MIPS 주소 지정 방식 문서의 검증 코드다. if __name__ == "__main__": 아래가 자체 테스트다.
# 19.MIPS 주소 지정 방식 문서의 값 확인: 분기 주소(PC 상대)와 점프 주소(의사 직접).
# 실제 어셈블러가 아니라 파이썬으로 짠 인코더·디코더와 작은 흉내기다.
# 실행: python3 19_mips-addressing-modes_verify.py
import random
REGS = ["zero", "at", "v0", "v1", "a0", "a1", "a2", "a3",
"t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7",
"s0", "s1", "s2", "s3", "s4", "s5", "s6", "s7",
"t8", "t9", "k0", "k1", "gp", "sp", "fp", "ra"]
# opcode·funct 값은 MIPS Green Sheet(Reference Data)의 표를 따른다.
R_FUNCT = {"sll": 0x00, "srl": 0x02, "sra": 0x03, "jr": 0x08,
"mfhi": 0x10, "mflo": 0x12, "mult": 0x18, "multu": 0x19,
"div": 0x1A, "divu": 0x1B,
"add": 0x20, "addu": 0x21, "sub": 0x22, "subu": 0x23,
"and": 0x24, "or": 0x25, "xor": 0x26, "nor": 0x27,
"slt": 0x2A, "sltu": 0x2B}
I_OP = {"beq": 0x04, "bne": 0x05, "addi": 0x08, "addiu": 0x09,
"slti": 0x0A, "sltiu": 0x0B, "andi": 0x0C, "ori": 0x0D,
"xori": 0x0E, "lui": 0x0F, "lb": 0x20, "lw": 0x23,
"lbu": 0x24, "sb": 0x28, "sw": 0x2B}
J_OP = {"j": 0x02, "jal": 0x03}
FUNCT_R = {v: k for k, v in R_FUNCT.items()}
OP_I = {v: k for k, v in I_OP.items()}
OP_J = {v: k for k, v in J_OP.items()}
SHIFTS = ("sll", "srl", "sra")
ZERO_EXT = ("andi", "ori", "xori", "lui")
MEMOPS = ("lw", "sw", "lb", "lbu", "sb")
MASK = 0xFFFFFFFF
def reg(name):
name = name.strip()
assert name.startswith("$"), name
name = name[1:]
return int(name) if name.isdigit() else REGS.index(name)
def rname(n):
return "$" + REGS[n]
def signed16(x):
x &= 0xFFFF
return x - 0x10000 if x & 0x8000 else x
def signed32(x):
x &= MASK
return x - (1 << 32) if x & 0x80000000 else x
def fields_r(op, rs, rt, rd, shamt, funct):
return (op << 26) | (rs << 21) | (rt << 16) | (rd << 11) | (shamt << 6) | funct
def fields_i(op, rs, rt, imm):
return (op << 26) | (rs << 21) | (rt << 16) | (imm & 0xFFFF)
def split_instr(text):
text = text.split("#")[0].strip()
parts = text.split(None, 1)
args = [a.strip() for a in parts[1].split(",")] if len(parts) > 1 else []
return parts[0], args
def target_of(tok, labels):
return labels[tok] if labels and tok in labels else int(tok, 0)
def encode(text, addr=0, labels=None):
"""어셈블리 한 줄을 32비트 기계어로 바꾼다. addr는 이 명령이 놓인 주소."""
m, a = split_instr(text)
if m in R_FUNCT:
f = R_FUNCT[m]
if m in SHIFTS: # sll rd, rt, shamt
sh = int(a[2], 0)
assert 0 <= sh < 32
return fields_r(0, 0, reg(a[1]), reg(a[0]), sh, f)
if m == "jr":
return fields_r(0, reg(a[0]), 0, 0, 0, f)
if m in ("mult", "multu", "div", "divu"):
return fields_r(0, reg(a[0]), reg(a[1]), 0, 0, f)
if m in ("mfhi", "mflo"):
return fields_r(0, 0, 0, reg(a[0]), 0, f)
return fields_r(0, reg(a[1]), reg(a[2]), reg(a[0]), 0, f) # add rd, rs, rt
if m in I_OP:
op = I_OP[m]
if m in MEMOPS: # lw rt, offset(rs)
off, base = a[1].rstrip(")").split("(")
off = int(off, 0)
assert -32768 <= off <= 32767
return fields_i(op, reg(base), reg(a[0]), off)
if m in ("beq", "bne"): # beq rs, rt, label
diff = target_of(a[2], labels) - (addr + 4)
assert diff % 4 == 0
off = diff // 4
assert -32768 <= off <= 32767, "분기 거리가 16비트를 넘는다"
return fields_i(op, reg(a[0]), reg(a[1]), off)
if m == "lui":
imm = int(a[1], 0)
assert 0 <= imm <= 0xFFFF
return fields_i(op, 0, reg(a[0]), imm)
imm = int(a[2], 0)
if m in ZERO_EXT:
assert 0 <= imm <= 0xFFFF
else:
assert -32768 <= imm <= 32767
return fields_i(op, reg(a[1]), reg(a[0]), imm) # addi rt, rs, imm
if m in J_OP:
t = target_of(a[0], labels)
assert t % 4 == 0
assert (t & 0xF0000000) == ((addr + 4) & 0xF0000000), "위 4비트가 다르다"
return (J_OP[m] << 26) | ((t >> 2) & 0x03FFFFFF)
raise ValueError("모르는 명령: " + text)
def split_fields(word):
return {"op": word >> 26, "rs": (word >> 21) & 31, "rt": (word >> 16) & 31,
"rd": (word >> 11) & 31, "shamt": (word >> 6) & 31, "funct": word & 63,
"imm": word & 0xFFFF, "addr": word & 0x03FFFFFF}
def decode(word, addr=0):
"""32비트 기계어를 어셈블리 한 줄로 되돌린다. 분기·점프의 목적지는 16진 주소로 적는다."""
f = split_fields(word)
if f["op"] == 0:
m = FUNCT_R[f["funct"]]
if m in SHIFTS:
return "%s %s, %s, %d" % (m, rname(f["rd"]), rname(f["rt"]), f["shamt"])
if m == "jr":
return "jr %s" % rname(f["rs"])
if m in ("mult", "multu", "div", "divu"):
return "%s %s, %s" % (m, rname(f["rs"]), rname(f["rt"]))
if m in ("mfhi", "mflo"):
return "%s %s" % (m, rname(f["rd"]))
return "%s %s, %s, %s" % (m, rname(f["rd"]), rname(f["rs"]), rname(f["rt"]))
if f["op"] in OP_J:
t = ((addr + 4) & 0xF0000000) | (f["addr"] << 2)
return "%s 0x%08x" % (OP_J[f["op"]], t)
m = OP_I[f["op"]]
if m in MEMOPS:
return "%s %s, %d(%s)" % (m, rname(f["rt"]), signed16(f["imm"]), rname(f["rs"]))
if m in ("beq", "bne"):
t = (addr + 4 + signed16(f["imm"]) * 4) & MASK
return "%s %s, %s, 0x%08x" % (m, rname(f["rs"]), rname(f["rt"]), t)
if m == "lui":
return "lui %s, 0x%x" % (rname(f["rt"]), f["imm"])
if m in ZERO_EXT:
return "%s %s, %s, 0x%x" % (m, rname(f["rt"]), rname(f["rs"]), f["imm"])
return "%s %s, %s, %d" % (m, rname(f["rt"]), rname(f["rs"]), signed16(f["imm"]))
def assemble(source, base=0x00400000):
"""여러 줄을 두 번 훑어 (주소, 기계어, 원문) 목록과 라벨 표를 돌려준다."""
labels, lines, addr = {}, [], base
for raw in source.strip().splitlines():
line = raw.split("#")[0].strip()
while ":" in line:
lab, line = line.split(":", 1)
labels[lab.strip()] = addr
line = line.strip()
if line:
lines.append((addr, line))
addr += 4
return [(a, encode(t, a, labels), t) for a, t in lines], labels
class Machine:
"""MIPS 일부를 흉내 내는 작은 기계. 기계어를 해독해 실행한다.
지연 분기는 흉내 내지 않는다(jal은 PC+4를 $ra에 넣는다)."""
def __init__(self, source, base=0x00400000, big_endian=True):
self.code, self.labels = assemble(source, base)
self.words = {a: w for a, w, _ in self.code}
self.text = {a: t for a, _, t in self.code}
self.r = [0] * 32
self.hi = self.lo = 0
self.mem = {}
self.pc = base
self.big = big_endian
self.steps = 0
self.log = []
def load_word(self, addr):
assert addr % 4 == 0, "워드 주소는 4의 배수여야 한다"
bs = [self.mem.get(addr + i, 0) for i in range(4)]
if not self.big:
bs.reverse()
return (bs[0] << 24) | (bs[1] << 16) | (bs[2] << 8) | bs[3]
def store_word(self, addr, val):
assert addr % 4 == 0, "워드 주소는 4의 배수여야 한다"
bs = [(val >> s) & 0xFF for s in (24, 16, 8, 0)]
if not self.big:
bs.reverse()
for i, b in enumerate(bs):
self.mem[addr + i] = b
def set(self, n, val):
if n != 0: # $zero는 써도 0이다
self.r[n] = val & MASK
def step(self):
pc = self.pc
f = split_fields(self.words[pc])
r, npc = self.r, pc + 4
rs, rt = r[f["rs"]], r[f["rt"]]
simm = signed16(f["imm"])
if f["op"] == 0:
m = FUNCT_R[f["funct"]]
if m in ("add", "sub"):
v = signed32(rs) + signed32(rt) if m == "add" else signed32(rs) - signed32(rt)
assert -2**31 <= v < 2**31, "오버플로 예외"
self.set(f["rd"], v)
elif m == "addu": self.set(f["rd"], rs + rt)
elif m == "subu": self.set(f["rd"], rs - rt)
elif m == "and": self.set(f["rd"], rs & rt)
elif m == "or": self.set(f["rd"], rs | rt)
elif m == "xor": self.set(f["rd"], rs ^ rt)
elif m == "nor": self.set(f["rd"], ~(rs | rt))
elif m == "slt": self.set(f["rd"], int(signed32(rs) < signed32(rt)))
elif m == "sltu": self.set(f["rd"], int(rs < rt))
elif m == "sll": self.set(f["rd"], rt << f["shamt"])
elif m == "srl": self.set(f["rd"], rt >> f["shamt"])
elif m == "sra": self.set(f["rd"], signed32(rt) >> f["shamt"])
elif m == "jr": npc = rs
elif m == "mult":
p = (signed32(rs) * signed32(rt)) & 0xFFFFFFFFFFFFFFFF
self.hi, self.lo = p >> 32, p & MASK
elif m == "multu":
p = rs * rt
self.hi, self.lo = p >> 32, p & MASK
elif m == "div":
a, b = signed32(rs), signed32(rt)
q = abs(a) // abs(b)
q = -q if (a < 0) != (b < 0) else q
self.lo, self.hi = q & MASK, (a - q * b) & MASK
elif m == "divu":
self.lo, self.hi = rs // rt, rs % rt
elif m == "mfhi": self.set(f["rd"], self.hi)
elif m == "mflo": self.set(f["rd"], self.lo)
elif f["op"] in OP_J:
if OP_J[f["op"]] == "jal":
self.set(31, pc + 4)
npc = ((pc + 4) & 0xF0000000) | (f["addr"] << 2)
else:
m = OP_I[f["op"]]
if m == "addi":
v = signed32(rs) + simm
assert -2**31 <= v < 2**31, "오버플로 예외"
self.set(f["rt"], v)
elif m == "addiu": self.set(f["rt"], rs + simm)
elif m == "slti": self.set(f["rt"], int(signed32(rs) < simm))
elif m == "sltiu": self.set(f["rt"], int(rs < (simm & MASK)))
elif m == "andi": self.set(f["rt"], rs & f["imm"])
elif m == "ori": self.set(f["rt"], rs | f["imm"])
elif m == "xori": self.set(f["rt"], rs ^ f["imm"])
elif m == "lui": self.set(f["rt"], f["imm"] << 16)
elif m == "lw": self.set(f["rt"], self.load_word((rs + simm) & MASK))
elif m == "sw": self.store_word((rs + simm) & MASK, rt)
elif m == "lb":
b = self.mem.get((rs + simm) & MASK, 0)
self.set(f["rt"], b - 256 if b & 0x80 else b)
elif m == "lbu": self.set(f["rt"], self.mem.get((rs + simm) & MASK, 0))
elif m == "sb": self.mem[(rs + simm) & MASK] = rt & 0xFF
elif m == "beq":
if rs == rt: npc = pc + 4 + simm * 4
elif m == "bne":
if rs != rt: npc = pc + 4 + simm * 4
self.pc = npc & MASK
self.steps += 1
return pc
def run(self, max_steps=100000, hook=None):
"""PC가 프로그램 밖으로 나가면 멈춘다."""
while self.pc in self.words:
pc = self.step()
if hook:
hook(self, pc)
assert self.steps < max_steps, "끝나지 않는다"
return self
def reg(self, name):
return self.r[reg(name)]
LOOP = """
add $s1, $zero, $zero
add $s0, $zero, $zero
Loop: slt $t0, $s0, $s2
beq $t0, $zero, Exit
sll $t1, $s0, 2
add $t1, $t1, $s3
lw $t2, 0($t1)
add $s1, $s1, $t2
addi $s0, $s0, 1
j Loop
Exit:
"""
def branch_target(pc, word):
return (pc + 4 + signed16(word & 0xFFFF) * 4) & MASK
def jump_target(pc, word):
return ((pc + 4) & 0xF0000000) | ((word & 0x03FFFFFF) << 2)
if __name__ == "__main__":
code, labels = assemble(LOOP)
words = {a: w for a, w, _ in code}
assert labels == {"Loop": 0x00400008, "Exit": 0x00400028}
assert words[0x00400008] == 0x0212402A and words[0x00400010] == 0x00104880
assert words[0x0040000C] == 0x11000006 and words[0x0040000C] & 0xFFFF == 6
assert words[0x00400024] == 0x08100002 and words[0x00400024] & 0x03FFFFFF == 0x0100002
assert (0x00400028 - 0x00400010) == 0x18 == 24 and 24 // 4 == 6
assert 0x00400008 // 4 == 0x0100002
assert branch_target(0x0040000C, 0x11000006) == 0x00400028
assert jump_target(0x00400024, 0x08100002) == 0x00400008
# 예제 1: 뒤로 가는 분기
w = encode("bne $t0, $zero, 0x00400004", 0x00400018)
assert w == 0x1500FFFA and signed16(w) == -6 and (0x00400004 - 0x0040001C) == -24
assert branch_target(0x00400018, w) == 0x00400004
# 예제 2: 기계어에서 갈 곳 찾기
assert 0x08100013 >> 26 == 2 and 0x08100013 & 0x03FFFFFF == 0x0100013
assert 0x0100013 * 4 == 0x040004C and jump_target(0x0040000C, 0x08100013) == 0x0040004C
assert decode(0x08100013, 0x0040000C) == "j 0x0040004c"
# 무작위 왕복: 식으로 구한 갈 곳이 인코더에 준 갈 곳과 같다
rng = random.Random(19)
for _ in range(2000):
pc = 0x00400000 + 4 * rng.randrange(100000)
t = pc + 4 + 4 * rng.randint(-32768, 32767)
w = encode("beq $s0, $s1, 0x%08x" % t, pc)
assert branch_target(pc, w) == t and signed16(w) == (t - (pc + 4)) // 4
t = ((pc + 4) & 0xF0000000) | (4 * rng.randrange(1 << 26))
w = encode("jal 0x%08x" % t, pc)
assert jump_target(pc, w) == t and (w & 0x03FFFFFF) == (t & 0x0FFFFFFF) >> 2
# 닿는 범위
assert 4 * 32768 == 131072 and 4 * 32767 == 131068 and 2 ** 28 == 256 * 2 ** 20
assert 32768 // 1024 == 32 and 131072 // 1024 == 128
pc = 0x00400010
assert encode("beq $s0, $s1, 0x%08x" % (pc + 4 + 131068), pc) & 0xFFFF == 0x7FFF
assert encode("beq $s0, $s1, 0x%08x" % (pc + 4 - 131072), pc) & 0xFFFF == 0x8000
for t in (pc + 4 + 131072, pc + 4 - 131076):
try:
encode("beq $s0, $s1, 0x%08x" % t, pc)
raise SystemExit("막지 못했다")
except AssertionError:
pass
try:
encode("j 0x10000000", pc) # 위 4비트가 다른 구역
raise SystemExit("막지 못했다")
except AssertionError:
pass
# 예제 3: 닿지 않는 분기를 bne + j로. 40,000줄 뒤
far = 0x00400010 + 4 + 4 * 40000
assert far == 0x00427114
code, _ = assemble("bne $s0, $s1, Skip\nj 0x%08x\nSkip:" % far, base=0x00400010)
assert [w for _, w, _ in code] == [0x16110001, 0x08109C45]
for a, b in ((5, 5), (5, 6)): # 같으면 먼 곳으로, 다르면 다음 줄로
pcv, w0, w1 = 0x00400010, code[0][1], code[1][1]
nxt = branch_target(pcv, w0) if a != b else pcv + 4
if nxt == pcv + 4:
nxt = jump_target(pcv + 4, w1)
assert nxt == (far if a == b else 0x00400018)
# 카드
assert encode("beq $s0, $s1, 0x00400040", 0x00400020) == 0x12110007
assert (0x00400040 - 0x00400024) == 0x1C == 28
assert decode(0x0C100004, 0x00400034) == "jal 0x00400010" and 0x0C100004 >> 26 == 3
m = Machine("jal F\nF: add $t0, $zero, $zero", base=0x00400034) # jal 뒤의 $ra
m.step()
assert m.reg("$ra") == 0x00400038
print("ALL CHECKS PASSED")