public void Test_BitTricks_Min_Unsigned()
{
Tools tools = this.CreateTools();
tools.StateConfig.Set_All_Reg_Off();
tools.StateConfig.RAX = true;
tools.StateConfig.RBX = true;
tools.StateConfig.RDX = true;
tools.StateConfig.CF = true;
string line1 = "sub rax, rbx";
string line2 = "sbb rdx, rdx"; // copy CF to all bits of edx
string line3 = "and rdx, rax";
string line4 = "add rbx, rdx";
{ // forward
State state = this.CreateState(tools);
BitVecExpr rax0 = state.Create(Rn.RAX);
BitVecExpr rbx0 = state.Create(Rn.RBX);
state = Runner.SimpleStep_Forward(line1, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line1 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line2, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line2 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line3, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line3 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line4, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line4 + "\", we know:\n" + state);
}
// ebx is minimum of ebx and eax
Context ctx = state.Ctx;
BitVecExpr rbx1 = state.Create(Rn.RBX);
rax0 = rax0.Translate(ctx) as BitVecExpr;
rbx0 = rbx0.Translate(ctx) as BitVecExpr;
BoolExpr t = ctx.MkEq(rbx1, ctx.MkITE(ctx.MkBVUGT(rax0, rbx0), rbx0, rax0));
{
state.Solver.Push();
state.Solver.Assert(t);
if (state.Solver.Check() != Status.SATISFIABLE)
{
if (LogToDisplay)
{
Console.WriteLine("UnsatCore has " + state.Solver.UnsatCore.Length + " elements");
}
foreach (BoolExpr b in state.Solver.UnsatCore)
{
if (LogToDisplay)
{
Console.WriteLine("UnsatCore=" + b);
}
}
Assert.Fail();
}
state.Solver.Pop();
}
{
state.Solver.Push();
state.Solver.Assert(ctx.MkNot(t));
if (state.Solver.Check() == Status.SATISFIABLE)
{
if (LogToDisplay)
{
Console.WriteLine("Model=" + state.Solver.Model);
}
Assert.Fail();
}
state.Solver.Pop();
}
Assert.AreEqual(Tv.ONE, ToolsZ3.GetTv(t, state.Solver, state.Ctx));
}
}
public void Test_BitTricks_Mod3()
{
/*
* mod3_A PROC
* ; parameter 1: rcx
* mov r8, 0aaaaaaaaaaaaaaabH ;; (scaled) reciprocal of 3
* mov rax, rcx
* mul r8 ;; multiply with reciprocal
* shr rdx, 1 ;; quotient
* lea r9, QWORD PTR [rdx+rdx*2] ;; back multiply with 3
* neg r9
* add rcx, r9 ;; subtract from dividend
* mov rax, rcx ;; remainder
* ret
* mod3_A ENDP
*
* mod3_B PROC
* ; parameter 1: rcx
* mov r8, 3
* mov rax, rcx
* xor rdx, rdx
* idiv r8
* mov rax, rdx
* ret
* mod3_B ENDP
*/
Tools tools = this.CreateTools(0);
tools.StateConfig.Set_All_Off();
tools.StateConfig.RAX = true;
tools.StateConfig.RCX = true;
tools.StateConfig.RDX = true;
tools.StateConfig.R8 = true;
tools.StateConfig.R9 = true;
tools.StateConfig.R10 = true;
string line0 = "mov rcx, r10";
string line1 = "mov r8, 0aaaaaaaaaaaaaaabH";
string line2 = "mov rax, rcx";
string line3 = "mul r8";
string line4 = "shr rdx, 1";
string line5 = "lea r9, QWORD PTR [rdx+rdx*2]";
string line6 = "neg r9";
string line7 = "add rcx, r9"; // rcx has result of
string line8 = "mov r8, 3";
string line9 = "mov rax, r10";
string line10 = "mov rdx, 0";
string line11 = "idiv r8";
if (false)
{
State state = this.CreateState(tools);
state = Runner.SimpleStep_Forward(line0, state);
state = Runner.SimpleStep_Forward(line1, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line1 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line2, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line2 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line3, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line3 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line4, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line4 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line5, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line5 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line6, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line6 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line7, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line7 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line8, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line8 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line9, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line9 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line10, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line10 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line11, state);
if (LogToDisplay)
{
Console.WriteLine("After \"" + line11 + "\", we know:\n" + state);
}
Context ctx = state.Ctx;
BoolExpr t = ctx.MkEq(state.Create(Rn.RCX), state.Create(Rn.RDX));
if (false)
{// this test does not seem to terminate
state.Solver.Push();
state.Solver.Assert(t);
if (state.Solver.Check() != Status.SATISFIABLE)
{
if (LogToDisplay)
{
Console.WriteLine("UnsatCore has " + state.Solver.UnsatCore.Length + " elements");
}
foreach (BoolExpr b in state.Solver.UnsatCore)
{
if (LogToDisplay)
{
Console.WriteLine("UnsatCore=" + b);
}
}
Assert.Fail();
}
state.Solver.Pop();
}
if (true)
{ // this test does not seem to terminate
state.Solver.Push();
state.Solver.Assert(ctx.MkNot(t));
if (state.Solver.Check() == Status.SATISFIABLE)
{
if (LogToDisplay)
{
Console.WriteLine("Model=" + state.Solver.Model);
}
Assert.Fail();
}
state.Solver.Pop();
}
Assert.AreEqual(Tv.ONE, ToolsZ3.GetTv(t, state.Solver, state.Ctx));
}
}
public void Test_BitTricks_Parallel_Search_GPR_1()
{
Tools tools = this.CreateTools();
tools.StateConfig.Set_All_Reg_Off();
tools.StateConfig.RBX = true;
tools.StateConfig.RCX = true;
tools.StateConfig.RDX = true;
string line1 = "mov ebx, 0x01_00_02_03"; // EBX contains four bytes
string line2 = "lea ecx, [ebx-0x01_01_01_01]"; // substract 1 from each byte
string line3 = "not ebx"; // invert all bytes
string line4 = "and ecx, ebx"; // and these two
string line5 = "and ecx, 80808080h";
{ // forward
State state = this.CreateState(tools);
BitVecExpr bytes = state.Create(Rn.EBX);
if (false)
{ // line 1
state = Runner.SimpleStep_Forward(line1, state);
//if (logToDisplay) Console.WriteLine("After \"" + line1 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line2, state);
//if (logToDisplay) Console.WriteLine("After \"" + line2 + "\", we know:\n" + state);
state = Runner.SimpleStep_Forward(line3, state);
//if (logToDisplay) Console.WriteLine("After \"" + line3 + "\", we know:\n" + state);
state = Runner.SimpleStep_Forward(line4, state);
//if (logToDisplay) Console.WriteLine("After \"" + line4 + "\", we know:\n" + state);
state = Runner.SimpleStep_Forward(line5, state);
//if (logToDisplay) Console.WriteLine("After \"" + line5 + "\", we know:\n" + state);
Context ctx = state.Ctx;
BitVecExpr zero = ctx.MkBV(0, 8);
bytes = bytes.Translate(ctx) as BitVecExpr;
BitVecExpr byte1 = ctx.MkExtract((1 * 8) - 1, (0 * 8), bytes);
BitVecExpr byte2 = ctx.MkExtract((2 * 8) - 1, (1 * 8), bytes);
BitVecExpr byte3 = ctx.MkExtract((3 * 8) - 1, (2 * 8), bytes);
BitVecExpr byte4 = ctx.MkExtract((4 * 8) - 1, (3 * 8), bytes);
{
// if at least one of the bytes is equal to zero, then ECX cannot be equal to zero
// if ECX is zero, then none of the bytes is equal to zero.
BoolExpr property = ctx.MkEq(
ctx.MkOr(
ctx.MkEq(byte1, zero),
ctx.MkEq(byte2, zero),
ctx.MkEq(byte3, zero),
ctx.MkEq(byte4, zero)
),
ctx.MkNot(ctx.MkEq(state.Create(Rn.ECX), ctx.MkBV(0, 32)))
);
TestTools.AreEqual(Tv.ONE, ToolsZ3.GetTv(property, state.Solver, state.Ctx));
}
{
state.Solver.Push();
BoolExpr p = ctx.MkOr(ctx.MkEq(byte1, zero), ctx.MkEq(byte2, zero), ctx.MkEq(byte3, zero), ctx.MkEq(byte4, zero));
state.Solver.Assert(p);
if (logToDisplay)
{
Console.WriteLine("After \"" + p + "\", we know:\n" + state);
}
state.Solver.Pop();
}
{
state.Solver.Push();
BoolExpr p = ctx.MkAnd(
ctx.MkEq(ctx.MkEq(byte1, zero), ctx.MkFalse()),
ctx.MkEq(ctx.MkEq(byte2, zero), ctx.MkFalse()),
ctx.MkEq(ctx.MkEq(byte3, zero), ctx.MkTrue()),
ctx.MkEq(ctx.MkEq(byte4, zero), ctx.MkFalse())
);
state.Solver.Assert(p);
if (logToDisplay)
{
Console.WriteLine("After \"" + p + "\", we know:\n" + state);
}
//state.Solver.Pop();
}
}
}
public void Test_BitTricks_Parallel_Search_GPR_2()
{
Tools tools = this.CreateTools();
tools.StateConfig.Set_All_Reg_Off();
tools.StateConfig.RAX = true;
tools.StateConfig.RBX = true;
tools.StateConfig.RCX = true;
tools.StateConfig.RSP = true;
string line1 = "mov rax, 0x80_80_80_80_80_80_80_80";
string line2 = "mov rsp, 0x01_01_01_01_01_01_01_01";
string line3 = "mov rbx, 0x01_02_03_04_05_06_07_08"; // EBX contains 8 bytes
string line4a = "mov rcx, rbx"; // cannot substract with lea, now we need an extra mov
string line4b = "sub rcx, rsp"; // substract 1 from each byte
string line5 = "not rbx"; // invert all bytes
string line6 = "and rcx, rbx"; // and these two
string line7 = "and rcx, rax";
{ // forward
State state = this.CreateState(tools);
BitVecExpr bytes = state.Create(Rn.RBX);
state = Runner.SimpleStep_Forward(line1, state);
state = Runner.SimpleStep_Forward(line2, state);
if (false)
{
state = Runner.SimpleStep_Forward(line3, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line3 + "\", we know:\n" + state);
}
}
state = Runner.SimpleStep_Forward(line4a, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line4a + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line4b, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line4b + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line5, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line5 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line6, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line6 + "\", we know:\n" + state);
}
state = Runner.SimpleStep_Forward(line7, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line7 + "\", we know:\n" + state);
}
{
// if at least one of the bytes is equal to zero, then ECX cannot be equal to zero
// if ECX is zero, then none of the bytes is equal to zero.
Context ctx = state.Ctx;
BitVecExpr zero8 = ctx.MkBV(0, 8);
bytes = bytes.Translate(ctx) as BitVecExpr;
BitVecExpr byte1 = ctx.MkExtract((1 * 8) - 1, (0 * 8), bytes);
BitVecExpr byte2 = ctx.MkExtract((2 * 8) - 1, (1 * 8), bytes);
BitVecExpr byte3 = ctx.MkExtract((3 * 8) - 1, (2 * 8), bytes);
BitVecExpr byte4 = ctx.MkExtract((4 * 8) - 1, (3 * 8), bytes);
BitVecExpr byte5 = ctx.MkExtract((5 * 8) - 1, (4 * 8), bytes);
BitVecExpr byte6 = ctx.MkExtract((6 * 8) - 1, (5 * 8), bytes);
BitVecExpr byte7 = ctx.MkExtract((7 * 8) - 1, (6 * 8), bytes);
BitVecExpr byte8 = ctx.MkExtract((8 * 8) - 1, (7 * 8), bytes);
BoolExpr property = ctx.MkEq(
ctx.MkOr(
ctx.MkEq(byte1, zero8),
ctx.MkEq(byte2, zero8),
ctx.MkEq(byte3, zero8),
ctx.MkEq(byte4, zero8),
ctx.MkEq(byte5, zero8),
ctx.MkEq(byte6, zero8),
ctx.MkEq(byte7, zero8),
ctx.MkEq(byte8, zero8)
),
ctx.MkNot(ctx.MkEq(state.Create(Rn.RCX), ctx.MkBV(0, 64)))
);
TestTools.AreEqual(Tv.ONE, ToolsZ3.GetTv(property, state.Solver, ctx));
}
}
}
public void Test_BitTricks_Min_Signed()
{
Tools tools = this.CreateTools();
tools.StateConfig.Set_All_Reg_Off();
tools.StateConfig.RAX = true;
tools.StateConfig.RBX = true;
tools.StateConfig.RDX = true;
return; // this trick does not seem to be correct?!
string line1 = "sub rax, rbx"; // Will not work if overflow here!
string line2 = "cqo"; // rdx1 = (rax0 > rbx0) ? -1 : 0
string line3 = "and rdx, rax"; // rdx2 = (rax0 > rbx0) ? 0 : (rax0 - rbx0)
string line4 = "add rbx, rdx"; // rbx1 = (rax0 > rbx0) ? (rbx0 + 0) : (rbx0 + rax0 - rbx0)
{ // forward
State state = this.CreateState(tools);
Context ctx = state.Ctx;
if (true)
{
ulong rax_value = 0x61a4292198602827;
ulong rbx_value = 0x8739140220c24080;
StateUpdate updateState = new StateUpdate("!PREVKEY", "!NEXTKEY", state.Tools);
updateState.Set(Rn.RAX, rax_value);
updateState.Set(Rn.RBX, rbx_value);
state.Update_Forward(updateState);
if (logToDisplay)
{
Console.WriteLine("Initially, we know:\n" + state);
}
}
BitVecExpr rax0 = state.Create(Rn.RAX);
BitVecExpr rbx0 = state.Create(Rn.RBX);
{
state.Solver.Assert(state.Ctx.MkNot(ToolsFlags.Create_OF_Sub(rax0, rbx0, rax0.SortSize, ctx))); // this code only works when there is no overflow in line1
}
{ // line 1
state = Runner.SimpleStep_Forward(line1, state);
// retrieve the overflow after line 1, OF has to be zero for the code to work
state.Solver.AssertAndTrack(ctx.MkNot(state.Create(Flags.OF)), ctx.MkBoolConst("OF-ZERO"));
Assert.AreEqual(Status.SATISFIABLE, state.Solver.Check());
if (logToDisplay)
{
Console.WriteLine("After \"" + line1 + "\", we know:\n" + state);
}
}
{ // line 2
state = Runner.SimpleStep_Forward(line2, state);
//if (logToDisplay) Console.WriteLine("After \"" + line2 + "\", we know:\n" + state);
BoolExpr t2 = ctx.MkEq(state.Create(Rn.RDX), ctx.MkITE(ctx.MkBVSGT(rax0, rbx0), ctx.MkBV(0xFFFF_FFFF_FFFF_FFFF, 64), ctx.MkBV(0, 64)));
//Assert.AreEqual(Tv5.ONE, ToolsZ3.GetTv5(t2, state.Solver, state.Ctx));
}
{
state = Runner.SimpleStep_Forward(line3, state);
//if (logToDisplay) Console.WriteLine("After \"" + line3 + "\", we know:\n" + state);
//BoolExpr t2 = ctx.MkEq(state.Get(Rn.RDX), ctx.MkITE(ctx.MkBVSGT(rax0, rbx0), ctx.MkBV(0, 64), ctx.MkBVSub(rax0, rbx0)));
//Assert.AreEqual(Tv5.ONE, ToolsZ3.GetTv5(t2, state.Solver, state.Ctx));
}
{
state = Runner.SimpleStep_Forward(line4, state);
if (logToDisplay)
{
Console.WriteLine("After \"" + line4 + "\", we know:\n" + state);
}
}
// ebx is minimum of ebx and eax
BitVecExpr rbx1 = state.Create(Rn.RBX);
BoolExpr t = ctx.MkEq(rbx1, ctx.MkITE(ctx.MkBVSGT(rax0, rbx0), rbx0, rax0));
if (false)
{
state.Solver.Push();
state.Solver.AssertAndTrack(t, ctx.MkBoolConst("MIN_RAX_RBX"));
Status s = state.Solver.Check();
if (logToDisplay)
{
Console.WriteLine("Status A = " + s + "; expected " + Status.SATISFIABLE);
}
if (s == Status.UNSATISFIABLE)
{
if (logToDisplay)
{
Console.WriteLine("UnsatCore has " + state.Solver.UnsatCore.Length + " elements");
}
foreach (BoolExpr b in state.Solver.UnsatCore)
{
if (logToDisplay)
{
Console.WriteLine("UnsatCore=" + b);
}
}
if (logToDisplay)
{
Console.WriteLine(state.Solver);
}
Assert.Fail();
}
state.Solver.Pop();
}
if (true)
{
state.Solver.Push();
state.Solver.Assert(ctx.MkNot(t), ctx.MkBoolConst("NOT_MIN_RAX_RBX"));
Status s = state.Solver.Check();
if (logToDisplay)
{
Console.WriteLine("Status B = " + s + "; expected " + Status.UNSATISFIABLE);
}
if (s == Status.SATISFIABLE)
{
if (logToDisplay)
{
Console.WriteLine("Model=" + state.Solver.Model);
}
Assert.Fail();
}
state.Solver.Pop();
}
Assert.AreEqual(Tv.ONE, ToolsZ3.GetTv(t, state.Solver, state.Ctx));
}
}
