def to_float(s, strict=False):
"""
Convert a raw mpf to a Python float. The result is exact if the
bitcount of s is <= 53 and no underflow/overflow occurs.
If the number is too large or too small to represent as a regular
float, it will be converted to inf or 0.0. Setting strict=True
forces an OverflowError to be raised instead.
"""
sign, man, exp, bc = s
if not man:
if s == fzero: return 0.0
if s == finf: return math_float_inf
if s == fninf: return -math_float_inf
return math_float_inf/math_float_inf
if sign:
man = -man
try:
if bc < 100:
return math.ldexp(man, exp)
# Try resizing the mantissa. Overflow may still happen here.
n = bc - 53
m = man >> n
return math.ldexp(m, exp + n)
except OverflowError:
if strict:
raise
# Overflow to infinity
if exp + bc > 0:
if sign:
return -math_float_inf
else:
return math_float_inf
# Underflow to zero
return 0.0
python类ldexp()的实例源码
def to_fixed(ctx, x, prec):
return int(math.ldexp(x, prec))
def to_float(s, strict=False):
"""
Convert a raw mpf to a Python float. The result is exact if the
bitcount of s is <= 53 and no underflow/overflow occurs.
If the number is too large or too small to represent as a regular
float, it will be converted to inf or 0.0. Setting strict=True
forces an OverflowError to be raised instead.
"""
sign, man, exp, bc = s
if not man:
if s == fzero: return 0.0
if s == finf: return math_float_inf
if s == fninf: return -math_float_inf
return math_float_inf/math_float_inf
if sign:
man = -man
try:
if bc < 100:
return math.ldexp(man, exp)
# Try resizing the mantissa. Overflow may still happen here.
n = bc - 53
m = man >> n
return math.ldexp(m, exp + n)
except OverflowError:
if strict:
raise
# Overflow to infinity
if exp + bc > 0:
if sign:
return -math_float_inf
else:
return math_float_inf
# Underflow to zero
return 0.0
def test_ends(self):
self.identical(self.MIN, ldexp(1.0, -1022))
self.identical(self.TINY, ldexp(1.0, -1074))
self.identical(self.EPS, ldexp(1.0, -52))
self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a^b < 0
a, b = abs(a), abs(b)
# exceptions: division by zero, overflow
if not b:
raise ZeroDivisionError("division by zero")
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError("int/int too large to represent as a float")
# find integer d satisfying 2**(d - 1) <= a/b < 2**d
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
# compute 2**-exp * a / b for suitable exp
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
# round-half-to-even: fractional part is r/b, which is > 0.5 iff
# 2*r > b, and == 0.5 iff 2*r == b.
if 2*r > b or 2*r == b and q % 2 == 1:
q += 1
result = math.ldexp(float(q), exp)
return -result if negative else result
def test_705836(self):
# SF bug 705836. "<f" and ">f" had a severe rounding bug, where a carry
# from the low-order discarded bits could propagate into the exponent
# field, causing the result to be wrong by a factor of 2.
import math
for base in range(1, 33):
# smaller <- largest representable float less than base.
delta = 0.5
while base - delta / 2.0 != base:
delta /= 2.0
smaller = base - delta
# Packing this rounds away a solid string of trailing 1 bits.
packed = struct.pack("<f", smaller)
unpacked = struct.unpack("<f", packed)[0]
# This failed at base = 2, 4, and 32, with unpacked = 1, 2, and
# 16, respectively.
self.assertEqual(base, unpacked)
bigpacked = struct.pack(">f", smaller)
self.assertEqual(bigpacked, string_reverse(packed))
unpacked = struct.unpack(">f", bigpacked)[0]
self.assertEqual(base, unpacked)
# Largest finite IEEE single.
big = (1 << 24) - 1
big = math.ldexp(big, 127 - 23)
packed = struct.pack(">f", big)
unpacked = struct.unpack(">f", packed)[0]
self.assertEqual(big, unpacked)
# The same, but tack on a 1 bit so it rounds up to infinity.
big = (1 << 25) - 1
big = math.ldexp(big, 127 - 24)
self.assertRaises(OverflowError, struct.pack, ">f", big)
def _write_float(f, x):
import math
if x < 0:
sign = 0x8000
x = x * -1
else:
sign = 0
if x == 0:
expon = 0
himant = 0
lomant = 0
else:
fmant, expon = math.frexp(x)
if expon > 16384 or fmant >= 1 or fmant != fmant: # Infinity or NaN
expon = sign|0x7FFF
himant = 0
lomant = 0
else: # Finite
expon = expon + 16382
if expon < 0: # denormalized
fmant = math.ldexp(fmant, expon)
expon = 0
expon = expon | sign
fmant = math.ldexp(fmant, 32)
fsmant = math.floor(fmant)
himant = long(fsmant)
fmant = math.ldexp(fmant - fsmant, 32)
fsmant = math.floor(fmant)
lomant = long(fsmant)
_write_ushort(f, expon)
_write_ulong(f, himant)
_write_ulong(f, lomant)
def test_ends(self):
self.identical(self.MIN, ldexp(1.0, -1022))
self.identical(self.TINY, ldexp(1.0, -1074))
self.identical(self.EPS, ldexp(1.0, -52))
self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a^b < 0
a, b = abs(a), abs(b)
# exceptions: division by zero, overflow
if not b:
raise ZeroDivisionError("division by zero")
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError("int/int too large to represent as a float")
# find integer d satisfying 2**(d - 1) <= a/b < 2**d
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
# compute 2**-exp * a / b for suitable exp
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
# round-half-to-even: fractional part is r/b, which is > 0.5 iff
# 2*r > b, and == 0.5 iff 2*r == b.
if 2*r > b or 2*r == b and q % 2 == 1:
q += 1
result = math.ldexp(float(q), exp)
return -result if negative else result
def test_705836(self):
# SF bug 705836. "<f" and ">f" had a severe rounding bug, where a carry
# from the low-order discarded bits could propagate into the exponent
# field, causing the result to be wrong by a factor of 2.
import math
for base in range(1, 33):
# smaller <- largest representable float less than base.
delta = 0.5
while base - delta / 2.0 != base:
delta /= 2.0
smaller = base - delta
# Packing this rounds away a solid string of trailing 1 bits.
packed = struct.pack("<f", smaller)
unpacked = struct.unpack("<f", packed)[0]
# This failed at base = 2, 4, and 32, with unpacked = 1, 2, and
# 16, respectively.
self.assertEqual(base, unpacked)
bigpacked = struct.pack(">f", smaller)
self.assertEqual(bigpacked, string_reverse(packed))
unpacked = struct.unpack(">f", bigpacked)[0]
self.assertEqual(base, unpacked)
# Largest finite IEEE single.
big = (1 << 24) - 1
big = math.ldexp(big, 127 - 23)
packed = struct.pack(">f", big)
unpacked = struct.unpack(">f", packed)[0]
self.assertEqual(big, unpacked)
# The same, but tack on a 1 bit so it rounds up to infinity.
big = (1 << 25) - 1
big = math.ldexp(big, 127 - 24)
self.assertRaises(OverflowError, struct.pack, ">f", big)
def _write_float(f, x):
import math
if x < 0:
sign = 0x8000
x = x * -1
else:
sign = 0
if x == 0:
expon = 0
himant = 0
lomant = 0
else:
fmant, expon = math.frexp(x)
if expon > 16384 or fmant >= 1 or fmant != fmant: # Infinity or NaN
expon = sign|0x7FFF
himant = 0
lomant = 0
else: # Finite
expon = expon + 16382
if expon < 0: # denormalized
fmant = math.ldexp(fmant, expon)
expon = 0
expon = expon | sign
fmant = math.ldexp(fmant, 32)
fsmant = math.floor(fmant)
himant = long(fsmant)
fmant = math.ldexp(fmant - fsmant, 32)
fsmant = math.floor(fmant)
lomant = long(fsmant)
_write_ushort(f, expon)
_write_ulong(f, himant)
_write_ulong(f, lomant)
def _write_float(f, x):
import math
if x < 0:
sign = 0x8000
x = x * -1
else:
sign = 0
if x == 0:
expon = 0
himant = 0
lomant = 0
else:
fmant, expon = math.frexp(x)
if expon > 16384 or fmant >= 1 or fmant != fmant: # Infinity or NaN
expon = sign|0x7FFF
himant = 0
lomant = 0
else: # Finite
expon = expon + 16382
if expon < 0: # denormalized
fmant = math.ldexp(fmant, expon)
expon = 0
expon = expon | sign
fmant = math.ldexp(fmant, 32)
fsmant = math.floor(fmant)
himant = long(fsmant)
fmant = math.ldexp(fmant - fsmant, 32)
fsmant = math.floor(fmant)
lomant = long(fsmant)
_write_ushort(f, expon)
_write_ulong(f, himant)
_write_ulong(f, lomant)
def test_ends(self):
self.identical(self.MIN, ldexp(1.0, -1022))
self.identical(self.TINY, ldexp(1.0, -1074))
self.identical(self.EPS, ldexp(1.0, -52))
self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a^b < 0
a, b = abs(a), abs(b)
# exceptions: division by zero, overflow
if not b:
raise ZeroDivisionError("division by zero")
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError("int/int too large to represent as a float")
# find integer d satisfying 2**(d - 1) <= a/b < 2**d
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
# compute 2**-exp * a / b for suitable exp
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
# round-half-to-even: fractional part is r/b, which is > 0.5 iff
# 2*r > b, and == 0.5 iff 2*r == b.
if 2*r > b or 2*r == b and q % 2 == 1:
q += 1
result = math.ldexp(q, exp)
return -result if negative else result
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
self.assertEqual(math.ldexp(1., -1000000), 0.)
self.assertEqual(math.ldexp(-1., -1000000), -0.)
self.assertEqual(math.ldexp(INF, 30), INF)
self.assertEqual(math.ldexp(NINF, -213), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10**10, 10**20, 10**40]:
self.assertEqual(math.ldexp(INF, -n), INF)
self.assertEqual(math.ldexp(NINF, -n), NINF)
self.assertEqual(math.ldexp(1., -n), 0.)
self.assertEqual(math.ldexp(-1., -n), -0.)
self.assertEqual(math.ldexp(0., -n), 0.)
self.assertEqual(math.ldexp(-0., -n), -0.)
self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
self.assertRaises(OverflowError, math.ldexp, 1., n)
self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEqual(math.ldexp(0., n), 0.)
self.assertEqual(math.ldexp(-0., n), -0.)
self.assertEqual(math.ldexp(INF, n), INF)
self.assertEqual(math.ldexp(NINF, n), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, n)))
def testLog2Exact(self):
#fixme brython.
# Check that we get exact equality for log2 of powers of 2.
actual = [math.log2(math.ldexp(1.0, n)) for n in range(-1074, 1024)]
expected = [float(n) for n in range(-1074, 1024)]
self.assertEqual(actual, expected)
def float_unpack(Q, size, le):
"""Convert a 32-bit or 64-bit integer created
by float_pack into a Python float."""
if size == 8:
MIN_EXP = -1021 # = sys.float_info.min_exp
MAX_EXP = 1024 # = sys.float_info.max_exp
MANT_DIG = 53 # = sys.float_info.mant_dig
BITS = 64
elif size == 4:
MIN_EXP = -125 # C's FLT_MIN_EXP
MAX_EXP = 128 # FLT_MAX_EXP
MANT_DIG = 24 # FLT_MANT_DIG
BITS = 32
else:
raise ValueError("invalid size value")
if Q >> BITS:
raise ValueError("input out of range")
# extract pieces
sign = Q >> BITS - 1
exp = (Q & ((1 << BITS - 1) - (1 << MANT_DIG - 1))) >> MANT_DIG - 1
mant = Q & ((1 << MANT_DIG - 1) - 1)
if exp == MAX_EXP - MIN_EXP + 2:
# nan or infinity
result = float('nan') if mant else float('inf')
elif exp == 0:
# subnormal or zero
result = math.ldexp(float(mant), MIN_EXP - MANT_DIG)
else:
# normal
mant += 1 << MANT_DIG - 1
result = math.ldexp(float(mant), exp + MIN_EXP - MANT_DIG - 1)
return -result if sign else result
def minimum_part_size(size_in_bytes, default_part_size=DEFAULT_PART_SIZE):
"""Calculate the minimum part size needed for a multipart upload.
Glacier allows a maximum of 10,000 parts per upload. It also
states that the maximum archive size is 10,000 * 4 GB, which means
the part size can range from 1MB to 4GB (provided it is one 1MB
multiplied by a power of 2).
This function will compute what the minimum part size must be in
order to upload a file of size ``size_in_bytes``.
It will first check if ``default_part_size`` is sufficient for
a part size given the ``size_in_bytes``. If this is not the case,
then the smallest part size than can accomodate a file of size
``size_in_bytes`` will be returned.
If the file size is greater than the maximum allowed archive
size of 10,000 * 4GB, a ``ValueError`` will be raised.
"""
# The default part size (4 MB) will be too small for a very large
# archive, as there is a limit of 10,000 parts in a multipart upload.
# This puts the maximum allowed archive size with the default part size
# at 40,000 MB. We need to do a sanity check on the part size, and find
# one that works if the default is too small.
part_size = _MEGABYTE
if (default_part_size * MAXIMUM_NUMBER_OF_PARTS) < size_in_bytes:
if size_in_bytes > (4096 * _MEGABYTE * 10000):
raise ValueError("File size too large: %s" % size_in_bytes)
min_part_size = size_in_bytes / 10000
power = 3
while part_size < min_part_size:
part_size = math.ldexp(_MEGABYTE, power)
power += 1
part_size = int(part_size)
else:
part_size = default_part_size
return part_size
def ldexp(node, i): return merge([node], lambda x: math.ldexp(x, i))
def test_ends(self):
self.identical(self.MIN, ldexp(1.0, -1022))
self.identical(self.TINY, ldexp(1.0, -1074))
self.identical(self.EPS, ldexp(1.0, -52))
self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))
