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authorFabrice Desclaux <fabrice.desclaux@cea.fr>2019-02-27 20:12:54 +0100
committerFabrice Desclaux <fabrice.desclaux@cea.fr>2019-03-05 16:52:51 +0100
commit944806c506446c918eb74c17a605f5f56d4b75e0 (patch)
treeba1d989b03bf8b5544c362a9f61b4e8d3284650f /miasm2/analysis/modularintervals.py
parent02bbb30efea4980c9d133947cbbf69fb599071ad (diff)
downloadmiasm-944806c506446c918eb74c17a605f5f56d4b75e0.tar.gz
miasm-944806c506446c918eb74c17a605f5f56d4b75e0.zip
Rename miasm2 to miasm
Diffstat (limited to 'miasm2/analysis/modularintervals.py')
-rw-r--r--miasm2/analysis/modularintervals.py530
1 files changed, 0 insertions, 530 deletions
diff --git a/miasm2/analysis/modularintervals.py b/miasm2/analysis/modularintervals.py
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--- a/miasm2/analysis/modularintervals.py
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-"""Intervals with a maximum size, supporting modular arithmetic"""
-
-from future.builtins import range
-from builtins import int as int_types
-from itertools import product
-
-from miasm2.core.interval import interval
-
-class ModularIntervals(object):
-    """Intervals with a maximum size, supporting modular arithmetic"""
-
-    def __init__(self, size, intervals=None):
-        """Instantiate a ModularIntervals of size @size
-        @size: maximum size of elements
-        @intervals: (optional) interval instance, or any type  supported by
-                    interval initialisation; element of the current instance
-        """
-        # Create or cast @intervals argument
-        if intervals is None:
-            intervals = interval()
-        if not isinstance(intervals, interval):
-            intervals = interval(intervals)
-        self.intervals = intervals
-        self.size = size
-
-        # Sanity check
-        start, end = intervals.hull()
-        if start is not None:
-            assert start >= 0
-        if end is not None:
-            assert end <= self.mask
-
-    # Helpers
-
-    @staticmethod
-    def size2mask(size):
-        """Return the bit mask of size @size"""
-        return (1 << size) - 1
-
-    def _range2interval(func):
-        """Convert a function taking 2 ranges to a function taking a ModularIntervals
-        and applying to the current instance"""
-        def ret_func(self, target):
-            ret = interval()
-            for left_i, right_i in product(self.intervals, target.intervals):
-                ret += func(self, left_i[0], left_i[1], right_i[0],
-                            right_i[1])
-            return self.__class__(self.size, ret)
-        return ret_func
-
-    def _range2integer(func):
-        """Convert a function taking 1 range and optional arguments to a function
-        applying to the current instance"""
-        def ret_func(self, *args):
-            ret = interval()
-            for x_min, x_max in self.intervals:
-                ret += func(self, x_min, x_max, *args)
-            return self.__class__(self.size, ret)
-        return ret_func
-
-    def _promote(func):
-        """Check and promote the second argument from integer to
-        ModularIntervals with one value"""
-        def ret_func(self, target):
-            if isinstance(target, int_types):
-                target = ModularIntervals(self.size, interval([(target, target)]))
-            if not isinstance(target, ModularIntervals):
-                raise TypeError("Unsupported operation with %s" % target.__class__)
-            if target.size != self.size:
-                raise TypeError("Size are not the same: %s vs %s" % (self.size,
-                                                                     target.size))
-            return func(self, target)
-        return ret_func
-
-    def _unsigned2signed(self, value):
-        """Return the signed value of @value, based on self.size"""
-        if (value & (1 << (self.size - 1))):
-            return -(self.mask ^ value) - 1
-        else:
-            return value
-
-    def _signed2unsigned(self, value):
-        """Return the unsigned value of @value, based on self.size"""
-        return value & self.mask
-
-    # Operation internals
-    #
-    # Naming convention:
-    # _range_{op}: takes 2 interval bounds and apply op
-    # _range_{op}_uniq: takes 1 interval bounds and apply op
-    # _interval_{op}: apply op on an ModularIntervals
-    # _integer_{op}: apply op on itself with possible arguments
-
-    def _range_add(self, x_min, x_max, y_min, y_max):
-        """Bounds interval for x + y, with
-         - x, y of size 'self.size'
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bound = self.mask
-        if (x_min + y_min <= max_bound and
-            x_max + y_max >= max_bound + 1):
-            # HD returns 0, max_bound; but this is because it cannot handle multiple
-            # interval.
-            # x_max + y_max can only overflow once, so returns
-            # [result_min, overflow] U [0, overflow_rest]
-            return interval([(x_min + y_min, max_bound),
-                             (0, (x_max + y_max) & max_bound)])
-        else:
-            return interval([((x_min + y_min) & max_bound,
-                              (x_max + y_max) & max_bound)])
-
-    _interval_add = _range2interval(_range_add)
-
-    def _range_minus_uniq(self, x_min, x_max):
-        """Bounds interval for -x, with
-         - x of size self.size
-         - @x_min <= x <= @x_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bound = self.mask
-        if (x_min == 0 and x_max != 0):
-            # HD returns 0, max_bound; see _range_add
-            return interval([(0, 0), ((- x_max) & max_bound, max_bound)])
-        else:
-            return interval([((- x_max) & max_bound, (- x_min) & max_bound)])
-
-    _interval_minus = _range2integer(_range_minus_uniq)
-
-    def _range_or_min(self, x_min, x_max, y_min, y_max):
-        """Interval min for x | y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bit = 1 << (self.size - 1)
-        while max_bit:
-            if ~x_min & y_min & max_bit:
-                temp = (x_min | max_bit) & - max_bit
-                if temp <= x_max:
-                    x_min = temp
-                    break
-            elif x_min & ~y_min & max_bit:
-                temp = (y_min | max_bit) & - max_bit
-                if temp <= y_max:
-                    y_min = temp
-                    break
-            max_bit >>= 1
-        return x_min | y_min
-
-    def _range_or_max(self, x_min, x_max, y_min, y_max):
-        """Interval max for x | y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bit = 1 << (self.size - 1)
-        while max_bit:
-            if x_max & y_max & max_bit:
-                temp = (x_max - max_bit) | (max_bit - 1)
-                if temp >= x_min:
-                    x_max = temp
-                    break
-                temp = (y_max - max_bit) | (max_bit - 1)
-                if temp >= y_min:
-                    y_max = temp
-                    break
-            max_bit >>= 1
-        return x_max | y_max
-
-    def _range_or(self, x_min, x_max, y_min, y_max):
-        """Interval bounds for x | y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        return interval([(self._range_or_min(x_min, x_max, y_min, y_max),
-                          self._range_or_max(x_min, x_max, y_min, y_max))])
-
-    _interval_or = _range2interval(_range_or)
-
-    def _range_and_min(self, x_min, x_max, y_min, y_max):
-        """Interval min for x & y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bit = (1 << (self.size - 1))
-        while max_bit:
-            if ~x_min & ~y_min & max_bit:
-                temp = (x_min | max_bit) & - max_bit
-                if temp <= x_max:
-                    x_min = temp
-                    break
-                temp = (y_min | max_bit) & - max_bit
-                if temp <= y_max:
-                    y_min = temp
-                    break
-            max_bit >>= 1
-        return x_min & y_min
-
-    def _range_and_max(self, x_min, x_max, y_min, y_max):
-        """Interval max for x & y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        max_bit = (1 << (self.size - 1))
-        while max_bit:
-            if x_max & ~y_max & max_bit:
-                temp = (x_max & ~max_bit) | (max_bit - 1)
-                if temp >= x_min:
-                    x_max = temp
-                    break
-            elif ~x_max & y_max & max_bit:
-                temp = (y_max & ~max_bit) | (max_bit - 1)
-                if temp >= y_min:
-                    y_max = temp
-                    break
-            max_bit >>= 1
-        return x_max & y_max
-
-    def _range_and(self, x_min, x_max, y_min, y_max):
-        """Interval bounds for x & y, with
-         - x, y of size @size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        return interval([(self._range_and_min(x_min, x_max, y_min, y_max),
-                          self._range_and_max(x_min, x_max, y_min, y_max))])
-
-    _interval_and = _range2interval(_range_and)
-
-    def _range_xor(self, x_min, x_max, y_min, y_max):
-        """Interval bounds for x ^ y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        From Hacker's Delight: Chapter 4
-        """
-        not_size = lambda x: x ^ self.mask
-        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)
-        max_xor = self._range_or_max(0,
-                                     self._range_and_max(x_min, x_max, not_size(y_max), not_size(y_min)),
-                                     0,
-                                     self._range_and_max(not_size(x_max), not_size(x_min), y_min, y_max))
-        return interval([(min_xor, max_xor)])
-
-    _interval_xor = _range2interval(_range_xor)
-
-    def _range_mul(self, x_min, x_max, y_min, y_max):
-        """Interval bounds for x * y, with
-         - x, y of size self.size
-         - @x_min <= x <= @x_max
-         - @y_min <= y <= @y_max
-         - operations are considered unsigned
-        This is a naive version, going to TOP on overflow"""
-        max_bound = self.mask
-        if y_max * x_max > max_bound:
-            return interval([(0, max_bound)])
-        else:
-            return interval([(x_min * y_min, x_max * y_max)])
-
-    _interval_mul = _range2interval(_range_mul)
-
-    def _range_mod_uniq(self, x_min, x_max, mod):
-        """Interval bounds for x % @mod, with
-         - x, @mod of size self.size
-         - @x_min <= x <= @x_max
-         - operations are considered unsigned
-        """
-        if (x_max - x_min) >= mod:
-            return interval([(0, mod - 1)])
-        x_max = x_max % mod
-        x_min = x_min % mod
-        if x_max < x_min:
-            return interval([(0, x_max), (x_min, mod - 1)])
-        else:
-            return interval([(x_min, x_max)])
-
-    _integer_modulo = _range2integer(_range_mod_uniq)
-
-    def _range_shift_uniq(self, x_min, x_max, shift, op):
-        """Bounds interval for x @op @shift with
-         - x of size self.size
-         - @x_min <= x <= @x_max
-         - operations are considered unsigned
-         - shift <= self.size
-        """
-        assert shift <= self.size
-        # Shift operations are monotonic, and overflow results in 0
-        max_bound = self.mask
-
-        if op == "<<":
-            obtain_max = x_max << shift
-            if obtain_max > max_bound:
-                # Overflow at least on max, best-effort
-                # result '0' often happen, include it
-                return interval([(0, 0), ((1 << shift) - 1, max_bound)])
-            else:
-                return interval([(x_min << shift, obtain_max)])
-        elif op == ">>":
-            return interval([((x_min >> shift) & max_bound,
-                              (x_max >> shift) & max_bound)])
-        elif op == "a>>":
-            # The Miasm2 version (Expr or ModInt) could have been used, but
-            # introduce unnecessary dependencies for this module
-            # Python >> is the arithmetic one
-            ashr = lambda x, y: self._signed2unsigned(self._unsigned2signed(x) >> y)
-            end_min, end_max = ashr(x_min, shift), ashr(x_max, shift)
-            end_min, end_max = min(end_min, end_max), max(end_min, end_max)
-            return interval([(end_min, end_max)])
-        else:
-            raise ValueError("%s is not a shifter" % op)
-
-    def _interval_shift(self, operation, shifter):
-        """Apply the shifting operation @operation with a shifting
-        ModularIntervals @shifter on the current instance"""
-        # Work on a copy of shifter intervals
-        shifter = interval(shifter.intervals)
-        if (shifter.hull()[1] >= self.size):
-            shifter += interval([(self.size, self.size)])
-        shifter &= interval([(0, self.size)])
-        ret = interval()
-        for shift_range in shifter:
-            for shift in range(shift_range[0], shift_range[1] + 1):
-                for x_min, x_max in self.intervals:
-                    ret += self._range_shift_uniq(x_min, x_max, shift, operation)
-        return self.__class__(self.size, ret)
-
-    def _range_rotate_uniq(self, x_min, x_max, shift, op):
-        """Bounds interval for x @op @shift with
-         - x of size self.size
-         - @x_min <= x <= @x_max
-         - operations are considered unsigned
-         - shift <= self.size
-        """
-        assert shift <= self.size
-        # Divide in sub-operations: a op b: a left b | a right (size - b)
-        if op == ">>>":
-            left, right = ">>", "<<"
-        elif op == "<<<":
-            left, right = "<<", ">>"
-        else:
-            raise ValueError("Not a rotator: %s" % op)
-
-        left_intervals = self._range_shift_uniq(x_min, x_max, shift, left)
-        right_intervals = self._range_shift_uniq(x_min, x_max,
-                                                 self.size - shift, right)
-
-        result = self.__class__(self.size, left_intervals) | self.__class__(self.size, right_intervals)
-        return result.intervals
-
-    def _interval_rotate(self, operation, shifter):
-        """Apply the rotate operation @operation with a shifting
-        ModularIntervals @shifter on the current instance"""
-        # Consider only rotation without repetition, and enumerate
-        # -> apply a '% size' on shifter
-        shifter %= self.size
-        ret = interval()
-        for shift_range in shifter:
-            for shift in range(shift_range[0], shift_range[1] + 1):
-                for x_min, x_max in self.intervals:
-                    ret += self._range_rotate_uniq(x_min, x_max, shift,
-                                                   operation)
-
-        return self.__class__(self.size, ret)
-
-    # Operation wrappers
-
-    @_promote
-    def __add__(self, to_add):
-        """Add @to_add to the current intervals
-        @to_add: ModularInstances or integer
-        """
-        return self._interval_add(to_add)
-
-    @_promote
-    def __or__(self, to_or):
-        """Bitwise OR @to_or to the current intervals
-        @to_or: ModularInstances or integer
-        """
-        return self._interval_or(to_or)
-
-    @_promote
-    def __and__(self, to_and):
-        """Bitwise AND @to_and to the current intervals
-        @to_and: ModularInstances or integer
-        """
-        return self._interval_and(to_and)
-
-    @_promote
-    def __xor__(self, to_xor):
-        """Bitwise XOR @to_xor to the current intervals
-        @to_xor: ModularInstances or integer
-        """
-        return self._interval_xor(to_xor)
-
-    @_promote
-    def __mul__(self, to_mul):
-        """Multiply @to_mul to the current intervals
-        @to_mul: ModularInstances or integer
-        """
-        return self._interval_mul(to_mul)
-
-    @_promote
-    def __rshift__(self, to_shift):
-        """Logical shift right the current intervals of @to_shift
-        @to_shift: ModularInstances or integer
-        """
-        return self._interval_shift('>>', to_shift)
-
-    @_promote
-    def __lshift__(self, to_shift):
-        """Logical shift left the current intervals of @to_shift
-        @to_shift: ModularInstances or integer
-        """
-        return self._interval_shift('<<', to_shift)
-
-    @_promote
-    def arithmetic_shift_right(self, to_shift):
-        """Arithmetic shift right the current intervals of @to_shift
-        @to_shift: ModularInstances or integer
-        """
-        return self._interval_shift('a>>', to_shift)
-
-    def __neg__(self):
-        """Negate the current intervals"""
-        return self._interval_minus()
-
-    def __mod__(self, modulo):
-        """Apply % @modulo on the current intervals
-        @modulo: integer
-        """
-
-        if not isinstance(modulo, int_types):
-            raise TypeError("Modulo with %s is not supported" % modulo.__class__)
-        return self._integer_modulo(modulo)
-
-    @_promote
-    def rotation_right(self, to_rotate):
-        """Right rotate the current intervals of @to_rotate
-        @to_rotate: ModularInstances or integer
-        """
-        return self._interval_rotate('>>>', to_rotate)
-
-    @_promote
-    def rotation_left(self, to_rotate):
-        """Left rotate the current intervals of @to_rotate
-        @to_rotate: ModularInstances or integer
-        """
-        return self._interval_rotate('<<<', to_rotate)
-
-    # Instance operations
-
-    @property
-    def mask(self):
-        """Return the mask corresponding to the instance size"""
-        return ModularIntervals.size2mask(self.size)
-
-    def __iter__(self):
-        return iter(self.intervals)
-
-    @property
-    def length(self):
-        return self.intervals.length
-
-    def __contains__(self, other):
-        if isinstance(other, ModularIntervals):
-            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