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# -*- coding: ascii -*-
#
# Util/_number_new.py : utility functions
#
# Written in 2008 by Dwayne C. Litzenberger <dlitz@dlitz.net>
#
# ===================================================================
# The contents of this file are dedicated to the public domain. To
# the extent that dedication to the public domain is not available,
# everyone is granted a worldwide, perpetual, royalty-free,
# non-exclusive license to exercise all rights associated with the
# contents of this file for any purpose whatsoever.
# No rights are reserved.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# ===================================================================
## NOTE: Do not import this module directly. Import these functions from Crypto.Util.number.
__revision__ = "$Id$"
__all__ = ['ceil_shift', 'ceil_div', 'floor_div', 'exact_log2', 'exact_div']
from Crypto.Util.python_compat import *
def ceil_shift(n, b):
"""Return ceil(n / 2**b) without performing any floating-point or division operations.
This is done by right-shifting n by b bits and incrementing the result by 1
if any '1' bits were shifted out.
"""
if not isinstance(n, (int, long)) or not isinstance(b, (int, long)):
raise TypeError("unsupported operand type(s): %r and %r" % (type(n).__name__, type(b).__name__))
assert n >= 0 and b >= 0 # I haven't tested or even thought about negative values
mask = (1L << b) - 1
if n & mask:
return (n >> b) + 1
else:
return n >> b
def ceil_div(a, b):
"""Return ceil(a / b) without performing any floating-point operations."""
if not isinstance(a, (int, long)) or not isinstance(b, (int, long)):
raise TypeError("unsupported operand type(s): %r and %r" % (type(a).__name__, type(b).__name__))
(q, r) = divmod(a, b)
if r:
return q + 1
else:
return q
def floor_div(a, b):
if not isinstance(a, (int, long)) or not isinstance(b, (int, long)):
raise TypeError("unsupported operand type(s): %r and %r" % (type(a).__name__, type(b).__name__))
(q, r) = divmod(a, b)
return q
def exact_log2(num):
"""Find and return an integer i >= 0 such that num == 2**i.
If no such integer exists, this function raises ValueError.
"""
if not isinstance(num, (int, long)):
raise TypeError("unsupported operand type: %r" % (type(num).__name__,))
n = long(num)
if n <= 0:
raise ValueError("cannot compute logarithm of non-positive number")
i = 0
while n != 0:
if (n & 1) and n != 1:
raise ValueError("No solution could be found")
i += 1
n >>= 1
i -= 1
assert num == (1L << i)
return i
def exact_div(p, d, allow_divzero=False):
"""Find and return an integer n such that p == n * d
If no such integer exists, this function raises ValueError.
Both operands must be integers.
If the second operand is zero, this function will raise ZeroDivisionError
unless allow_divzero is true (default: False).
"""
if not isinstance(p, (int, long)) or not isinstance(d, (int, long)):
raise TypeError("unsupported operand type(s): %r and %r" % (type(p).__name__, type(d).__name__))
if d == 0 and allow_divzero:
n = 0
if p != n * d:
raise ValueError("No solution could be found")
else:
(n, r) = divmod(p, d)
if r != 0:
raise ValueError("No solution could be found")
assert p == n * d
return n
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