pub fn trace() -> RowMajorMatrix<F> {
        // The trace containing all values, with all multiplicities set to zero.
        let mut initial_trace = RowMajorMatrix::new(
            zeroed_f_vec(NUM_ROWS * NUM_BYTE_PREPROCESSED_COLS),
            NUM_BYTE_PREPROCESSED_COLS,
        );

        // Record all the necessary operations for each byte lookup.
        let opcodes = ByteOpcode::all();

        // Iterate over all options for pairs of bytes `a` and `b`.
        for (row_index, (b, c)) in (0..=u8::MAX).cartesian_product(0..=u8::MAX).enumerate() {
            let b = b as u8;
            let c = c as u8;
            let col: &mut BytePreprocessedCols<F> = initial_trace.row_mut(row_index).borrow_mut();

            // Set the values of `b` and `c`.
            col.b = F::from_canonical_u8(b);
            col.c = F::from_canonical_u8(c);

            // Iterate over all operations for results and updating the table map.
            for opcode in opcodes.iter() {
                match opcode {
                    ByteOpcode::AND => {
                        let and = b & c;
                        col.and = F::from_canonical_u8(and);
                        ByteLookupEvent::new(*opcode, and as u16, 0, b, c)
                    }
                    ByteOpcode::OR => {
                        let or = b | c;
                        col.or = F::from_canonical_u8(or);
                        ByteLookupEvent::new(*opcode, or as u16, 0, b, c)
                    }
                    ByteOpcode::XOR => {
                        let xor = b ^ c;
                        col.xor = F::from_canonical_u8(xor);
                        ByteLookupEvent::new(*opcode, xor as u16, 0, b, c)
                    }
                    ByteOpcode::SLL => {
                        let sll = b << (c & 7);
                        col.sll = F::from_canonical_u8(sll);
                        ByteLookupEvent::new(*opcode, sll as u16, 0, b, c)
                    }
                    ByteOpcode::U8Range => ByteLookupEvent::new(*opcode, 0, 0, b, c),
                    ByteOpcode::ShrCarry => {
                        let (res, carry) = shr_carry(b, c);
                        col.shr = F::from_canonical_u8(res);
                        col.shr_carry = F::from_canonical_u8(carry);
                        ByteLookupEvent::new(*opcode, res as u16, carry, b, c)
                    }
                    ByteOpcode::LTU => {
                        let ltu = b < c;
                        col.ltu = F::from_bool(ltu);
                        ByteLookupEvent::new(*opcode, ltu as u16, 0, b, c)
                    }
                    ByteOpcode::MSB => {
                        let msb = (b & 0b1000_0000) != 0;
                        col.msb = F::from_bool(msb);
                        ByteLookupEvent::new(*opcode, msb as u16, 0, b, 0)
                    }
                    ByteOpcode::U16Range => {
                        let v = ((b as u32) << 8) + c as u32;
                        col.value_u16 = F::from_canonical_u32(v);
                        ByteLookupEvent::new(*opcode, v as u16, 0, 0, 0)
                    }
                };
            }
        }

        initial_trace
    }
Creates the preprocessed byte trace.

This function returns a `trace` which is a matrix containing all possible byte operations.
crates/core/machine/src/bytes/mod.rs