def from_decimal(cls, dec):
from decimal import Decimal
if isinstance(dec, numbers.Integral):
dec = Decimal(int(dec))
elif not isinstance(dec, Decimal):
raise TypeError(
"%s.from_decimal() only takes Decimals, not %r (%s)" %
(cls.__name__, dec, type(dec).__name__))
return cls(*dec.as_integer_ratio())
def from_decimal(cls, dec):
"""Converts a finite Decimal instance to a rational number, exactly."""
from decimal import Decimal
if isinstance(dec, numbers.Integral):
dec = Decimal(int(dec))
elif not isinstance(dec, Decimal):
raise TypeError(
"%s.from_decimal() only takes Decimals, not %r (%s)" %
(cls.__name__, dec, type(dec).__name__))
return cls(*dec.as_integer_ratio())
def from_decimal(cls, dec):
"""Converts a finite Decimal instance to a rational number, exactly."""
from decimal import Decimal
if isinstance(dec, numbers.Integral):
dec = Decimal(int(dec))
elif not isinstance(dec, Decimal):
raise TypeError(
"%s.from_decimal() only takes Decimals, not %r (%s)" %
(cls.__name__, dec, type(dec).__name__))
return cls(*dec.as_integer_ratio())
class Note:
decimal_two = Decimal(2)
def __init__(self, note_num=60, note_len=Decimal(0.25), is_rest=False):
self.midi_num = note_num
self.note_len = Decimal(note_len)
self.is_rest = is_rest
# checks if the note has a valid length
# returns true if the note is a multiple of a nonpositive power of two
def is_valid_length(self):
numer, denom = map(Decimal, self.note_len.as_integer_ratio())
log = denom.log10() / self.decimal_two.log10()
return math.ceil(log) == math.floor(log) and numer <= denom
def __str__(self):
return "(Note number = {}, length = {}, is_rest = {})".format(self.midi_num,self.note_len, self.is_rest)
adjusted() return the adjusted exponent
as_integer_ratio() return a pair (n, d) of integers that represent the given Decimal instance as a fraction
as_tuple() return a named tuple DecimalTuple(sign, digits, exponent)
copy_abs() return the absolute value of the argument
copy_sign(other) return a copy of the first operand with the sign set to be the same as other
exp() return the value of the (natural) exponential function e**x at the given number
quantize(exp, rounding=None) round a number to a fixed exponent
Rounding modes
decimal.ROUND_CEILING round towards Infinity
decimal.ROUND_FLOOR round towards -Infinity
decimal.ROUND_UP round away from zero
decimal.ROUND_DOWN round towards zero
decimal.ROUND_HALF_UP round to nearest with ties going away from zero.
decimal.ROUND_HALF_DOWN round to nearest with ties going towards zero
decimal.ROUND_HALF_EVEN round to nearest with ties going to nearest even integer
"""
import decimal
from decimal import Decimal
a = Decimal(-139) + Decimal('-2e-5') + Decimal('1.53')
print(a)
print(a.adjusted()) # the position of the most significant digit with respect to the decimal point
print(a.as_integer_ratio())
print(a.as_tuple()) # sign 0 for positive or 1 for negative
print(a.copy_abs(), a.quantize(Decimal('1.000'), rounding=decimal.ROUND_UP))
b = Decimal(15)
print(a, b, a + b, a - b, a * b, a / b)
from decimal import Decimal, getcontext
# incorrect
getcontext().prec = 100
t = 0
for i in range(2, 100):
s = Decimal(i).sqrt()
if s.as_integer_ratio()[1] != 1:
for i in str(s)[2:]:
t += int(i)
print(t)
print(t)
def lecture_graphe(path):
f = open(path)
# Parse du nombre de sommets
try:
nb_sommets = Decimal(f.readline())
if nb_sommets.as_integer_ratio()[1] != 1:
raise Exception
nb_sommets = int(nb_sommets)
if nb_sommets <= 0:
raise Exception
except:
print('SyntaxError:', 'Erreur à la ligne 1, le nombre de sommets doit être un nombre entier positif non nul')
f.close()
return None
# Parse du nombre d'arcs
try:
nb_arcs = Decimal(f.readline())
if nb_arcs.as_integer_ratio()[1] != 1:
raise Exception
nb_arcs = int(nb_arcs)
if nb_arcs < 0:
raise Exception
except:
print('SyntaxError:', 'Erreur à la ligne 2, le nombre de d\'arcs doit être un nombre entier')
f.close()
return None
arcs = []
i = 2
# Déclaration des arcs
for line in f.readlines():
i += 1
line = line.strip().split(' ')
# Nombre d'arguments dans la lignes
if len(line) != 3:
print('SyntaxError:', f'Erreur à la ligne {i}, l\'arc ne contient pas le bon nombre de valeurs')
f.close()
return None
# Parse de l'argument 1
try:
line[0] = Decimal(line[0])
if line[0].as_integer_ratio()[1] != 1:
raise Exception
line[0] = int(line[0])
if not 0 <= line[0] < nb_sommets:
raise Exception
except:
print('SyntaxError:', f'Erreur à la ligne {i}, le sommet de départ n\'existe pas')
f.close()
return None
# Parse de l'argument 2
try:
line[1] = Decimal(line[1])
if line[1].as_integer_ratio()[1] != 1:
raise Exception
line[1] = int(line[1])
if not 0 <= line[1] < nb_sommets:
raise Exception
except:
print('SyntaxError:', f'Erreur à la ligne {i}, le sommet d\'arrivée n\'existe pas')
f.close()
return None
# Parse de l'argument 3
try:
line[2] = Decimal(line[2])
except:
print('SyntaxError:', f'Erreur à la ligne {i}, la pondération de l\'arc doit être un nombre')
f.close()
return None
# Ajout de l'arc à la liste
arcs.append(line)
# Vérification du nombre d'arcs
difference_arcs = len(arcs) - nb_arcs
if (difference_arcs != 0):
accord_pluriel = "s" if abs(difference_arcs) > 1 else ""
print('SyntaxError:', f'{abs(difference_arcs)} arc{accord_pluriel} {"manquant" if difference_arcs < 0 else "supplémentaire"}{accord_pluriel} dans la déclaration du graphe')
f.close()
return None
f.close()
return nb_sommets, nb_arcs, arcs
