#include <stdio.h>
#include <stdlib.h>
#include <math.h>
//for multithreading
#include <pthread.h>
#include <assert.h>
//for sleep
#include <unistd.h>

#define DOUBLEMODE 0
#define DOUBLEERRORMODE 1
#define RATIOMODE 2

#ifndef MODE
#define MODE DOUBLEMODE
#endif

#define NUM_THREADS 6

#if MODE == DOUBLEERRORMODE
#include "double-error.h"
#define VALUETYPE double_error
#define EXPTYPE double_error
#elif MODE == RATIOMODE
#include "ratio.h"
#define VALUETYPE rational
#define EXPTYPE unsigned int
#else
#include "double.h"
#define VALUETYPE double
#define EXPTYPE double
#endif

/*length of the support of f*/
static const int N=24;

/*order of the derivative to consider.*/
static const int K=3;

/*given function df[0] on domain [0,M-1], compute derivatives f' until f^{(K)} and store them in df[1] to df[K]*/
void differentiate(VALUETYPE* f, VALUETYPE* df, int D){
	VALUETYPE df0[D];
	/*Set zeroth derivative to be f.*/
	for(int i=0; i<D; i++){
		df0[i] = f[i];
		df[i] = f[i];
	}
	for(int k=1; k<=K; k++){
		/*Compute kth derivative of f from (k-1)th.*/
		for(int i=0; i<D; i++) df[i] = difference(df0[(i+1)%D], df0[i]);
		for(int i=0; i<D; i++) df0[i] = df[i];
	}

	/*
	printf("df    ");
	for(int i=0;i<D;i++) printf("%+6.1f ",to_double(df[i]));
	printf("\n");
	*/
}

/*given function f on domain [0,D-1] compute pth root of integral of |f|^p*/
VALUETYPE integratep(VALUETYPE* f, EXPTYPE p, int D){
	VALUETYPE integralp = convert_int(0);
	for(int i=0;i<D;i++){
		VALUETYPE padd = power(absolute(f[i]),p);
		integralp = sum(integralp,padd);
	}
	return integralp;
}

void compute_maximalfunction(VALUETYPE* f, VALUETYPE* Mf, int D){
	/*Sf[i][j] will be the integral of f on [min(i,j),max(i,j)]*/
	//VALUETYPE Sf[N][N];
	/*Af[i][j] will be the average of f on [min(i,j),max(i,j)]*/
	//VALUETYPE Af[N][N];
	/*Apparently may become too big for stack or something.*/
	VALUETYPE* Sf[N];
	VALUETYPE* Af[N];
	for(int i=0; i<D;i++){
		Sf[i] = malloc(N*sizeof(VALUETYPE));
		Af[i] = malloc(N*sizeof(VALUETYPE));
	}

	for(int i=0; i<D; i++) {
		Sf[i][i] = f[i];
		Af[i][i] = f[i];
	}
	
	for(int n=1; n<D; n++){
		/*Recursively compute all integrals and averages over intervals of increasing length*/
		for(int i=0; i<D; i++){
			Sf[i][(i+n)%D] = sum(Sf[i][(i+n-1)%D], f[(i+n)%D]);
			Af[i][(i+n)%D] = ratio(Sf[i][(i+n)%D],convert_int(n+1));
		}
	}
	
	/*Compute maximal function by picking the largest average*/
	for(int i=0; i<D; i++){
		Mf[i] = Af[i][i];
		for(int j=1; j<=D; j++){
			Mf[i] = maximum(Af[i][(i+j)%D], Mf[i]);
			Mf[i] = maximum(Af[(i-j+D)%D][i], Mf[i]);
		}
	}

	/*Print computed functions and averages*/
	/*
	printf("Mf    ");
	for(int i=0;i<D;i++) printf("%+0.1f ",to_double(Mf[i]));
	printf("\n");
	for(int i=0;i<D;i++){
		for(int j=0;j<D;j++) printf("%0.1f ",to_double(Af[i][j]));
		printf("\n");
	}
	*/

	for(int i=0; i<D; i++){
		free(Sf[i]);
		free(Af[i]);
	}
}

void compute(EXPTYPE p, int t, int D){
	/*allocate memory for f*/
	VALUETYPE f[N];
	/*Initiate f to be zero everywhere.*/
	for(int i=0; i<D; i++) f[i] = convert_int(0);
	//for(int i=0; i<N; i++) f[N+i] = rand() %2;
	/*In the middle of the domain set f to the values encoded in bit string t*/
	for(int i=0; i<D; i++) f[i] = convert_int((t >> i) & 1);
	//if(i%3==0) f[2*N+i+K/2] = 1;

	VALUETYPE Mf[N];
	compute_maximalfunction(f,Mf,D);

	/*Allocate memory for derivatives.*/
	VALUETYPE df[N];
	VALUETYPE dMf[N];

	/*Compute Kth derivative of f and Mf*/
	differentiate(f,df,D);
	differentiate(Mf,dMf,D);

	/*Print derivatives*/
	/*
	for(int k=0; k<=K; k++){
		printf("f  %d: ",k);
		for(int i=0; i<D; i++) printf("%+0.1f ",df[k][i]);
		printf("\n");
		printf("Mf %d: ",k);
		for(int i=0; i<D; i++) printf("%+0.1f ",dMf[k][i]);
		printf("\n");
	}
	*/

	/*Compute L^p norm of derivatives*/
	VALUETYPE intdfp = integratep(df,p,D);
	VALUETYPE intdMfp = integratep(dMf,p,D);

	//printf("%d: %f / %f = %f\n",k,intdMfp[k],intdfp[k],intdMfp[k]/intdfp[k]);

	/*Compute ||Mf^{(k)}||_p/||f^{(k)}||_p.*/

	VALUETYPE r = ratio(intdMfp, intdfp);

	//printf("%.3d: %.3f  \n",t,r);
	/*Print f and ||Mf^{(k)}||_p/||f^{(k)}||_p if the latter is close to 1/2.*/
	//if(to_double(r)>.4997)
	//if(to_double(r)>=.58)
	if(to_double(r)>.53)
	{
		printf("f: ");
		for(int i=0; i<D; i++) printf("%1.0f ",to_double(f[i]));
		printf("\n");
		char s[128];
		root_to_string(s,r,p);
		printf("%s\n",s);
	}
}

struct Args {EXPTYPE* p; int* D; int* t; };

void* perform_work(void* arguments){
	struct Args *args = arguments;
	EXPTYPE p = *(args->p);
	int* D = args->D;
	int* s = args->t;

	while(*D <= N){
		if(*s <= (1 << *D)-2){
			int t = *s;
			*s = t+1;
			compute(p,t,*D);
		}
		else {
			*s = 0;
			*D = *D+1;
		}
	}
	return NULL;
}

int main() {
	/*exponent p of the L^p norm to consider*/
	EXPTYPE p = to_exptype(1);

	/*Iterate over all strings of 0s and 1s with length N. Those will represent f.*/
	int t = 1;
	int D = 1;

	//for(int t=1; t<=(1 << N)-1; t++){
		//compute(N,K,D,p,t);
	//}

	struct Args args = {&p, &D, &t};

	pthread_t threads[NUM_THREADS];
	int result_code;

	for (int i = 0; i < NUM_THREADS; i++) {
		printf("In main: Creating thread %d.\n", i);
		result_code = pthread_create(&threads[i], NULL, perform_work, &args);
		assert(!result_code);
		usleep(1000*100);
	}

	// wait for each thread to complete
	for (int i = 0; i < NUM_THREADS; i++) {
		result_code = pthread_join(threads[i], NULL);
		assert(!result_code);
		printf("In main: Thread %d has ended.\n", i);
	}

	return 0;
}