Convert to src-layout ta/nix

1 files changed, 525 insertions, 0 deletions

diff --git a/src/miasm/analysis/modularintervals.py b/src/miasm/analysis/modularintervals.py
new file mode 100644
index 00000000..67eda9dc
--- /dev/null
+++ b/src/miasm/analysis/modularintervals.py
@@ -0,0 +1,525 @@
+"""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 miasm.core.interval import interval
+from miasm.core.utils import size2mask
+
+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
+    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 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] <= 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