#include "bignum.h"
Bignum fact(int N){
	static Bignum X;X=intToBignum(1);
	for(int i=1;i<=N;i++) X=mulAbs(X,i);
	return X;

}
Bignum maxSqrt(Bignum A){
	int PN=int(sqrt((double)A.Num[A.Len]))+1;
	int BaseM1=Base-1, SQB=(int)(sqrt((double)Base)+0.5);
	static Bignum X; X.Len=(A.Len+1)/2;
	if(A.Len % 2==0){
		if(PN<SQB) return hightFigures(false,X.Len,PN*10);
		for(int i=1;i<=X.Len;i++) X.Num[i]=Base-1;
	}
	else if(PN<SQB) {
		X.Num[X.Len]=PN;
		for(int i=1;i<X.Len;i++)X.Num[i]=0;
	}
	else{
		X.Num[X.Len]=SQB-1;
		for(int i=1;i<X.Len;i++)X.Num[i]=Base-1;
	}
	return X;
}
Bignum minSqrt(Bignum A){
	int XLen=(A.Len+1)/2;
	int PN=int(sqrt((double)A.Num[A.Len]));
	if(A.Len % 2==0)return hightFigures(false,XLen,PN*10);
    else return hightFigures(false,XLen,PN);
}
int sqrDebug=true;
Bignum sqrt(Bignum A){
	if(sqrDebug) printf("\n--------- sqrt Check start-----");
	Bignum maxS=maxSqrt(A),M, S;
	if(sqrDebug){printf("\n maxS     = ");printBignum(maxS);}
	M=mulAbs(maxS,maxS);
	int chk;chk=compAbs(M,A);
	if(chk<=0) S= maxS;
	else{
		Bignum minS=minSqrt(A);
		if(sqrDebug){ printf("\n minS     = ");printBignum(minS);}
	 	S=divAbs(addAbs(minS,maxS),2);
		M=mulAbs(S,S);chk=compAbs(M,A);
		while(chk!=0){
			if(chk>0) maxS=copyBignum(S);
			else if(chk<0) minS=copyBignum(S);
			S=divAbs(addAbs(minS,maxS),2);chk=compAbs(S,minS);
			if(chk==0) break;
			M=mulAbs(S,S);
			chk=compAbs(M,A);
		}
	}	
	if(sqrDebug){
		printf("\n--------- sqrt Check ----------");
		printf("\n A        = ");printBignum(A);
	    printf("\n S        = ");printBignum(S);
		M=addAbs(S,1);printf("\n S + 1    = ");printBignum(M);
		M=mulAbs(M,M);printf("\n (S+1)^ 2 = ");printBignum(M);
		M=mulAbs(S,S);printf("\n S ^ 2    = ");printBignum(M);
		M=subAbs(A,M);printf("\n 差       = ");printBignum(M);
		printf("\n-------------------------------");
	}
	return S;

}
Bignum compPi(int MX){ //マチンの公式によるπの計算。MXは計算桁数
// π=16(��(-1)^k / ((2k + 1)・5^(2k - 1)) -4(��(-1)^k / ((2k + 1)・239^(2k - 1)))
  int MXX;MXX = MX + 1; Bignum Pi,T,K,U;
  Pi = intToBignum(0);T = hightFigures(false, MXX, 16); T = divAbs(T, 5); //最上位桁を16とする
  K = intToBignum(1); U = copyBignum(T);
  do{
    Pi = addBig(Pi, U); T = divAbs(T, 25); K = addAbs(K, 2); U = divBig(T, K);
	Pi = subBig(Pi, U); T = divAbs(T, 25); K = addAbs(K, 2); U = divBig(T, K);
  }while (U.Len !=0);
  T = hightFigures(false, MXX, 4);
  Bignum N239, N239sq; N239 = intToBignum(239);N239sq = mulAbs(N239, N239);
  T = divAbs(T, N239); K = intToBignum(1); U = copyBignum(T);
  do{
    Pi = subBig(Pi, U); T = divBig(T, N239sq); K = addAbs(K, 2); U = divBig(T, K);
  	Pi = addBig(Pi, U); T = divBig(T, N239sq); K = addAbs(K, 2); U = divBig(T, K);
  } while(U.Len!=0);
  return Pi;
}
Bignum compE(int MX){ //自然対数の底(e:ネイピア数）の計算
// e^x = �肺^k / k! で x = 1として計算する
  int MXX;MXX = MX + 1; Bignum E,T,K;
   E = hightFigures(false, MXX, 1); T=E; K=intToBignum(1);
  do{
	  E=addBig(E,T); K=addAbs(K,1);T=divBig(T,K);
  } while(T.Len!=0);
  return E; 
}
int main(void){//テストメイン
	int numA[]={0,10,10,10};
	int numB[]={0,10,10};
	Bignum A=integerArrayToBigNumber(false, numA, 3);
    Bignum B=integerArrayToBigNumber(false, numB, 2);
	printf("\n stringToBignum = ");
	printBignum(stringToBignum("-12345678"));
	char str[256];
	int N= bigToString(stringToBignum("123456789"),str, 256);
	printf("\n bigToString =%s",str);
	printf("\n A = ");
	printBignum(A);
	printf("\n B = ");
	printBignum(B);
	Bignum X; X= sqrt(stringToBignum("99999999999999999"));
	printf("\n sqrt(a)  = ");printBignum(X);

	int R;
    printf("\n A == A ");
	printf("%s", eqBig(A,A)?"true":"false");
    printf("\n A == B ");
	printf("%s", eqBig(A,B)?"true":"false");
	printf("\n A != A ");
	printf("%s", neqBig(A,A)?"true":"false");
    printf("\n A != B ");
	printf("%s", neqBig(A,B)?"true":"false");
    printf("\n A > A ");
	printf("%s", gtBig(A,A)?"true":"false");
    printf("\n A > B ");
	printf("%s", gtBig(A,B)?"true":"false");
	printf("\n B > A ");
	printf("%s", gtBig(B,A)?"true":"false");
	printf("\n A < A ");
	printf("%s", ltBig(A,A)?"true":"false");
    printf("\n A < B ");
	printf("%s", ltBig(A,B)?"true":"false");
	printf("\n B < A ");
	printf("%s", ltBig(B,A)?"true":"false");
	printf("\n A >= A ");
	printf("%s", geBig(A,A)?"true":"false");
    printf("\n A >= B ");
	printf("%s", geBig(A,B)?"true":"false");
	printf("\n B >= A ");
	printf("%s", geBig(B,A)?"true":"false");
	printf("\n A <= A ");
	printf("%s", leBig(A,A)?"true":"false");
    printf("\n A <= B ");
	printf("%s", leBig(A,B)?"true":"false");
	printf("\n B <= A ");
	printf("%s", leBig(B,A)?"true":"false");
	printf("\n - intToBigNum(65532) = ");
	printBignum(minus(intToBignum(65532)));

	printf("\n A+10=");
	printBignum(addAbs(A,10));
	printf("\n A+B=");
	printBignum(addAbs(A,B));
	printf("\n A*B=");
	printBignum(mulAbs(A,B));
	
	printf("\n %d", compAbs(A,B));
    printf("\n A-B=");
	printBignum(subAbs(A,B));
	 printf("\n B*99=");
	printBignum(mulAbs(B,99));
	 printf("\n A*B=");
	printBignum(mulAbs(A,B));
	printf("\nB+A*B=");
	printBignum(mulAbs(B,A,B));
	printf("\n");
	printBignum(divQRAbs(A,8,&R));
	printf("余り=%d",R);
	QRData QR=divQRAbs(A,B);
	printf("\n divQRAbs A/B 商　");
	printBignum(QR.Q);
	printf("\n divQRAbs A/B 余り　");
	printBignum(QR.R);
	QR.Q=divAbs(A,B);
	printf("\n divAbs A/B 商　");
	printBignum(QR.Q);
	QR.R=modAbs(A,B);
	printf("\n divAbs A/B 余り　");
	printBignum(QR.R);
	printf("\n π =　");
	printSeperate(compPi(503));//1000桁求めるには,1006桁で計算し後を無視
	printf("\n e =　");
	printSeperate(compE(503));//1000桁求めるには,1006桁で計算し後を無視

	printf("\n\n 階乗の計算\n");
	for(int i=1;i<=50;i++){
		printf("\n %2d! = ",i); printBignum(fact(i));
	}
	getchar();
	return 0;
}