From c6e74e0b980f567f93cb46786e344f410ca83555 Mon Sep 17 00:00:00 2001
From: Julian Weigt <juw@posteo.de>
Date: Wed, 7 Jan 2026 21:13:50 +0000
Subject: Loop over all derivatives up to whatever limit and print depending on
 order of derivative.

---
 charf.c | 114 ++++++++++++++++++++++++++++++++++++++++++----------------------
 1 file changed, 76 insertions(+), 38 deletions(-)

(limited to 'charf.c')

diff --git a/charf.c b/charf.c
index 3dd9d5e..c6a32c3 100644
--- a/charf.c
+++ b/charf.c
@@ -29,7 +29,7 @@
 #endif
 
 /*maximum length of the support of f*/
-static const int N=16;
+static const int N=24;
 
 /*given function df[0] on domain [0,M-1], compute derivatives f' until f^{(K)} and store f^{(K)} in df*/
 void differentiate(VALUETYPE* f, VALUETYPE* df, int D, int K){
@@ -114,52 +114,91 @@ void compute_maximalfunction(VALUETYPE* f, VALUETYPE* Mf, int D){
 	}
 }
 
-void compute(int K, EXPTYPE p, int D, VALUETYPE* f){
+void compute(EXPTYPE p, int D, VALUETYPE* f){
 	VALUETYPE Mf[N];
+	/*This is the only O(D^2) operation in here so makes a lot of sense to only compute once and avoid repeating it.*/
 	compute_maximalfunction(f,Mf,D);
 
 	/*Allocate memory for derivatives.*/
-	VALUETYPE df[N];
-	VALUETYPE dMf[N];
+	VALUETYPE df[2][N];
+	VALUETYPE dMf[2][N];
 
-	/*Compute Kth derivative of f and Mf*/
-	differentiate(f,df,D,K);
-	differentiate(Mf,dMf,D,K);
-
-	/*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");
+	for(int i=0; i<D; i++){
+		df[1][i] = f[i];
+		df[0][i] = f[i];
+		dMf[0][i] = Mf[i];
+		dMf[1][i] = Mf[i];
 	}
-	*/
 
-	/*Compute L^p norm of derivatives*/
-	VALUETYPE intdfp = integratep(df,p,D);
-	VALUETYPE intdMfp = integratep(dMf,p,D);
+	VALUETYPE tmp[N];
 
-	//printf("%d: %f / %f = %f\n",k,intdMfp[k],intdfp[k],intdMfp[k]/intdfp[k]);
+	for(int k=1; k<=16; k++){
+		/*Compute kth derivative of f and Mf*/
+		differentiate(df[(k+1)%2],df[k%2],D,1);
+		differentiate(dMf[(k+1)%2],dMf[k%2],D,1);
+		
+		/*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 ||Mf^{(k)}||_p/||f^{(k)}||_p.*/
+		/*Compute L^p norm of derivatives*/
+		VALUETYPE intdfp = integratep(df[k%2],p,D);
+		VALUETYPE intdMfp = integratep(dMf[k%2],p,D);
 
-	VALUETYPE r = ratio(intdMfp, intdfp);
+		//printf("%d: %f / %f = %f\n",k,intdMfp[k],intdfp[k],intdMfp[k]/intdfp[k]);
 
-	//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);
+		/*Compute ||Mf^{(k)}||_p/||f^{(k)}||_p.*/
+
+		VALUETYPE r = ratio(intdMfp, intdfp);
+		double t = to_double(r);
+		if(
+		//(k==1 && t>.9)
+		//||
+		//(k==2 && t>=.5)
+		//||
+		(k==3 && t>.53)
+		//||
+		//(k==4 && t>=.5)
+		||
+		(k==5 && t>=.58)
+		||
+		(k==6 && t>=.58)
+		||
+		(k==7 && t>=.69)
+		||
+		(k==8 && t>=.83)
+		||
+		(k==9 && t>=.8699)
+		||
+		(k==10 && t>=.919)
+		||
+		(k==11 && t>=.97)
+		||
+		(k==12 && t>=.97)
+		||
+		(k==13 && t>=.98)
+		||
+		(k==14 && t>=.98)
+		||
+		(k==15 && t>=.9817)
+		||
+		(k==16 && t>=.9817)
+		){
+			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("ratio for %dth derivative: %s\n",k,s);
+		}
 	}
 }
 
@@ -188,13 +227,12 @@ int generate_function(VALUETYPE* f, int i){
 /*Goes through all functions indexed by those numbers which equal the thread number module NUM_THREADS.*/
 void* compute_chunk(void* arguments){
 	int i = *((int*)arguments);
-	int K = 3;
 	EXPTYPE p = int_to_exptype(1);
 
 	VALUETYPE f[N];
 	int d = generate_function(f,i);
 	while(d >= 0){
-		compute(K,p,d,f);
+		compute(p,d,f);
 		i += NUM_THREADS;
 		d = generate_function(f,i);
 	}	
-- 
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