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| author | Fabrice Desclaux <fabrice.desclaux@cea.fr> | 2019-02-27 20:12:54 +0100 |
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| committer | Fabrice Desclaux <fabrice.desclaux@cea.fr> | 2019-03-05 16:52:51 +0100 |
| commit | 944806c506446c918eb74c17a605f5f56d4b75e0 (patch) | |
| tree | ba1d989b03bf8b5544c362a9f61b4e8d3284650f /miasm2/analysis/modularintervals.py | |
| parent | 02bbb30efea4980c9d133947cbbf69fb599071ad (diff) | |
| download | miasm-944806c506446c918eb74c17a605f5f56d4b75e0.tar.gz miasm-944806c506446c918eb74c17a605f5f56d4b75e0.zip | |
Rename miasm2 to miasm
Diffstat (limited to 'miasm2/analysis/modularintervals.py')
| -rw-r--r-- | miasm2/analysis/modularintervals.py | 530 |
1 files changed, 0 insertions, 530 deletions
diff --git a/miasm2/analysis/modularintervals.py b/miasm2/analysis/modularintervals.py deleted file mode 100644 index 2195598b..00000000 --- a/miasm2/analysis/modularintervals.py +++ /dev/null @@ -1,530 +0,0 @@ -"""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 |