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Problem 3: CPU emulator

Description

To understand how the computer executes your program, let me give a short introduction to CPU. The CPU basically contains 2 parts: registers and ALU. You can consider registers as an array. Each cell of this array has a name (for example, x0, x1, x2, $\dots$, x31 in RISC-V), and can store a single number. Arithmetic calculations (addition, subscription, multiplication, division, ...) are done by ALU.

When executing your program, the assembly codes (written in binary) are sent to CPU. Each line of assembly code specifies some operation of registers, and CPU will use a special register named PC (program counter) to identify the current execution line number. For example, if the code is add x3 x1 x2, then CPU will take the values in registers x1 and x2, add them up and store the result in the register x3. This is shown in the figure below (only 5 registers shown here). Then, the CPU increments PC by 1 to execute the next instruction.

In this problem, you are required to implement a toy emulator which is able to execute a very simple assembly language (similar to RISC-V). You only need to consider 6 registers, named x0, x1, x2, x3, x4 and x5, all in lowercase, and each register stores a 16-bit integer. The x0 register is a special one, whose value is always zero. Also, there are only has 6 instructions in this assembly language: add, sub, mul, div, let and print, which are introduced below.

In this problem, we use a 16-bit machine code. An example of a 16-bit instruction is as follows.

The instructions add, sub, mul and div are similar. The syntax is shown in the following table. Note that in these operations, the imm part is discarded.

The let instruction is used to assign value to a register. The syntax is:

where r1 is the name of some register (x0 to x5), and imm is an integer within the range $\left[0,2^7-1\right]$. In this instruction, the r2 part is discarded and the imm part is used. For example, the execution of instruction let x1 80 is shown below.

Also, we need a print instruction to print the value in some register so that we can test whether the execution result is correct. For example, if the value in register x1 is 5, your emulator should print x1 = 5 on the screen when the instruction print x1 is executed. The r2 part is also discarded in this instruction.

Notes:

1. In the div instruction, the division result is truncated towards zero, and the denominator will always be non-zero.
2. Value in all registers should be initialized to 0 before execution.
3. Remember that the value in x0 is always zero. Any instruction that attempts to modify it should have no effect.
4. We only consider unsigned immediate in this problem.

Input format

• The first line of the input is a number n, indicating the total lines of code. The following n lines are the instructions written in hexadecimal.

Output format

• Your emulator should execute the input program, and only print the result when a print instruction is executed. It is guaranteed that the input and output are both non-empty.

Example

Input:

2
0x8401
0xA400

Output:

x1 = 1

Explanation:

• 0x8401 is 1000010000000001 in binary, whose opcode is 100, r1 is 001 (x1), r2 is 000 (x0) and imm is 0000001 (1). From the opcode we know that this is a let instruction, so the instruction is let x1 1.
• 0xA400 is 1010010000000000 in binary, whose opcode is 101 and r1 is 001 (x1). This is a print instruction, so the instruction is print x1.

Note

Your program will not be compiled and linked against the math library, so do not use the functions in <math.h>.