sm-plugins/SteamCore/scripting/steamcore/bigint.sp
2017-02-26 00:25:51 +01:00

634 lines
16 KiB
SourcePawn

/***
bigint.inc - Big Integers Operation Library Functions
Version: 0.1
Date: 28-12-2014
Author: Statik
Provides some arithmetic and logical maths functions to operate
with big integers.
**UNFINISHED**
***/
#if defined _BigInt_included
#endinput
#endif
#define _BigInt_included
stock modpowBigInt(base[], exponent[], modulus[], nBase, output[], oSize) // http://en.wikipedia.org/wiki/Modular_exponentiation
{ // Modular exponentiation, Right-to-left binary method (binary exponentiation + memory efficient method)
new eSize = getBigIntSize(exponent);
new mSize = getBigIntSize(modulus);
new auxSize = (mSize+1)*2; // output and base (pow base) are never bigger than modulus
decl aux[auxSize];
decl auxBase[auxSize]; // Is used as a replacemente of the power base, not the numeric base
decl auxExponent[eSize+1];
new parity[2];
output[0] = 1;
output[1] = -1;
copyBigInt(base, auxBase, auxSize);
copyBigInt(exponent, auxExponent, eSize+1);
modBigInt(base, modulus, nBase, auxBase, auxSize);
while (isBiggerThanBigNumber(auxExponent, {0,-1})) // exponent > 0
{
fulldivBigInt(auxExponent, {2,-1}, nBase, auxExponent, eSize+1, parity, sizeof(parity));
if (parity[0] == 1) // (exponent % 2) == 1 / Is exponent odd?
{
multBigInt(output, auxBase, nBase, aux, auxSize);
modBigInt(aux, modulus, nBase, output, oSize);
}
multBigInt(auxBase, auxBase, nBase, auxBase, auxSize);
modBigInt(auxBase, modulus, nBase, auxBase, auxSize);
}
}
stock powBigInt(number[], exponent[], base, output[], oSize) // Exponentiation by squaring recursive algorithm **UNFINISHED**
{ // http://en.wikipedia.org/wiki/Exponentiation_by_squaring
new nSize = getBigIntSize(number);
new eSize = getBigIntSize(exponent);
if (!isBiggerThanBigNumber(exponent, {0,-1})) // Exponent is 0
{
output[0] = 1;
output[1] = -1;
return;
}
if (!isBiggerThanBigNumber(exponent, {1,-1})) // Exponent is 1
{
for (new i = 0; i <= nSize; i++)
{
output[i] = number[i];
}
return;
}
new bool:isExponentEven = (exponent[0] % 2) == 0;
multBigInt(number, number, base, output, oSize); // number^2
if (!isBiggerThanBigNumber(exponent, {2,-1})) return;
if (isExponentEven)
{
//powBigInt(output, exponent/2, base, output, oSize);
}
else
{
//powBigInt(output, exponent-1/2, base, output, oSize);
}
}
stock multBigInt(n1[], n2[], base, output[], oSize)
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
if (n1Size < 40000 && n2Size < 40000)
{
standardMult(n1, n2, base, output, oSize);
}
else
{
karatsubaMult(n1, n2, base, output, oSize);
}
}
stock divBigInt(n1[], n2[], base, output[], oSize)
{
new n2Size = getBigIntSize(n2);
decl remainder[n2Size+1]; // Remainder is never bigger than divisor/denominator
fulldivBigInt(n1, n2, base, output, oSize, remainder, n2Size+1);
}
stock modBigInt(n1[], n2[], base, output[], oSize)
{
new n1Size = getBigIntSize(n1);
decl quotient[n1Size+1]; // Quotient is never bigger than dividend/numerator
fulldivBigInt(n1, n2, base, quotient, n1Size+1, output, oSize);
}
stock fulldivBigInt(n1[], n2[], base, quotient[], qSize, remainder[], rSize)
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
if (qSize < (n1Size+1)) return;
if (!isBiggerThanBigNumber(n2, {0,-1})) // n2 == 0
return;
if (n2Size > n1Size)
{
quotient[0] = 0;
quotient[1] = -1;
copyBigInt(n1, remainder, rSize);
return;
}
decl tempRemainder[rSize+1];
tempRemainder[0] = -1;
quotient[n1Size] = -1;
new i;
for (i = n1Size-1; i >= 0; i--)
{
leftShiftBigInt(tempRemainder, 1);
trimBigInt(tempRemainder);
tempRemainder[0] = n1[i];
quotient[i] = 0;
while (!isBiggerThanBigNumber(n2, tempRemainder)) // (tempRemainder >= n2)
{
subBigInt(tempRemainder, n2, base, tempRemainder, rSize);
quotient[i]++;
}
}
copyBigInt(tempRemainder, remainder, rSize);
trimBigInt(quotient);
}
stock karatsubaMult(n1[], n2[], base, output[], oSize) // Karatsuba recursive algorithm
{ // http://en.wikipedia.org/wiki/Karatsuba_algorithm#Pseudo_Code_Implementation
if (oSize < 2) return;
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
if (n1Size == 1 || n2Size == 1) // Base case
{
standardMult(n1, n2, base, output, oSize);
return;
}
new m = (n1Size > n2Size) ? n1Size : n2Size;
new m2 = m/2;
decl l1[oSize], h1[oSize];
decl l2[oSize], h2[oSize];
splitBigIntAt(n1, m2, l1, oSize, h1, oSize);
splitBigIntAt(n2, m2, l2, oSize, h2, oSize);
decl z0[oSize]; // <-
karatsubaMult(l1, l2, base, z0, oSize);
//standardMult(l1, l2, base, z0, oSize);
decl z1[oSize]; // <-
decl l1plush1[oSize];
decl l2plush2[oSize];
addBigInt(l1, h1, base, l1plush1, oSize);
addBigInt(l2, h2, base, l2plush2, oSize);
karatsubaMult(l1plush1, l2plush2, base, z1, oSize);
//standardMult(l1plush1, l2plush2, base, z1, oSize);
decl z2[oSize]; // <-
karatsubaMult(h1, h2, base, z2, oSize);
//standardMult(h1, h2, base, z2, oSize);
decl z3[oSize]; // <-
subBigInt(z1, z2, base, z3, oSize);
subBigInt(z3, z0, base, z3, oSize);
leftShiftBigInt(z2, 2*m2);
leftShiftBigInt(z3, m2);
addBigInt(z2, z3, base, output, oSize);
addBigInt(output, z0, base, output, oSize);
trimBigInt(output);
}
stock standardMult(n1[], n2[], base, output[], oSize)
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
new bool:n1b = isBiggerThanBigNumber(n1, n2); // Is n1 bigger
new sSize = (n1b) ? n2Size : n1Size; // Smallest size
new bSize = (n1b) ? n1Size : n2Size; // Biggest size
new carry = 0;
decl value[sSize][oSize];
new temp, i, u;
for (i = 0; i < sSize; i++)
{
for (u = 0; u < bSize; u++)
{
temp = n1[(n1b)?u:i] * n2[(n1b)?i:u] + carry;
if (temp >= base)
{
carry = temp / base;
value[i][u] = temp % base;
}
else
{
carry = 0;
value[i][u] = temp;
}
}
if (carry != 0)
{
value[i][u] = carry;
value[i][u+1] = -1;
carry = 0;
}
else
{
value[i][u] = -1;
}
leftShiftBigInt(value[i], i);
}
output[0] = -1; // Initializes output
for (i = 0; i < sSize; i++)
{
addBigInt(output, value[i], base, output, oSize);
}
trimBigInt(output);
}
stock addBigInt(n1[], n2[], base, output[], oSize) // Standard algorithm
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
new carry = 0;
new temp;
new i;
for (i = 0; (i < n1Size || i < n2Size); i++)
{
if (i == oSize) return;
if (i >= n1Size) temp = n2[i] + carry;
else if (i >= n2Size) temp = n1[i] + carry;
else temp = n1[i] + n2[i] + carry;
if (temp >= base)
{
output[i] = temp - base;
carry = 1;
}
else
{
output[i] = temp;
carry = 0;
}
}
if (carry == 1) // Adds the last carry
{
output[i] = carry;
output[i+1] = -1;
}
else output[i] = -1;
trimBigInt(output);
}
stock subBigInt(n1[], n2[], base, output[], oSize) // Standard algorithm
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
new carry = 0;
new temp;
new i;
for (i = 0; (i < n1Size || i < n2Size); i++)
{
if (i == oSize) return;
if (i >= n1Size) temp = n2[i] - carry;
else if (i >= n2Size) temp = n1[i] - carry;
else temp = n1[i] - n2[i] - carry;
if (temp < 0)
{
output[i] = temp + base;
carry = 1;
}
else
{
output[i] = temp;
carry = 0;
}
}
output[i] = -1;
trimBigInt(output);
}
stock bool:splitBigIntAt(number[], index, lowOut[], loSize, highOut[], hoSize)
{
new nSize = getBigIntSize(number);
if (index == 0) return false;
if (index >= nSize) return false;
if (index >= loSize) return false;
if (nSize-index >= hoSize) return false;
new i;
for (i = 0; i < index; i++)
{
lowOut[i] = number[i];
}
lowOut[i] = -1;
trimBigInt(lowOut);
for (i = index; i < nSize; i++)
{
highOut[i-index] = number[i];
}
highOut[i-index] = -1;
trimBigInt(highOut);
return true;
}
stock bool:isEqualToBigNumber(n1[], n2[])
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
if (n1Size != n2Size) return false;
for (new i = 0; i < n1Size; i++)
{
if (n1[i] != n2[i]) return false;
}
return true;
}
stock bool:isBiggerThanBigNumber(n1[], n2[])
{
new n1Size = getBigIntSize(n1);
new n2Size = getBigIntSize(n2);
if (n1Size > n2Size) return true;
if (n1Size < n2Size) return false;
for (new i = (n1Size-1); i >= 0; i--)
{
if (n1[i] == n2[i]) continue;
else if (n1[i] > n2[i]) return true;
else return false;
}
return false; // In case both numbers are the same
}
stock leftShiftBigInt(number[], digits) // Logical shift
{
if (digits == 0) return;
new nSize = getBigIntSize(number);
decl temp[nSize+1];
for (new i = 0; i <= nSize; i++) // Creates a backup
{
temp[i] = number[i];
}
for (new a = 0; a < digits; a++) // Fills with zeros
{
number[a] = 0;
}
for (new i = 0; i <= nSize; i++) // Puts the backup back in
{
number[i+digits] = temp[i];
}
trimBigInt(number);
}
stock trimBigInt(number[]) // Removes left padded zeros
{
new nSize = getBigIntSize(number);
for (new zeros = 0; number[nSize-zeros-1] == 0; zeros++)
{
if (nSize-zeros-1 != 0) number[nSize-zeros-1] = -1;
}
}
stock copyBigInt(number[], output[], oSize)
{
new nSize = getBigIntSize(number);
if (oSize <= nSize) return;
for (new i = 0; i <= nSize; i++)
{
output[i] = number[i];
}
}
stock getBigIntSize(number[])
{
new i;
for (i = 0; number[i] != -1; i++){}
return i;
}
stock toBase256BigInt(number[], output[], oLength)
{
new nSize = getBigIntSize(number);
new finalLength = nSize/2 + (nSize%2);
if (oLength < finalLength) return 0;
new i;
new high, low;
for (i = 0; i < finalLength; i++)
{
if ((i == finalLength-1) && nSize%2 == 1)
high = 0;
else
high = number[i*2+1];
low = number[i*2];
output[finalLength-i-1] = (high << 4) + low;
}
return finalLength;
}
stock bool:hexString2BigInt(const String:hexString[], output[], oSize)
{
new i;
new temp[oSize];
for(i = 0; hexString[i] != 0; i++)
{
if (i >= oSize) return false;
temp[i] = hexChar2Int(hexString[i]);
if (temp[i] == -1) return false;
}
// Inverts number string
for (new u = 0; u < i; u++)
{
output[u] = temp[i-u-1];
}
output[i] = -1; // Terminates the number string
trimBigInt(output);
return true;
}
stock bool:bigInt2HexString(input[], String:hexString[], hsSize)
{
new nSize = getBigIntSize(input);
new i;
for (i = 0; i < (hsSize-1); i++)
{
if (i == nSize) break;
if ((hexString[i] = int2HexChar(input[nSize-i-1])) == -1) return false;
}
hexString[i] = 0;
return true;
}
stock hexChar2Int(input)
{
if(input >= '0' && input <= '9')
return input - '0';
if(input >= 'A' && input <= 'F')
return input - 'A' + 10;
if(input >= 'a' && input <= 'f')
return input - 'a' + 10;
return -1;
}
stock int2HexChar(input)
{
if (input >= 0 && input <= 9)
return input + '0';
if (input >= 10 && input <= 16)
return input + 'A' - 10;
return -1;
}
/*
test()
{
// LOTS OF TESTS
PrintDebug(caller, "Modulus size: %i", getBigIntSize(modulus));
/// Addition test
new n1[] = {0xC,9,4,9,0xF,0,-1};
new n2[] = {0,0x3,5,7,-1};
decl String:s1[7];
decl String:s2[7];
bigInt2HexString(n1, s1, sizeof(s1));
bigInt2HexString(n2, s2, sizeof(s2));
PrintDebug(caller, "HEX 1 : %s", s1);
PrintDebug(caller, "HEX 2 : %s", s2);
new a[20];
addBigInt(n1, n2, 16, a, sizeof(a));
new String:sa[20];
bigInt2HexString(a, sa, sizeof(sa));
PrintDebug(caller, "HEX 1 + HEX 2 = %s", sa);
/// Split test
new n3[] = {4,6,8,2,5,7,3,4,7,2,-1};
new n4[15];
new n5[15];
splitBigIntAt(n3, 5, n4, sizeof(n4), n5, sizeof(n5));
new String:s3[30];
new String:s4[15];
new String:s5[15];
bigInt2HexString(n3, s3, sizeof(s3));
bigInt2HexString(n4, s4, sizeof(s4));
bigInt2HexString(n5, s5, sizeof(s5));
PrintDebug(caller, "%s splitted at index %i", s3, 5);
PrintDebug(caller, "Low: %s", s4);
PrintDebug(caller, "High: %s", s5);
/// Subtraction test
new n6[] = {3,1,3,5,5,9,6,9,-1};
new n7[] = {1,3,5,6,9,6,9,2,-1};
decl String:s6[10];
decl String:s7[10];
bigInt2HexString(n6, s6, sizeof(s6));
bigInt2HexString(n7, s7, sizeof(s7));
new n8[10];
new String:s8[10];
subBigInt(n6, n7, 16, n8, sizeof(n8));
bigInt2HexString(n8, s8, sizeof(s8));
PrintDebug(caller, "Subtracting %s to %s...", s7, s6);
PrintDebug(caller, "Result: %s", s8);
/// Shift test
new n9[] = {3,7,9,1,5,7,8,1,-1};
decl String:s9[15];
bigInt2HexString(n9, s9, sizeof(s9));
PrintDebug(caller, "Shifting %s 3 numbers to left", s9);
leftShiftBigInt(n9, 3);
bigInt2HexString(n9, s9, sizeof(s9));
PrintDebug(caller, "Result: %s", s9);
/// Standard multiplication test
new n10[] = {3,1,3,5,5,9,6,9,-1};
new n11[] = {1,3,5,6,9,6,9,2,-1};
decl String:s10[10];
decl String:s11[10];
bigInt2HexString(n10, s10, sizeof(s10));
bigInt2HexString(n11, s11, sizeof(s11));
new n12[30];
new String:s12[30];
standardMult(n10, n11, 16, n12, sizeof(n12));
bigInt2HexString(n12, s12, sizeof(s12));
PrintDebug(caller, "Multiplying (standard) %s to %s...", s10, s11);
PrintDebug(caller, "Result: %s", s12);
/// Karatsuba multiplication test
new n13[] = {3,1,3,5,5,9,6,9,-1};
new n14[] = {1,3,5,6,9,6,9,2,-1};
decl String:s13[10];
decl String:s14[10];
bigInt2HexString(n13, s13, sizeof(s13));
bigInt2HexString(n14, s14, sizeof(s14));
new n15[30];
new String:s15[30];
karatsubaMult(n13, n14, 16, n15, sizeof(n15));
bigInt2HexString(n15, s15, sizeof(s15));
PrintDebug(caller, "Multiplying (karatsuba) %s to %s...", s13, s14);
PrintDebug(caller, "Result: %s", s15);
/// Exponentiation test
new n16[] = {3,4,5,6,2,5,-1};
new n17[] = {0,1,-1};
decl String:s16[20];
decl String:s17[20];
bigInt2HexString(n16, s16, sizeof(s16));
bigInt2HexString(n17, s17, sizeof(s17));
new n18[30];
new String:s18[30];
powBigInt(n16, n17, 16, n18, sizeof(n18));
bigInt2HexString(n18, s18, sizeof(s18));
PrintDebug(caller, "Exponentiating %s to %s...", s16, s17);
PrintDebug(caller, "Result: %s", s18);
/// Division test
new n19[] = {9,0xC,7,2,-1};
new n20[] = {6,2,6,-1};
decl String:s19[20];
decl String:s20[20];
bigInt2HexString(n19, s19, sizeof(s19));
bigInt2HexString(n20, s20, sizeof(s20));
new n21[30];
new String:s21[30];
new n22[30];
new String:s22[30];
fulldivBigInt(n19, n20, 16, n21, sizeof(n21), n22, sizeof(n22));
bigInt2HexString(n21, s21, sizeof(s21));
bigInt2HexString(n22, s22, sizeof(s22));
PrintDebug(caller, "Dividing %s to %s...", s19, s20);
PrintDebug(caller, "Quotient: %s - Remainder: %s", s21, s22);
/// PKCS#1 v1.5 Padding Scheme test
//decl String:aux[1024] = "BE629EA2D835880BF2572379CC751C5FA44F4A09B6F8CE5CB52C53EEDD0314E77AC827219E78DB1473BBA7BBE8BABC85C02CBC308B75375AE7C4B3AA31A491BB08D1946328F2B1BCE3E07E96D1CFF5E95A553C083A424CD5F6B7F2B55F89B958F0AE3B80A94CF5FEB3BD9417ABD09E1A42456E99128169CCEC176FDF7D2893A5";
new k = strlen(hexModulus);
new String:paddedMessage[k+1];
pkcs1v15Pad(message, k, paddedMessage, k+1);
PrintDebug(caller, "Padding message: %s with %i length modulus ", message, k);
PrintDebug(caller, "Result: %i - %s", strlen(paddedMessage), paddedMessage);
/// Modular exponentiation test
decl n23[1024];
decl n24[20];
decl n25[1024];
hexString2BigInt(paddedMessage, n23, 1024);
hexString2BigInt(hexExponent, n24, 20);
hexString2BigInt(hexModulus, n25, 1024);
//new n23[] = {3,2,-1};
//new n24[] = {5,-1};
//new n25[] = {6,2,6,-1};
new String:s23[1024];
new String:s24[40];
new String:s25[1024];
new n26[1024];
new String:s26[1024];
modpowBigInt(n23, n24, n25, 16, n26, sizeof(n26));
bigInt2HexString(n23, s23, sizeof(s23));
bigInt2HexString(n24, s24, sizeof(s24));
bigInt2HexString(n25, s25, sizeof(s25));
bigInt2HexString(n26, s26, sizeof(s26));
PrintDebug(caller, "Modular Power Test");
PrintDebug(caller, "base = %s", s23);
PrintDebug(caller, "exponent = %s", s24);
PrintDebug(caller, "modulus = %s", s25);
PrintDebug(caller, "Result size: %i, result = \n%s", getBigIntSize(n26), s26);
}
*/