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from struct import pack, unpack
from bitarray import bitarray
from bitarray.util import ba2int, int2ba
class Double:
def __init__(self, x=0.0):
if isinstance(x, (float, int)):
self.from_float(float(x))
elif isinstance(x, str):
self.from_string(x)
else:
raise TypeError("float or str expected")
def __float__(self):
a = self.to_bitarray()
return unpack("<d", a.tobytes())[0]
def __str__(self):
a = self.to_bitarray()
a.reverse()
return "%s %s %s" % (a[0], a[1:12].to01(), a[12:].to01())
def __repr__(self):
return 'Double("%s")' % str(self)
def from_float(self, x):
a = bitarray(pack("<d", x), endian="little")
self.from_bitarray(a)
def from_string(self, s):
a = bitarray(s, endian="little")
if len(a) != 64:
raise ValueError("64 bits expected")
a.reverse()
self.from_bitarray(a)
def from_bitarray(self, a):
if len(a) != 64 or a.endian != "little":
raise ValueError("litten endian bitarray of length 64 expected")
self.sign = a[63]
self.exponent = ba2int(a[52:63]) - 1023
self.fraction = a[0:52]
def to_bitarray(self):
if len(self.fraction) != 52:
raise ValueError("fraction must be a bitarray of length 52")
a = bitarray(self.fraction, endian="little")
a.extend(int2ba(self.exponent + 1023, length=11, endian="little"))
a.append(self.sign)
return a
def info(self):
print("float: %r" % float(self))
print(str(self))
print("sign = %d" % self.sign)
print("exponent = %d" % self.exponent)
d = Double()
d.exponent = 0
d.fraction = self.fraction
x = float(d)
if self.exponent == -1023:
x -= 1
print("fraction = %.17f" % x)
exponent = self.exponent
if exponent == -1023:
exponent = -1022
x *= pow(2.0, exponent)
if self.sign:
x = -x
print(" --> %r" % x)
# ---------------------------------------------------------------------------
from math import pi, inf, nan, isnan
from random import getrandbits, randint
import unittest
from bitarray.util import urandom
EXAMPLES = [
( 0.0, "0 00000000000 " + 52 * "0"),
( 1.0, "0 01111111111 " + 52 * "0"),
( 1.5, "0 01111111111 1" + 51 * "0"),
( 2.0, "0 10000000000 " + 52 * "0"),
( 5.0, "0 10000000001 01" + 50 * "0"),
(-5.0, "1 10000000001 01" + 50 * "0"),
# smallest number > 1
(1.0000000000000002, "0 01111111111 " + 51 * "0" + "1"),
# minimal subnormal double
(4.9406564584124654e-324, "0 00000000000 " + 51 * "0" + "1"),
# maximal subnormal double
(2.2250738585072009e-308, "0 00000000000 " + 52 * "1"),
# minimal normal double
(2.2250738585072014e-308, "0 00000000001 " + 52 * "0"),
# maximal (normal) double
(1.7976931348623157e+308, "0 11111111110 " + 52 * "1"),
( inf, "0 11111111111 " + 52 * "0"),
(-inf, "1 11111111111 " + 52 * "0"),
( 1/3, "0 01111111101 " + 26 * "01"),
( pi, "0 10000000000 "
"1001001000011111101101010100010001000010110100011000"),
# largest number exactly representated as integer
(2 ** 53 - 1, "0 10000110011 " + 52 * "1"),
]
class DoubleTests(unittest.TestCase):
def test_zero(self):
d = Double()
self.assertEqual(float(d), 0.0)
self.assertEqual(d.sign, 0)
self.assertEqual(d.exponent, -1023)
self.assertEqual(d.fraction, bitarray(52))
def test_examples(self):
for x, s in EXAMPLES:
for d in Double(x), Double(s):
self.assertEqual(float(d), x)
self.assertEqual(str(d), s)
def test_nan(self):
s = "0 11111111111 1" + 51 * "0"
for x in nan, s:
d = Double(x)
self.assertEqual(str(d), s)
self.assertTrue(isnan(float(d)))
def test_nan_msg(self):
msg = urandom(52)
d = Double()
d.exponent = 1024
d.fraction = msg
x = float(d)
self.assertEqual(type(x), float)
self.assertTrue(isnan(x))
e = Double(x)
self.assertEqual(e.exponent, 1024)
self.assertEqual(e.fraction, msg)
def test_exponent52(self):
for _ in range(1000):
d = Double()
d.fraction = urandom(52, endian="little")
d.exponent = 52
d.sign = getrandbits(1)
i = (1 << 52) + ba2int(d.fraction)
if d.sign:
i = -i
self.assertEqual(float(d), i)
def test_exact_ints(self):
for _ in range(1000):
i = getrandbits(randint(1, 53))
if i == 0:
continue
d = Double(i)
self.assertEqual(d.sign, 0)
a = int2ba(i, endian="little")
a.pop()
n = len(a)
self.assertEqual(d.exponent, n)
a = bitarray(52 - n, endian="little") + a
self.assertEqual(d.fraction, a)
if __name__ == '__main__':
import sys
if len(sys.argv) > 1:
for arg in sys.argv[1:]:
d = Double(eval(arg))
d.info()
else:
unittest.main()
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