wa = Word(a);
			let wb = Word(b);
			let wcin = Word(cin_word);
			let (sum, cout) = wa.iadd32_cin_cout(wb, wcin);

			// Each 32-bit half is added independently with its carry-in
			let lo_sum = (a as u32 as u64) + (b as u32 as u64) + (cin_lo as u64);
			let hi_sum = ((a >> 32) as u32 as u64) + ((b >> 32) as u32 as u64) + (cin_hi as u64);
			let expected_sum = (lo_sum as u32 as u64) | ((hi_sum as u32 as u64) << 32);
			assert_eq!(sum.0, expected_sum);

			// Carry computation: cout = (a & b) | ((a ^ b) & !sum)
			let expected_cout = (a & b) | ((a ^ b) & !expected_sum);
			assert_eq!(cout.0, expected_cout);

			// Zero cin should match iadd_cout_32
			let (sum0, cout0) = wa.iadd_cout_32(wb);
			let (sum1, cout1) = wa.iadd32_cin_cout(wb, Word::ZERO);
			assert_eq!(sum0, sum1);
			assert_eq!(cout0, cout1);
		}

		#[test]
		fn prop_iadd_cin_cout(a in any::<u64>(), b in any::<u64>(), cin in 0u64..=1) {
			let wa = Word(a);
			let wb = Word(b);
			let wcin = Word(cin);
			let (sum, cout) = wa.iadd_cin_cout(wb, wcin);

			// Basic addition with carry
			let expected_sum = a.wrapping_add(b).wrapping_add(cin);
			assert_eq!(sum.0, expected_sum);

			// Carry computation: cout at each bit position
			let expected_cout = (a & b) | ((a ^ b) & !expected_sum);
			assert_eq!(cout.0, expected_cout);

			// Without carry in, same as regular addition
			let (sum0, cout0) = wa.iadd_cin_cout(wb, Word::ZERO);
			let full_sum = a.wrapping_add(b);
			assert_eq!(sum0.0, full_sum);
			assert_eq!(cout0.0, (a & b) | ((a ^ b) & !full_sum));
		}

		#[test]
		fn prop_isub_bin_bout(a in any::<u64>(), b in any::<u64>(), bin in 0u64..=1) {
			let wa = Word(a);
			let wb = Word(b);
			let wbin = Word(bin);
			let (diff, bout) = wa.isub_bin_bout(wb, wbin);

			// Basic subtraction with borrow
			let expected_diff = a.wrapping_sub(b).wrapping_sub(bin);
			assert_eq!(diff.0, expected_diff);

			// Borrow computation: bout = (!a & b) | (!(a ^ b) & diff)
			let expected_bout = (!a & b) | (!(a ^ b) & expected_diff);
			assert_eq!(bout.0, expected_bout);

			// Without borrow in
			let (diff0, bout0) = wa.isub_bin_bout(wb, Word::ZERO);
			let expected = a.wrapping_sub(b);
			assert_eq!(diff0.0, expected);
			assert_eq!(bout0.0, (!a & b) | (!(a ^ b) & expected));
		}

		#[test]
		fn prop_shr_32(val in any::<u64>(), shift in 0u32..64) {
			let w = Word(val);
			let result = w.shr_32(shift);

			// Result should be the full value shifted right, then masked to 32 bits
			let expected = (val >> shift) & 0xFFFFFFFF;
			assert_eq!(result.0, expected);

			// Shifting by 0 gives lower 32 bits
			assert_eq!(w.shr_32(0).0, val & 0xFFFFFFFF);

			// Shifting by 32 or more gives upper bits or zeros
			if shift >= 32 {
				assert_eq!(result.0, (val >> shift) & 0xFFFFFFFF);
			}
		}
		#[test]
		fn prop_rotr(val in any::<u64>(), rotate in 0u32..128) {
			let w = Word(val);
			let result = w.rotr(rotate);

			// Rotation is modulo 64
			let rotate_mod = rotate % 64;
			let expected = val.rotate_right(rotate_mod);
			assert_eq!(result.0, expected);

			// Rotation by 0 or 64 is identity
			assert_eq!(w.rotr(0), w);
			assert_eq!(w.rotr(64), w);

			// Double rotation
			let r1 = rotate % 64;
			let r2 = (64 - r1) % 64;
			if r1 != 0 {
				assert_eq!(w.rotr(r1).rotr(r2), w);
			}
		}

		#[test]
		fn prop_imul(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);
			let (hi, lo) = wa.imul(wb);

			// Check against native 128-bit multiplication
			let result = (a as u128) * (b as u128);
			assert_eq!(hi.0, (result >> 64) as u64);
			assert_eq!(lo.0, result as u64);

			// Multiplication by 0 gives 0
			let (hi0, lo0) = wa.imul(Word::ZERO);
			assert_eq!(hi0, Word::ZERO);
			assert_eq!(lo0, Word::ZERO);

			// Multiplication by 1 is identity
			let (hi1, lo1) = wa.imul(Word::ONE);
			assert_eq!(hi1, Word::ZERO);
			assert_eq!(lo1, wa);

			// Commutative
			let (hi_ab, lo_ab) = wa.imul(wb);
			let (hi_reversed, lo_reversed) = wb.imul(wa);
			assert_eq!(hi_ab, hi_reversed);
			assert_eq!(lo_ab, lo_reversed);
		}

		#[test]
		fn prop_sll32(val in any::<u64>(), shift in 0u32..32) {
			let w = Word(val);
			let result = w.sll32(shift);

			// Extract 32-bit halves
			let lo = val as u32;
			let hi = (val >> 32) as u32;

			// Expected result: each half shifted independently
			let expected_lo = ((lo << shift) as u64) & 0xFFFFFFFF;
			let expected_hi = ((hi << shift) as u64) << 32;
			let expected = expected_lo | expected_hi;

			assert_eq!(result.0, expected);

			// Shifting by 0 is identity
			assert_eq!(w.sll32(0), w);

			// Shifting by 31 should move MSB of each half to sign bit
			let w_test = Word(0x40000001_40000001);
			let result_31 = w_test.sll32(31);
			assert_eq!(result_31.0, 0x80000000_80000000);

			// Test that shift amount is masked to 5 bits
			assert_eq!(w.sll32(shift), w.sll32(shift | 0x20));
		}

		#[test]
		fn prop_srl32(val in any::<u64>(), shift in 0u32..32) {
			let w = Word(val);
			let result = w.srl32(shift);

			// Extract 32-bit halves
			let lo = val as u32;
			let hi = (val >> 32) as u32;

			// Expected result: each half shifted independently
			let expected_lo = (lo >> shift) as u64;
			let expected_hi = ((hi >> shift) as u64) << 32;
			let expected = expected_lo | expected_hi;

			assert_eq!(result.0, expected);

			// Shifting by 0 is identity
			assert_eq!(w.srl32(0), w);

			// Shifting by 31 should move LSB to bit 0, clearing upper bits
			let w_test = Word(0x80000000_80000000);
			let result_31 = w_test.srl32(31);
			assert_eq!(result_31.0, 0x00000001_00000001);

			// Test that shift amount is masked to 5 bits
			assert_eq!(w.srl32(shift), w.srl32(shift | 0x20));
		}

		#[test]
		fn prop_sra32(val in any::<u64>(), shift in 0u32..32) {
			let w = Word(val);
			let result = w.sra32(shift);

			// Extract 32-bit halves as signed
			let lo = val as u32 as i32;
			let hi = (val >> 32) as u32 as i32;

			// Expected result: each half arithmetic shifted independently
			let expected_lo = ((lo >> shift) as u32) as u64;
			let expected_hi = (((hi >> shift) as u32) as u64) << 32;
			let expected = expected_lo | expected_hi;

			assert_eq!(result.0, expected);

			// Shifting by 0 is identity
			assert_eq!(w.sra32(0), w);

			// Sign extension test: negative values extend sign bit
			let w_neg = Word(0x80000000_80000000);
			let result_1 = w_neg.sra32(1);
			assert_eq!(result_1.0, 0xC0000000_C0000000);

			// Sign extension test: positive values extend 0
			let w_pos = Word(0x40000000_40000000);
			let result_1_pos = w_pos.sra32(1);
			assert_eq!(result_1_pos.0, 0x20000000_20000000);

			// Shifting by 31 gives all 0s or all 1s in each half
			let result_31 = w.sra32(31);
			let expected_lo_31 = if lo < 0 { 0xFFFFFFFF } else { 0 };
			let expected_hi_31 = if hi < 0 { 0xFFFFFFFF00000000 } else { 0 };
			assert_eq!(result_31.0, expected_lo_31 | expected_hi_31);

			// Test that shift amount is masked to 5 bits
			assert_eq!(w.sra32(shift), w.sra32(shift | 0x20));
		}

		#[test]
		fn prop_rotr32(val in any::<u64>(), rotate in 0u32..32) {
			let w = Word(val);
			let result = w.rotr32(rotate);

			// Extract 32-bit halves
			let lo = val as u32;
			let hi = (val >> 32) as u32;

			// Expected result: each half rotated independently
			let expected_lo = lo.rotate_right(rotate) as u64;
			let expected_hi = ((hi.rotate_right(rotate)) as u64) << 32;
			let expected = expected_lo | expected_hi;

			assert_eq!(result.0, expected);

			// Rotating by 0 is identity
			assert_eq!(w.rotr32(0), w);

			// Rotating by 32 is identity (due to masking to 5 bits)
			assert_eq!(w.rotr32(32), w.rotr32(0));

			// Test that rotate amount is masked to 5 bits
			assert_eq!(w.rotr32(rotate), w.rotr32(rotate | 0x20));

			// Rotation is circular - rotating by n then 32-n gives identity
			if rotate > 0 && rotate < 32 {
				let w_test = Word(0x12345678_9ABCDEF0);
				let rotated = w_test.rotr32(rotate);
				let back = rotated.rotr32(32 - rotate);
				assert_eq!(back, w_test);
			}
		}

		#[test]
		fn prop_smul(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);
			let (hi, lo) = wa.smul(wb);

			// Check against native 128-bit signed multiplication
			let result = (a as i64 as i128) * (b as i64 as i128);
			assert_eq!(hi.0, (result >> 64) as u64);
			assert_eq!(lo.0, result as u64);

			// Multiplication by 0 gives 0
			let (hi0, lo0) = wa.smul(Word::ZERO);
			assert_eq!(hi0, Word::ZERO);
			assert_eq!(lo0, Word::ZERO);

			// Multiplication by 1 is identity
			let (hi1, lo1) = wa.smul(Word::ONE);
			let expected_hi = if (a as i64) < 0 { Word(0xFFFFFFFFFFFFFFFF) } else { Word::ZERO };
			assert_eq!(hi1, expected_hi);
			assert_eq!(lo1, wa);

			// Multiplication by -1 negates
			let (hi_neg, lo_neg) = wa.smul(Word(0xFFFFFFFFFFFFFFFF));
			let neg_result = -(a as i64 as i128);
			assert_eq!(hi_neg.0, (neg_result >> 64) as u64);
			assert_eq!(lo_neg.0, neg_result as u64);

			// Commutative
			let (hi_ab, lo_ab) = wa.smul(wb);
			let (hi_reversed, lo_reversed) = wb.smul(wa);
			assert_eq!(hi_ab, hi_reversed);
			assert_eq!(lo_ab, lo_reversed);
		}

		#[test]
		fn prop_wrapping_sub(a in any::<u64>(), b in any::<u64>()) {
			let wa = Word(a);
			let wb = Word(b);
			let result = wa.wrapping_sub(wb);

			assert_eq!(result.0, a.wrapping_sub(b));

			// Subtracting 0 is identity
			assert_eq!(wa.wrapping_sub(Word::ZERO), wa);

			// Subtracting itself gives 0
			assert_eq!(wa.wrapping_sub(wa), Word::ZERO);

			// Adding then subtracting cancels
			let sum = Word(a.wrapping_add(b));
			assert_eq!(sum.wrapping_sub(wb), wa);
		}

		#[test]
		fn prop_conversions(val in any::<u64>()) {
			let word = Word::from_u64(val);
			assert_eq!(word.as_u64(), val);
			assert_eq!(word, Word(val));

			// Round trip
			assert_eq!(Word::from_u64(word.as_u64()), word);
		}

		#[test]
		fn prop_debug_format(val in any::<u64>()) {
			let word = Word(val);
			let debug_str = format!("{:?}", word);
			assert!(debug_str.starts_with("Word(0x"));
			assert!(debug_str.ends_with(")"));
			// Check the hex value is correct (lowercase)
			let expected = format!("Word({:#018x})", val);
			assert_eq!(debug_str, expected);
		}
	}

	#[test]
	fn test_32bit_shift_edge_cases() {
		// Test sll32 edge cases
		let w1 = Word(0x12345678_9ABCDEF0);
		assert_eq!(w1.sll32(4).0, 0x23456780_ABCDEF00);
		assert_eq!(w1.sll32(16).0, 0x56780000_DEF00000);

		// Test that upper bits don't affect lower half and vice versa
		let w2 = Word(0xFFFFFFFF_00000000);
		assert_eq!(w2.sll32(1).0, 0xFFFFFFFE_00000000);
		let w3 = Word(0x00000000_FFFFFFFF);
		assert_eq!(w3.sll32(1).0, 0x00000000_FFFFFFFE);

		// Test srl32 edge cases
		assert_eq!(w1.srl32(4).0, 0x01234567_09ABCDEF);
		assert_eq!(w1.srl32(16).0, 0x00001234_00009ABC);

		// Test sra32 with mixed sign bits
		let w4 = Word(0x80000000_7FFFFFFF); // Negative upper, positive lower
		assert_eq!(w4.sra32(1).0, 0xC0000000_3FFFFFFF);
		assert_eq!(w4.sra32(31).0, 0xFFFFFFFF_00000000);

		let w5 = Word(0x7FFFFFFF_80000000); // Positive upper, negative lower
		assert_eq!(w5.sra32(1).0, 0x3FFFFFFF_C0000000);
		assert_eq!(w5.sra32(31).0, 0x00000000_FFFFFFFF);

		// Test boundary values
		let all_ones = Word(0xFFFFFFFF_FFFFFFFF);
		assert_eq!(all_ones.sll32(1).0, 0xFFFFFFFE_FFFFFFFE);
		assert_eq!(all_ones.srl32(1).0, 0x7FFFFFFF_7FFFFFFF);
		assert_eq!(all_ones.sra32(1).0, 0xFFFFFFFF_FFFFFFFF);

		let alternating = Word(0xAAAAAAAA_55555555);
		assert_eq!(alternating.sll32(1).0, 0x55555554_AAAAAAAA);
		assert_eq!(alternating.srl32(1).0, 0x55555555_2AAAAAAA);
		assert_eq!(alternating.sra32(1).0, 0xD5555555_2AAAAAAA);

		// Test zero shifts
		assert_eq!(w1.sll32(0), w1);
		assert_eq!(w1.srl32(0), w1);
		assert_eq!(w1.sra32(0), w1);

		// Test that shifts are independent between halves
		let w6 = Word(0x00000001_00000000);
		assert_eq!(w6.sll32(31).0, 0x80000000_00000000);
		assert_eq!(w6.srl32(1).0, 0x00000000_00000000);

		// Test rotr32 edge cases
		let w7 = Word(0x80000001_80000001);
		assert_eq!(w7.rotr32(1).0, 0xC0000000_C0000000);
		assert_eq!(w7.rotr32(31).0, 0x00000003_00000003);

		// Test rotr32 rotation wrapping
		let w8 = Word(0x12345678_9ABCDEF0);
		assert_eq!(w8.rotr32(4).0, 0x81234567_09ABCDEF);
		assert_eq!(w8.rotr32(16).0, 0x56781234_DEF09ABC);

		// Test rotr32 with different values in each half
		let w9 = Word(0xFFFF0000_0000FFFF);
		assert_eq!(w9.rotr32(16).0, 0x0000FFFF_FFFF0000);

		// Test rotr32 zero rotation
		assert_eq!(w8.rotr32(0), w8);
	}

	#[test]
	fn test_word_serialization_round_trip() {
		let mut rng = StdRng::seed_from_u64(0);
		let word = Word::from_u64(rng.next_u64());

		let mut buf = Vec::new();
		word.serialize(&mut buf).unwrap();

		let deserialized = Word::deserialize(&mut buf.as_slice()).unwrap();
		assert_eq!(word, deserialized);
	}
}