def __mul__(self, other: "Float") -> "Float":
"""
Binary Mul 연산 ( * )을 위한 operator overloading
:param other: Float 타입 가정
:return: 새로운 Float 객체로 return
"""
a_frac = BitOperation.fraction_bits(self.fractions)
b_frac = BitOperation.fraction_bits(other.fractions)
exp, _ = Arithmetic.add_bits(self.exponents, other.exponents, self.exponent_len)
bias = Arithmetic.str_to_integer('127', self.exponent_len)
exp, _ = Arithmetic.raw_sub_bits(exp, bias)
extra = BitOperation.empty_bits(self.fraction_len + 1)
mul = a_frac
over = BitOperation.empty_bits(self.fraction_len + 1)
for bit in b_frac[:0:-1]:
if bit:
extra, overflow = Arithmetic.raw_add_bits(extra, mul)
if overflow:
over, _ = Arithmetic.add_bits(over, BitOperation.num_map['1'], self.fraction_len+1)
mul = BitOperation.raw_lshift_bits(mul, 1)
if BitOperation.is_empty(mul):
break
res = BitOperation.empty_bits(self.fraction_len + 1)
mul = a_frac
for bit in b_frac:
if bit:
res, overflow = Arithmetic.raw_add_bits(res, mul)
if overflow:
res = BitOperation.raw_rshift_bits(res, 1)
res[0] = overflow
exp, _ = Arithmetic.add_bits(exp, BitOperation.num_map['1'], self.exponent_len)
mul = BitOperation.raw_rshift_bits(mul, 1)
mul = BitOperation.raw_rshift_bits(mul, 1)
if BitOperation.is_empty(mul):
break
res, _ = Arithmetic.raw_add_bits(res, over)
res = res[1:]
return Float(exp, res, self.sign ^ other.sign)
def equalize_exponent(a_exp: List[Bit], a_frac: List[Bit],
b_exp: List[Bit], b_frac: List[Bit]):
"""
두 float 값의 exponent 값이 같게 만들고 fraction을 조정함
:param a_exp: a의 exponent ( 지수 )
:param a_frac: a의 fraction ( 가수 )
:param b_exp: b의 exponent ( 지수 )
:param b_frac: b의 fraction ( 가수 )
:return: 같은 exponent, exponent에 맞춰 조정된 a의 fraction, exponent에 맞춰 조정된 b의 fraction
"""
a_frac = BitOperation.fraction_bits(a_frac)
b_frac = BitOperation.fraction_bits(b_frac)
if BitOperation.raw_ge_bits(a_exp, b_exp):
b_frac = Arithmetic.shift_fraction(a_exp, b_exp, b_frac)
exp = a_exp
else:
a_frac = Arithmetic.shift_fraction(b_exp, a_exp, a_frac)
exp = b_exp
return exp, a_frac, b_frac
def __truediv__(self, other: "Float") -> "Float":
"""
Binary Div 연산 ( / )을 위한 operator overloading
:param other: Float 타입 가정
:return: 새로운 Float 객체로 return
"""
if other.is_zero():
if self.is_zero():
return self.nan()
if self.sign ^ other.sign:
return -self.inf()
return self.inf()
remain = BitOperation.fraction_bits(self.fractions)
div = BitOperation.fraction_bits(other.fractions)
exp, _ = Arithmetic.sub_bits(self.exponents, other.exponents, self.exponent_len)
bias = Arithmetic.str_to_integer('127', self.exponent_len)
exp, _ = Arithmetic.raw_add_bits(exp, bias)
res = BitOperation.empty_bits(self.fraction_len+1)
one = BitOperation.fit_bits(BitOperation.num_map['1'], self.fraction_len+1)
for i in range(self.fraction_len, -1, -1):
if BitOperation.raw_ge_bits(remain, div):
remain, _ = Arithmetic.raw_sub_bits(remain, div)
quotient = BitOperation.raw_lshift_bits(one, i)
res = BitOperation.raw_or_bits(res, quotient)
remain = BitOperation.raw_lshift_bits(remain, 1)
else:
div = BitOperation.raw_rshift_bits(div, 1)
if BitOperation.first_bit_index(res) != 0:
res = BitOperation.raw_lshift_bits(res, 1)
exp, _ = Arithmetic.sub_bits(exp, BitOperation.num_map['1'], self.exponent_len)
return Float(exp, res[1:], self.sign ^ other.sign)