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num7.py
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num7.py
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''' --- SUPREME PRECISION GENERAL PURPOSE ARITHMETIC-LOGIC DECIMAL CLASS --- (SEE DOC AT THE END) '''
class Num:
''' object self attributes list allowed '''
__slots__ = ('d', 'n', 'n0', 'n1', 'n2', 'L_n0', 'L_n1')
''' class VARIABLES list '''
pi = '3.141592654'
e = '2.718281828'
''' class METHODS list '''
def f_fund_fr(self, i, y) -> 'Num':
''' french financing month mortgage (high precision) '''
i = Num(i) / 100
return (self*i) / (1-(1+i)**-y) / 12 #
def f_fund_IEEE754(S, i, y) -> float:
''' french financing month mortgage (high speed) '''
i = i / 100
return (S*i) / (1-(1+i)**-y) / 12
def f_perf(self, sob) -> 'Num':
''' percentage performance value (direct ratio) '''
sob = Num(sob) #allowing float string as: '2.3'
return (-self + sob) / self * 100
def f_perf_time(self, sob) -> tuple:
''' percentage and relative magnitude order time performance value (inverse ratio) '''
sob = Num(sob) #allowing float string as: '2.3'
self= Num(self)
R = ((self - sob) / sob * 100)
return R, -sob/self+1 if sob>self else self/sob-1 # tuple
def f_price_over(self, t = 22) -> 'Num':
''' add or sub a percentage value to a base price '''
t = Num(t) #allowing float string as: '2.3'
self += self * t / 100
return self
def f_price_spinoff(self, t = 22) -> 'Num':
''' spin off percentage tax value from a base price '''
t = Num(t) #allowing float string as: '2.3'
return self / ((100+t) / 100)
def f_fileread(filename = 'nums.txt') -> list:
''' read a number strings column from disk '''
FILE = [ls for line in open(filename, 'r') if (ls:=line.strip())]
cart = [Num(str(N)) if '.' in N else Num(str(N)+'.0') for N in FILE]
return cart
def f_filewrite(L: list, filename = 'nums.txt') -> None:
''' write a number strings column on disk '''
lines = [f'{str(i)}\n' for i in L]
with open(filename, 'a') as FILE:
FILE.writelines(lines)
return None
def str(self) -> str:
''' return Num string '''
return self.__str__()
def repr(self) -> str:
''' return Num representation string '''
return self.__repr__()
def is_numstr(n) -> bool:
''' is_numstr to check numeric string validation '''
if type(n) != str:
return False
if 'E' in n.upper():
n = Num.exp2num(n)
nv = n.split('.')
if len(nv) != 2 or not (type(int(nv[0])) == int and nv[1].isdigit()):
return False
n0 = nv[0].strip().replace('_', ''); L_n0 = len(n0) #clear space, '_'
n1 = nv[1] ; L_n1 = len(n1)
if n0[0] == '-': #negative
n2 = '-'; n0 = n0[1:]
elif n0[0] == '+': #positive
n2 = '+'; n0 = n0[1:]
else:
n2 = '' #positive
if L_n0 > 1:
n0 = n0.lstrip('0') #clear LEFT zeros
if not len(n0): #if ''
n0 = '0'
if L_n1 > 1:
n1 = n1.rstrip('0') #clear RIGTH zeros
if not len(n1): #if ''
n1 = '0'
n = n2 + n0 + '.' + n1 #set all number cleaned
if n0 == '0' and n1 == '0': # zero get not any sign == BE CAREFUL!
if n2 == '-' or n[0] == '+':
return False
return True
def is_numint(self) -> bool:
''' is_numint checks if integer num '''
if self.n1 == '0':
return True
return False
def is_numfloat(self) -> bool:
''' is_numfloat checks if floating point num '''
if self.n1 != '0':
return True
return False
def is_numeven(self) -> bool:
''' is_numeven checks if even num '''
if self.is_numint():
if self % 2:
return False
return True
raise ValueError("Num.is_numeven => Num, must be integer value: ", self)
def is_numodd(self) -> bool:
''' is_numodd checks if odd num '''
if self.is_numint():
if self % 2:
return True
return False
raise ValueError("Num.is_numodd => Num, must be integer value:", self)
def exp2num(s) -> str:
''' convert a scientific notation number to string numeric '''
if type(s) != str:
raise ValueError("Num.exp2num => type not valid:", s)
s = s.strip().upper()
be = s.split('E'); be0 = be[0]; be1 = be[1]
if len(be) > 2:
raise ValueError("Num.exp2num => scientific notation not valid:", s)
try:
float(be0); float(be1)
except:
raise ValueError("Num.exp2num => scientific notation not valid:", s)
if be1 == '-0' or be1 == '+0':
raise ValueError("Num.exp2num => zero can not be signed:", s)
POS = False if '-' in be0 else True
EXP = int(be1);
bf = be[0].split('.');
size = len(bf)
if size != 1:
bf0 = bf[0]; bf1 = bf[1]
bf0 = '-' + bf0[1:].lstrip('0') if '-' in bf0 else bf0
bf0 = '' + bf0[1:].lstrip('0') if '+' in bf0 else bf0
else:
bf0 = be0[1:].lstrip('0') if '+' in be[0] else be[0]
bf0 = '-' + be0[1:].lstrip('0') if '-' in be[0] else bf0
L_bf0 = len(bf0) #base length
if EXP >= 0:
if POS: #positive integer base
if size == 1:
return bf0 + EXP*'0' + '.0' #'2e3'
#size == 2 floating point base
L_bf1 = len(bf[1]) #base decs length
r = bf0 + bf1 + (EXP-L_bf1)*'0'
DOT = 1 if (EXP-L_bf1) < 0 else 0
s_CHECK = r[0:L_bf0+EXP] + '.'*DOT + r[L_bf0+EXP:]
if '.' in s_CHECK:
return s_CHECK #'2.3456e3'
return s_CHECK + '.0' #'2.3e3'
#negative integer base
be0 = be0[0]+'0'+be0[1:].lstrip('0')
if size == 1: #negative integer base
return be0 + EXP*'0' + '.0' #'-2e3' #'-1123e2'
#size == 2 floating point base
L_bf1 = len(bf[1]) #base decs length
r = bf[0] + bf[1] + (EXP-L_bf1)*'0'
DOT = 1 if (EXP-L_bf1) < 0 else 0
s_CHECK = r[0:L_bf0+EXP] + '.'*DOT + r[L_bf0+EXP:]
if '.' in s_CHECK:
return s_CHECK #'-1.123e2'
return s_CHECK + '.0' #'-1.123e3'
#EXP < 0
DOT = L_bf0+EXP; #clear zero on positives only
if POS: #POS > 0:
if DOT > 0:
if size != 1:
return bf0[0:DOT] + '.' + bf[0][EXP:] + bf[1]
return bf0[0:DOT] + '.' + bf0[DOT:] #'224422e-4'
if size != 1:
return '0.' + (-DOT)*'0' + bf0 + bf1 #'112.3e-13'
return '0.' + (-DOT)*'0' + bf0 #'2e-3'
#POS=false base < 0
DOT -= 1; L_bf0 -= 1
if size == 1: #negative integer base
if DOT > 0:
return be0[0:EXP] + '.' + be0[EXP:] #'-22e-1'
s_TEST = be0[1:]
return '-0.' + (-DOT)*'0' + s_TEST #'-2522e-4' '-2522e-5'
#size == 2 floating point base
if DOT > 0:
return bf[0][0:EXP] + '.' + bf[0][EXP:] + bf[1] #'-112.9e-2'
return '-0.' + (-DOT)*'0' + bf[0][1:] + bf[1] #'-112.9e-3'
def ieee754(self) -> str:
''' float to IEEE754 conversion '''
return f'{float(self):.80f}'.rstrip('0')
def float2num(f) -> 'Num':
''' float to Num conversion '''
return Num(str(f))
def float2num_list(L: list) -> list:
''' float to Num list conversion '''
return [Num((i) if type(i)==int else str(i)) for i in L]
def num2exp(ob) -> str:
''' convert a Num object to scientific notation string '''
if type(ob) != Num:
raise ValueError("Num.num2exp => type not valid:", ob)
if ob.n1 == '0': #EXP >= 0
e = ob.L_n0 - 1
CHECK = (ob.n0[0] + '.' + ob.n0[1:]).rstrip('0')
if CHECK[-1] == '.':
CHECK += '0'
return ob.n2 + CHECK + 'e' + str(e)
if ob.n0 == '0': #EXP < 0
n1 = ob.n1.lstrip('0')
L_n1 = len(n1)
e = ob.L_n1 - L_n1 + 1
if L_n1 == 1:
return ob.n2 + n1 + '.0' + 'e' + str(-e)
return ob.n2 + n1[-L_n1:-L_n1+1] + '.' + n1[-L_n1+1:] + 'e' + str(-e)
e = ob.L_n0 - 1
return ob.n2 + ob.n0[0] + '.' + ob.n0[1:] + ob.n1 + 'e' + str(e)
def numint(self) -> 'Num':
''' Num integer truncation '''
return Num(self.n2 + self.n0 + '.0')
def trunc(self, d = 0) -> 'Num':
''' Num floating point truncation '''
m = Num(10)**d
return Num(int(self * m), d) / m
def round_floor(self, d = 0) -> 'Num': #relative value (real number R)
''' Num floor rounding '''
''' relative round down: 0.12 => 0.1 -0.12 => -0.2 '''
if self >= 0: #positives and zero
return self.trunc(d)
#negatives
e = Num('1.0', d) / Num('10.0')**d
if d >= 0:
t = self.trunc(d) - e; t2 = self - e
return self if t == t2 else t
if e < self:
return self
t = self.trunc(d) - e; t2 = self - e
return self if t == t2 else t
def round(self, d = 2) -> 'Num':
''' Num half up rounding '''
''' COMMON STANDARD -relative round_half_ceil: 0.15 => 0.2 -0.15 => -0.1 '''
temp = (self + Num('0.5') * Num('10.0')**-d).round_floor(d)
return temp
def round_bank(self, d = 2) -> 'Num':
''' Num half even rounding '''
if d < 0:
d = -d; e = 10**d
return (self / Num(e)).round_bank(0) * e
of = d - self.L_n1
if of >= 0:
return Num(self.n) #0.5 => 0.5 (no round)
else:
if not d: #integer rounding (d=0)
a = int(self.n0); b = int(self.n1[0:1]); c = self.n1[1:].rstrip('0')
if b > 5:
a += 1
return Num(self.n2 + str(a) + '.0') #12.51 => 13.0 integer
elif b == 5:
if a % 2: #odd
a += 1
return Num(self.n2 + str(a) + '.0') #13.5 => 14.0 integer
elif c != '': #even overflow
a += 1
return Num(self.n2 + str(a) + '.0') #12.51 => 13.0 integer
else: #even
if not a:# a == 0
return Num('0.0')
return Num(self.n2 + str(a) + '.0') #12.5 => 12.0 integer -0.5 => 0.0
else:
if int(self.n0) >= 1:
return Num(self.n2 + str(a) + '.0') #12.3 => 12.0 integer
return Num('0.0') #0.3 => 0.0 #Num(self.n2 + '0.0')
# floating point rounding (d>0)
a = int(self.n1[d-1:d]); b = int(self.n1[d:d+1]); c = self.n1[d+1:].rstrip('0')
if b > 5:
a += 1; of2 = 1
if a > 9: #flag carry
while a > 9:
b = 0; s = self.n1[d-of2-1:d-of2]
if not s:
return Num(self.n2 + str(int(self.n0)+1) + '.0') #3.99 => 4.0
a = int(s); a += 1; of2 += 1
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-of2] + str(a)) #3.095 => 3.1
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-1] + str(a)) #3.1415 => 3.142
elif b == 5:
if a % 2: #odd
a += 1; of2 = 1
while a > 9:
b = 0; s = self.n1[d-of2-1:d-of2]
if not s:
return Num(self.n2 + str(int(self.n0)+1) + '.0') #3.95 => 4.0
a = int(s); a += 1; of2 += 1
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-of2] + str(a)) #3.095 => 3.1
elif c != '': #even overflow
a += 1
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-1] + str(a)) #12.51 => 13.0 integer
else:
if not a:# a == 0
return Num('0.0')
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-1] + str(a)) #even 5.65 => 5.6 -0.05 => 0.0
else:
try:
return Num(self.n2 + self.n0 + '.' + self.n1[0:d-1] + str(a)) #3.1415 => 3.14 #-0.02 => -0.0 ERROR!
except:
return Num('0.0') #-0.02 => 0.0 OK.
def round_ceil(self, d = 0) -> 'Num':
''' Num ceil rounding '''
''' relative round up: 0.12 => 0.2 -0.12 => -0.1 '''
if self <= 0: #negatives and zero
return self.trunc(d)
#positives
e = Num('1.0', d) / Num('10.0') ** d
if d <= 0:
t = self.trunc(d) + e; t2 = self + e
return self if t == t2 else t
if e > self:
return self
t = self.trunc(d) + e; t2 = self + e
return self if t == t2 else t
def reduce(itb, init=None, f=lambda x, y: x+y):
''' used by sum() '''
i = iter(itb)
x = next(i) if init is None else init
for y in i:
x = f(Num(x), Num(y))
return x
def sum(*multi_args: tuple) -> 'Num':
''' calculator sum method '''
return Num.reduce(multi_args)
def mean(*multi_args: tuple) -> 'Num':
''' calculator mean method '''
return Num.reduce(multi_args)/len(multi_args)
def min(L: list) -> 'Num':
''' calculator min method '''
return min([Num(i) for i in L])
def max(L: list) -> 'Num':
''' calculator max method '''
return max([Num(i) for i in L])
def root_i(n, i = 3, d = 80) -> 'Num':
''' calculator ith root method '''
if not i:
return('1.0')
n = Num(n, d); i = Num(i)
if i.is_numeven() and n.n2:
raise ValueError("Num.root_i => Negative number:", n)
if i < 0:
n = 1/n
i = -i
i = int(i)
sign = '-' if n < 0 else ''
n = abs(Num(n))
n = n.str()
n0, _, n1 = n.partition('.')
n = n0 + n1
W = i * d - len(n1) #set precision
n = n + W*'0' if W >= 0 else n[:W] #integer conversion
z = n = int(n)
s = z + 1
while z<s: #Newton's method
s = z
try:
t = (i-1)*s + n//s**(i-1)
except:
raise ValueError("Num.root_i => d parameter too low:", d)
z = t//i
s = str(s)
if d: #floating point conversion with clearing zeros
s = '0' * (1 + d - len(s)) + s
r = (s[:-d] + '.' +s[-d:]).rstrip('0')
s = r + '0' if r[-1] == '.' else r
return Num(sign + s)
return Num(sign + s + '.0') #integer conversion
def sqrt(n, d = 80) -> 'Num':
''' calculator square root method '''
n = Num(n)
if n.L_n0 > 80 and d == 80:
return Num.sqr(n, n.L_n0)
return Num.sqr(n, d)
def sqr(n, d = 80) -> 'int Num':
''' square root method => used by sqrt() '''
''' sqr(n, d = 80) method runs on python3 trying to be more human style
and so overcoming sqrt() integer arithmetic limits. (math library function)
'''
d = abs(int(d))
if type(n) == int: #only integer square root (not floating point)
if n < 0:
raise ValueError("Num.sqr => Negative number:", n)
if not n: # zero
return 0 #
L = len(str(n))+1 >> 1 #two division to obtain integer root size
r = 10**L #Newton's method
q = n // r
while r > q:
r = r+q >> 1 #two division
q = n // r
return r #
if type(n) == Num: #str
nv = str(n).split('.')
if int(nv[0]) < 0:
raise ValueError("Num.sqr => Negative number:", n)
n0 = nv[0]; L_n0 = len(n0)
n1 = nv[1]; L_n1 = len(n1)
if n0 + '.' + n1 == '0.0': # 0.0
return Num('0.0')
L_rx = len(str(n0))+1 >> 1 #X2Division - root digit length
L_n1 = len(n1) #floating digit number
if n0 == '0': # 0 < n < 1
shift = L_n1+1 >> 1 #X2Division - decimal point position
ds = d - shift
if L_n1 % 2: #odd (dispari):
op = n1 + '0' + ds*'00'
else: #even (pari)
op = n1 + ds*'00'
r1 = str(Num.sqr(int(op), 0))
r1_len = len(r1)
if ds > 0:
return Num('0.' + (shift-r1_len+ds)*'0' + r1)
return Num('0.' + ((shift-r1_len)*'0' + r1)[0:d])
elif n1 == '0':
root = str(Num.sqr(int(n0 + d * '00'), 0))
if not d:
return Num(root[0:L_rx] + '.0')
return Num(root[0:L_rx] + '.' + root[L_rx:])
else:
if L_n1 % 2: #odd (dispari)
temp = str(Num.sqr(int(n0 + n1 + '0' + (d-1)*'00'), 0))
return Num(temp[0:L_rx] + '.' + temp[L_rx:L_rx+d])
else: #even (pari)
temp = str(Num.sqr(int(n0 + n1 + (d-1)*'00'), 0))
return Num(temp[0:L_rx] + '.' + temp[L_rx:L_rx+d])
if type(n) == float:
raise ValueError("Num.sqr => 'float', type not valid:", n)
else:
raise ValueError("Num.sqr => Type not valid:", n)
def _divi_(n, div, d=3) -> str:
''' division between signed integer number '''
'''
It runs the division between signed integer numbers only and the quotient
is a floating point string of arbitrary precision (default 3 digits).
'''
if not div:
raise Exception('Num._divi_ => ZeroDivisionError: Num division by zero')
n = int(n); div = int(div)
n_si = True if n < 0 else False
div_si = True if div < 0 else False
n = abs(n); div = abs(div); d = abs(int(d))
q = n // div; s = str(q) + '.'; k = d #result s
while k > 0:
r = n % div; n = r * 10; r = n // div; s += str(r); k -= 1
if not (n_si or div_si) or n_si and div_si: #positive
if not d:
return s + '0'
return s
else: #negative
if not d:
r = '-' + s + '0'
if r == '-0.0':
return '0.0'
return r
return '-' + s
def __hash__(self) -> int:
if int(self.n1): #floating point
return hash(self.n)
else: #integer
return int(self.n2 + self.n0)
def __init__(self, n, d = 80) -> 'Num':
''' Num object constructor '''
#VALIDATION n
if type(n) == int:
n = str(n) + '.0' # SUFFIX .0 FOR 'int' type
if type(n) == float:
raise ValueError("Num.__init__ => float, type not valid:", n)
if type(n) == Num:
self.d = n.d
self.n = n.n
self.n0 = n.n0
self.n1 = n.n1
self.n2 = n.n2
self.L_n0 = n.L_n0
self.L_n1 = n.L_n1
return None
if type(n) != str:
raise ValueError("Num.__init__ => type not valid:", n)
if 'E' in n.upper():
n = Num.exp2num(n)
nv = n.split('.')
if len(nv) != 2 or not (type(int(nv[0])) == int and nv[1].isdigit()): #.isnumeric() .isdigit() .isdecimal()
raise ValueError("Num.__init__ => number format not valid:", n)
self.n0 = nv[0].strip().replace('_', ''); self.L_n0 = len(self.n0) #clear space, '_'
self.n1 = nv[1] ; self.L_n1 = len(self.n1)
if self.n0[0] == '-': #negative
self.n2 = '-'; self.n0 = self.n0[1:]
elif self.n0[0] == '+': #positive
self.n2 = ''; self.n0 = self.n0[1:]
else:
self.n2 = '' #positive
if self.L_n0 > 1:
self.n0 = self.n0.lstrip('0') #clear LEFT zeros
if not len(self.n0): #if ''
self.n0 = '0'
if self.L_n1 > 1:
self.n1 = self.n1.rstrip('0') #clear RIGHT zeros
if not len(self.n1): #if ''
self.n1 = '0'
self.L_n0 = len(self.n0); self.L_n1 = len(self.n1) #check for new len
self.n = self.n2 + self.n0 + '.' + self.n1 #set all number cleaned
if self.n0 == '0' and self.n1 == '0': # zero get not any sign == BE CAREFUL!
if self.n2 == '-' or n[0] == '+':
raise ValueError("Num.__init__ => zero can not be signed:", n)
self.d = d if d > self.L_n1 else self.L_n1 #precision
def __bool__(self) -> bool:
''' not logic unary operator '''
return False if self.n == '0.0' else True
def __invert__(self) -> 'Num':
''' (~) not unary bitwise operator '''
if not Num.is_numint(self) or self.n2: #only positive integer
raise TypeError("Num.__invert__ => only positive integer allowed:", self)
t = ''
for bit in bin(int(self.n0))[2:]:
t += '0' if bit == '1' else '1'
return Num(int(t, 2))
def __and__(self, sob) -> int:
''' (&) overloading binary & operator (Bitwise AND) '''
if not Num.is_numint(self) or self.n2: #only positive integer
raise TypeError("Num.__and__ => only positive integer allowed:", self)
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if not Num.is_numint(sob) and sob >= 0: #only integer
raise TypeError("Num.__and__ => only positive integer allowed:", sob)
if type(sob) != Num:
raise TypeError("Num.__and__ => type not valid:", sob)
return int(self.n0) & int(sob.n0)
def __rand__(self, sob) -> int:
''' (&) swap operands binary AND bitwise operator '''
return Num(sob).__and__(self)
def __or__(self, sob) -> int:
''' (|) overloading binary | operator (Bitwise OR) '''
if not Num.is_numint(self) or self.n2: #only positive integer
raise TypeError("Num.__or__ => only positive integer allowed:", self)
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if not Num.is_numint(sob): #only integer
raise TypeError("Num.__or__ => only positive integer allowed:", self)
if type(sob) != Num:
raise TypeError("Num.__or__ => type not valid:", sob)
return int(self.n0) | int(sob.n0)
def __ror__(self, sob) -> int:
''' (|) swap operands binary OR bitwise operator '''
return Num(sob).__or__(self)
def __xor__(self, sob) -> int:
''' (^) overloading binary ^ operator (Bitwise XOR) '''
if not Num.is_numint(self) or self.n2: #only positive integer
raise TypeError("Num.__xor__ => only positive integer allowed:", self)
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if not Num.is_numint(sob): #only integer
raise TypeError("Num.__xor__ => only positive integer allowed:", self)
if type(sob) != Num:
raise TypeError("Num.__xor__ => type not valid:", sob)
return int(self.n0) ^ int(sob.n0)
def __rxor__(self, sob) -> int:
''' (^) swap operands binary XOR bitwise operator '''
return Num(sob).__xor__(self)
def __abs__(self) -> 'Num':
''' (built-in abs function) Return the absolute value of a number '''
return Num(self.n if self.n2 == '' else self.n[1:])
def abs(self) -> 'Num':
''' abs method calculator '''
return Num(self).__abs__()
def add(a, b) -> 'Num':
''' (+) calculator addition method '''
return Num(a) + Num(b)
def __add__(self, sob) -> 'Num':
''' (+) overloading binary plus operator -used by built-in method sum() '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__add__( => type not valid:", sob)
if self.L_n1 < sob.L_n1:
x1 = int(self.n2 + self.n0 + self.n1 + (sob.L_n1-self.L_n1)*'0')
x2 = int(sob.n2 + sob.n0 + sob.n1)
elif self.L_n1 > sob.L_n1:
x1 = int(self.n2 + self.n0 + self.n1)
x2 = int(sob.n2 + sob.n0 + sob.n1 + (self.L_n1-sob.L_n1)*'0')
else:
x1 = int(self.n2 + self.n0 + self.n1)
x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = x1+x2
if not x3: #zero result addition
return Num('0.0')
xt = str(x3)
xt_L = len(xt)
xt_D = sob.L_n1 if sob.L_n1 > self.L_n1 else self.L_n1
if x3 < 0: #Negative add
ze = xt_D-xt_L+1
if ze >= 0: #-1 < Negative add < 0
xtr = '-0' + '.' + ze*'0' + xt[1:]
return Num(xtr)
else: #Positive sub
ze = xt_D-xt_L
if ze >= 0: #0 < Positive add < 1
xtr = '0' + '.' + ze*'0' + xt[0:]
return Num(xtr)
return Num(xt[0:-xt_D] + '.' + xt[-xt_D:])
def inc(self, sob = 1) -> 'Num':
''' increment variable adding method -object modify by self reference '''
telf = self + sob
self.d = telf.d
self.n = telf.n
self.n0 = telf.n0
self.n1 = telf.n1
self.n2 = telf.n2
self.L_n0 = telf.L_n0
self.L_n1 = telf.L_n1
return self
def incmul(self, sob = 10) -> 'Num':
''' increment variable multiplying method -object modify by self reference '''
telf = self * sob
self.d = telf.d
self.n = telf.n
self.n0 = telf.n0
self.n1 = telf.n1
self.n2 = telf.n2
self.L_n0 = telf.L_n0
self.L_n1 = telf.L_n1
return self
def dec(self, sob = 1) -> 'Num':
''' decrement variable subtracting method -object modify by self reference '''
telf = self - sob
self.d = telf.d
self.n = telf.n
self.n0 = telf.n0
self.n1 = telf.n1
self.n2 = telf.n2
self.L_n0 = telf.L_n0
self.L_n1 = telf.L_n1
return self
def decdiv(self, sob = 10) -> 'Num':
''' decrement variable dividing method -object modify by self reference '''
telf = self / sob
self.d = telf.d
self.n = telf.n
self.n0 = telf.n0
self.n1 = telf.n1
self.n2 = telf.n2
self.L_n0 = telf.L_n0
self.L_n1 = telf.L_n1
return self
def clear(self) -> 'Num':
''' clear variable '''
telf = self
self.d = telf.d
self.n = '0.0'
self.n0 = '0'
self.n1 = '0'
self.n2 = ''
self.L_n0 = 1
self.L_n1 = 1
return self
''' (+) swap operands binary plus operator -mandatory by built-in method sum() '''
__radd__ = __add__
def sub(a, b) -> 'Num':
''' (-) calculator subtract method '''
return Num(a) - Num(b)
def __sub__(self, sob) -> 'Num':
''' (-) overloading binary minus operator '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__add__( => type not valid:", sob)
if self.L_n1 < sob.L_n1:
x1 = int(self.n2 + self.n0 + self.n1 + (sob.L_n1-self.L_n1)*'0')
x2 = int(sob.n2 + sob.n0 + sob.n1)
elif self.L_n1 > sob.L_n1:
x1 = int(self.n2 + self.n0 + self.n1)
x2 = int(sob.n2 + sob.n0 + sob.n1 + (self.L_n1-sob.L_n1)*'0')
else:
x1 = int(self.n2 + self.n0 + self.n1)
x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = x1-x2
if not x3: #zero result subtraction
return Num('0.0')
xt = str(x3)
xt_L = len(xt)
xt_D = sob.L_n1 if sob.L_n1 > self.L_n1 else self.L_n1
if x3 < 0: #Negative sub
ze = xt_D-xt_L+1
if ze >= 0: #-1 < Negative sub < 0
xtr = '-0' + '.' + ze*'0' + xt[1:]
return Num(xtr)
else: #Positive sub
ze = xt_D-xt_L
if ze >= 0: #0 < Positive sub < 1
xtr = '0' + '.' + ze*'0' + xt[0:]
return Num(xtr)
return Num(xt[0:-xt_D] + '.' + xt[-xt_D:])
def __rsub__(self, sob) -> 'Num':
''' (-) swap operands binary minus operator '''
return Num(sob).__sub__(self)
def mul(a, b) -> 'Num':
''' (*) calculator multiplication method '''
return Num(a) * Num(b)
def __mul__(self, sob) -> 'Num':
''' (*) overloading binary multiply operator '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__mul__ => type not valid:", sob)
x1 = int(self.n2 + self.n0 + self.n1); x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = x1*x2
if not x3: #multiply with 0
return Num('0.0')
xt = str(x3); xt_L = len(xt); xt_D = self.L_n1 + sob.L_n1
if x3 < 0: #Negative
ze = xt_D-xt_L+1
if ze >= 0:
return Num('-0' + '.' + ze*'0' + xt[1:])
return Num(xt[0:-xt_D] + '.' + xt[-xt_D:])
ze = xt_D-xt_L
if ze >= 0:
return Num('0' + '.' + ze*'0' + xt[0:])
return Num(xt[0:-xt_D] + '.' + xt[-xt_D:])
def __lshift__(self, sob) -> 'Num':
''' (<<) left shift binary operator -multiplying for 10 powers '''
return self * 10**int(Num(sob)) #
def __rlshift__(self, sob) -> 'Num':
''' (<<) swap operands left shift binary operator '''
return Num(sob).__lshift__(self)
''' (*) swap operands binary multiplication operator '''
__rmul__ = __mul__
def div(a, b) -> 'Num':
''' (/) calculator division method '''
return Num(a) / Num(b)
def __truediv__(self, sob) -> 'Num':
''' (/) overloading binary floating point division operator '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__truediv__ => type not valid:", sob)
if sob == '0.0':
raise Exception('Num.__truediv__ => ZeroDivisionError: Num division by zero')
if self.n == '0.0':
return Num('0.0')
if self.L_n1 > sob.L_n1:
ze = self.L_n1 - sob.L_n1
x1 = int(self.n2 + self.n0 + self.n1); x2 = int(sob.n2 + sob.n0 + sob.n1 + ze*'0')
x3 = Num._divi_(x1, x2, self.d if self.d > sob.d else sob.d)
else:
ze = sob.L_n1 - self.L_n1
x1 = int(self.n2 + self.n0 + self.n1 + ze*'0'); x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = Num._divi_(x1, x2, self.d if self.d > sob.d else sob.d)
return Num(x3)
def __rtruediv__(self, sob) -> 'Num':
''' (/) swap operands floating point division binary operator '''
return Num(sob).__truediv__(self)
def __floordiv__(self, sob) -> 'Num':
''' (//) overloading integer division binary operator '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__floordiv__ => type not valid:", sob)
if self.n == '0.0':
return Num('0.0')
if self.L_n1 > sob.L_n1:
ze = self.L_n1 - sob.L_n1
x1 = int(self.n2 + self.n0 + self.n1); x2 = int(sob.n2 + sob.n0 + sob.n1 + ze*'0')
x3 = Num._divi_(x1, x2, 0)
else:
ze = sob.L_n1 - self.L_n1
x1 = int(self.n2 + self.n0 + self.n1 + ze*'0'); x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = Num._divi_(x1, x2, 0)
return Num(x3)
def __rfloordiv__(self, sob) -> 'Num':
''' (//) swap operands integer division binary operator '''
return Num(sob).__floordiv__(self)
def __mod__(self, sob) -> 'Num':
''' (%) overloading module binary operator (Num floating point division remainder) '''
if type(sob) == int or Num.is_numstr(sob):
sob = Num(sob)
if type(sob) != Num:
raise TypeError("Num.__floordiv__ => type not valid:", sob)
if self.n == '0.0':
return Num('0.0')
if self.L_n1 > sob.L_n1:
ze = self.L_n1 - sob.L_n1
x1 = int(self.n2 + self.n0 + self.n1); x2 = int(sob.n2 + sob.n0 + sob.n1 + ze*'0')
x3 = Num._divi_(x1, x2, 0)
else:
ze = sob.L_n1 - self.L_n1
x1 = int(self.n2 + self.n0 + self.n1 + ze*'0'); x2 = int(sob.n2 + sob.n0 + sob.n1)
x3 = Num._divi_(x1, x2, 0)
return self - (Num(x3) * sob)
def __rmod__(self, sob) -> 'Num':
''' (%) swap operands module operator (integer division remainder) '''
return Num(sob).__mod__(self)
def divmod(self, sob) -> tuple:
''' (// %) calculator divmod return a tuple (self // sob, self % sob) '''
Q = Num(self).__floordiv__(Num(sob))
R = Num(self).__mod__(Num(sob))
return Q, R
def __divmod__(self, sob) -> tuple:
''' (divmod built-in method) return a tuple (self // sob, self % sob) '''
Q = (self).__floordiv__((sob))
R = (self).__mod__((sob))
return Q, R
def __rdivmod__(self, sob) -> 'Num':
''' (divmod built-in method) swap operands '''
return Num(sob).__divmod__(self)
def __rshift__(self, sob) -> 'Num':
''' (>>) right shift binary operator -dividing for ten powers '''
sob = Num(sob)
t = sob + self.L_n1
self.d = t if t > self.d else self.d
return self / 10**int(sob)
def __rrshift__(self, sob) -> 'Num':
''' (>>) swap operands right shift binary operator '''
return Num(sob).__rshift__(self)
def __eq__(self, sob) -> bool: #== !=
''' (== !=) overloading equal and not equal logic binary operators '''
sob = Num(sob)
return True if self.n == sob.n else False
def __gt__(self, sob) -> bool: #>
''' (>) overloading greater logic binary operator '''
sob = Num(sob)
if int(self.n2+self.n0) > int(sob.n2+sob.n0):
return True
if int(self.n2+self.n0) == int(sob.n2+sob.n0):
d_L1 = self.L_n1 - sob.L_n1
if d_L1 > 0:
a = int(self.n2+self.n1); b = int(sob.n2+sob.n1+abs(d_L1)*'0')
if a > b:
return True
elif d_L1 < 0:
a = int(self.n2+self.n1+abs(d_L1)*'0'); b = int(sob.n2+sob.n1)
if a > b:
return True
else:
return True if int(self.n2+self.n1) > int(sob.n2+sob.n1) else False
return False
def __ge__(self, sob) -> bool: #>=
''' (>=) overloading greater or equal logic binary operator '''
return True if self > sob or self == sob else False
def __lt__(self, sob) -> bool: #<
''' (<) overloading less logic binary operator '''
return False if self >= sob else True #
def __le__(self, sob) -> bool: #<=
''' (<=) overloading less or equal logic binary operator '''
return False if self > sob else True #
def __len__(self) -> int:
''' overloading built-in method len() '''
return len(self.n)
def len(self) -> tuple:
''' return a tuple with num lengths before and after floating point dot '''
return len(self.n0), 0 if len(self.n1) == 1 and self.n1 == '0' else len(self.n1)
def __neg__(self) -> 'Num':
''' overloading unary operator - '''
return Num(self.n[1:]) if self.n2 == '-' else Num('-' + self.n)
def __pos__(self) -> 'Num':
''' overloading unary operator + '''
return Num(self.n)
def __int__(self) -> int:
''' (built-in int method) Num to int (truncation) - great loss precision! '''
return int(self.n2 + self.n0)
def int(self) -> int:
''' (truncation) Num to int method - great loss precision! '''
return self.__int__()
def __float__(self) -> float:
''' Num to float (loss precision!) '''
return float(self.n)
def pow(self, e) -> 'Num':
''' pow method calculator '''
return Num(self).__pow__(Num(e))
def __pow__(self, e) -> 'Num': #argument e mandatory,
''' (**) overloading power binary operator and used by built-in function pow() '''
if type(e) != int and type(e) != Num:
raise ValueError("Num.__pow__ => type not valid:", e)
if type(e) == int or type(e) == Num and e.is_numint():
if self == Num('0.0') and e == 0:
raise ValueError("Num.__pow__ => undetermined:", e)
if e < 0:
b = i = Num('1.0') / self #
e = -e
while e > 1:
b *= i
e -= 1
else:
b = Num('1.0')
while e > 0:
b *= self #Num(self.n)
e -= 1
return b
raise ValueError("Num.__pow__ => Num, must be integer value:", e)
def __rpow__(self, sob) -> 'Num':
''' (**) swap operands power binary operator '''
return Num(sob).__pow__(self)
def __round__(self, d = 2) -> 'Num':
''' built-in function round() '''
return self.round(d)
def __trunc__(self) -> int:
''' like math.trunc() function '''
return self.__int__()
def __str__(self) -> str:
''' built-in function str() '''
return self.n
def __repr__(self) -> str: #almost like __str__ (obj representation in REPL)
''' built-in function repr() '''
return str('Num(\'' + self.n + '\')')
def __format__(self, spec) -> str: