From b7835be8db1d6d2ef60bbe9e972cb708c0fee8c0 Mon Sep 17 00:00:00 2001
From: Julian Weigt <juw@posteo.de>
Date: Sun, 18 Jan 2026 13:28:25 +0100
Subject: =?UTF-8?q?Allow=20p=3D=E2=88=9E=20in=20program=20and=20adjust=20a?=
 =?UTF-8?q?nd=20generalize=20printing=20accordingly.?=
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---
 charf.c        | 32 +++++++++++++++++++++-----------
 double-error.c | 40 +++++++++++++++++++++++++++++++---------
 double-error.h | 12 +++++++++---
 double.c       | 36 ++++++++++++++++++++++++++----------
 double.h       |  8 +++++++-
 ratio.c        | 53 ++++++++++++++++++++++++++++++++++++++++-------------
 ratio.h        |  8 +++++++-
 7 files changed, 141 insertions(+), 48 deletions(-)

diff --git a/charf.c b/charf.c
index c33a88d..520e8cb 100644
--- a/charf.c
+++ b/charf.c
@@ -68,8 +68,8 @@ void differentiate(VALUETYPE* f, VALUETYPE* df, int D, int k){
 VALUETYPE integratep(VALUETYPE* f, EXPTYPE p, int D){
 	VALUETYPE integralp = int_to_valuetype(0);
 	for(int i=0; i<D; i++){
-		VALUETYPE padd = power(absolute(f[i]),p);
-		integralp = sum(integralp,padd);
+		if(exptype_is_infinite(p)) integralp = maximum(integralp,absolute(f[i]));
+		else integralp = sum(integralp,power(absolute(f[i]),p));
 	}
 	return integralp;
 }
@@ -172,20 +172,26 @@ void format_result(char* s, int index, int k, EXPTYPE p, VALUETYPE r, int format
 	if(format == FORMAT_TEXT){
 		strcpy(s,"f: ");
 		int l = 3;
-		for(int i=0; i<d; i++) l += sprintf(s+l,"%2.0f ",valuetype_to_double(f[i]));
-		for(int i=d; i<N; i++) l += sprintf(s+l,"   ");
+		for(int i=0; i<d; i++){
+			char v[8];
+			valuetype_to_string(v,f[i]);
+			l += sprintf(s+l,"%s ",v);
+		}
+		for(int i=d; i<N; i++) l += sprintf(s+l,"  ");
+		char e[16];
 		char rts[128];
+		exptype_to_string(e,p);
 		root_to_string(rts,r,p);
-		l += sprintf(s+l,"|f^(%d)|_1/%2.1f: %s",k,exptype_to_double(p),rts);
+		l += sprintf(s+l,"|f^(%d)|_%s: %s",k,e,rts);
 	}
 	else if(format == FORMAT_LATEX){
 		int l = 0;
 		char v[128];
 		root_to_latex(v,r,p);
-		l += sprintf(s+l,"$%d$ & %s",k,v);
+		l += sprintf(s+l,"$%d$ & $%s$",k,v);
 		for(int i=0; i<d; i++){
 			valuetype_to_latex(v,f[i]);
-			l += sprintf(s+l,"& %s ",v);
+			l += sprintf(s+l,"& $%s$ ",v);
 		}
 		for(int i=d; i<N; i++) l += sprintf(s+l,"& ");
 	}
@@ -270,13 +276,15 @@ void format_results(char* text, EXPTYPE exponents[P], VALUETYPE ratios[K+1][P],
 	char beginningp[P][1024];
 	char endp[P][1024];
 	char newline[4];
+	char e[8];
 	
 	if(format == FORMAT_TEXT){
 		strcpy(beginning,"Current records:");
 		strcpy(end,"");
 
 		for(int p=0; p<P; p++){
-			sprintf(beginningp[p],"exponent %2.1f:",exptype_to_double(exponents[p]));
+			exptype_to_string(e,exponents[p]);
+			sprintf(beginningp[p],"exponent %s:",e);
 			strcpy(endp[p],"");
 		}
 
@@ -295,8 +303,9 @@ void format_results(char* text, EXPTYPE exponents[P], VALUETYPE ratios[K+1][P],
 		for(int n=1; n<N; n++) strcat(f,"& ");
 		strcat(f,"\\\\\n\\hline");
 		for(int p=0; p<P; p++){
-			sprintf(beginningp[p],"$p=%1.0f$:\n\n\\begin{tabular}%s\n%s",exptype_to_double(exponents[p]),h,f);
-			strcpy(endp[p],"\\end{tabular}\n");
+			exptype_to_latex(e,exponents[p]);
+			sprintf(beginningp[p],"\\begin{table}\n\\begin{tabular}%s\n%s",h,f);
+			sprintf(endp[p],"\\end{tabular}\n\\caption{$p=%s$:}\n\\end{table}",e);
 		}
 		strcpy(newline,"\\\\");
 	}
@@ -360,7 +369,8 @@ int main() {
 	int num_exponents[K+1];
 	EXPTYPE exponents[P];
 	exponents[0] = int_to_exptype(1);
-	exponents[1] = int_to_exptype(2);
+	//exponents[1] = int_to_exptype(2);
+	exponents[1] = infinity_to_exptype();
 
 	pthread_t threads[NUM_THREADS];
 	Args args[NUM_THREADS];
diff --git a/double-error.c b/double-error.c
index 9490671..8df0974 100644
--- a/double-error.c
+++ b/double-error.c
@@ -16,13 +16,17 @@ double_error int_to_valuetype(int i){
 	return de;
 }
 
-double_error int_to_exptype(double d){
+double_error int_to_exptype(int i){ return int_to_valuetype(i); }
+
+double_error infinity_to_exptype(){
 	double_error de;
-	de.v = d;
-	de.e = EPS*fabs(d) + DBL_MIN;
+	de.v = INFINITY;
+	de.e = 0;
 	return de;
 }
 
+bool exptype_is_infinite(double_error d){ return d.v == INFINITY; }
+
 double_error sum(double_error de1, double_error de2){
 	double_error de;
 	de.v = de1.v + de2.v;
@@ -113,27 +117,45 @@ double valuetype_to_double(double_error de){ return de.v; }
 double exptype_to_double(double_error de){ return de.v; }
 
 int valuetype_to_string(char* s, double_error de){
-	sprintf(s,"%f… +/- %6.1e",de.v,de.e);
+	if(de.e == 0.0){
+		if(de.v == 0.0 || de.v == 1.0 || de.v == 2.0 || de.v == 4.0 || de.v == 8.0 || de.v == 16.0) sprintf(s,"%d", (int)de.v);
+		else sprintf(s,"%4.3f…",de.v);
+	}
+	else sprintf(s,"%4.3f… +/- %6.1e",de.v,de.e);
 	return 0;
 }
 
+int exptype_to_string(char* s, double_error de){
+	if(exptype_is_infinite(de)) return sprintf(s,"inf");
+	else return valuetype_to_string(s,de);
+}
+
 int valuetype_to_latex(char* s, double_error de){
 	if(de.e == 0.0){
-		if(de.v == 0.0) sprintf(s,"$0$");
-		else if(de.v == 1.0) sprintf(s,"$1$");
+		if(de.v == 0.0 || de.v == 1.0 || de.v == 2.0 || de.v == 4.0 || de.v == 8.0 || de.v == 16.0) sprintf(s,"%d", (int)de.v);
+		else sprintf(s,"%4.3f\\ldots",de.v);
 	}
-	else sprintf(s,"$%4.3f\\ldots\\pm\\texttt{%1.0e}$",de.v,de.e);
+	else sprintf(s,"%4.3f\\ldots\\pm\\texttt{%1.0e}",de.v,de.e);
 	return 0;
 }
 
+int exptype_to_latex(char* s, double_error de){ 
+	if(exptype_is_infinite(de)) return sprintf(s,"\\infty");
+	else return valuetype_to_latex(s,de);
+}
+
 int root_to_string(char* s, double_error de, double_error p){
-	double_error de1p = power(de,ratio(int_to_valuetype(1),p));
+	double_error de1p;
+	if(exptype_is_infinite(p)) de1p = de;
+	else de1p = power(de,ratio(int_to_valuetype(1),p));
 	valuetype_to_string(s,de1p);
 	return 0;
 }
 
 int root_to_latex(char* s, double_error de, double_error p){
-	double_error de1p = power(de,ratio(int_to_valuetype(1),p));
+	double_error de1p;
+	if(exptype_is_infinite(p)) de1p = de;
+	else de1p = power(de,ratio(int_to_valuetype(1),p));
 	valuetype_to_latex(s,de1p);
 	return 0;
 }
diff --git a/double-error.h b/double-error.h
index d89b9b8..dbfe283 100644
--- a/double-error.h
+++ b/double-error.h
@@ -7,7 +7,11 @@ typedef struct {double v; double e;} double_error;
 
 double_error int_to_valuetype(int);
 
-double_error int_to_exptype(double);
+double_error int_to_exptype(int);
+
+double_error infinity_to_exptype();
+
+bool exptype_is_infinite(double_error);
 
 bool is_greater_certainly(double_error,double_error);
 
@@ -29,12 +33,14 @@ double_error power(double_error,double_error);
 
 double valuetype_to_double(double_error);
 
-double exptype_to_double(double_error);
-
 int valuetype_to_string(char*,double_error);
 
 int valuetype_to_latex(char*,double_error);
 
+int exptype_to_string(char*,double_error);
+
+int exptype_to_latex(char*,double_error);
+
 int root_to_string(char*,double_error,double_error);
 
 int root_to_latex(char*,double_error,double_error);
diff --git a/double.c b/double.c
index 09fcc28..0799e7d 100644
--- a/double.c
+++ b/double.c
@@ -8,6 +8,10 @@ double int_to_valuetype(int i){ return (double) i; }
 
 double int_to_exptype(double d){ return d; }
 
+double infinity_to_exptype(){ return INFINITY; }
+
+bool exptype_is_infinite(double d){ return d==INFINITY; }
+
 double sum(double d1, double d2){ return d1+d2; }
 
 double difference(double d1, double d2){ return d1-d2; }
@@ -31,26 +35,38 @@ double power(double d, double p) { return pow(d,p); }
 
 double valuetype_to_double(double d){ return d; }
 
-double exptype_to_double(double d){ return d; }
-
 int valuetype_to_string(char* s, double d){
-	sprintf(s,"%f",d);
+	if( d == 0.0 || d == 1.0 || d == 2.0 || d == 4.0 || d == 8.0 || d == 16.0 ) sprintf(s,"%d", (int)d);
+	else sprintf(s,"%4.3f",d);
 	return 0;
 }
 
-int valuetype_to_latex(char* s, double d){
-	if( d == 0.0) sprintf(s,"$0$");
-	else if( d == 1.0) sprintf(s,"$1$");
-	else sprintf(s,"$%4.3f$",d);
-	return 0;
+int valuetype_to_latex(char* s, double d){ return valuetype_to_string(s,d); }
+
+int exptype_to_string(char *s, double p){ 
+	if(exptype_is_infinite(p)){
+		sprintf(s,"inf");
+		return 0;
+	}
+	else return valuetype_to_string(s,p);
+}
+
+int exptype_to_latex(char *s, double p){
+	if(exptype_is_infinite(p)){
+		sprintf(s,"\\infty");
+		return 0;
+	}
+	else return valuetype_to_latex(s,p);
 }
 
 int root_to_string(char* s, double d, double p){
-	valuetype_to_string(s,pow(d,1.0/p));
+	if(exptype_is_infinite(p)) valuetype_to_string(s,d);
+	else valuetype_to_string(s,pow(d,1.0/p));
 	return 0;
 }
 
 int root_to_latex(char* s, double d, double p){
-	valuetype_to_latex(s,pow(d,1.0/p));
+	if(exptype_is_infinite(p)) valuetype_to_latex(s,d);
+	else valuetype_to_latex(s,pow(d,1.0/p));
 	return 0;
 }
diff --git a/double.h b/double.h
index 303f911..032d994 100644
--- a/double.h
+++ b/double.h
@@ -7,6 +7,10 @@ double int_to_valuetype(int);
 
 double int_to_exptype(double);
 
+double infinity_to_exptype();
+
+bool exptype_is_infinite(double);
+
 bool is_greater_certainly(double,double);
 
 bool is_greater_possibly(double,double);
@@ -27,7 +31,9 @@ double power(double,double);
 
 double valuetype_to_double(double);
 
-double exptype_to_double(double);
+int exptype_to_string(char*,double);
+
+int exptype_to_latex(char*,double);
 
 int valuetype_to_string(char*,double);
 
diff --git a/ratio.c b/ratio.c
index ecc20fb..fa7dc17 100644
--- a/ratio.c
+++ b/ratio.c
@@ -37,6 +37,10 @@ rational int_to_valuetype(int i){
 	return r;
 }
 
+unsigned int infinity_to_exptype(){ return UINT_MAX; }
+
+bool exptype_is_infinite(num p){ return p == UINT_MAX; }
+
 unsigned int int_to_exptype(unsigned int i){ return i; } 
 
 num gcd(num a, num b){
@@ -129,7 +133,17 @@ rational power(rational r, unsigned int p){
 	return s;
 }
 
-double exptype_to_double(int r){ return (double)r; }
+int exptype_to_string(char *s, unsigned int p){
+	if(exptype_is_infinite(p)) sprintf(s,"inf",p);
+	else sprintf(s,"%d",p);
+	return 0;
+}
+
+int exptype_to_latex(char *s, unsigned int p){
+	if(exptype_is_infinite(p)) sprintf(s,"\\infty",p);
+	else sprintf(s,"%d",p);
+	return 0;
+}
 
 double valuetype_to_double(rational r){
 	double i;
@@ -138,34 +152,47 @@ double valuetype_to_double(rational r){
 }
 
 int valuetype_to_string(char* s, rational r){
-	double f = valuetype_to_double(r);
-	sprintf(s,"%llu / %llu = %f… +/- %6.1e",r.n,r.d,f,f*DBL_EPSILON);
+	if(r.d == 1) {
+		if(r.n == 0) sprintf(s,"0");
+		else if(r.s) sprintf(s,"-%lld",r.n);
+		else if(!r.s) sprintf(s,"%lld",r.n);
+	}
+	else{
+		double f = valuetype_to_double(r);
+		sprintf(s,"%llu / %llu = %f… +/- %6.1e",r.n,r.d,f,f*DBL_EPSILON);
+	}
 	return 0;
 }
 
 int valuetype_to_latex(char* s, rational r){
 	if(r.d == 1) {
-		if(r.n == 0) sprintf(s,"$0$");
-		else if(r.s) sprintf(s,"$-%lld$",r.n);
-		else if(!r.s) sprintf(s,"$%lld$",r.n);
+		if(r.n == 0) sprintf(s,"0");
+		else if(r.s) sprintf(s,"-%lld",r.n);
+		else if(!r.s) sprintf(s,"%lld",r.n);
 	}
 	else{
 		double f = valuetype_to_double(r);
-		sprintf(s,"$\\frac{%llu}{%llu} = %4.3f\\ldots$",r.n,r.d,f);
-		//sprintf(s,"$\\frac{%llu}{%llu} = %3.2f\\ldots \\pm  %1.0e$",r.n,r.d,f,f*DBL_EPSILON);
+		sprintf(s,"\\frac{%llu}{%llu} = %4.3f\\ldots",r.n,r.d,f);
+		//sprintf(s,"\\frac{%llu}{%llu} = %3.2f\\ldots \\pm  %1.0e",r.n,r.d,f,f*DBL_EPSILON);
 	}
 	return 0;
 }
 
 int root_to_string(char* s, rational r, unsigned int p){
-	double f = pow(valuetype_to_double(r),1.0/p);
-	sprintf(s,"(%llu / %llu)^1/%i = %f… +/- %6.1e",r.n,r.d,p,f,2*DBL_EPSILON*f);
+	if(exptype_is_infinite(p) || p == 1) valuetype_to_string(s,r);
+	else{
+		double f = pow(valuetype_to_double(r),1.0/p);
+		sprintf(s,"(%llu / %llu)^1/%i = %f… +/- %6.1e",r.n,r.d,p,f,2*DBL_EPSILON*f);
+	}
 	return 0;
 }
 
 int root_to_latex(char* s, rational r, unsigned int p){
-	double f = pow(valuetype_to_double(r),1.0/p);
-	sprintf(s,"$\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %4.3f\\ldots$",r.n,r.d,p,f);
-	//sprintf(s,"$\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %3.2f\\ldots \\pm  %1.0e$",r.n,r.d,p,f,2*DBL_EPSILON*f);
+	if(exptype_is_infinite(p) || p == 1) valuetype_to_latex(s,r);
+	else{
+		double f = pow(valuetype_to_double(r),1.0/p);
+		sprintf(s,"\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %4.3f\\ldots",r.n,r.d,p,f);
+		//sprintf(s,"\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %3.2f\\ldots \\pm  %1.0e",r.n,r.d,p,f,2*DBL_EPSILON*f);
+	}
 	return 0;
 }
diff --git a/ratio.h b/ratio.h
index 87e210d..d17f0ae 100644
--- a/ratio.h
+++ b/ratio.h
@@ -9,6 +9,10 @@ rational int_to_valuetype(int);
 
 unsigned int int_to_exptype(unsigned int);
 
+unsigned int infinity_to_exptype();
+
+bool exptype_is_infinite(unsigned int);
+
 bool is_greater_certainly(rational,rational);
 
 bool is_greater_possibly(rational,rational);
@@ -29,7 +33,9 @@ rational power(rational,unsigned int);
 
 double valuetype_to_double(rational);
 
-double exptype_to_double(int);
+int exptype_to_string(char*,unsigned int);
+
+int exptype_to_latex(char*,unsigned int);
 
 int valuetype_to_string(char*,rational r);
 
-- 
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