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ContFrac.cpp
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#include "stdafx.h"
const std::string sq = "^2";
extern mpz_t Bi_L1, Bi_L2, Bi_H1, Bi_H2, Bi_K1, Bi_K2;
extern long long g_Disc;
extern long long g_A, g_B, g_D, g_F;
extern mpz_t Dp_NUM, Dp_DEN;
extern unsigned long long SqrtDisc;
extern long long g_CY1, g_CY0;
extern long long g_A2, g_B2;
extern int NbrSols, NbrCo;
extern bool teach;
long long g_A1, g_B1;
int NbrEqs, EqNbr;
std::string UU = "";
std::string VU = "";
std::string UL = "";
std::string VL = "";
std::string UL1 = "";
std::string VL1 = "";
std::string FP = "";
/*******************************************/
/* NextConv: */
/* BigInteger tmp = Prev * A1 + Act * B1; */
/* Act = Prev * A2 + Act * B2; */
/* Prev = Tmp; */
/*******************************************/
void NextConv(mpz_t Bi_Prev, mpz_t Bi_Act, const long long A1,
const long long A2, const long long B1, const long long B2) {
mpz_t t1, t2, tmp;
/*std::cout << "**temp NextConv: Prev = ";
ShowLargeNumber(Bi_Prev);
std::cout << " Act =";
ShowLargeNumber(Bi_Act);
std::cout << " A1 =" << A1 << " A2=" << A2 << " B1=" << B1 << " B2=" << B2 << "\n"; */
mpz_inits(t1, t2, tmp, NULL);
mpz_mul_si(t1, Bi_Prev, A1); // t1 = Prev * A1
mpz_mul_si(t2, Bi_Act, B1); // t2 = Act * B1
mpz_add(tmp, t1, t2); // tmp = Prev * A1 + Act * B1
mpz_mul_si(t1, Bi_Prev, A2); // t1 = Prev * A2
mpz_mul_si(t2, Bi_Act, B2); // t2 = Act * B2
mpz_add(Bi_Act, t1, t2); // act = Prev * A2 + Act * B2
mpz_set(Bi_Prev, tmp); // Prev = Tmp
mpz_clears(t1, t2, tmp, NULL); // avoid memory leakage
/* temporary */
/*std::cout << "**exit NextConv: Prev = ";
ShowLargeNumber(Bi_Prev);
std::cout << " Act =";
ShowLargeNumber(Bi_Act);
std::cout << "\n\n";*/
/* end temporary */
}
/* uses global variables Bi_L1, Bi_L2, g_A, g_B, g_D, g_F, g_CY0, g_CY1*/
bool ShowHomoSols(int type, mpz_t Bi_SHH, mpz_t Bi_SHK, long long s, long long T,
const long long MagnifY, const std::string eqX, const std::string eqY) {
assert(_CrtCheckMemory());
/*std::cout << "**temp ShowHomoSols: s=" << s << " T=" << T << " MagnifY=" << MagnifY << "\n";
std::cout << "Bi_SH1="; ShowLargeNumber(Bi_SH1);
std::cout << " Bi_SHK1="; ShowLargeNumber(Bi_SHK1); std::cout << "\n";*/
int i;
std::string U = (type == 4 ? "'" : "");
std::string X1 = "X";
std::string Y1 = (MagnifY == 1 ? "Y" : "Y'");
if (teach) {
ShowLargeXY(Y1, "Z", Bi_SHH, Bi_SHK, true, eqX, eqY);
std::cout << "Since " << X1 << U << "0 = ";
if (T>1) {
std::cout << T << " " << UU << U << "0 = " << T << " (";
}
ShowLin(s, -g_F, 0, VU + "0", "Z0");
if (T>1) {
std::cout << ")\nand " << Y1 << "0 = " << T << " V0";
}
printf(":\n");
}
MultAddLargeNumbers(s*T, Bi_SHH, -g_F*T, Bi_SHK, Bi_L1); // result stored in Bi_L1
MultLargeNumber(T, Bi_SHH, Bi_L2);
/*std::cout << "**temp ShowHomoSols(1) Bi_L1="; ShowLargeNumber(Bi_L1);
std::cout << " Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";*/
if (type == 4) {
if (teach) {
ShowLargeXY(X1 + U, Y1 + U, Bi_L1, Bi_L2, false, "", "");
}
for (i = (IsZero(Bi_L1) && IsZero(Bi_L2) ? 1 : 0); i<2; i++) {
AddLarge(Bi_L2, -g_CY0, Bi_L2);
//std::cout << "**temp ShowHomoSols(2) Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";
if (teach) {
std::cout << Y1 << "0 = (";
ShowLin(0, i == 0 ? 1 : -1, -g_CY0, "", Y1 + "0");
std::cout << ")/" << par(g_CY1) << "\n";
}
if (tDivLargeNumber(Bi_L2, g_CY1, Bi_L2) != 0) {
//std::cout << "**temp ShowHomoSols(3) Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";
if (teach) {
printf("It is not an integer number. \n");
}
}
else {
//std::cout << "**temp ShowHomoSols(4) Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";
if (teach) {
std::cout << X1 << "0 = (";
ShowLin(i == 0 ? 1 : -1, -g_B, -g_D, X1 + "0", Y1 + "0");
std::cout << ") / " << par(2 * g_A) << "\n";
}
AddLarge(Bi_L1, -g_D, Bi_L1); // L1 -= D
MultAddLargeNumbers(1, Bi_L1, -g_B, Bi_L2, Bi_L1); // store result in L1
//std::cout << "**temp ShowHomoSols(5) Bi_L1="; ShowLargeNumber(Bi_L1); std::cout << "\n";
if (tDivLargeNumber(Bi_L1, 2 * g_A, Bi_L1) != 0) {
//std::cout << "**temp ShowHomoSols(6) Bi_L1="; ShowLargeNumber(Bi_L1); std::cout << "\n";
if (teach) {
printf("It is not an integer number. \n");
}
}
else {
//std::cout << "**temp ShowHomoSols(7) Bi_L1="; ShowLargeNumber(Bi_L1); std::cout << "\n";
if (teach) {
if (MagnifY != 1) {
ShowLargeXY(X1, Y1, Bi_L1, Bi_L2, false, "", "");
std::cout << "Since Y = " << MagnifY << Y1;
}
putchar('\n');
}
MultLargeNumber(MagnifY, Bi_L2, Bi_L2);
ShowLargeXY("X", "Y", Bi_L1, Bi_L2, false, "", "");
/*std::cout << "**temp ShowHomoSols(8) returns true: Bi_L1="; ShowLargeNumber(Bi_L1);
std::cout << " Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";*/
return true;
}
}
//gmp_printf("**temp ShowHomoSols(9) Bi_L1= %lld*%Zd + %lld*%Zd =", -s*T, Bi_SH1, g_F*T, Bi_SHK1);
MultAddLargeNumbers(-s*T, Bi_SHH, g_F*T, Bi_SHK, Bi_L1);
MultLargeNumber(-T, Bi_SHH, Bi_L2);
/*ShowLargeNumber(Bi_L1);
std::cout << " Bi_L2="; ShowLargeNumber(Bi_L2); std::cout << "\n";*/
}
}
else {
if (teach) {
if (MagnifY != 1) {
ShowLargeXY(X1, Y1, Bi_L1, Bi_L2, false, "", "");
std::cout << "Since " << Y1 << " = " << MagnifY << "Y";
}
putchar('\n');
}
MultLargeNumber(MagnifY, Bi_L2, Bi_L2);
if (teach) {
ShowLargeXY("X", "Y", Bi_L1, Bi_L2, false, "", "");
ChangeSign(Bi_L1);
ChangeSign(Bi_L2);
ShowLargeXY("X", "Y", Bi_L1, Bi_L2, false, "", "");
ChangeSign(Bi_L1);
ChangeSign(Bi_L2);
}
/*std::cout << "**temp ShowHomoSols(10) returns true: Bi_L1=";
ShowLargeNumber(Bi_L1);
std::cout << " Bi_L2=";
ShowLargeNumber(Bi_L2);
std::cout << "\n";*/
return true;
}
//std::cout << "**temp ShowHomoSols(11) returns false \n";
return false; // solution not found
}
/***************************************************************************
* type = 1: Find convergents *
* type = 2: Find convergents for x^2 + Bxy + ACy^2 = 1 (recursion) *
* type = 3: Find convergents for modified equation in homogeneous equation *
* type = 4: Find convergents for modified equation in complete solution *
* type = 5: Find convergents for x^2 + Bxy + ACy^2 = 1 (mod B^2-4AC) *
* returns true if there are solutions, otherwise false *
* uses global variables DP_NUM, DP_DEN, Bi_H1, Bi_H2, Bi_K1, Bi_K2, NbrCo *
* NbrEqs, Eqnbr, NbrSols, g_F, g_A1, g_A2, g_B1, g_B2 *
****************************************************************************/
bool ContFrac(const mpz_t Dp_A, int type, const int SqrtSign, long long s, long long T,
long long MagnifY, long long A) {
/*std::cout << "**temp ContFrac: type=" << type << " SqrtSign=" << SqrtSign << " s=" << s;
std::cout << " T=" << T << " MagnifY=" << MagnifY << " A=" << A << "\n";
std::cout << "Dp_NUM=" << numToString(Dp_NUM);
std::cout << " Dp_DEN=" << numToString(Dp_DEN) << "\n";*/
long long P, Z, M, P1, M1, Tmp, K, L, Mu;
mpz_t Dp_P, Dp_M, Dp_Z, Dp_G, Dp_Mu, Dp_K, Dp_L, Dp_M1, Dp_P1, Dp_zz;
long long H1ModCY1 = 1, H2ModCY1 = 0, K1ModCY1 = 0, K2ModCY1 = 1;
bool Sols = true, secondDo = true;
int Conv;
int Co = -1;
std::string U = (type == 4 ? "'" : "");
std::string X1 = "X";
std::string Y1 = (MagnifY == 1 ? "Y" : "Y'");
assert(_CrtCheckMemory());
mpz_inits(Dp_P,Dp_M, Dp_Z, Dp_G, Dp_Mu, Dp_K, Dp_L, Dp_M1, Dp_P1, Dp_zz, NULL);
if (IsOne(Dp_A)) {
/* Dp_A = 1 */
mpz_set_si(Bi_H1, SqrtSign);
mpz_set_si(Bi_K1, 0);
/*std::cout << "**temp ContFrac Bi_H1="; ShowLargeNumber(Bi_H1);
std::cout << " Bi_K1="; ShowLargeNumber(Bi_K1); std::cout << "\n";*/
if (type == 1) {
ShowLargeXY(X1, Y1, Bi_H1, Bi_K1, true, "", "");
mpz_clears(Dp_P, Dp_M, Dp_Z, Dp_G, Dp_Mu, Dp_K, Dp_L, Dp_M1, Dp_P1, Dp_zz, NULL);
//std::cout << "** temp ContFrac returns true (1) - solution(s) found\n";
assert(_CrtCheckMemory());
return true; /* Indicate there are solutions */
}
if ((type == 3 || type == 4) && (g_Disc != 5 || A*g_F<0)) {
if (ShowHomoSols(type, Bi_H1, Bi_K1, s, T, MagnifY, "", "")) {
mpz_clears(Dp_P, Dp_M, Dp_Z, Dp_G, Dp_Mu, Dp_K, Dp_L, Dp_M1, Dp_P1, Dp_zz, NULL);
//std::cout << "**temp ContFrac(2) - solution found\n";
assert(_CrtCheckMemory());
return true; /* Indicate there are solutions */
}
}
}
/* Paso = 1: Quick scan for solutions */
/* Paso = 2: Show actual solutions */
for (int Paso = (type == 2 || g_Disc == 5 && A*g_F>0 && (type == 3 || type == 4) ? 2 : 1);
Sols && Paso <= 2; Paso++) {
Conv = 0;
Sols = false;
mpz_set(Dp_P, Dp_DEN); // P = DEN
if (SqrtSign < 0) {
ChSign(Dp_P);
}
LongToDoublePrecLong(SqrtDisc + (IsNeg(Dp_P) ? 1 : 0), Dp_K);
//std::cout << " Dp_K=" << numToString(Dp_K) << "(1)\n";
if (SqrtSign < 0) {
SubtDoublePrecLong(Dp_K, Dp_NUM, Dp_K); // K -= NUM
//std::cout << " Dp_K=" << numToString(Dp_K) << "(2)\n";
}
else {
AddLarge(Dp_K, Dp_NUM, Dp_K); // K += NUM
//std::cout << " Dp_K=" << numToString(Dp_K) << "(3)\n";
}
//std::cout << " Dp_DEN=" << numToString(Dp_DEN);
Z = DivDoublePrec(Dp_K, Dp_P); // Z = K/P
//std::cout << " Dp_K=" << numToString(Dp_K) << " Dp_P=" << numToString(Dp_P) << "\n";
LongToDoublePrecLong(Z, Dp_M); // M = Z (=K/P)
Mult2LargeNumbers(Dp_M, Dp_DEN, Dp_K); // K = M*DEN
//std::cout << " Dp_K=" << numToString(Dp_K) << " Z=" << Z;
SubtDoublePrecLong(Dp_K, Dp_NUM, Dp_M); // M = K-NUM
//std::cout << " Dp_M=" << numToString(Dp_M) << "(4)\n";
if (SqrtSign < 0) {
ChSign(Dp_M);
}
/* type = 4: Find convergents for modified equation in complete solution */
if (type == 4) {
H2ModCY1 = Z%g_CY1;
}
/* type = 5: Find convergents for x^2 + Bxy + ACy^2 = 1 (mod B^2-4AC) */
if (type == 5) {
g_A1 = g_B2 = 1;
g_A2 = Z%T;
g_B1 = 0;
}
else {
mpz_set_si(Bi_H1, SqrtSign);
mpz_set_si(Bi_H2, Z*SqrtSign);
mpz_set_si(Bi_K1, 0);
mpz_set(Bi_K2, Bi_H1);
/*std::cout << "**temp ContFrac Bi_H1="; ShowLargeNumber(Bi_H1);
std::cout << " Bi_H2="; ShowLargeNumber(Bi_H2);
std::cout << " Bi_K1="; ShowLargeNumber(Bi_K1);
std::cout << " Bi_K2="; ShowLargeNumber(Bi_K2); std::cout << "\n";*/
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
Co = -1;
mpz_set_si(Dp_K, -1); // K = -1
mpz_set_si(Dp_L, -1); // L = -1
//std::cout << " Dp_K=" << numToString(Dp_K) << "(6)\n";
/* set Mu */
switch (type) {
case 1: // find convergents
LongToDoublePrecLong(-2 * g_F*SqrtSign, Dp_Mu);
break;
case 3: // find convergents for modified equation in homogeneous equation
case 4: // find convergents for modified equation in complete solution
LongToDoublePrecLong(-2 * SqrtSign, Dp_Mu);
break;
default: // type = 2 or 5
mpz_set(Dp_Mu, Dp_DEN); // Mu = DEN
if (SqrtSign > 0) {
ChSign(Dp_Mu);
//std::cout << "**temp ContFrac(3A) Dp_Mu= " << numToString(Dp_Mu) << " (revsign)\n";
}
}
/*std::cout << "**temp ContFrac(3B) Dp_Mu= " << numToString(Dp_Mu);
std::cout << " Dp_K=" << numToString(Dp_K);
std::cout << " Dp_P1=" << numToString(Dp_P1) << "\n";*/
do {
LongToDoublePrecLong(g_Disc, Dp_Z); // Z = Disc
//std::cout << "**temp ContFrac Dp_Z=" << numToString(Dp_Z) << "(3D)\n";
Mult2LargeNumbers(Dp_M, Dp_M, Dp_G); // G = M*M
//std::cout << "**temp ContFrac Dp_G=" << numToString(Dp_G) << "\n";
SubtDoublePrecLong(Dp_Z, Dp_G, Dp_G); // G = Z-G = Disc -M*M
//std::cout << "**temp ContFrac Dp_G=" << numToString(Dp_G) << "\n";
DivideDoublePrecLong(Dp_G, Dp_P, Dp_P1); // P1 = (Disc-M*M)/P
//std::cout << "**temp ContFrac Dp_P1=" << numToString(Dp_P1) << "\n";
/* Z = SqrtDisc +(1 or 0, depending on sign of P1) */
LongToDoublePrecLong(SqrtDisc + (IsNeg(Dp_P1) ? 1 : 0), Dp_Z);
AddLarge(Dp_Z, Dp_M, Dp_K); // K = M+Z
//std::cout << "**temp ContFrac Dp_K=" << numToString(Dp_K) << "\n";
/* round Z to a multiple of P1 */
Z = DivDoublePrec(Dp_K, Dp_P1); // Z = K/P1
LongToDoublePrecLong(Z, Dp_G); // G = Z = K/P1
Mult2LargeNumbers(Dp_G, Dp_P1, Dp_Z); // Z=G*P1 i.e Z rounded to multiple of P1
//std::cout << "**temp ContFrac Dp_Z=" << numToString(Dp_Z) << "\n";
SubtDoublePrecLong(Dp_Z, Dp_M, Dp_M1); // M1 = Z-M
//std::cout << " **temp ContFrac Dp_M1=" << numToString(Dp_M1) << "\n";
mpz_add_si(Dp_zz, Dp_M, SqrtDisc); // Dp_zz = SqrtDisc + DP_M
if (Co<0 &&
(mpz_cmp_si(Dp_P, 0) > 0) &&
(mpz_cmp (Dp_P, Dp_zz) <= 0) &&
(mpz_cmp_si(Dp_M, 0) > 0) &&
(mpz_cmp_si(Dp_M, SqrtDisc) <= 0) ) {
/* if (P > 0 & P <= SqrtDisc+M & M > 0 & M < SqrtDisc) */
Co = 0;
mpz_set(Dp_K, Dp_P); // K = P
mpz_set(Dp_L, Dp_M); // L = M
//std::cout << "**temp ContFrac(4) Dp_K=" << numToString(Dp_K);
//std::cout << " Dp_L=" << numToString(Dp_L) << "\n";
}
/*std::cout << "**temp ContFrac(5) type=" << type << " Co=" << Co;
std::cout << " Dp_P=" << numToString(Dp_P);
std::cout << " Dp_Mu=" << numToString(Dp_Mu);
std::cout << " Dp_K=" << numToString(Dp_K);
std::cout << " Dp_P1=" << numToString(Dp_P1) << "\n";*/
if (type == 1 && AreEqual(Dp_P, Dp_Mu) ) {
// Solution found
if (Co % 2 == 0 || !AreEqual(Dp_K, Dp_P1)) {
if (Paso == 2) {
if (g_A2 != 0) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
ShowLargeXY(X1, Y1, Bi_H2, Bi_K2, true, "NUM(" + numToStr(Conv) + ") = ",
"DEN(" + numToStr(Conv) + ") = ");
}
Sols = true;
}
secondDo = false;
//std::cout << "**temp ContFrac(5A)\n";
break;
}
if (type == 3 || type == 4) {
if (Co == 0 && A*g_F>0 && g_Disc == 5) { /* Solution found */
if (Paso == 1) {
secondDo = false;
Sols = true;
//std::cout << "**temp ContFrac(6)\n";
break;
}
else {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
ChangeSign(Bi_H2);
AddLarge(Bi_H1, Bi_H2, Bi_H2);
ChangeSign(Bi_H2);
ChangeSign(Bi_K2);
AddLarge(Bi_K1, Bi_K2, Bi_K2);
ChangeSign(Bi_K2);
if (ShowHomoSols(type, Bi_H2, Bi_K2, s, T, MagnifY,
"NUM(" + numToStr(Conv) + ") - NUM(" + numToStr(Conv - 1) + ") = ",
"DEN(" + numToStr(Conv) + ") - DEN(" + numToStr(Conv - 1) + ") = ")) {
secondDo = false;
Sols = true;
//std::cout << "**temp ContFrac(7) - solution found\n";
break;
}
AddLarge(Bi_H1, Bi_H2, Bi_H2);
AddLarge(Bi_K1, Bi_K2, Bi_K2);
}
}
if (AreEqual(Dp_P1, Dp_Mu)) {
// Solution found
if (Co % 2 == 0 || !AreEqual(Dp_K, Dp_P1) || !AreEqual(Dp_L, Dp_M1) ) {
if (Paso == 2) {
if (g_A2 != 0) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
if (ShowHomoSols(type, Bi_H2, Bi_K2, s, T, MagnifY, "NUM(" + numToStr(Conv) + ") = ",
"DEN(" + numToStr(Conv) + ") = ")) {
secondDo = false;
Sols = true;
//std::cout << "**temp ContFrac(8) - solution found\n";
break;
}
}
else {
if (type == 4) {
Tmp = H2ModCY1*T;
if ((Tmp - g_CY0) % g_CY1 == 0 || (Tmp + g_CY0) % g_CY1 == 0) {
secondDo = false;
Sols = true;
//std::cout << "**temp ContFrac(9)\n";
break;
}
}
else {
secondDo = false;
Sols = true;
//std::cout << "**temp ContFrac(10)\n";
break;
}
}
}
}
if (Paso == 1 && type == 4) {
Tmp = (H1ModCY1 + Z*H2ModCY1) % g_CY1;
H1ModCY1 = H2ModCY1;
H2ModCY1 = Tmp;
Tmp = (K1ModCY1 + Z*K2ModCY1) % g_CY1;
K1ModCY1 = K2ModCY1;
K2ModCY1 = Tmp;
}
}
mpz_set(Dp_M, Dp_M1); // M = M1
mpz_set(Dp_P, Dp_P1); // P = P1
if (Co == 0) {
Co = 1;
}
if (type == 5) {
Tmp = (g_A1 + Z*g_A2) % T;
g_A1 = g_A2; g_A2 = Tmp;
Tmp = (g_B1 + Z*g_B2) % T;
g_B1 = g_B2; g_B2 = Tmp;
}
ChSign(Dp_Mu);
if (Paso == 2) {
if (g_A2 != 0 && Z>(quintillion / 10 - g_A1) / g_A2 ||
g_B2 != 0 && Z>(quintillion / 10 - g_B1) / g_B2) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
g_A1 += Z*g_A2;
g_B1 += Z*g_B2;
Tmp = g_A1; g_A1 = g_A2; g_A2 = Tmp; // swap A1 and A2
Tmp = g_B1; g_B1 = g_B2; g_B2 = Tmp; // swap B1 and B2
}
Conv++;
} while (Co<0);
if (!secondDo) {
continue; // go to next step (paso = 2)
}
Mu = DoublePrecToLong(Dp_Mu);
L = DoublePrecToLong(Dp_L);
K = DoublePrecToLong(Dp_K);
M = DoublePrecToLong(Dp_M);
P = DoublePrecToLong(Dp_P);
do {
P1 = (g_Disc - M*M) / P; /* P & Q should be > 0 (See Knuth Ex 4.5.3-12) */
Z = (SqrtDisc + M) / P1;
M1 = Z*P1 - M;
if (type == 1 && P == Mu) { /* Solution found */
if (Co % 2 == 0 || K != P1 || L != M1) {
if (Paso == 2) {
if (g_A2 != 0) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
ShowLargeXY(X1, Y1, Bi_H1, Bi_K1, true, "NUM(" + numToStr(Conv) + ") = ",
"DEN(" + numToStr(Conv) + ") = ");
}
Sols = true;
}
//std::cout << "**temp ContFrac(11)\n";
break;
}
if (type == 3 || type == 4) {
if ((Co & 1) == 0 && A*g_F>0 && g_Disc == 5) { /* Solution found */
if (Paso == 1) {
Sols = true;
//std::cout << "**temp ContFrac(12)\n";
break;
}
else {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
ChangeSign(Bi_H2);
AddLarge(Bi_H1, Bi_H2, Bi_H2);
ChangeSign(Bi_H2);
ChangeSign(Bi_K2);
AddLarge(Bi_K1, Bi_K2, Bi_K2);
ChangeSign(Bi_K2);
if (ShowHomoSols(type, Bi_H2, Bi_K2, s, T, MagnifY,
"NUM(" + numToStr(Conv) + ") - NUM(" + numToStr(Conv - 1) + ") = ",
"DEN(" + numToStr(Conv) + ") - DEN(" + numToStr(Conv - 1) + ") = ")) {
Sols = true;
//std::cout << "**temp ContFrac(13) - solution found\n";
break;
}
AddLarge(Bi_H1, Bi_H2, Bi_H2); // H2 = H1 + H2
AddLarge(Bi_K1, Bi_K2, Bi_K2); // K2 = K1 + K2
}
}
if (P1 == Mu) { /* Solution found */
if (Co % 2 == 0 || K != P1 || L != M1) {
if (Paso == 2) {
if (g_A2 != 0) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
if (ShowHomoSols(type, Bi_H2, Bi_K2, s, T, MagnifY,
"NUM(" + numToStr(Conv) + ") = ",
"DEN(" + numToStr(Conv) + ") = ")) {
Sols = true;
//std::cout << "**temp ContFrac(14) - solution found\n";
break;
}
}
else {
if (type == 4) {
Tmp = H2ModCY1*T;
if ((Tmp - g_CY0) % g_CY1 == 0 || (Tmp + g_CY0) % g_CY1 == 0) {
Sols = true;
break;
}
}
else {
Sols = true;
//std::cout << "**temp ContFrac(15)\n";
break;
}
}
}
}
if (Paso == 1 && type == 4) {
Tmp = (H1ModCY1 + Z*H2ModCY1) % g_CY1;
H1ModCY1 = H2ModCY1;
H2ModCY1 = Tmp;
Tmp = (K1ModCY1 + Z*K2ModCY1) % g_CY1;
K1ModCY1 = K2ModCY1;
K2ModCY1 = Tmp;
}
}
Co++;
if (Co % 5000 == 0) {
std::cout << "Conv: " << Co << " (Eq " << EqNbr << " of " << NbrEqs << ") \n";
std::cout << NbrSols << " solution" << (NbrSols == 1 ? "\n" : "s\n");
}
if (Co % 5000 == 2500) {
std::cout << NbrSols << " solution" << (NbrSols == 1 ? "\n" : "s\n");
}
M = M1;
P = P1;
if (type == 2 && P1 == Mu) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
Sols = true;
//std::cout << "**temp ContFrac(17)\n";
break;
}
if (type == 5) {
if (P1 == Mu) {
NbrCo = Co;
Sols = true;
//std::cout << "**temp ContFrac(18) NbrCo=" << NbrCo << "\n";
break;
}
else {
Tmp = (g_A1 + Z*g_A2) % T;
g_A1 = g_A2; g_A2 = Tmp;
Tmp = (g_B1 + Z*g_B2) % T;
g_B1 = g_B2; g_B2 = Tmp;
}
}
Mu = -Mu;
if (Paso == 2) {
if (g_A2 != 0 && Z>(quintillion / 10 - g_A1) / g_A2 || g_B2 != 0 && Z>(quintillion / 10 - g_B1) / g_B2) {
NextConv(Bi_H1, Bi_H2, g_A1, g_A2, g_B1, g_B2);
NextConv(Bi_K1, Bi_K2, g_A1, g_A2, g_B1, g_B2);
g_A1 = g_B2 = 1;
g_A2 = g_B1 = 0;
}
g_A1 += Z*g_A2; g_B1 += Z*g_B2;
Tmp = g_A1; g_A1 = g_A2; g_A2 = Tmp; // swap A1 and A2
Tmp = g_B1; g_B1 = g_B2; g_B2 = Tmp; // swap B1 and B2
}
Conv++;
/*std::cout << "**temp ContFrac(18A) NbrCo=" << NbrCo << " Co=" << Co;
std::cout << " K=" << K << " P=" << P << " L=" << L << " M=" << M << "\n";*/
} while (NbrCo>0 ? Co != NbrCo : Co % 2 != 0 || K != P || L != M);
//std::cout << "**temp ContFrac(18B)\n";
/* type = 5: Find convergents for x^2 + Bxy + ACy^2 = 1 (mod B^2-4AC) */
if (type == 5) {
//std::cout << "**temp ContFrac(19)\n";
break; // break out of for loop
}
} /* end for */
//std::cout << "**temp ContFrac returns " << Sols << "\n";
mpz_clears(Dp_P, Dp_M, Dp_Z, Dp_G, Dp_Mu, Dp_K, Dp_L, Dp_M1, Dp_P1, Dp_zz, NULL);
assert(_CrtCheckMemory());
return Sols;
}
/******************************************************************************
* H = Constant term *
* T = Divisor of the square part of the constant term *
* A = X^2 coefficient *
* B = XY coefficient *
* C = Y^2 coefficient *
* SCFstr = Nothing or apostrophe (complete quad equation) *
* called from solveEquation *
* overwrites global variable g_F, Bi_L1, Bi_L2, DP_NUM, DP_DEN, disc, *
* sqrtdisc, NbrSols *
*******************************************************************************/
void SolContFrac(long long H, long long T, long long A, long long B, long long C,
std::string SCFstr) {
long long factor[64] = { 0 };
long long P[64] = { 0 };
long long Q[64] = { 0 };
long long Dif[64] = { 0 }; /* Holds difference */
long long mod[64] = { 0 };
long long pos[64] = { 0 };
long long Tmp, q, s, t, v, Pp, dif, Sol1, Sol2, Modulo;
long long Tmp1 = SqrtDisc;
mpz_t Dp_Tmp2, Dp_Tmp3;
long long Tmp4 = g_Disc;
long long ValA, ValB, ValC, ValF, ValAM, ValBM, ValCM;
long long VarD, VarK, VarQ, VarR, VarV, VarW, VarX, VarY, VarY1;
mpz_t Dp_A, Dp_B, Dp_C, Dp_R, Dp_S, Dp_T;
mpz_t Bi_Xcopy, Bi_Ycopy;
int index, index2, cont;
int NbrFactors;
long long gcdAF, MagnifY;
int cuenta = 0;
long long OrigA, OrigC;
bool ShowHR = false;
mpz_inits(Dp_A, Dp_B, Dp_C, Dp_R, Dp_S, Dp_T, Dp_Tmp2, Dp_Tmp3, Bi_Xcopy, Bi_Ycopy, NULL);
//std::cout << "**temp SolContFrac: H=" << H << " T=" << T << " A=" << A << " B=" << B << " C=" << C << "\n";;
mpz_set(Dp_Tmp2, Dp_NUM); // copy global NUM to local Tmp2
mpz_set(Dp_Tmp3, Dp_DEN); // copy global DEN to l.ocal Tmp3
g_F = H / T / T;
if (teach && T>1) {
std::cout << "Since " << T << " * " << T << " is a divisor of the constant term ("
<< H << "), the solutions should be " << T << " times the solutions of ";
ShowEq(A, B, C, 0, 0, g_F, "u", "v");
printf(" = 0.\n");
if (abs(g_F) != 1) {
printf(" Let F be the constant term.");
}
putchar('\n');
UU = "U";
VU = "V";
UL = "u";
VL = "v";
FP = "F";
}
if (teach && T == 1) {
UU = "X" + SCFstr;
VU = "Y" + SCFstr;
UL = "x" + SCFstr;
VL = "y" + SCFstr;
FP = "f" + SCFstr;
}
gcdAF = gcd(A, g_F);
OrigA = A;
OrigC = C;
if (teach && gcdAF > 1) {
std::cout << "Since gcd(A,F) = gcd(" << A << "," << g_F << ") = " << gcdAF
<< " > 1, we have to replace y = ny' where n is a divisor of gcd(A,F).\n";
}
for (MagnifY = 1; MagnifY*MagnifY <= gcdAF; MagnifY++) {
do {
if (gcdAF / MagnifY*MagnifY != gcdAF) {
continue; // if MagnifY^2 is a not factor of gcdAF skip to next value
}
if (teach) {
if (ShowHR) {
//w("<HR>");
}
else {
ShowHR = true;
}
}
MagnifY = gcdAF / MagnifY;
g_F = H / T / T / MagnifY;
ValF = abs(g_F);
A = OrigA / MagnifY;
C = OrigC*MagnifY;
ValA = (A + ValF) % ValF;
ValB = (B + ValF) % ValF;
ValC = (C + ValF) % ValF;
if (teach) {
if (MagnifY != 1) {
std::cout << "Let y = " << MagnifY << "y' We obtain: ";
}
putchar('\n');
ShowEq(A, B, C, 0, 0, g_F, "x", "y'");
printf(" = 0\n");
}
/* Find factors of F, store in array factors */
NbrFactors = 0;
Tmp = ValF;
if (Tmp == 1) {
factor[NbrFactors++] = 1;
}
else {
while ((Tmp % 2) == 0) {
factor[NbrFactors++] = 2;
Tmp /= 2;
}
while ((Tmp % 3) == 0) {
factor[NbrFactors++] = 3;
Tmp /= 3;
}
s = 5; /* Sequence of divisors 5, 7, 11, 13, 17, 19,... */
do {
while ((Tmp%s) == 0) {
factor[NbrFactors++] = s;
Tmp /= s;
}
s += 2;
while ((Tmp%s) == 0) {
factor[NbrFactors++] = s;
Tmp /= s;
}
s += 4;
} while (s*s <= Tmp);
if (Tmp != 1) {
factor[NbrFactors++] = Tmp;
}
}
/* complete list of prime factors of F now in array F */
mod[NbrFactors] = Tmp = 1;
Pp = (2 * ValA) % ValF;
for (index = NbrFactors - 1; index >= 0; index--) {
P[index] = Pp;
Tmp *= factor[index];
mod[index] = Tmp;
Pp = MultMod(MultMod(Pp, factor[index], ValF), factor[index], ValF);
}
Modulo = factor[NbrFactors - 1]; // get largest prime factor
ValAM = (ValA + Modulo) % Modulo;
ValBM = (ValB + Modulo) % Modulo;
ValCM = (ValC + Modulo) % Modulo;
if (ValAM == 0) { /* Linear equation: sol=-C/B */
Sol1 = Sol2 = MultMod(Modulo - ValCM, ModInv(ValBM, Modulo), Modulo);
}
else { /* Quadratic equation Ax^2+Bx+C=0 (mod F) */
if (Modulo>2) {
Sol1 = MultMod(ValBM, ValBM, Modulo) - MultMod(4 * ValAM, ValCM, Modulo);
if (Sol1<0) { Sol1 += Modulo; }
/* Find square root of Sol1 mod Modulo */
if (Sol1 == 0) { /* if double root: sol = -t/2a */
Sol1 = Sol2 = MultMod(ModInv((2 * ValAM + Modulo) % Modulo, Modulo), ((-ValBM) + Modulo) % Modulo, Modulo);
}
else {
if (ModPow(Sol1, (Modulo - 1) / 2, Modulo) == 1) { /* if sols exist */
if (Modulo % 8 == 5) {
s = ModPow(2 * Sol1, (Modulo - 5) / 8, Modulo);
Sol1 = MultMod(MultMod(MultMod(MultMod(2 * Sol1, s, Modulo), s, Modulo) - 1, Sol1, Modulo), s, Modulo);
}
else {
if (Modulo % 8 != 1) {
Sol1 = ModPow(Sol1, (Modulo + 1) / 4, Modulo);
}
else {
VarR = 1;
VarQ = Modulo - 1;
while (VarQ % 2 == 0) {
VarQ /= 2;
VarR *= 2;
}
VarX = 2;
while (true) {
VarY = ModPow(VarX, VarQ, Modulo);
if (ModPow(VarY, VarR / 2, Modulo) != 1) { break; }
VarX++;
}
VarX = ModPow(Sol1, (VarQ - 1) / 2, Modulo);
VarV = MultMod(Sol1, VarX, Modulo);
VarW = MultMod(VarV, VarX, Modulo);
while (VarW != 1) {
VarK = 1; VarD = VarW;
while (VarD != 1) {
VarD = MultMod(VarD, VarD, Modulo);
VarK *= 2;
}
VarD = ModPow(VarY, VarR / VarK / 2, Modulo);
VarY1 = MultMod(VarD, VarD, Modulo);
VarR = VarK;
VarV = MultMod(VarV, VarD, Modulo);
VarW = MultMod(VarW, VarY1, Modulo);
VarY = VarY1;
} /* end while */
Sol1 = VarV;
} /* end modulo 8 = 1 */
}
s = ModInv((2 * ValAM) % Modulo, Modulo);
Sol2 = MultMod((Modulo + Sol1 - ValBM) % Modulo, s, Modulo);
Sol1 = MultMod((2 * Modulo - Sol1 - ValBM) % Modulo, s, Modulo);
}
else { /* No solution exists */
Sol1 = Sol2 = -1;
}
}
}
else { /* Modulo <= 2 */
if (Modulo == 2) {
switch ((int)ValBM * 2 + (int)ValCM) {
case 0: /* A = 1, B = 0, C = 0 */
Sol1 = Sol2 = 0; /* Solution only for s=0 */
break;
case 1: /* A = 1, B = 0, C = 1 */
Sol1 = Sol2 = 1; /* Solution only for s=1 */
break;
case 2: /* A = 1, B = 1, C = 0 */
Sol1 = 0; /* Solution for s=0 and s=1 */
Sol2 = 1;
break;
default: /* A = 1, B = 1, C = 1 */
Sol1 = Sol2 = -1; /* No solutions */
break;
}
} /* End Modulo = 2 */
else { /* Modulo = 1 */
Sol1 = Sol2 = 0;
}
}
} /* End Quadratic Equation */
//std::cout << "**temp SolContFrac: Sol1 =" << Sol1 << " Sol2=" << Sol2 << "\n";
ValAM = (ValA + ValF) % ValF;
ValBM = (ValB + ValF) % ValF;
ValCM = (ValC + ValF) % ValF;
if (teach) {
UL1 = UL;
VL1 = VL + (MagnifY == 1 ? "" : "'");
std::cout << "Let " << UL1 << " = s" << VL1 << " - " << FP << "z, so [-(as" << sq << " + bs + c)/"
<< FP << "]" << VL1 << sq << " + (2as + b)" << VL1 << "z - a" << FP << "z" << sq << " = 1.\nSo \n";
ShowEq(A, 0, 0, B, 0, C, "s", "");
std::cout << " should be multiple of " << ValF << "\n";
}
NbrEqs = EqNbr = 0;
int sol = 0;
t = Sol1;
/* if Sol1 >= 0 execute loop twice, otherwise not at all */
for (cont = (Sol1<0 ? 2 : 0); cont<2; cont++) {
index = NbrFactors - 1;
v = mod[index];
dif = 0;
q = (MultMod((MultMod(ValAM, t, ValF) + ValBM) % ValF, t, ValF) + ValCM) % ValF; /* q%v = 0 */
while (true) {
if (q%v == 0) {
if (index == 0) { /* Solution found */
NbrEqs++;
if (teach) {
s = t*mod[1];
for (index2 = 1; index2<NbrFactors; index2++) {
s += pos[index2] * mod[index2 + 1];
}
s = s%ValF;
if (sol == 0) {
sol = 1;
std::cout << "This holds for s = " << s;
}
else {
std::cout << ", " << s;
}
}
else {
if (sol == 0)
sol = 1;
}
}
else { /* solution not found */
pos[index] = t;
t = 0;
for (index2 = index; index2<NbrFactors; index2++) {
t += pos[index2] * mod[index2 + 1];
}
t = t%ValF;
Dif[index] = dif;
Q[index] = q;
dif = MultMod((MultMod((2 * t + v) % ValF, ValAM, ValF) + ValBM) % ValF, v, ValF);
Pp = P[--index];
t = 0; v = mod[index];
continue;
}
}
if (index != NbrFactors - 1 && ++t < factor[index]) {
q = (q + dif) % ValF;
dif = (dif + Pp) % ValF;
continue;
}
else {
while (++index < NbrFactors) {
t = pos[index];
v = mod[index]; /* Restore previous values */
if (index < NbrFactors - 1 && ++t < factor[index]) {
Pp = P[index];
dif = Dif[index];
q = (Q[index] + dif) % ValF;
dif = (dif + Pp) % ValF;
break; // exit from 'while' loop
}
}
if (index >= NbrFactors) {
break;
}
}
}
if (Sol1 == Sol2) {
break; /* Do not process double root */
}
t = Sol2;
}
if (teach) {
if (sol == 0) {
printf("No values of s makes the previous assertion true. \n");
SqrtDisc = Tmp1;