}
/*
*@overload
*Overloaded function tgamma_stirl
*Takes one parameter
*Uses some defined policy as default
*
*@z - argument of gamma function
*returns gamma(z)
*/
template <class T>
T tgamma_stirl(T z)
{
return polygamma(z,boost::math::policies::policy<>());
}
//Examples for the use of functions
typedef boost::multiprecision::cpp_dec_float_100 float100;
bernoulli<float100> bn1; //precomputes and stores first 100 bernoulli numbers as default constructor is called
std::cout<<bn1.get_bernoulli_num(10); //prints 10th bernoulli number
bernoulli<float100> bn2(50) //precomputes and stores first 50 bernoulli numbers as specified in parameterized constructor
std::cout<<polygamma<float100>(3,2) //prints polygamma of 3 for order 2
std::cout<<lgamma_stirl<float100>(30); //prints ln(gamma(30)) using stirling's approximation
std::cout<<tgamma_stirl<float100>(30); //prints gamma(30)
bool EvalScript(vector<vector<unsigned char> >& stack, const CScript& script, const CTransaction& txTo, unsigned int nIn, int nHashType)
{
CAutoBN_CTX pctx;
CScript::const_iterator pc = script.begin();
CScript::const_iterator pend = script.end();
CScript::const_iterator pbegincodehash = script.begin();
vector<bool> vfExec;
vector<valtype> altstack;
if (script.size() > 10000)
return false;
int nOpCount = 0;
try
{
while (pc < pend)
{
bool fExec = !count(vfExec.begin(), vfExec.end(), false);
//
// Read instruction
//
opcodetype opcode;
valtype vchPushValue;
if (!script.GetOp(pc, opcode, vchPushValue))
return false;
if (vchPushValue.size() > 5000)
return false;
if (opcode > OP_16 && nOpCount++ > 200)
return false;
if (fExec && opcode <= OP_PUSHDATA4)
stack.push_back(vchPushValue);
else if (fExec || (OP_IF <= opcode && opcode <= OP_ENDIF))
switch (opcode)
{
//
// Push value
//
case OP_1NEGATE:
case OP_1:
case OP_2:
case OP_3:
case OP_4:
case OP_5:
case OP_6:
case OP_7:
case OP_8:
case OP_9:
case OP_10:
case OP_11:
case OP_12:
case OP_13:
case OP_14:
case OP_15:
case OP_16:
{
// ( -- value)
CBigNum bn((int)opcode - (int)(OP_1 - 1));
stack.push_back(bn.getvch());
}
break;
//
// Control
//
case OP_NOP:
case OP_NOP1: case OP_NOP2: case OP_NOP3: case OP_NOP4: case OP_NOP5:
case OP_NOP6: case OP_NOP7: case OP_NOP8: case OP_NOP9: case OP_NOP10:
break;
case OP_VER:
case OP_VERIF:
case OP_VERNOTIF:
{
return false;
}
break;
case OP_IF:
case OP_NOTIF:
{
// <expression> if [statements] [else [statements]] endif
bool fValue = false;
if (fExec)
{
if (stack.size() < 1)
return false;
valtype& vch = stacktop(-1);
fValue = CastToBool(vch);
if (opcode == OP_NOTIF)
fValue = !fValue;
stack.pop_back();
}
vfExec.push_back(fValue);
}
break;
case OP_ELSE:
{
if (vfExec.empty())
return false;
vfExec.back() = !vfExec.back();
}
break;
case OP_ENDIF:
{
if (vfExec.empty())
return false;
vfExec.pop_back();
}
break;
case OP_VERIFY:
{
// (true -- ) or
// (false -- false) and return
if (stack.size() < 1)
return false;
bool fValue = CastToBool(stacktop(-1));
if (fValue)
stack.pop_back();
else
return false;
}
break;
case OP_RETURN:
{
return false;
}
break;
//
// Stack ops
//
case OP_TOALTSTACK:
{
if (stack.size() < 1)
return false;
altstack.push_back(stacktop(-1));
stack.pop_back();
}
break;
case OP_FROMALTSTACK:
{
if (altstack.size() < 1)
return false;
stack.push_back(altstacktop(-1));
altstack.pop_back();
}
break;
case OP_2DROP:
{
// (x1 x2 -- )
stack.pop_back();
stack.pop_back();
}
break;
case OP_2DUP:
{
// (x1 x2 -- x1 x2 x1 x2)
if (stack.size() < 2)
return false;
valtype vch1 = stacktop(-2);
valtype vch2 = stacktop(-1);
stack.push_back(vch1);
stack.push_back(vch2);
}
break;
case OP_3DUP:
{
// (x1 x2 x3 -- x1 x2 x3 x1 x2 x3)
if (stack.size() < 3)
return false;
valtype vch1 = stacktop(-3);
valtype vch2 = stacktop(-2);
valtype vch3 = stacktop(-1);
stack.push_back(vch1);
stack.push_back(vch2);
stack.push_back(vch3);
}
break;
case OP_2OVER:
{
// (x1 x2 x3 x4 -- x1 x2 x3 x4 x1 x2)
if (stack.size() < 4)
return false;
valtype vch1 = stacktop(-4);
valtype vch2 = stacktop(-3);
stack.push_back(vch1);
stack.push_back(vch2);
}
break;
case OP_2ROT:
{
// (x1 x2 x3 x4 x5 x6 -- x3 x4 x5 x6 x1 x2)
if (stack.size() < 6)
return false;
valtype vch1 = stacktop(-6);
valtype vch2 = stacktop(-5);
stack.erase(stack.end()-6, stack.end()-4);
stack.push_back(vch1);
stack.push_back(vch2);
}
break;
case OP_2SWAP:
{
// (x1 x2 x3 x4 -- x3 x4 x1 x2)
if (stack.size() < 4)
return false;
swap(stacktop(-4), stacktop(-2));
swap(stacktop(-3), stacktop(-1));
}
break;
case OP_IFDUP:
{
// (x - 0 | x x)
if (stack.size() < 1)
return false;
valtype vch = stacktop(-1);
if (CastToBool(vch))
stack.push_back(vch);
}
break;
case OP_DEPTH:
{
// -- stacksize
CBigNum bn(stack.size());
stack.push_back(bn.getvch());
}
break;
case OP_DROP:
{
// (x -- )
if (stack.size() < 1)
return false;
stack.pop_back();
}
break;
case OP_DUP:
{
// (x -- x x)
if (stack.size() < 1)
return false;
valtype vch = stacktop(-1);
stack.push_back(vch);
}
break;
case OP_NIP:
{
// (x1 x2 -- x2)
if (stack.size() < 2)
return false;
stack.erase(stack.end() - 2);
}
break;
case OP_OVER:
{
// (x1 x2 -- x1 x2 x1)
if (stack.size() < 2)
return false;
valtype vch = stacktop(-2);
stack.push_back(vch);
}
break;
case OP_PICK:
case OP_ROLL:
{
// (xn ... x2 x1 x0 n - xn ... x2 x1 x0 xn)
// (xn ... x2 x1 x0 n - ... x2 x1 x0 xn)
if (stack.size() < 2)
return false;
int n = CBigNum(stacktop(-1)).getint();
stack.pop_back();
if (n < 0 || n >= stack.size())
return false;
valtype vch = stacktop(-n-1);
if (opcode == OP_ROLL)
stack.erase(stack.end()-n-1);
stack.push_back(vch);
}
break;
case OP_ROT:
{
// (x1 x2 x3 -- x2 x3 x1)
// x2 x1 x3 after first swap
// x2 x3 x1 after second swap
if (stack.size() < 3)
return false;
swap(stacktop(-3), stacktop(-2));
swap(stacktop(-2), stacktop(-1));
}
break;
case OP_SWAP:
{
// (x1 x2 -- x2 x1)
if (stack.size() < 2)
return false;
swap(stacktop(-2), stacktop(-1));
}
break;
case OP_TUCK:
{
// (x1 x2 -- x2 x1 x2)
if (stack.size() < 2)
return false;
valtype vch = stacktop(-1);
stack.insert(stack.end()-2, vch);
}
break;
//
// Splice ops
//
case OP_CAT:
{
// (x1 x2 -- out)
if (stack.size() < 2)
return false;
valtype& vch1 = stacktop(-2);
valtype& vch2 = stacktop(-1);
vch1.insert(vch1.end(), vch2.begin(), vch2.end());
stack.pop_back();
if (stacktop(-1).size() > 5000)
return false;
}
break;
case OP_SUBSTR:
{
// (in begin size -- out)
if (stack.size() < 3)
return false;
valtype& vch = stacktop(-3);
int nBegin = CBigNum(stacktop(-2)).getint();
int nEnd = nBegin + CBigNum(stacktop(-1)).getint();
if (nBegin < 0 || nEnd < nBegin)
return false;
if (nBegin > vch.size())
nBegin = vch.size();
if (nEnd > vch.size())
nEnd = vch.size();
vch.erase(vch.begin() + nEnd, vch.end());
vch.erase(vch.begin(), vch.begin() + nBegin);
stack.pop_back();
stack.pop_back();
}
break;
case OP_LEFT:
case OP_RIGHT:
{
// (in size -- out)
if (stack.size() < 2)
return false;
valtype& vch = stacktop(-2);
int nSize = CBigNum(stacktop(-1)).getint();
if (nSize < 0)
return false;
if (nSize > vch.size())
nSize = vch.size();
if (opcode == OP_LEFT)
vch.erase(vch.begin() + nSize, vch.end());
else
vch.erase(vch.begin(), vch.end() - nSize);
stack.pop_back();
}
break;
case OP_SIZE:
{
// (in -- in size)
if (stack.size() < 1)
return false;
CBigNum bn(stacktop(-1).size());
stack.push_back(bn.getvch());
}
break;
//
// Bitwise logic
//
case OP_INVERT:
{
// (in - out)
if (stack.size() < 1)
return false;
valtype& vch = stacktop(-1);
for (int i = 0; i < vch.size(); i++)
vch[i] = ~vch[i];
}
break;
case OP_AND:
case OP_OR:
case OP_XOR:
{
// (x1 x2 - out)
if (stack.size() < 2)
return false;
valtype& vch1 = stacktop(-2);
valtype& vch2 = stacktop(-1);
MakeSameSize(vch1, vch2);
if (opcode == OP_AND)
{
for (int i = 0; i < vch1.size(); i++)
vch1[i] &= vch2[i];
}
else if (opcode == OP_OR)
{
for (int i = 0; i < vch1.size(); i++)
vch1[i] |= vch2[i];
}
else if (opcode == OP_XOR)
{
for (int i = 0; i < vch1.size(); i++)
vch1[i] ^= vch2[i];
}
stack.pop_back();
}
break;
case OP_EQUAL:
case OP_EQUALVERIFY:
//case OP_NOTEQUAL: // use OP_NUMNOTEQUAL
{
// (x1 x2 - bool)
if (stack.size() < 2)
return false;
valtype& vch1 = stacktop(-2);
valtype& vch2 = stacktop(-1);
bool fEqual = (vch1 == vch2);
// OP_NOTEQUAL is disabled because it would be too easy to say
// something like n != 1 and have some wiseguy pass in 1 with extra
// zero bytes after it (numerically, 0x01 == 0x0001 == 0x000001)
//if (opcode == OP_NOTEQUAL)
// fEqual = !fEqual;
stack.pop_back();
stack.pop_back();
stack.push_back(fEqual ? vchTrue : vchFalse);
if (opcode == OP_EQUALVERIFY)
{
if (fEqual)
stack.pop_back();
else
return false;
}
}
break;
//
// Numeric
//
case OP_1ADD:
case OP_1SUB:
case OP_2MUL:
case OP_2DIV:
case OP_NEGATE:
case OP_ABS:
case OP_NOT:
case OP_0NOTEQUAL:
{
// (in -- out)
if (stack.size() < 1)
return false;
if (stacktop(-1).size() > nMaxNumSize)
return false;
CBigNum bn(stacktop(-1));
switch (opcode)
{
case OP_1ADD: bn += bnOne; break;
case OP_1SUB: bn -= bnOne; break;
case OP_2MUL: bn <<= 1; break;
case OP_2DIV: bn >>= 1; break;
case OP_NEGATE: bn = -bn; break;
case OP_ABS: if (bn < bnZero) bn = -bn; break;
case OP_NOT: bn = (bn == bnZero); break;
case OP_0NOTEQUAL: bn = (bn != bnZero); break;
}
stack.pop_back();
stack.push_back(bn.getvch());
}
break;
case OP_ADD:
case OP_SUB:
case OP_MUL:
case OP_DIV:
case OP_MOD:
case OP_LSHIFT:
case OP_RSHIFT:
case OP_BOOLAND:
case OP_BOOLOR:
case OP_NUMEQUAL:
case OP_NUMEQUALVERIFY:
case OP_NUMNOTEQUAL:
case OP_LESSTHAN:
case OP_GREATERTHAN:
case OP_LESSTHANOREQUAL:
case OP_GREATERTHANOREQUAL:
case OP_MIN:
case OP_MAX:
{
// (x1 x2 -- out)
if (stack.size() < 2)
return false;
if (stacktop(-2).size() > nMaxNumSize ||
stacktop(-1).size() > nMaxNumSize)
return false;
CBigNum bn1(stacktop(-2));
CBigNum bn2(stacktop(-1));
CBigNum bn;
switch (opcode)
{
case OP_ADD:
bn = bn1 + bn2;
break;
case OP_SUB:
bn = bn1 - bn2;
break;
case OP_MUL:
if (!BN_mul(&bn, &bn1, &bn2, pctx))
return false;
break;
case OP_DIV:
if (!BN_div(&bn, NULL, &bn1, &bn2, pctx))
return false;
break;
case OP_MOD:
if (!BN_mod(&bn, &bn1, &bn2, pctx))
return false;
break;
case OP_LSHIFT:
if (bn2 < bnZero || bn2 > CBigNum(2048))
return false;
bn = bn1 << bn2.getulong();
break;
case OP_RSHIFT:
if (bn2 < bnZero || bn2 > CBigNum(2048))
return false;
bn = bn1 >> bn2.getulong();
break;
case OP_BOOLAND: bn = (bn1 != bnZero && bn2 != bnZero); break;
case OP_BOOLOR: bn = (bn1 != bnZero || bn2 != bnZero); break;
case OP_NUMEQUAL: bn = (bn1 == bn2); break;
case OP_NUMEQUALVERIFY: bn = (bn1 == bn2); break;
case OP_NUMNOTEQUAL: bn = (bn1 != bn2); break;
case OP_LESSTHAN: bn = (bn1 < bn2); break;
case OP_GREATERTHAN: bn = (bn1 > bn2); break;
case OP_LESSTHANOREQUAL: bn = (bn1 <= bn2); break;
case OP_GREATERTHANOREQUAL: bn = (bn1 >= bn2); break;
case OP_MIN: bn = (bn1 < bn2 ? bn1 : bn2); break;
case OP_MAX: bn = (bn1 > bn2 ? bn1 : bn2); break;
}
stack.pop_back();
stack.pop_back();
stack.push_back(bn.getvch());
if (opcode == OP_NUMEQUALVERIFY)
{
if (CastToBool(stacktop(-1)))
stack.pop_back();
else
return false;
}
}
break;
case OP_WITHIN:
{
// (x min max -- out)
if (stack.size() < 3)
return false;
if (stacktop(-3).size() > nMaxNumSize ||
stacktop(-2).size() > nMaxNumSize ||
stacktop(-1).size() > nMaxNumSize)
return false;
CBigNum bn1(stacktop(-3));
CBigNum bn2(stacktop(-2));
CBigNum bn3(stacktop(-1));
bool fValue = (bn2 <= bn1 && bn1 < bn3);
stack.pop_back();
stack.pop_back();
stack.pop_back();
stack.push_back(fValue ? vchTrue : vchFalse);
}
break;
//
// Crypto
//
case OP_RIPEMD160:
case OP_SHA1:
case OP_SHA256:
case OP_HASH160:
case OP_HASH256:
{
// (in -- hash)
if (stack.size() < 1)
return false;
valtype& vch = stacktop(-1);
valtype vchHash((opcode == OP_RIPEMD160 || opcode == OP_SHA1 || opcode == OP_HASH160) ? 20 : 32);
if (opcode == OP_RIPEMD160)
RIPEMD160(&vch[0], vch.size(), &vchHash[0]);
else if (opcode == OP_SHA1)
SHA1(&vch[0], vch.size(), &vchHash[0]);
else if (opcode == OP_SHA256)
SHA256(&vch[0], vch.size(), &vchHash[0]);
else if (opcode == OP_HASH160)
{
uint160 hash160 = Hash160(vch);
memcpy(&vchHash[0], &hash160, sizeof(hash160));
}
else if (opcode == OP_HASH256)
{
uint256 hash = Hash(vch.begin(), vch.end());
memcpy(&vchHash[0], &hash, sizeof(hash));
}
stack.pop_back();
stack.push_back(vchHash);
}
break;
case OP_CODESEPARATOR:
{
// Hash starts after the code separator
pbegincodehash = pc;
}
break;
case OP_CHECKSIG:
case OP_CHECKSIGVERIFY:
{
// (sig pubkey -- bool)
if (stack.size() < 2)
return false;
valtype& vchSig = stacktop(-2);
valtype& vchPubKey = stacktop(-1);
////// debug print
//PrintHex(vchSig.begin(), vchSig.end(), "sig: %s\n");
//PrintHex(vchPubKey.begin(), vchPubKey.end(), "pubkey: %s\n");
// Subset of script starting at the most recent codeseparator
CScript scriptCode(pbegincodehash, pend);
// Drop the signature, since there's no way for a signature to sign itself
scriptCode.FindAndDelete(CScript(vchSig));
bool fSuccess = CheckSig(vchSig, vchPubKey, scriptCode, txTo, nIn, nHashType);
stack.pop_back();
stack.pop_back();
stack.push_back(fSuccess ? vchTrue : vchFalse);
if (opcode == OP_CHECKSIGVERIFY)
{
if (fSuccess)
stack.pop_back();
else
return false;
}
}
break;
case OP_CHECKMULTISIG:
case OP_CHECKMULTISIGVERIFY:
{
// ([sig ...] num_of_signatures [pubkey ...] num_of_pubkeys -- bool)
int i = 1;
if (stack.size() < i)
return false;
int nKeysCount = CBigNum(stacktop(-i)).getint();
if (nKeysCount < 0)
return false;
int ikey = ++i;
i += nKeysCount;
if (stack.size() < i)
return false;
int nSigsCount = CBigNum(stacktop(-i)).getint();
if (nSigsCount < 0 || nSigsCount > nKeysCount)
return false;
int isig = ++i;
i += nSigsCount;
if (stack.size() < i)
return false;
// Subset of script starting at the most recent codeseparator
CScript scriptCode(pbegincodehash, pend);
// Drop the signatures, since there's no way for a signature to sign itself
for (int k = 0; k < nSigsCount; k++)
{
valtype& vchSig = stacktop(-isig-k);
scriptCode.FindAndDelete(CScript(vchSig));
}
bool fSuccess = true;
while (fSuccess && nSigsCount > 0)
{
valtype& vchSig = stacktop(-isig);
valtype& vchPubKey = stacktop(-ikey);
// Check signature
if (CheckSig(vchSig, vchPubKey, scriptCode, txTo, nIn, nHashType))
{
isig++;
nSigsCount--;
}
ikey++;
nKeysCount--;
// If there are more signatures left than keys left,
// then too many signatures have failed
if (nSigsCount > nKeysCount)
fSuccess = false;
}
while (i-- > 0)
stack.pop_back();
stack.push_back(fSuccess ? vchTrue : vchFalse);
if (opcode == OP_CHECKMULTISIGVERIFY)
{
if (fSuccess)
stack.pop_back();
else
return false;
}
}
break;
default:
return false;
}
// Size limits
if (stack.size() + altstack.size() > 1000)
return false;
}
}
catch (...)
{
return false;
}
if (!vfExec.empty())
return false;
return true;
}
