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number.py
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number.py
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#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""
The module include all number-related function and class. It could operate truly value and
symbolic value.
"""
import io
import math
import struct
import ctypes
import z3
import utils
u8 = i8 = u16 = i16 = u32 = i32 = u64 = i64 = int
f32 = f64 = float
def int2u8(i: int) -> u8:
if utils.is_all_real(i):
return i & 0xFF
return z3.Extract(7, 0, i)
def int2i8(i: int) -> i8:
if utils.is_all_real(i):
i = i & 0xFF
if i & 0x80:
return i - 0x100
return i
return z3.Extract(7, 0, i)
def int2u16(i: int) -> u16:
if utils.is_all_real(i):
return i & 0xFFFF
return z3.Extract(15, 0, i)
def int2i16(i: int) -> i16:
if utils.is_all_real(i):
i = i & 0xFFFF
if i & 0x8000:
return i - 0x10000
return i
return z3.Extract(15, 0, i)
def int2u32(i: int) -> u32:
if utils.is_all_real(i):
return i & 0xFFFFFFFF
return z3.Extract(31, 0, i)
def int2i32(i: int) -> i32:
if utils.is_all_real(i):
i = i & 0xFFFFFFFF
if i & 0x80000000:
return i - 0x100000000
return i
return z3.Extract(31, 0, i)
def int2u64(i: int) -> u64:
if utils.is_all_real(i):
return i & 0xFFFFFFFFFFFFFFFF
return z3.Extract(63, 0, i)
def int2i64(i: int) -> i64:
if utils.is_all_real(i):
i = i & 0xFFFFFFFFFFFFFFFF
if i & 0x8000000000000000:
return i - 0x10000000000000000
return i
return z3.Extract(63, 0, i)
def i322f32(i: i32) -> f32:
if utils.is_all_real(i):
i = int2i32(i)
return struct.unpack('<f', struct.pack('<i', i))[0]
return z3.fpToFP(i, z3.Float32())
def f322i32(f: f32) -> i32:
if utils.is_all_real(f):
return struct.unpack('<i', struct.pack('<f', f))[0]
return z3.fpToIEEEBV(f, z3.Float32())
def i642f64(i: i64) -> f64:
if utils.is_all_real(i):
i = int2i64(i)
return struct.unpack('<i', struct.pack('<q', i))[0]
return z3.fpToFP(i, z3.Float64())
def f642i64(f: f64) -> i64:
if utils.is_all_real(f):
return struct.unpack('<q', struct.pack('<d', f))[0]
return z3.fpToIEEEBV(f, z3.Float64())
class LittleEndian:
@staticmethod
def u8(r: bytes):
return struct.unpack('<B', r)[0]
@staticmethod
def i8(r: bytes):
return struct.unpack('<b', r)[0]
@staticmethod
def u16(r: bytes):
return struct.unpack('<H', r)[0]
@staticmethod
def i16(r: bytes):
return struct.unpack('<h', r)[0]
@staticmethod
def u32(r: bytes):
return struct.unpack('<I', r)[0]
@staticmethod
def i32(r: bytes):
return struct.unpack('<i', r)[0]
@staticmethod
def u64(r: bytes):
return struct.unpack('<Q', r)[0]
@staticmethod
def i64(r: bytes):
return struct.unpack('<q', r)[0]
@staticmethod
def f32(r: bytes):
return struct.unpack('<f', r)[0]
@staticmethod
def f64(r: bytes):
return struct.unpack('<d', r)[0]
@staticmethod
def pack_u8(n: u8):
return struct.pack('<B', n)
@staticmethod
def pack_i8(n: i8):
return struct.pack('<b', n)
@staticmethod
def pack_u16(n: u16):
return struct.pack('<H', n)
@staticmethod
def pack_i16(n: i16):
return struct.pack('<h', n)
@staticmethod
def pack_u32(n: u32):
return struct.pack('<I', n)
@staticmethod
def pack_i32(n: i32):
return struct.pack('<i', n)
@staticmethod
def pack_u64(n: u64):
return struct.pack('<Q', n)
@staticmethod
def pack_i64(n: i64):
return struct.pack('<q', n)
@staticmethod
def pack_f32(n: f32):
return struct.pack('<f', n)
@staticmethod
def pack_f64(n: f64):
return struct.pack('<d', n)
class BigEndian:
@staticmethod
def u8(r: bytes):
return struct.unpack('>B', r)[0]
@staticmethod
def i8(r: bytes):
return struct.unpack('>b', r)[0]
@staticmethod
def u16(r: bytes):
return struct.unpack('>H', r)[0]
@staticmethod
def i16(r: bytes):
return struct.unpack('>h', r)[0]
@staticmethod
def u32(r: bytes):
return struct.unpack('>I', r)[0]
@staticmethod
def i32(r: bytes):
return struct.unpack('>i', r)[0]
@staticmethod
def u64(r: bytes):
return struct.unpack('>Q', r)[0]
@staticmethod
def i64(r: bytes):
return struct.unpack('>q', r)[0]
@staticmethod
def f32(r: bytes):
return struct.unpack('>f', r)[0]
@staticmethod
def f64(r: bytes):
return struct.unpack('>d', r)[0]
@staticmethod
def pack_u8(n: u8):
return struct.pack('>B', n)
@staticmethod
def pack_i8(n: i8):
return struct.pack('>b', n)
@staticmethod
def pack_u16(n: u16):
return struct.pack('>H', n)
@staticmethod
def pack_i16(n: i16):
return struct.pack('>h', n)
@staticmethod
def pack_u32(n: u32):
return struct.pack('>I', n)
@staticmethod
def pack_i32(n: i32):
return struct.pack('>i', n)
@staticmethod
def pack_u64(n: u64):
return struct.pack('>Q', n)
@staticmethod
def pack_i64(n: i64):
return struct.pack('>q', n)
@staticmethod
def pack_f32(n: f32):
return struct.pack('>f', n)
@staticmethod
def pack_f64(n: f64):
return struct.pack('>d', n)
class MemoryLoad:
@staticmethod
def i8(r: list):
if utils.is_all_real(r[0]):
return ctypes.c_int8(r[0]).value
else:
return r[0]
@staticmethod
def u8(r: list):
return r[0]
@staticmethod
def i16(r: list):
if utils.is_all_real(r[0], r[1]):
return ctypes.c_int16(r[0] + (r[1] << 8)).value
else:
for i in range(len(r)):
r[i] = utils.to_symbolic(r[i], 8)
return z3.Concat(r[1], r[0])
@staticmethod
def u16(r: list):
if utils.is_all_real(r[0], r[1]):
return ctypes.c_uint16(r[0] + (r[1] << 8)).value
else:
for i in range(len(r)):
r[i] = utils.to_symbolic(r[i], 8)
return z3.Concat(r[1], r[0])
@staticmethod
def i32(r: list):
if utils.is_all_real(r[0], r[1], r[2], r[3]):
return ctypes.c_int32(r[0] + (r[1] << 8) + (r[2] << 16) + (r[3] << 24)).value
else:
for i in range(len(r)):
r[i] = utils.to_symbolic(r[i], 8)
return z3.Concat(r[3], r[2], r[1], r[0])
@staticmethod
def u32(r: list):
if utils.is_all_real(r[0], r[1], r[2], r[3]):
return ctypes.c_uint32(r[0] + (r[1] << 8) + (r[2] << 16) + (r[3] << 24)).value
else:
for i in range(len(r)):
r[i] = utils.to_symbolic(r[i], 8)
return z3.Concat(r[3], r[2], r[1], r[0])
@staticmethod
def i64(r: list):
if utils.is_all_real(r[0], r[1], r[2], r[3], r[4], r[5], r[6], r[7]):
return ctypes.c_int64(r[0] + (r[1] << 8) + (r[2] << 16) + (r[3] << 24) +
(r[4] << 32) + (r[5] << 40) + (r[6] << 48) + (r[7] << 56)).value
else:
for i in range(len(r)):
r[i] = utils.to_symbolic(r[i], 8)
return z3.Concat(r[7], r[6], r[5], r[4], r[3], r[2], r[1], r[0])
@staticmethod
def u64(r: list):
# if utils.is_all_real(r[0], r[1], r[2], r[3], r[4], r[5], r[6], r[7]):
# return ctypes.c_int64(r[0] + (r[1] << 8) + (r[2] << 16) + (r[3] << 24) +
# (r[4] << 32) + (r[5] << 40) + (r[6] << 48) + (r[7] << 56)).value
# else:
# for i in range(len(r)):
# r[i] = utils.to_symbolic(r[i], 8)
# return z3.Concat(r[7], r[6], r[5], r[4], r[3], r[2], r[1], r[0])
return MemoryLoad.i64(r)
class MemoryStore:
@staticmethod
def pack_i8(n: i8):
if utils.is_all_real(n):
return [n & 0xFF]
else:
return [n]
@staticmethod
def pack_u8(n: u8):
if utils.is_all_real(n):
return [n & 0xFF]
else:
return [n]
@staticmethod
def pack_i16(n: i16):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n)]
@staticmethod
def pack_u16(n: u16):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n)]
@staticmethod
def pack_i32(n: i32):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8, (n & 0xFF0000) >> 16, (n & 0xFF000000) >> 24]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n), z3.Extract(23, 16, n), z3.Extract(31, 24, n)]
@staticmethod
def pack_u32(n: u32):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8, (n & 0xFF0000) >> 16, (n & 0xFF000000) >> 24]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n), z3.Extract(23, 16, n), z3.Extract(31, 24, n)]
@staticmethod
def pack_i64(n: i64):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8, (n & 0xFF0000) >> 16, (n & 0xFF000000) >> 24, (n & 0xFF00000000) >> 32,
(n & 0xFF0000000000) >> 40, (n & 0xFF000000000000) >> 48, (n & 0xFF000000000000) >> 56]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n), z3.Extract(23, 16, n), z3.Extract(31, 24, n),
z3.Extract(39, 32, n), z3.Extract(47, 40, n), z3.Extract(55, 48, n), z3.Extract(63, 56, n)]
@staticmethod
def pack_u64(n: i64):
if utils.is_all_real(n):
return [n & 0xFF, (n & 0xFF00) >> 8, (n & 0xFF0000) >> 16, (n & 0xFF000000) >> 24, (n & 0xFF00000000) >> 32,
(n & 0xFF0000000000) >> 40, (n & 0xFF000000000000) >> 48, (n & 0xFF000000000000) >> 56]
else:
return [z3.Extract(7, 0, n), z3.Extract(15, 8, n), z3.Extract(23, 16, n), z3.Extract(31, 24, n),
z3.Extract(39, 32, n), z3.Extract(47, 40, n), z3.Extract(55, 48, n), z3.Extract(63, 56, n)]
@staticmethod
def pack_f32(n: f32):
if utils.is_all_real(n):
float_bytes = struct.pack('<f', n)
return [float_bytes for float_byte in float_bytes]
f32_bv = z3.fpToIEEEBV(n)
return [z3.Extract(7, 0, f32_bv), z3.Extract(15, 8, f32_bv),
z3.Extract(23, 16, f32_bv), z3.Extract(31, 24, f32_bv)]
@staticmethod
def pack_f64(n: f64):
if utils.is_all_real(n):
double_bytes = struct.pack('<d', n)
return [double_byte for double_byte in double_bytes]
f64_bv = z3.fpToIEEEBV(n)
return [z3.Extract(7, 0, f64_bv), z3.Extract(15, 8, f64_bv),
z3.Extract(23, 16, f64_bv), z3.Extract(31, 24, f64_bv),
z3.Extract(39, 32, f64_bv), z3.Extract(47, 40, f64_bv),
z3.Extract(55, 48, f64_bv), z3.Extract(63, 56, f64_bv)]
def leb(reader, maxbits=32, signed=False):
if isinstance(reader, (bytes, bytearray)):
reader = io.BytesIO(reader)
r = 0
s = 0
b = 0
i = 0
a = bytearray()
while True:
byte = ord(reader.read(1))
i += 1
a.append(byte)
r |= ((byte & 0x7F) << s)
s += 7
if (byte & 0x80) == 0:
break
b += 1
assert b <= math.ceil(maxbits / 7.0)
if signed and (s < maxbits) and (byte & 0x40):
r |= -(1 << s)
return i, r, a
def rotl_u32(x: int, k: int):
x = int2u32(x)
k = int2u32(k)
n = 32
s = k & (n - 1)
return ((x << s) | (x >> (n - s))) & 0xFFFFFFFF
def rotl_u64(x: int, k: int):
x = int2u64(x)
k = int2u64(k)
n = 64
s = k & (n - 1)
return ((x << s) | (x >> (n - s))) & 0xFFFFFFFF
def rotr_u32(x: int, k: int):
return rotl_u32(x, -k)
def rotr_u64(x: int, k: int):
return rotl_u64(x, -k)
def idiv_s(a, b):
return a // b if a * b > 0 else (a + (-a % b)) // b
def irem_s(a, b):
return a % b if a * b > 0 else -(-a % b)