mirror of
https://github.com/cea-sec/miasm
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Ajax
528 lines
19 KiB
Python
528 lines
19 KiB
Python
"""Intervals with a maximum size, supporting modular arithmetic"""
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from itertools import product
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from miasm2.core.interval import interval
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class ModularIntervals(object):
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"""Intervals with a maximum size, supporting modular arithmetic"""
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def __init__(self, size, intervals=None):
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"""Instanciate a ModularIntervals of size @size
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@size: maximum size of elements
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@intervals: (optional) interval instance, or any type supported by
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interval initialisation; element of the current instance
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"""
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# Create or cast @intervals argument
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if intervals is None:
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intervals = interval()
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if not isinstance(intervals, interval):
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intervals = interval(intervals)
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self.intervals = intervals
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self.size = size
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# Sanity check
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start, end = intervals.hull()
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if start is not None:
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assert start >= 0
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if end is not None:
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assert end <= self.mask
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# Helpers
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@staticmethod
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def size2mask(size):
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"""Return the bit mask of size @size"""
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return (1 << size) - 1
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def _range2interval(func):
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"""Convert a function taking 2 ranges to a function taking a ModularIntervals
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and applying to the current instance"""
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def ret_func(self, target):
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ret = interval()
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for left_i, right_i in product(self.intervals, target.intervals):
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ret += func(self, left_i[0], left_i[1], right_i[0],
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right_i[1])
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return self.__class__(self.size, ret)
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return ret_func
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def _range2integer(func):
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"""Convert a function taking 1 range and optional arguments to a function
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applying to the current instance"""
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def ret_func(self, *args):
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ret = interval()
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for x_min, x_max in self.intervals:
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ret += func(self, x_min, x_max, *args)
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return self.__class__(self.size, ret)
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return ret_func
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def _promote(func):
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"""Check and promote the second argument from integer to
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ModularIntervals with one value"""
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def ret_func(self, target):
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if isinstance(target, (int, long)):
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target = ModularIntervals(self.size, interval([(target, target)]))
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if not isinstance(target, ModularIntervals):
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raise TypeError("Unsupported operation with %s" % target.__class__)
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if target.size != self.size:
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raise TypeError("Size are not the same: %s vs %s" % (self.size,
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target.size))
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return func(self, target)
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return ret_func
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def _unsigned2signed(self, value):
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"""Return the signed value of @value, based on self.size"""
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if (value & (1 << (self.size - 1))):
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return -(self.mask ^ value) - 1
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else:
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return value
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def _signed2unsigned(self, value):
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"""Return the unsigned value of @value, based on self.size"""
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return value & self.mask
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# Operation internals
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#
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# Naming convention:
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# _range_{op}: takes 2 interval bounds and apply op
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# _range_{op}_uniq: takes 1 interval bounds and apply op
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# _interval_{op}: apply op on an ModularIntervals
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# _integer_{op}: apply op on itself with possible arguments
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def _range_add(self, x_min, x_max, y_min, y_max):
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"""Bounds interval for x + y, with
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- x, y of size 'self.size'
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bound = self.mask
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if (x_min + y_min <= max_bound and
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x_max + y_max >= max_bound + 1):
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# HD returns 0, max_bound; but this is because it cannot handle multiple
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# interval.
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# x_max + y_max can only overflow once, so returns
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# [result_min, overflow] U [0, overflow_rest]
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return interval([(x_min + y_min, max_bound),
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(0, (x_max + y_max) & max_bound)])
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else:
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return interval([((x_min + y_min) & max_bound,
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(x_max + y_max) & max_bound)])
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_interval_add = _range2interval(_range_add)
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def _range_minus_uniq(self, x_min, x_max):
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"""Bounds interval for -x, with
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- x of size self.size
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- @x_min <= x <= @x_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bound = self.mask
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if (x_min == 0 and x_max != 0):
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# HD returns 0, max_bound; see _range_add
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return interval([(0, 0), ((- x_max) & max_bound, max_bound)])
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else:
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return interval([((- x_max) & max_bound, (- x_min) & max_bound)])
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_interval_minus = _range2integer(_range_minus_uniq)
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def _range_or_min(self, x_min, x_max, y_min, y_max):
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"""Interval min for x | y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bit = 1 << (self.size - 1)
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while max_bit:
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if ~x_min & y_min & max_bit:
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temp = (x_min | max_bit) & - max_bit
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if temp <= x_max:
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x_min = temp
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break
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elif x_min & ~y_min & max_bit:
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temp = (y_min | max_bit) & - max_bit
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if temp <= y_max:
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y_min = temp
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break
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max_bit >>= 1
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return x_min | y_min
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def _range_or_max(self, x_min, x_max, y_min, y_max):
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"""Interval max for x | y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bit = 1 << (self.size - 1)
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while max_bit:
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if x_max & y_max & max_bit:
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temp = (x_max - max_bit) | (max_bit - 1)
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if temp >= x_min:
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x_max = temp
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break
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temp = (y_max - max_bit) | (max_bit - 1)
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if temp >= y_min:
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y_max = temp
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break
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max_bit >>= 1
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return x_max | y_max
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def _range_or(self, x_min, x_max, y_min, y_max):
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"""Interval bounds for x | y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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return interval([(self._range_or_min(x_min, x_max, y_min, y_max),
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self._range_or_max(x_min, x_max, y_min, y_max))])
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_interval_or = _range2interval(_range_or)
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def _range_and_min(self, x_min, x_max, y_min, y_max):
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"""Interval min for x & y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bit = (1 << (self.size - 1))
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while max_bit:
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if ~x_min & ~y_min & max_bit:
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temp = (x_min | max_bit) & - max_bit
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if temp <= x_max:
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x_min = temp
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break
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temp = (y_min | max_bit) & - max_bit
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if temp <= y_max:
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y_min = temp
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break
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max_bit >>= 1
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return x_min & y_min
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def _range_and_max(self, x_min, x_max, y_min, y_max):
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"""Interval max for x & y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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max_bit = (1 << (self.size - 1))
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while max_bit:
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if x_max & ~y_max & max_bit:
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temp = (x_max & ~max_bit) | (max_bit - 1)
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if temp >= x_min:
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x_max = temp
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break
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elif ~x_max & y_max & max_bit:
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temp = (y_max & ~max_bit) | (max_bit - 1)
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if temp >= y_min:
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y_max = temp
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break
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max_bit >>= 1
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return x_max & y_max
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def _range_and(self, x_min, x_max, y_min, y_max):
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"""Interval bounds for x & y, with
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- x, y of size @size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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return interval([(self._range_and_min(x_min, x_max, y_min, y_max),
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self._range_and_max(x_min, x_max, y_min, y_max))])
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_interval_and = _range2interval(_range_and)
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def _range_xor(self, x_min, x_max, y_min, y_max):
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"""Interval bounds for x ^ y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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From Hacker's Delight: Chapter 4
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"""
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not_size = lambda x: x ^ self.mask
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min_xor = self._range_and_min(x_min, x_max, not_size(y_max), not_size(y_min)) | self._range_and_min(not_size(x_max), not_size(x_min), y_min, y_max)
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max_xor = self._range_or_max(0,
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self._range_and_max(x_min, x_max, not_size(y_max), not_size(y_min)),
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0,
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self._range_and_max(not_size(x_max), not_size(x_min), y_min, y_max))
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return interval([(min_xor, max_xor)])
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_interval_xor = _range2interval(_range_xor)
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def _range_mul(self, x_min, x_max, y_min, y_max):
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"""Interval bounds for x * y, with
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- x, y of size self.size
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- @x_min <= x <= @x_max
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- @y_min <= y <= @y_max
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- operations are considered unsigned
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This is a naive version, going to TOP on overflow"""
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max_bound = self.mask
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if y_max * x_max > max_bound:
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return interval([(0, max_bound)])
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else:
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return interval([(x_min * y_min, x_max * y_max)])
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_interval_mul = _range2interval(_range_mul)
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def _range_mod_uniq(self, x_min, x_max, mod):
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"""Interval bounds for x % @mod, with
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- x, @mod of size self.size
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- @x_min <= x <= @x_max
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- operations are considered unsigned
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"""
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if (x_max - x_min) >= mod:
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return interval([(0, mod - 1)])
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x_max = x_max % mod
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x_min = x_min % mod
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if x_max < x_min:
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return interval([(0, x_max), (x_min, mod - 1)])
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else:
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return interval([(x_min, x_max)])
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_integer_modulo = _range2integer(_range_mod_uniq)
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def _range_shift_uniq(self, x_min, x_max, shift, op):
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"""Bounds interval for x @op @shift with
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- x of size self.size
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- @x_min <= x <= @x_max
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- operations are considered unsigned
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- shift <= self.size
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"""
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assert shift <= self.size
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# Shift operations are monotonic, and overflow results in 0
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max_bound = self.mask
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if op == "<<":
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obtain_max = x_max << shift
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if obtain_max > max_bound:
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# Overflow at least on max, best-effort
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# result '0' often happen, include it
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return interval([(0, 0), ((1 << shift) - 1, max_bound)])
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else:
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return interval([(x_min << shift, obtain_max)])
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elif op == ">>":
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return interval([((x_min >> shift) & max_bound,
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(x_max >> shift) & max_bound)])
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elif op == "a>>":
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# The Miasm2 version (Expr or ModInt) could have been used, but
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# introduce unnecessary dependencies for this module
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# Python >> is the arithmetic one
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ashr = lambda x, y: self._signed2unsigned(self._unsigned2signed(x) >> y)
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end_min, end_max = ashr(x_min, shift), ashr(x_max, shift)
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end_min, end_max = min(end_min, end_max), max(end_min, end_max)
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return interval([(end_min, end_max)])
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else:
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raise ValueError("%s is not a shifter" % op)
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def _interval_shift(self, operation, shifter):
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"""Apply the shifting operation @operation with a shifting
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ModularIntervals @shifter on the current instance"""
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# Work on a copy of shifter intervals
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shifter = interval(shifter.intervals)
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if (shifter.hull()[1] >= self.size):
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shifter += interval([(self.size, self.size)])
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shifter &= interval([(0, self.size)])
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ret = interval()
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for shift_range in shifter:
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for shift in xrange(shift_range[0], shift_range[1] + 1):
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for x_min, x_max in self.intervals:
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ret += self._range_shift_uniq(x_min, x_max, shift, operation)
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return self.__class__(self.size, ret)
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def _range_rotate_uniq(self, x_min, x_max, shift, op):
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"""Bounds interval for x @op @shift with
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- x of size self.size
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- @x_min <= x <= @x_max
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- operations are considered unsigned
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- shift <= self.size
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"""
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assert shift <= self.size
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# Divide in sub-operations: a op b: a left b | a right (size - b)
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if op == ">>>":
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left, right = ">>", "<<"
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elif op == "<<<":
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left, right = "<<", ">>"
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else:
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raise ValueError("Not a rotator: %s" % op)
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left_intervals = self._range_shift_uniq(x_min, x_max, shift, left)
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right_intervals = self._range_shift_uniq(x_min, x_max,
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self.size - shift, right)
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result = self.__class__(self.size, left_intervals) | self.__class__(self.size, right_intervals)
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return result.intervals
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def _interval_rotate(self, operation, shifter):
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"""Apply the rotate operation @operation with a shifting
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ModularIntervals @shifter on the current instance"""
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# Consider only rotation without repetition, and enumerate
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# -> apply a '% size' on shifter
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shifter %= self.size
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ret = interval()
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for shift_range in shifter:
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for shift in xrange(shift_range[0], shift_range[1] + 1):
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for x_min, x_max in self.intervals:
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ret += self._range_rotate_uniq(x_min, x_max, shift,
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operation)
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return self.__class__(self.size, ret)
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# Operation wrappers
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@_promote
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def __add__(self, to_add):
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"""Add @to_add to the current intervals
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@to_add: ModularInstances or integer
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"""
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return self._interval_add(to_add)
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@_promote
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def __or__(self, to_or):
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"""Bitwise OR @to_or to the current intervals
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@to_or: ModularInstances or integer
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"""
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return self._interval_or(to_or)
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@_promote
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def __and__(self, to_and):
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"""Bitwise AND @to_and to the current intervals
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@to_and: ModularInstances or integer
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"""
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return self._interval_and(to_and)
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@_promote
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def __xor__(self, to_xor):
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"""Bitwise XOR @to_xor to the current intervals
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@to_xor: ModularInstances or integer
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"""
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return self._interval_xor(to_xor)
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@_promote
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def __mul__(self, to_mul):
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"""Multiply @to_mul to the current intervals
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@to_mul: ModularInstances or integer
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"""
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return self._interval_mul(to_mul)
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@_promote
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def __rshift__(self, to_shift):
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"""Logical shift right the current intervals of @to_shift
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@to_shift: ModularInstances or integer
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"""
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return self._interval_shift('>>', to_shift)
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@_promote
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def __lshift__(self, to_shift):
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"""Logical shift left the current intervals of @to_shift
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@to_shift: ModularInstances or integer
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"""
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return self._interval_shift('<<', to_shift)
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@_promote
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def arithmetic_shift_right(self, to_shift):
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"""Arithmetic shift right the current intervals of @to_shift
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@to_shift: ModularInstances or integer
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"""
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return self._interval_shift('a>>', to_shift)
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def __neg__(self):
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"""Negate the current intervals"""
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return self._interval_minus()
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def __mod__(self, modulo):
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"""Apply % @modulo on the current intervals
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@modulo: integer
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"""
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if not isinstance(modulo, (int, long)):
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raise TypeError("Modulo with %s is not supported" % modulo.__class__)
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return self._integer_modulo(modulo)
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@_promote
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def rotation_right(self, to_rotate):
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"""Right rotate the current intervals of @to_rotate
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@to_rotate: ModularInstances or integer
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"""
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return self._interval_rotate('>>>', to_rotate)
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@_promote
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def rotation_left(self, to_rotate):
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"""Left rotate the current intervals of @to_rotate
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@to_rotate: ModularInstances or integer
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"""
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return self._interval_rotate('<<<', to_rotate)
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# Instance operations
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@property
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def mask(self):
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"""Return the mask corresponding to the instance size"""
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return ModularIntervals.size2mask(self.size)
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def __iter__(self):
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return iter(self.intervals)
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@property
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def length(self):
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return self.intervals.length
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def __contains__(self, other):
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if isinstance(other, ModularIntervals):
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other = other.intervals
|
|
return other in self.intervals
|
|
|
|
def __str__(self):
|
|
return "%s (Size: %s)" % (self.intervals, self.size)
|
|
|
|
def size_update(self, new_size):
|
|
"""Update the instance size to @new_size
|
|
The size of elements must be <= @new_size"""
|
|
|
|
# Increasing size is always safe
|
|
if new_size < self.size:
|
|
# Check that current values are indeed included in the new range
|
|
assert self.intervals.hull()[1] <= ModularIntervals.size2mask(new_size)
|
|
|
|
self.size = new_size
|
|
|
|
# For easy chainning
|
|
return self
|
|
|
|
# Mimic Python's set operations
|
|
|
|
@_promote
|
|
def union(self, to_union):
|
|
"""Union set operation with @to_union
|
|
@to_union: ModularIntervals instance"""
|
|
return ModularIntervals(self.size, self.intervals + to_union.intervals)
|
|
|
|
@_promote
|
|
def update(self, to_union):
|
|
"""Union set operation in-place with @to_union
|
|
@to_union: ModularIntervals instance"""
|
|
self.intervals += to_union.intervals
|
|
|
|
@_promote
|
|
def intersection(self, to_intersect):
|
|
"""Intersection set operation with @to_intersect
|
|
@to_intersect: ModularIntervals instance"""
|
|
return ModularIntervals(self.size, self.intervals & to_intersect.intervals)
|
|
|
|
@_promote
|
|
def intersection_update(self, to_intersect):
|
|
"""Intersection set operation in-place with @to_intersect
|
|
@to_intersect: ModularIntervals instance"""
|
|
self.intervals &= to_intersect.intervals
|