def str_to_minor(real: List[Bit], val: str, digit: int,
length: int) -> (List[Bit], int):
"""
소수점 아래의 값을 표현하는 문자열을 읽어 Bit List를 생성하는 함수
:param real: 소수점 위의 값의 Bit List
:param val: 소수점 아래의 값을 표현하는 문자열
:param digit: 소수점 위의 자리수
:param length: 원하는 Bit List의 길이
:return: 문자열 실수값에 해당하는 Bit List, 자리수
"""
real, ten = BitOperation.equalize_bit_length(
real, BitOperation.num_map['10'], length)
base = BitOperation.fit_bits(BitOperation.num_map['1'], length)
twenty = BitOperation.raw_lshift_bits(ten, 1)
remain = BitOperation.empty_bits(length)
shift = 1
index = 0
while True:
if index < len(val) and index < 6:
remain = Arithmetic.raw_mul_bits(remain, twenty)
next_digit = BitOperation.lshift_bits(
BitOperation.num_map[val[index]], shift, length)
remain, _ = Arithmetic.raw_add_bits(remain, next_digit)
index += 1
shift += 1
base = Arithmetic.raw_mul_bits(base, ten)
else:
remain = BitOperation.raw_lshift_bits(remain, 1)
if BitOperation.is_empty(BitOperation.raw_or_bits(
remain, real)):
return real, -127
real = BitOperation.raw_lshift_bits(real, 1)
if BitOperation.raw_ge_bits(remain, base):
real, _ = Arithmetic.add_bits(real, BitOperation.num_map['1'],
length)
remain, _ = Arithmetic.sub_bits(remain, base, length)
if BitOperation.first_bit_index(real) == 0:
remain = BitOperation.raw_lshift_bits(remain, 1)
if BitOperation.raw_ge_bits(remain, base):
real = BitOperation.or_bits(real,
BitOperation.num_map['1'],
length)
break
elif BitOperation.is_empty(real):
digit -= 1
return real, digit
def __add__(self, other: "Float") -> "Float":
"""
Binary Add 연산 ( + )을 위한 operator overloading
exponent를 같은 값으로 만든 후 fraction 덧셈 연산
:param other: Float 타입 가정
:return: 새로운 Float 객체로 return
"""
exp, a_frac, b_frac = Arithmetic.equalize_exponent(self.exponents, self.fractions, other.exponents,
other.fractions)
if BitOperation.raw_ge_bits(a_frac, b_frac):
sign = self.sign
else:
sign = other.sign
if self.sign ^ other.sign:
res, overflow = Arithmetic.sub_bits(a_frac, b_frac, self.fraction_len+1)
if sign:
res = Arithmetic.decomplement_bits(res, self.fraction_len+1)
else:
res, overflow = Arithmetic.add_bits(a_frac, b_frac, self.fraction_len+1)
if overflow:
res.insert(0, overflow)
res = res[:-1]
exp, _ = Arithmetic.add_bits(exp, BitOperation.num_map['1'], self.exponent_len)
first = BitOperation.first_bit_index(res)
if first != 0:
res, _ = Arithmetic.add_bits(res, BitOperation.num_map['1'], self.fraction_len + 1)
exp, _ = Arithmetic.raw_sub_bits(exp, Arithmetic.str_to_integer(str(first), self.exponent_len))
frac = BitOperation.raw_lshift_bits(res, first)[1:]
return Float(exp, frac, 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)