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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
//for multithreading
#include <pthread.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=16;
/*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 D, VALUETYPE* f){
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);
}
}
/*Writes into f the values of the function indexed by i. Returns the size of the support of f, or -1 if there is no function with that index.*/
int generate_function(VALUETYPE* f, int i){
int s=0;
int d=1;
while(d <= N){
/*number of strings of length d that are not all 0s or all 1s*/
int powd = (1<<d)-2;
if(i-s >= powd){
s += powd;
d++;
}
else {
int t = i-s+1;
/*Set f to the values encoded in bit string t which is a value between 1 and powd = (1<<d)-2.*/
for(int n=0; n<d; n++) f[n] = convert_int((t >> n) & 1);
return d;
}
}
return -1;
}
typedef struct {
EXPTYPE p;
VALUETYPE** f;
int i;
}Args;
/*Goes through all functions indexed by those numbers which equal the thread number module NUM_THREADS.*/
void* compute_chunk(void* arguments){
Args *args = arguments;
EXPTYPE p = args->p;
int i = args->i;
VALUETYPE f[N];
int d = generate_function(f,i);
while(d >= 0){
compute(p,d,f);
i += NUM_THREADS;
d = generate_function(f,i);
}
}
int main() {
/*exponent p of the L^p norm to consider*/
EXPTYPE p = to_exptype(1);
pthread_t threads[NUM_THREADS];
Args args[NUM_THREADS];
int result_code;
for (int i = 0; i < NUM_THREADS; i++) {
printf("In main: Creating thread %d.\n", i);
args[i] = (Args){.p=p, .i=i};
result_code = pthread_create(&threads[i], NULL, compute_chunk, &(args[i]));
}
// wait for each thread to complete
for (int i = 0; i < NUM_THREADS; i++) {
result_code = pthread_join(threads[i], NULL);
printf("In main: Thread %d has ended.\n", i);
}
return 0;
}
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