April 22, 2018
(1) test1
computes differences in zeros
(2) test2
computes Dirichlet products
(3) test2a
isolates different values in zeta function zeros
(4) test2b
finds maxima and minima in Dirichlet products (for computing scaling factors)
(5) test2c
computes scaling factors
(6) test2d
extrapolates scaling factors
(7) test2e
does Mobius inversion
(8) test3
convolves zeros and differences with Mobius function
(9) test3a
finds minima of convolutions with Mobius function
(10) test4
computes Dirichlet inverses
(11) test4a
finds maxima and minimum of Dirichlet inverses
(12) test5
computes probit function
(13) test5a
computes probit function, fixed-point arithmetic used
(13) test8
computes generalized Ramanujan sums
(14) test9
tests Mobius, Dirichlet inverses subroutines
(15) test10
compares output of probit program to sqrt(2)*erfinv(2*p-1)
(16) test11
computes convolutions of differences of zeros with Mobius function at x
values that are the products of the successive primes
/******************************************************************************/
/* */
/* COMPUTE DIFFERENCES OF ZEROS (test1) */
/* 03/09/18 (dkc) */
/* */
/******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "zerosi.h"
//
unsigned int numzeros=201; // number of zeros
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int inc=0; // offset in computing differences (0 for next)
unsigned int clip=0; // if set, use threshold
//double delta=2.0; // threshold
double delta=0.4; // threshold for theta'
//
//
void main () {
unsigned int i;
long double temp,maxdif,mindif;
FILE *Outfp;
Outfp = fopen("out1.dat","w");
if (Outfp==NULL)
return;
if (scale!=0) {
for (i=0; i<(numzeros+inc+1); i++)
riem[i]=riem[i]/log(riem[i]);
}
maxdif=-1000000.0;
mindif=1000000.0;
for (i=1; i<numzeros; i++) {
temp=riem[i+inc]-riem[i-1];
if ((clip!=0)&&(temp>delta))
continue;
if (temp>maxdif)
maxdif=temp;
if (temp<mindif)
mindif=temp;
fprintf(Outfp," %llf, \n",temp);
}
printf("mindif=%llf, maxdif=%llf \n",mindif,maxdif);
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C COMPUTE DIRICHLET PRODUCTS (test2) C
C 04/22/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "table2.h"
#include "zerosi.h" // 100000 zeros
//#include "zeros1.h" // 20001 zeros of the Riemann zeta function
//#include "rand.h" // 2001 uniformly distributed values
extern char *malloc();
unsigned int pcheck(unsigned int N, unsigned int p, unsigned int pprod,
unsigned int subcur, unsigned int size, unsigned int *table);
double interp1(double ND, double ND1, unsigned int I,
double init, double *out);
unsigned int primed(unsigned int *out, unsigned int tsize,
unsigned int *table,unsigned int limit);
//
unsigned int MAXN=100000;
unsigned int I=1; // number of values to interpolate
unsigned int numlim=100000;
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int check=1; // check if N is prime, etc.
unsigned int p=2; // power of prime (up to 17 complete)
unsigned int pprod=1; // if set when p>1 and odd, do primes and combinations
unsigned int subcur=0; // sub-curves, set to 0 to do all
// 0, 1, 2 for p=3
// 0, 1, 2 for p=5
// 0, 1, 2, 3 for p=7
// 0, 1, 2, 3 for p=9
// 0, 1, 2, 3, 4 for p=11
// 0, 1, 2, 3, 4, 5, 6 for p=13
// 0, 1, 2, 3, 4, 5, 6 for p=15
// 0, 1, 2, 3, 4, 5, 6 for p=17;
unsigned int rnd=0; // if set, scale up the standard uniform distribution
double rndfact=5600.0; // factor
unsigned int tsize=17984; // prime look-up table size
//
void main() {
unsigned int i,N,count,t1size;
unsigned int *table1;
double *output;
double init,sum,max;
double min,temp;
FILE *Outfp;
Outfp = fopen("out2.dat","w");
output=(double*) malloc(800008);
if (output==NULL) {
printf("not enough memory \n");
return;
}
table1=(unsigned int*) malloc(800008);
if (table1==NULL) {
printf("not enough memory \n");
return;
}
t1size=primed(table1,tsize,table,250000); // make larger prime look-up table
printf("prime look-up table size=%d, last prime=%d \n",t1size,table1[t1size-1]);
if (rnd!=0) {
for (i=0; i<MAXN; i++)
riem[i]=riem[i]*rndfact;
}
if (scale!=0) {
for (i=0; i<MAXN; i++)
riem[i]=riem[i]/log(riem[i]);
}
init=riem[0];
for (i=0; i<(numlim+1); i++)
init=interp1(riem[i],riem[i+1],I,init,&output[i*I]);
//
count=0;
min=10000000;
max=0.0;
for (N=1; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<=N; i++) {
if (N==(N/i)*i)
sum=sum+output[N/i-1];
}
if (check!=0) {
if (pcheck(N,p,pprod,subcur,t1size,table1)==1) {
count=count+1;
temp=sum-output[0];
if (temp>max)
max=temp;
if (temp<min)
min=temp;
fprintf(Outfp," %llf, \n",temp);
}
}
else
fprintf(Outfp," %llf, \n",sum);
}
printf("count=%d, max=%llf, min=%llf \n",count,max,min);
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C ISOLATE DIFFERENT VALUES IN ZETA FUNCTION ZEROS (test2a) C
C 01/30/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "table2.h"
//#include "out2e.h"
#include "zerosi.h" // 100000 zeros of the Riemann zeta function
unsigned int pcheck(unsigned int N, unsigned int p, unsigned int pprod,
unsigned int subcur, unsigned int size, unsigned int *table);
//
unsigned int MAXN=11000;
unsigned int p=3; // power of prime (up to 17 complete)
unsigned int pprod=1; // if set when p>1 and odd, do primes and combinations
unsigned int subcur=1; // sub-curves, set to 0 to do all
// 0, 1, 2 for p=3
// 0, 1, 2 for p=5
// 0, 1, 2, 3 for p=7
// 0, 1, 2, 3 for p=9
// 0, 1, 2, 3, 4 for p=11
// 0, 1, 2, 3, 4, 5, 6 for p=13
// 0, 1, 2, 3, 4, 5, 6 for p=15
// 0, 1, 2, 3, 4, 5, 6 for p=17;
unsigned int tsize=17984;
//
void main() {
unsigned int N,count;
FILE *Outfp;
Outfp = fopen("out2a.dat","w");
count=0;
for (N=1; N<=MAXN; N++) {
if (pcheck(N,p,pprod,subcur,tsize,table)==1) {
count=count+1;
fprintf(Outfp," %llf, \n",riem[N-1]);
}
}
printf("count=%d \n",count);
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C COMPUTE DIRICHLET PRODUCTS, FOR SCALING FACTORS (test2b) C
C 04/14/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "table2.h"
#include "zerosi.h"
extern char *malloc();
unsigned int pcheck(unsigned int N, unsigned int p, unsigned int pprod,
unsigned int subcur, unsigned int size, unsigned int *table);
double interp1(double ND, double ND1, unsigned int I,
double init, double *out);
//
unsigned int hmax=22;
unsigned int I=1;
unsigned int numlim=50000;
unsigned int delta=500;
// 100000>=I*numlim>=hmax*delta
unsigned int p=3; // power of prime (up to 17 complete)
unsigned int pprod=1; // products of powers of primes
unsigned int subcur=1; // sub-curves, set to 0 to do all
// 0, 1, 2 for p=3
// 0, 1, 2 for p=5
// 0, 1, 2, 3 for p=7
// 0, 1, 2, 3 for p=9
// 0, 1, 2, 3, 4 for p=11
// 0, 1, 2, 3, 4, 5, 6 for p=13
// 0, 1, 2, 3, 4, 5, 6 for p=15
// 0, 1, 2, 3, 4, 5, 6 for p=17;
unsigned int maxmin=1; // if set, output maximum
unsigned int tsize=17984;
//
void main() {
unsigned int h,i,N,count,MAXN;
double *output;
double init,sum,max;
double min,temp;
FILE *Outfp;
Outfp = fopen("out2b.dat","w");
output=(double*) malloc(800008);
if (output==NULL) {
printf("not enough memory \n");
return;
}
init=riem[0];
for (i=0; i<(numlim+1); i++)
init=interp1(riem[i],riem[i+1],I,init,&output[i*I]);
//
for (h=1; h<=hmax; h++) {
MAXN=h*delta;
count=0;
min=10000000;
max=0.0;
for (N=1; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<=N; i++) {
if (N==(N/i)*i)
sum=sum+output[N/i-1];
}
if (pcheck(N,p,pprod,subcur,tsize,table)==1) {
count=count+1;
temp=sum-output[0];
if (temp>max)
max=temp;
if (temp<min)
min=temp;
}
}
printf("h=%d, count=%d, max=%llf, min=%llf \n",h,count,max,min);
if (maxmin!=0)
fprintf(Outfp," %llf, \n",max);
else
fprintf(Outfp," %llf, \n",min);
}
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C COMPUTE SCALING FACTORS (test2c) C
C 04/14/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "out2b1.h"
#include "out2b2.h"
unsigned int hmax=20;
long double min1=83.619076;
long double min2=66.318290;
//
void main() {
unsigned int h;
long double factor;
FILE *Outfp;
Outfp = fopen("out2c.dat","w");
for (h=1; h<=hmax; h++) {
factor=(max1[h-1]-min1)/(max2[h-1]-min2);
printf("max1=%llf max2=%llf factor=%llf \n",max1[h-1],max2[h-1],factor);
fprintf(Outfp," %llf, \n",factor);
}
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C EXTEND QUADRATIC CURVE (test2d) C
C 04/14/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
void main() {
unsigned int i;
double temp,temp1,p1,p2,p3;
FILE *Outfp;
Outfp = fopen("out2d.dat","w");
p1=-0.00007625;
p2=.001507;
p3=1.805;
for (i=1; i<=6; i++) {
temp=p1*(double)i*(double)i;
temp1=p2*(double)i;
temp=temp+temp1+p3;
printf(" %llf \n",temp);
fprintf(Outfp," %llf \n",temp);
}
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C MOBIUS INVERSION (test2e) C
C 04/14/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "table2.h"
#include "out2.h"
int mobius(unsigned int a, unsigned int *table, unsigned int tsize);
unsigned int NMAX=11000;
unsigned int scalup=1;
double factor=1.811297;
double norm=66.318290;
void main() {
unsigned int tsize=17984;
unsigned int i,N;
double sum;
FILE *Outfp;
Outfp = fopen("out2e.dat","w");
if (scalup!=0) {
for (i=0; i<NMAX; i++)
riem[i]=(riem[i]+norm)*factor;
}
for (N=1; N<=NMAX; N++) {
sum=0.0;
for (i=1; i<=N; i++) {
if (N==(N/i)*i) {
sum=sum+riem[i-1]*mobius(N/i,table,tsize);
}
}
fprintf(Outfp," %llf, \n",sum);
}
fclose(Outfp);
return;
}
/******************************************************************************
* *
* COMPUTE CONVOLUTION WITH MOBIUS FUNCTION (test3) *
* 04/20/18 (dkc) *
* *
* Normally distributed. *
* *
******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "zerosi.h"
#include "table2.h"
extern char *malloc();
int mobius(unsigned int a, unsigned int *table, unsigned int tsize);
unsigned int pcheck(unsigned int N, unsigned int p, unsigned int pprod,
unsigned int subcur, unsigned int size, unsigned int *table);
unsigned int primed(unsigned int *out, unsigned int tsize,
unsigned int *table,unsigned int limit);
//
unsigned int MAXN=100000; // maximum N value (or upper bound if "check!=0")
unsigned int newcnt=100000; // for curves and sub-curves ("check" not equal to 0)
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int diff=1; // if set, take differences
unsigned int inc=0; // offset for differences (0 for next)
//
unsigned int check=1; // check if N is prime, etc.
unsigned int p=4; // power of prime (up to 17 complete)
unsigned int pprod=1; // if set when p>1 and odd, do primes and combinations
unsigned int subcur=0; // sub-curves, set to 0 to do all
// 0, 1, 2 for p=3
// 0, 1, 2 for p=5
// 0, 1, 2, 3 for p=7
// 0, 1, 2, 3 for p=9
// 0, 1, 2, 3, 4 for p=11
// 0, 1, 2, 3, 4, 5, 6 for p=13
// 0, 1, 2, 3, 4, 5, 6 for p=15
// 0, 1, 2, 3, 4, 5, 6 for p=17;
unsigned int tsize=17984;
void main () {
unsigned int i,N,count,t1size;
unsigned int *table1;
double sum;
double max,min;
FILE *Outfp;
Outfp = fopen("out3.dat","w");
if (Outfp==NULL)
return;
table1=(unsigned int*) malloc(800008);
if (table1==NULL) {
printf("not enough memory \n");
return;
}
t1size=primed(table1,tsize,table,250000); // make larger prime look-up table
printf("prime look-up table size=%d, last prime=%d \n",t1size,table1[t1size-1]);
//
count=0;
max=0.0;
min=1000000;
for (N=1; N<=MAXN; N++) {
if (check!=0) {
if (pcheck(N,p,pprod,subcur,t1size,table1)==1) {
count=count+1;
if (count>newcnt)
goto zskip;
}
else
continue;
}
sum=0.0;
for (i=1; i<=N; i++) {
if (N==(N/i)*i) {
if (scale==0) {
if (diff==0)
sum=sum+riem[i-1]*mobius(i,table1,t1size);
else
sum=sum+(riem[i+inc]-riem[i-1])*mobius(i,table1,t1size);
}
else {
if (diff==0)
sum=sum+riem[i-1]/log(riem[i-1])*mobius(i,table1,t1size);
else
sum=sum+(riem[i+inc]/log(riem[i+inc])-riem[i-1]/log(riem[i-1]))*mobius(i,table1,t1size);
}
}
}
if (sum>max)
max=sum;
if (sum<min)
min=sum;
printf("sum=%llf, N=%d \n",sum,N);
fprintf(Outfp," %llf, \n",sum);
}
count=count+1;
zskip:
printf("max=%llf min=%llf count=%d \n",max,min,count-1);
fclose(Outfp);
return;
}
/******************************************************************************
* *
* FIND MINIMA OF CONVOLUTIONS OF ZEROS WITH THE MOBIUS FUNCTION (test3a) *
* 03/08/16 (dkc) *
* *
* The output (y(x)) is a step function where values drop at x values having *
* a large number of small prime divisors (square-free). When the difference *
* between every other zeta function zero is considered, the number of prime *
* factors is usually non-decreasing. *
* *
******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "zerosi.h"
#include "table2.h"
int mobius(unsigned int a, unsigned int *table, unsigned int tsize);
//
unsigned int iters=10000; // number of iterations
unsigned int delta=1; // amount to increment index
//
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int outmin=0; // select minimum or maximum
unsigned int diff=1; // if set, take differences
unsigned int inc=0; // offset for differences (0 for next)
//
void main () {
unsigned int h,i,N;
unsigned int tsize=17984; // prime look-up table size
unsigned int MAXN,savind,savind1;
double sum;
double max,min,oldmin,oldmax;
FILE *Outfp;
Outfp = fopen("out3a.dat","w");
if (Outfp==NULL)
return;
//
oldmin=1000000.0;
oldmax=-1.0;
for (h=1; h<=iters; h++) {
// if (h!=(h/2)*2)
// continue;
if (h==(h/1000)*1000)
printf("h=%d \n",h);
MAXN=h*delta;
max=0.0;
min=1000000;
savind=1;
savind1=1;
for (N=1; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<=N; i++) {
if (N==(N/i)*i) {
if (scale==0) {
if (diff==0)
sum=sum+riem[i-1]*mobius(i,table,tsize);
else
sum=sum+(riem[i+inc]-riem[i-1])*mobius(i,table,tsize);
}
else {
if (diff==0)
sum=sum+riem[i-1]/log(riem[i-1])*mobius(i,table,tsize);
else
sum=sum+(riem[i+inc]/log(riem[i+inc])-riem[i-1]/log(riem[i-1]))*mobius(i,table,tsize);
}
}
}
if (sum>max) {
max=sum;
savind1=MAXN;
}
if (sum<min) {
min=sum;
savind=MAXN;
}
}
if (outmin!=0) {
if (min<oldmin) {
printf("h=%d, min=%llf index=%d \n",MAXN,min,savind);
oldmin=min;
}
}
else {
if (max>oldmax) {
printf("h=%d, max=%llf index=%d \n",MAXN,max,savind1);
oldmax=max;
}
}
if (outmin!=0)
fprintf(Outfp," %llf \n",min);
else
fprintf(Outfp," %llf \n",max);
}
fclose(Outfp);
return;
}
/******************************************************************************
* *
* COMPUTE DIRICHLET INVERSE (test4) *
* 03/08/18 (dkc) *
* *
* Normally distributed. Probit bounds upper part of sorted curve but not *
* the bottom. For differences, probit is bounded and the mean of the *
* distribution is almost zero. *
* *
******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "zerosi.h"
//#include "out4.h"
extern char *malloc();
void dirinv(double *input, double *output, unsigned int size);
//
unsigned int MAXN=1000;
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int diff=1; // if set, input differences of zeros
unsigned int inc=1; // offset for differences (0 for next zero)
unsigned int sort=0; // if set, sort output
//
void main () {
unsigned int i,N,index;
double *dirin,temp,min,max;
double *output;
FILE *Outfp;
Outfp = fopen("out4.dat","w");
if (Outfp==NULL)
return;
output=(double*) malloc(800008);
if (output==NULL) {
printf("not enough memory \n");
return;
}
dirin=(double*) malloc(800008);
if (dirin==NULL) {
printf("not enough memory \n");
return;
}
//
// Dirichlet inverse
//
for (N=1; N<=MAXN; N++) {
if (scale!=0) {
if (diff==0)
dirin[N-1]=riem[N-1]/log(riem[N-1]);
else
dirin[N-1]=riem[N+inc]/log(riem[N+inc])-riem[N-1]/log(riem[N-1]);
}
else {
if (diff==0)
dirin[N-1]=riem[N-1];
else
dirin[N-1]=riem[N+inc]-riem[N-1];
}
}
dirinv(dirin,output,MAXN);
//
// sort
//
if (sort!=0) {
min=1000000.0;
index=0;
for (N=0; N<MAXN; N++) {
min=output[N];
index=N;
for (i=N+1; i<MAXN; i++) {
if (output[i]<min) {
min=output[i];
index=i;
}
}
if (index!=N) {
temp=output[N];
output[N]=output[index];
output[index]=temp;
}
}
}
min=1000000.0;
max=0.0;
for (N=1; N<=MAXN; N++) {
if (output[N-1]>max)
max=output[N-1];
if (output[N-1]<min)
min=output[N-1];
fprintf(Outfp," %llf, \n",output[N-1]);
}
printf("min=%llf max=%llf \n",min,max);
fclose(Outfp);
return;
}
/******************************************************************************
* *
* COMPUTE MAXIMA AND MINIMA OF DIRICHLET INVERSES (test4a) *
* 03/08/18 (dkc) *
* *
* Dirichlet inverses of the differences of zeta function zeros are computed. *
* The inverses are normally distributed and the means of the distributions *
* are almost zero. The probit function is bounded by the inverses. The *
* minima or maxima of the distributions are output. *
* *
******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "zerosi.h"
extern char *malloc();
void dirinv(double *input, double *output, unsigned int size);
//
unsigned int hmax=5000; // maximum h value
unsigned int delta=1; // h increment
unsigned int outmin=0; // select minimum or maximum
//
unsigned int diff=1; // if set, take differences
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int inc=1; // offset for differences (0 for next zero)
unsigned int outall=0; // if set, output all minima or maxima
unsigned int sort=0; // if set, sort output
//
void main () {
unsigned int h,MAXN,N;
double *dirin,max,min,oldmin,oldmax;
double *output;
FILE *Outfp;
Outfp = fopen("out4a.dat","w");
if (Outfp==NULL)
return;
output=(double*) malloc(800008);
if (output==NULL) {
printf("not enough memory \n");
return;
}
dirin=(double*) malloc(800008);
if (dirin==NULL) {
printf("not enough memory \n");
return;
}
//
// Dirichlet inverse
//
oldmin=1000000;
oldmax=-1.0;
for (h=1; h<=hmax; h++) {
MAXN=h*delta;
if (delta!=1)
printf("MAXN=%d \n",MAXN);
if ((MAXN+inc)>999999)
break;
// if ((MAXN>630)&&(delta==1)) {
// if (MAXN!=(MAXN/30)*30)
// continue;
// }
for (N=1; N<=MAXN; N++) {
if (scale!=0) {
if (diff!=0)
dirin[N-1]=riem[N+inc]/log(riem[N+inc])-riem[N-1]/log(riem[N-1]);
else
dirin[N-1]=riem[N-1]/log(riem[N-1]);
}
else {
if (diff!=0)
dirin[N-1]=riem[N+inc]-riem[N-1];
else
dirin[N-1]=riem[N-1];
}
}
dirinv(dirin,output,MAXN);
if ((h==1)&&(delta==1))
fprintf(Outfp," %llf \n",output[0]);
min=1000000.0;
max=0.0;
for (N=1; N<=MAXN; N++) {
if (output[N-1]>max)
max=output[N-1];
if (output[N-1]<min)
min=output[N-1];
}
if (min<oldmin) {
if (outmin!=0)
printf("h=%d, min=%llf \n",MAXN,min);
oldmin=min;
}
if (max>oldmax) {
if (outmin==0)
printf("h=%d, max=%llf \n",MAXN,max);
oldmax=max;
}
if (outmin==0) {
if (outall==0)
fprintf(Outfp," %llf \n",oldmax);
else
fprintf(Outfp," %llf \n",max);
}
else {
if (outall==0)
fprintf(Outfp," %llf \n",oldmin);
else
fprintf(Outfp," %llf \n",min);
}
}
fclose(Outfp);
return;
}
/******************************************************************************/
/* */
/* COMPUTE PROBIT FUNCTION (test5) */
/* 03/09/18 (dkc) */
/* */
/* Steinbrecher and Shaw's method is used. Matlab uses sqrt(2)*erfinv(2p-1). */
/* For MAXN=1000, Matlab doesn't appear to compute the tails very accurately. */
/* */
/* 03/16/18 Changed initial p value from 0 to 1/(MAXN+1) (optional). */
/* */
/******************************************************************************/
#include <math.h>
#include <stdio.h>
unsigned int MAXN=99999;
unsigned int pzero=0; // if set, start with p=0
unsigned int takeabs=0;
void main () {
long double sum,pi,save[10],p,temp,temp1,savep[601],pio4,pinc,d[300],savpos;
long double oldsum,maxsum,oldmax;
unsigned int i,j,k,maxk,first;
FILE *Outfp;
Outfp = fopen("out5.dat","w");
if (Outfp==NULL)
return;
pi=3.14159265358979323846;
pio4=pi/4.0;
save[0]=1.0;
save[1]=pio4*(save[0]);
save[2]=pio4*(save[0]*save[1]+save[1]*save[0]/6.0);
save[3]=pio4*(save[0]*save[2]+save[1]*save[1]/6.0+save[2]*save[0]/15.0);
save[4]=pio4*(save[0]*save[3]+save[1]*save[2]/6.0+save[2]*save[1]/15.0+save[3]*save[0]/28.0);
save[5]=pio4*(save[0]*save[4]+save[1]*save[3]/6.0*save[2]*save[2]/15.0+save[3]*save[1]/28.0+save[4]*save[0]/45.0);
maxk=200;
d[0]=1.0;
for (k=1; k<=maxk; k++) {
sum=0.0;
for (j=0; j<k; j++) {
sum=sum+d[j]*d[k-1-j]/(double)(j+1)/(double)(2*j+1);
}
sum=sum*pio4;
d[k]=sum;
// if (d[k]!=save[k]) {
// printf(" k=%d %llf %llf \n",k,d[k],save[k]);
// return;
// }
}
first=1;
p=0.0;
if (pzero==0) {
pinc=1.0/(double)(MAXN+1);
p=p+pinc;
}
else
pinc=1.0/(double)MAXN;
for (i=0; i<MAXN; i++) {
temp=2*p-1;
temp1=1.0;
for (k=0; k<=(2*maxk+1); k++) {
savep[k]=temp1;
temp1=temp1*temp;
}
sum=0.0;
for (k=0; k<=maxk; k++)
sum=sum+d[k]/(double)(2*k+1)*savep[2*k+1];
sum=sum*sqrt(pi/2.0);
if (i==0)
maxsum=sum;
if (i==1)
oldmax=sum;
if (takeabs!=0) {
if (sum<0.0)
sum=-sum;
}
if ((sum>0.0)&&(first!=0)) {
savpos=oldsum;
first=0;
}
// printf("p=%llf %llf \n",p,sum);
fprintf(Outfp," %llf, \n",sum);
oldsum=sum;
p=p+pinc;
}
//
printf("smallest value=%llf \n",maxsum);
printf("next smallest value=%llf \n",oldmax);
printf("last negative value=%llf \n",savpos);
fclose(Outfp);
return;
}
/******************************************************************************/
/* */
/* COMPUTE PROBIT FUNCTION (test5a) */
/* 03/16/18 (dkc) */
/* */
/* Steinbrecher and Shaw's method is used. Matlab uses sqrt(2)*erfinv(2p-1). */
/* For MAXN=1000, Matlab doesn't appear to compute the tails very accurately. */
/* */
/* The floating point results (presumably having a 53-bit mantissa) are */
/* compared to results using 62 bit fixed-point arithmetic. No significant */
/* difference was found. */
/* */
/* 03/16/18 Changed initial p value from 0 to 1/(MAXN+1). */
/* */
/******************************************************************************/
#include <math.h>
#include <stdio.h>
void mul64_64(unsigned int a0, unsigned int a2, unsigned int m0,
unsigned int m2, unsigned int *product);
void div128_64(unsigned int a0, unsigned int a1, unsigned int a2,
unsigned int a3, unsigned int *quotient, unsigned int d2,
unsigned int d3);
void add64(unsigned int *a, unsigned int *b);
void shift(unsigned int A[2], unsigned int B[2], unsigned int shift);
void lshiftn(unsigned int *a, unsigned int *b, unsigned int shift, unsigned
int n);
void add128(unsigned int *a, unsigned int *b);
void sub128(unsigned int *a, unsigned int *b);
//
unsigned int MAXN=99999;
unsigned int takeabs=0;
//
void main () {
long double sum,pi,p,temp,temp1,savep[601],pio4,pinc,d[300],savpos;
long double oldsum,maxsum,oldmax,sqpi2,temp2,temp3,temp4,maxdif;
unsigned int i,j,k,maxk,first,Z[4],SQP[2];
unsigned int D[300*4],P[4],Q[4],S[4],T[2],PI[2],PI4[2],SP[601*4],PINC[4],PR[4];
FILE *Outfp;
Outfp = fopen("out5a.dat","w");
if (Outfp==NULL)
return;
pi=3.14159265358979323846;
// 3.243F6 A8885 A308D 31319 8A2E0 37073
sqpi2=1.25331413732; // sqrt(pi/2)
SQP[0]=0x140d931f;
SQP[1]=0xf6762ea7;
PI[0]=0x3243F6A8;
PI[1]=0x885A308D;
PI4[0]=PI[0];
PI4[1]=PI[1];
T[0]=0;
T[1]=2;
add64(T,PI4);
shift(PI4,PI4,2);
pio4=pi/4.0;
maxk=200;
d[0]=1.0;
D[0]=0x08000000;
D[1]=0;
D[2]=0;
D[3]=0;
for (k=1; k<=maxk; k++) {
sum=0.0;
S[0]=0;
S[1]=0;
S[2]=0;
S[3]=0;
for (j=0; j<k; j++) {
sum=sum+d[j]*d[k-1-j]/(double)(j+1)/(double)(2*j+1);
mul64_64(D[4*j],D[4*j+1],D[4*(k-1-j)],D[4*(k-1-j)+1],P);
div128_64(P[0],P[1],P[2],P[3],Q,0,(j+1)*(2*j+1));
add128(Q,S);
}
sum=sum*pio4;
mul64_64(S[0],S[1],PI4[0],PI4[1],P);
d[k]=sum;
lshiftn(P,P,9,4);
D[4*k]=P[0];
D[4*k+1]=P[1];
D[4*k+2]=P[2];
D[4*k+3]=P[3];
}
maxdif=0.0;
Z[0]=0;
Z[1]=0;
Z[2]=0;
Z[3]=0;
first=1;
p=0.0;
pinc=1.0/(double)(MAXN+1);
p=p+pinc;
div128_64(0x40000000,0,0,0,PINC,0,MAXN+1);
PR[0]=0;
PR[1]=0;
PR[2]=0;
PR[3]=0;
add128(PINC,PR);
for (i=0; i<MAXN; i++) {
temp=2*p-1;
temp1=1.0;
S[0]=0x40000000; // 1
S[1]=0;
S[2]=0;
S[3]=0;
SP[0]=S[0];
SP[1]=S[1];
SP[2]=S[2];
SP[3]=S[3];
P[0]=PR[0]; // p
P[1]=PR[1];
P[2]=PR[2];
P[3]=PR[3];
lshiftn(P,P,1,4); // 2*p
sub128(S,P); // 1-2*p
if ((P[0]&0x80000000)!=0)
sub128(Z,P);
S[0]=P[0];
S[1]=P[1];
S[2]=P[2];
S[3]=P[3];
for (k=0; k<=(2*maxk+1); k++) {
savep[k]=temp1;
temp1=temp1*temp;
SP[4*k+4]=P[0];
SP[4*k+5]=P[1];
SP[4*k+6]=P[2];
SP[4*k+7]=P[3];
mul64_64(P[0],P[1],S[0],S[1],Q);
lshiftn(Q,Q,2,4);
P[0]=Q[0];
P[1]=Q[1];
P[2]=Q[2];
P[3]=Q[3];
}
sum=0.0;
S[0]=0;
S[1]=0;
S[2]=0;
S[3]=0;
for (k=0; k<=maxk; k++) {
div128_64(D[4*k],D[4*k+1],D[4*k+2],D[4*k+3],Q,0,2*k+1);
mul64_64(SP[4*(2*k+1)],SP[4*(2*k+1)+1],Q[0],Q[1],Q);
lshiftn(Q,Q,5,4);
add128(Q,S);
sum=sum+d[k]/(double)(2*k+1)*savep[2*k+1];
}
sum=sum*sqrt(pi/2.0);
mul64_64(S[0],S[1],SQP[0],SQP[1],P);
lshiftn(P,S,3,4);
//
// compare results
//
temp2=sum;
if (temp2<0.0)
temp2=-temp2;
temp3=((double)S[0]+(double)S[1]/65536.0/65536.0)/65536.0/8192.0;
temp4=temp2-temp3;
if (temp4<0.0)
temp4=-temp4;
if (temp4>maxdif)
maxdif=temp4;
// printf("sum=%llf, %llf \n",sum,((double)S[0]+(double)S[1]/65536.0/65536.0)/65536.0/8192.0);
//
if (i==0)
maxsum=sum;
if (i==1)
oldmax=sum;
if (takeabs!=0) {
if (sum<0.0)
sum=-sum;
}
if ((sum>0.0)&&(first!=0)) {
savpos=oldsum;
first=0;
}
fprintf(Outfp," %llf, \n",sum);
oldsum=sum;
p=p+pinc;
add128(PINC,PR);
}
//
printf("\n");
printf("maximum difference=%llf \n",maxdif);
printf("smallest value=%llf \n",maxsum);
printf("next smallest value=%llf \n",oldmax);
printf("last negative value=%llf \n",savpos);
fclose(Outfp);
return;
}
/******************************************************************************
* *
* 64x64 BIT MULTIPLY (UNSIGNED) *
* 01/12/07 (dkc) *
* *
******************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum);
void mul64_64(unsigned int a0, unsigned int a2, unsigned int m0,
unsigned int m2, unsigned int *product) {
unsigned int a1,a3,m1,m3,temp;
unsigned int p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
unsigned int s0,s1,s2,s3;
unsigned int c1,c2,c3;
a1=a0&0xffff;
a0=a0>>16;
a3=a2&0xffff;
a2=a2>>16;
m1=m0&0xffff;
m0=m0>>16;
m3=m2&0xffff;
m2=m2>>16;
p0=a0*m0;
p1=a0*m1;
p2=a1*m0;
p3=a0*m2;
p4=a1*m1;
p5=a2*m0;
p6=a0*m3;
p7=a1*m2;
p8=a2*m1;
p9=a3*m0;
p10=a1*m3;
p11=a2*m2;
p12=a3*m1;
p13=a2*m3;
p14=a3*m2;
p15=a3*m3;
s3=p15+(p14<<16);
c3=carry(p15,(p14<<16),s3);
temp=s3+(p13<<16);
c3+=carry(s3,(p13<<16),temp);
s3=temp;
s2=p12+(p14>>16);
c2=carry(p12,(p14>>16),s2);
temp=s2+(p13>>16);
c2+=carry(s2,(p13>>16),temp);
s2=temp;
temp=s2+p11;
c2+=carry(s2,p11,temp);
s2=temp;
temp=s2+p10;
c2+=carry(s2,p10,temp);
s2=temp;
temp=s2+(p9<<16);
c2+=carry(s2,(p9<<16),temp);
s2=temp;
temp=s2+(p8<<16);
c2+=carry(s2,(p8<<16),temp);
s2=temp;
temp=s2+(p7<<16);
c2+=carry(s2,(p7<<16),temp);
s2=temp;
temp=s2+(p6<<16);
c2+=carry(s2,(p6<<16),temp);
s2=temp;
s1=p5+(p9>>16);
c1=carry(p5,(p9>16),s1);
temp=s1+(p8>>16);
c1+=carry(s1,(p8>>16),temp);
s1=temp;
temp=s1+(p7>>16);
c1+=carry(s1,(p7>>16),temp);
s1=temp;
temp=s1+(p6>>16);
c1+=carry(s1,(p6>>16),temp);
s1=temp;
temp=s1+p4;
c1+=carry(s1,p4,temp);
s1=temp;
temp=s1+p3;
c1+=carry(s1,p3,temp);
s1=temp;
temp=s1+(p2<<16);
c1+=carry(s1,(p2<<16),temp);
s1=temp;
temp=s1+(p1<<16);
c1+=carry(s1,(p1<<16),temp);
s1=temp;
s0=p0+(p2>>16);
s0=s0+(p1>>16);
temp=s2+c3;
c2+=carry(s2,c3,temp);
s2=temp;
temp=s1+c2;
c1+=carry(s1,c2,temp);
s1=temp;
s0=s0+c1;
*product=s0;
*(product+1)=s1;
*(product+2)=s2;
*(product+3)=s3;
return;
}
/*****************************************************************************/
/* */
/* 128/64 BIT DIVIDE (UNSIGNED) */
/* 01/12/07 (dkc) */
/* */
/*****************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum);
unsigned int lmbd(unsigned int mode, unsigned int a);
void div128_64(unsigned int a0, unsigned int a1, unsigned int a2,
unsigned int a3, unsigned int *quotient, unsigned int d2,
unsigned int d3) {
unsigned int i,d0,d1,dshift,ashift,count,flag;
unsigned int shift,c,c0,c1,c2,temp,temp0,temp1,temp2,temp3;
if (d2==0) {
if ((a0==0)&&(a1==0)&&(a2==0)&&(a3<d3)) {
*quotient=0;
*(quotient+1)=0;
*(quotient+2)=0;
*(quotient+3)=0;
return;
}
}
else {
if ((a0==0)&&(a1==0)&&(a2<d2)) {
*quotient=0;
*(quotient+1)=0;
*(quotient+2)=0;
*(quotient+3)=0;
return;
}
}
dshift=lmbd(1,d2);
if (d2==0)
dshift+=lmbd(1,d3);
dshift+=64;
ashift=lmbd(1,a0);
if (a0==0)
ashift+=lmbd(1,a1);
if ((a0|a1)==0)
ashift+=lmbd(1,a2);
if ((a0|a1|a2)==0)
ashift+=lmbd(1,a3);
shift=dshift-ashift;
count=shift+1;
d0=0;
d1=0;
if (shift<32) {
if (shift!=0) {
d1=d2>>(32-shift);
d2=(d2<<shift)|(d3>>(32-shift));
}
else
d1=0; // added to get MSVC to work
d3=d3<<shift;
flag=3;
shift=32-shift;
}
else {
shift=shift-32;
d1=d2;
d2=d3;
d3=0;
if (shift<32) {
if (shift!=0) {
d0=d1>>(32-shift);
d1=(d1<<shift)|(d2>>(32-shift));
}
else
d0=0; // added to get MSVC to work
d2=d2<<shift;
flag=2;
shift=32-shift;
}
else {
shift=shift-32;
d0=d1;
d1=d2;
d2=0;
if (shift<32) {
if (shift!=0) // added to get MSVC to work
d0=(d0<<shift)|(d1>>(32-shift));
d1=d1<<shift;
flag=1;
shift=32-shift;
}
else {
shift=shift-32;
d0=d1;
d1=0;
d0=d0<<shift;
flag=0;
shift=32-shift;
}
}
}
d0=~d0;
d1=~d1;
d2=~d2;
d3=~d3;
temp=d3+1;
c=carry(d3,1,temp);
d3=temp;
temp=d2+c;
c=carry(d2,c,temp);
d2=temp;
temp=d1+c;
c=carry(d1,c,temp);
d1=temp;
d0=d0+c;
for (i=0; i<count; i++) {
temp3=a3+d3;
c2=carry(a3,d3,temp3);
temp=a2+c2;
c1=carry(a2,c2,temp);
temp2=temp+d2;
c1+=carry(temp,d2,temp2);
temp=a1+c1;
c0=carry(a1,c1,temp);
temp1=temp+d1;
c0+=carry(temp,d1,temp1);
temp0=a0+d0+c0;
if ((temp0>>31)==0) {
a0=temp0<<1;
if ((temp1>>31)!=0)
c=1;
else
c=0;
a0=a0+c;
a1=temp1<<1;
if ((temp2>>31)!=0)
c=1;
else
c=0;
a1=a1+c;
a2=temp2<<1;
if ((temp3>>31)!=0)
c=1;
else
c=0;
a2=a2+c;
a3=temp3<<1;
a3=a3+1;
}
else {
a0=a0<<1;
if ((a1>>31)!=0)
c=1;
else
c=0;
a0=a0+c;
a1=a1<<1;
if ((a2>>31)!=0)
c=1;
else
c=0;
a1=a1+c;
a2=a2<<1;
if ((a3>>31)!=0)
c=1;
else
c=0;
a2=a2+c;
a3=a3<<1;
}
}
shift=shift-1;
if (flag==3) {
a0=0;
a1=0;
a2=0;
a3=a3<<shift;
a3=a3>>shift;
}
else {
if (flag==2) {
a0=0;
a1=0;
a2=a2<<shift;
a2=a2>>shift;
}
else {
if (flag==1) {
a0=0;
a1=a1<<shift;
a1=a1>>shift;
}
else {
a0=a0<<shift;
a0=a0>>shift;
}
}
}
*quotient=a0;
*(quotient+1)=a1;
*(quotient+2)=a2;
*(quotient+3)=a3;
return;
}
/******************************************************************************
* *
* 64-BIT ADD *
* 01/12/07 (dkc) *
* *
******************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum);
void add64(unsigned int *a, unsigned int *b) {
unsigned int high0,high1,low0,low1,templo,temphi,c;
high0=*a;
low0=*(a+1);
high1=*b;
low1=*(b+1);
templo=low0+low1;
c=carry(low0,low1,templo);
temphi=high0+high1+c;
*b=temphi;
*(b+1)=templo;
return;
}
/*****************************************************************************/
/* */
/* RIGHT-SHIFT 64 BITS */
/* 10/16/09 (dkc) */
/* */
/*****************************************************************************/
void shift(unsigned int A[2], unsigned int B[2], unsigned int shift) {
unsigned int temp;
B[0]=A[0];
B[1]=A[1];
while (shift>31) {
B[1]=B[0];
B[0]=0;
shift=shift-32;
}
if (shift==0)
return;
B[1]=B[1]>>shift;
temp=B[0]<<(32-shift);
B[1]=B[1]|temp;
B[0]=B[0]>>shift;
return;
}
/*****************************************************************************/
/* */
/* LEFT-SHIFT 32*N BITS */
/* 10/16/09 (dkc) */
/* */
/*****************************************************************************/
void lshiftn(unsigned int *a, unsigned int *b, unsigned int shift, unsigned
int n) {
unsigned int i;
for (i=0; i<n; i++)
*(b+i)=*(a+i);
while (shift>31) {
for (i=0; i<n-1; i++)
*(b+i)=*(b+i+1);
*(b+n-1)=0;
shift=shift-32;
}
if (shift==0)
return;
for (i=0; i<n-1; i++)
*(b+i)=(*(b+i)<<shift)|(*(b+i+1)>>(32-shift));
*(b+n-1)=*(b+n-1)<<shift;
return;
}
/******************************************************************************
* *
* 128-BIT ADD *
* 01/12/07 (dkc) *
* *
******************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum);
void add128(unsigned int *a, unsigned int *b) {
unsigned int a0,a1,a2,a3,b0,b1,b2,b3;
unsigned int s0,s1,s2,s3,temp,c1,c2,c3;
a0=*a;
a1=*(a+1);
a2=*(a+2);
a3=*(a+3);
b0=*b;
b1=*(b+1);
b2=*(b+2);
b3=*(b+3);
s3=a3+b3;
c3=carry(a3,b3,s3);
s2=a2+b2;
c2=carry(a2,b2,s2);
s1=a1+b1;
c1=carry(a1,b1,s1);
s0=a0+b0;
temp=s2+c3;
c2+=carry(s2,c3,temp);
s2=temp;
temp=s1+c2;
c1+=carry(s1,c2,temp);
s1=temp;
s0=s0+c1;
*b=s0;
*(b+1)=s1;
*(b+2)=s2;
*(b+3)=s3;
return;
}
/******************************************************************************
* *
* 128-BIT SUBTRACT *
* 01/12/07 (dkc) *
* *
******************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum);
void sub128(unsigned int *a, unsigned int *b) {
unsigned int a0,a1,a2,a3,b0,b1,b2,b3;
unsigned int s0,s1,s2,s3,temp,c,c1,c2,c3;
a0=*a;
a1=*(a+1);
a2=*(a+2);
a3=*(a+3);
b0=*b;
b1=*(b+1);
b2=*(b+2);
b3=*(b+3);
b0=~b0;
b1=~b1;
b2=~b2;
b3=~b3;
temp=b3+1;
c=carry(b3,1,temp);
b3=temp;
temp=b2+c;
c=carry(b2,c,temp);
b2=temp;
temp=b1+c;
c=carry(b1,c,temp);
b1=temp;
b0=b0+c;
s3=a3+b3;
c3=carry(a3,b3,s3);
s2=a2+b2;
c2=carry(a2,b2,s2);
s1=a1+b1;
c1=carry(a1,b1,s1);
s0=a0+b0;
temp=s2+c3;
c2+=carry(s2,c3,temp);
s2=temp;
temp=s1+c2;
c1+=carry(s1,c2,temp);
s1=temp;
s0=s0+c1;
*b=s0;
*(b+1)=s1;
*(b+2)=s2;
*(b+3)=s3;
return;
}
/*****************************************************************************/
/* */
/* LEFT-MOST BIT DETECTION */
/* 01/12/07 (dkc) */
/* */
/*****************************************************************************/
unsigned int lmbd(unsigned int mode, unsigned int a) {
unsigned int i,mask,count;
if (mode==0)
a=~a;
if (a==0)
return(32);
count=0;
mask=0x80000000;
for (i=0; i<32; i++) {
if ((a&mask)!=0)
break;
count+=1;
mask>>=1;
}
return(count);
}
/*****************************************************************************/
/* */
/* CARRY */
/* 01/12/07 (dkc) */
/* */
/*****************************************************************************/
unsigned int carry(unsigned int a, unsigned int b, unsigned int sum) {
unsigned int c;
if ((a&b)>>31!=0)
c=1;
else {
if ((a|b)>>31==0)
c=0;
else {
if (sum>=0x80000000)
c=0;
else
c=1;
}
}
return c;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C COMPUTE RAMANUJAN SUMS (test8) C
C 01/30/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "table2.h"
#include "zerosi.h" // 100000 zeros
extern char *malloc();
unsigned int pcheck(unsigned int N, unsigned int p, unsigned int pprod,
unsigned int subcur, unsigned int size, unsigned int *table);
double interp1(double ND, double ND1, unsigned int I,
double init, double *out);
unsigned int euclid(unsigned int d, unsigned int e);
//
unsigned int MAXN=1000;
unsigned int I=1; // number of values to interpolate
unsigned int numlim=1000;
unsigned int scale=0; // if set, divide zeros by their logarithms
unsigned int check=0; // check if N is prime, etc.
unsigned int p=1; // power of prime (up to 17 complete)
unsigned int kay=19; // k
unsigned int pprod=1; // if set when p>1 and odd, do primes and combinations
unsigned int subcur=0; // sub-curves, set to 0 to do all
// 0, 1, 2 for p=3
// 0, 1, 2 for p=5
// 0, 1, 2, 3 for p=7
// 0, 1, 2, 3 for p=9
// 0, 1, 2, 3, 4 for p=11
// 0, 1, 2, 3, 4, 5, 6 for p=13
// 0, 1, 2, 3, 4, 5, 6 for p=15
// 0, 1, 2, 3, 4, 5, 6 for p=17;
unsigned int outscale=0; // if set, divide output by logarithms
unsigned int tsize=17984;
//
void main() {
unsigned int i,N,count,d;
double *output;
double init,sum;
FILE *Outfp;
Outfp = fopen("out8.dat","w");
output=(double*) malloc(800008);
if (output==NULL) {
printf("not enough memory \n");
return;
}
if (scale!=0) {
for (i=0; i<MAXN; i++)
riem[i]=riem[i]/log(riem[i]);
}
init=riem[0];
for (i=0; i<(numlim+1); i++)
init=interp1(riem[i],riem[i+1],I,init,&output[i*I]);
//
count=0;
for (N=1; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<=N; i++) {
d=euclid(i,kay);
if (N==(N/d)*d) {
sum=sum+output[d-1]*output[kay/d-1];
}
}
if (check!=0) {
if (pcheck(N,p,pprod,subcur,tsize,table)==1) {
count=count+1;
fprintf(Outfp," %llf, \n",sum-output[0]);
}
}
else {
if (outscale==0)
fprintf(Outfp," %llf, \n",sum);
else
fprintf(Outfp," %llf, \n",sum/log(sum));
}
}
printf("count=%d \n",count);
fclose(Outfp);
return;
}
/******************************************************************************
* *
* TEST PHI AND MOBIUS SUBROUTINES (test9) *
* 04/02/10 (dkc) *
* *
******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "table2.h"
extern char *malloc();
int liouvill(unsigned int a, unsigned int *table, unsigned int tsize);
unsigned int phi(unsigned int a, unsigned int *table, unsigned int tsize);
int mobius(unsigned int a, unsigned int *table, unsigned int tsize);
void dirinv(double *input, double *output, unsigned int count);
unsigned int MAXN=20;
double input[20]={
0.187385,
-0.242368,
-0.272794,
0.000679,
-0.330931,
0.341767,
-0.387108,
0.000040,
-0.038278,
0.408796,
-0.468534,
-0.008380,
-0.510324,
0.481443,
0.416066,
-0.039088,
-0.575670,
0.053345,
-0.614358,
-0.022332};
void main () {
double sum;
unsigned int i,j,N;
unsigned int tsize=17984;
int k;
double *recur;
double *dirin;
int *save;
int *save1;
save=(int*) malloc(8008);
if (save==NULL) {
printf("not enough memory \n");
return;
}
save1=(int*) malloc(8008);
if (save1==NULL) {
printf("not enough memory \n");
return;
}
recur=(double*) malloc(8008);
if (recur==NULL) {
printf("not enough memory \n");
return;
}
dirin=(double*) malloc(8008);
if (dirin==NULL) {
printf("not enough memory \n");
return;
}
//
// compute phi function
//
printf("phi and mobius\n");
save[0]=1;
save1[0]=1;
printf(" %d %d %d \n",1,1,1);
for (i=2; i<=MAXN; i++) {
j=phi(i,table,tsize);
k=mobius(i,table,tsize);
save[i-1]=j;
save1[i-1]=k;
printf(" %d %d %d \n",i,j,k);
}
//
// compute Dirichlet inverse (phi function)
//
printf("\n");
printf("inverse of completely multiplicative function \n");
for (i=1; i<=MAXN; i++) {
k=save[i-1]*save1[i-1];
printf(" %d %d %d %d \n",i,save[i-1],save1[i-1],k);
}
printf("\n");
printf("inverse of phi function (gives strange function) \n");
//
// compute Dirichlet inverse (phi function)
//
recur[0]=1.0/(double)save[0];
printf(" %d %llf \n",1,recur[0]);
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+save[N/i-1]*recur[i-1];
}
recur[N-1]=-1.0/(double)save[0]*sum;
printf(" %d %llf \n",N,recur[N-1]);
}
//
// compute Dirichlet inverse (Liouville function)
//
printf("\n");
printf("inverse of completely multiplicative function \n");
for (i=1; i<=MAXN; i++) {
k=liouvill(i, table, tsize);
save[i-1]=k;
printf(" %d %d %d %d \n",i,k,save1[i-1],k*save1[i-1]);
save1[i-1]=k*save1[i-1];
}
printf("\n");
printf("inverse of Liouville function (gives abs of Mobius) \n");
//
// compute Dirichlet inverse (Liouville function)
//
recur[0]=1.0/(double)save[0];
printf(" %d %llf \n",1,recur[0]);
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+save[N/i-1]*recur[i-1];
}
recur[N-1]=-1.0/(double)save[0]*sum;
printf(" %d %llf %d \n",N,recur[N-1],save1[N-1]);
}
printf("\n");
printf("compute inverse of inverse \n");
for (i=0; i<MAXN; i++)
save1[i]=(int)recur[i];
recur[0]=1.0/(double)save1[0];
printf(" %d %llf \n",1,recur[0]);
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+save1[N/i-1]*recur[i-1];
}
recur[N-1]=-1.0/(double)save1[0]*sum;
printf(" %d %llf %d \n",N,recur[N-1],save1[N-1]);
}
//
// call subroutine
//
printf("\n");
printf("same as above, computed using subroutine \n");
for (i=0; i<MAXN; i++)
dirin[i]=(double)save[i];
dirinv(dirin,recur,MAXN);
for (i=0; i<MAXN; i++)
printf(" %d %llf \n",i+1,recur[i]);
//
// compute Dirichlet inverse (constant function)
//
printf("\n");
printf("inverse of a constant function (1 in this case, gives Mobius) \n");
recur[0]=1.0/(double)1;
printf(" %d %llf \n",1,recur[0]);
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+recur[i-1];
}
if (sum!=0.0)
recur[N-1]=-1.0/(double)sum;
else
recur[N-1]=0.0;
printf(" %d %llf %d \n",N,recur[N-1],save1[N-1]);
}
//
// compute Dirichlet inverse
//
printf("\n");
printf("inverse of inverse of zeta function zeros \n");
recur[0]=1.0/input[0];
printf(" %d %llf \n",1,recur[0]);
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+input[N/i-1]*recur[i-1];
}
recur[N-1]=-1.0/(double)input[0]*sum;
printf(" %d %llf %llf \n",N,recur[N-1],input[N-1]);
}
return;
}
/******************************************************************************/
/* */
/* TEST PROBIT PROGRAM (test10) */
/* 03/15/18 (dkc) */
/* *;
/* Compare output of the probit program (test 5) to sqrt(2)*erfinv(2*p-1) */
/* (computed by Matlab). */
/* */
/******************************************************************************/
#include <math.h>
#include <stdio.h>
#include "out5a.dat"
#include "out5b.dat"
//
unsigned int numbp=1000; // number of probability increments
//
void main () {
unsigned int i;
long double temp,maxdif,mindif,sum1,sum2;
FILE *Outfp;
Outfp = fopen("out10.dat","w");
if (Outfp==NULL)
return;
maxdif=-1000000.0;
mindif=1000000.0;
sum1=0.0;
sum2=0.0;
for (i=0; i<numbp; i++) {
sum1=sum1+prob1[i];
sum2=sum2+prob2[i];
temp=prob1[i]-prob2[i];
if (temp<0.0)
temp=-temp;
if (temp>maxdif)
maxdif=temp;
if (temp<mindif)
mindif=temp;
printf(" %llf \n",temp);
fprintf(Outfp," %llf, \n",temp);
}
printf("mindif=%llf, maxdif=%llf \n",mindif,maxdif);
printf("sum1=%llf, sum2=%llf \n",sum1,sum2);
fclose(Outfp);
return;
}
/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C CONVOLUTIONS OF DIFFERENCES OF ZEROS WITH MOBIUS FUNCTION AT PRODUCTS OF C
c SUCCESSIVE PRIMES (test11) C
C 03/19/18 (DKC) C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
#include "zerosi.h"
#include "table2.h"
extern char *malloc();
//
unsigned int MAXN=4;
int inc=1; // starts with 1
//
void main() {
unsigned int i,j,k,p,t,u,index;
double sum,temp;
unsigned int *f;
FILE *Outfp;
Outfp = fopen("out11.dat","w");
f=(unsigned int*) malloc(800008);
if (f==NULL) {
printf("not enough memory \n");
return;
}
//
temp=riem[inc]-riem[0];
printf("sum=%llf \n",temp);
f[0]=1;
f[1]=0;
//
f[2]=2;
f[3]=1;
//
f[4]=3;
f[5]=1;
//
f[6]=2*3;
f[7]=0;
//
index=2;
k=4;
sum=-riem[1]+riem[1+inc]-riem[2]+riem[2+inc]+riem[5]-riem[5+inc];
printf("sum=%llf \n",temp-sum);
//printf("\n");
for (i=0; i<MAXN; i++) {
p=table[index];
index=index+1;
for (j=0; j<k; j++) {
f[2*j+k*2]=f[2*j]*p;
f[2*j+k*2+1]=f[2*j+1]^1;
t=f[2*j+k*2];
u=f[2*j+k*2+1];
printf("t=%d u=%d \n",t,u);
if (u==1)
sum=sum-riem[t-1]+riem[t+inc-1];
else
sum=sum+riem[t-1]-riem[t+inc-1];
}
printf("sum=%llf \n",temp-sum);
printf("\n");
k=k*2;
}
fclose(Outfp);
return;
}
/*****************************************************************************/
/* */
/* DIRICHLET INVERSE */
/* 03/15/18 (dkc) */
/* */
/*****************************************************************************/
void dirinv(double *input, double *output, unsigned int MAXN) {
unsigned int i,N;
double sum;
output[0]=1.0/input[0];
for (N=2; N<=MAXN; N++) {
sum=0.0;
for (i=1; i<N; i++) {
if (N==(N/i)*i)
sum=sum+input[N/i-1]*output[i-1];
}
output[N-1]=-1.0/input[0]*sum;
}
return;
}
/*****************************************************************************/
/* */
/* EUCLIDEAN G.C.D. */
/* 11/14/06 (dkc) */
/* */
/*****************************************************************************/
unsigned int euclid(unsigned int d, unsigned int e) {
unsigned int a,b,temp;
a=d;
b=e;
if (b>a) {
temp=a;
a=b;
b=temp;
}
loop:
temp=a-(a/b)*b;
a=b;
b=temp;
if (b!=0) goto loop;
return(a);
}
/******************************************************************************
* *
* INTERPOLATE BETWEEN FRACTIONS *
* 04/02/10 (dkc) *
* *
******************************************************************************/
#include <math.h>
double interp1(double ND, double ND1, unsigned int I, double init,
double *out) {
unsigned int i;
double F,inc;
inc=(ND1-ND)/(double)I;
F=init;
for (i=0; i<I; i++) {
out[i]=F;
F=F+inc;
}
return ND1;
}
/******************************************************************************
* *
* COMPUTE LIOUVILLE FUNCTION *
* 04/02/10 (dkc) *
* *
******************************************************************************/
#include <math.h>
int liouvill(unsigned int a, unsigned int *table, unsigned int tsize) {
unsigned int i,b,count,p;
if (a==1)
return(1);
count=0;
for (i=0; i<tsize; i++) {
p=table[i];
if (p>a)
break;
if (a==(a/p)*p) {
b=a;
while (b==(b/p)*p) {
count=count+1;
b=b/p;
}
}
}
if ((count&1)==0)
return 1;
else
return -1;
}
/******************************************************************************
* *
* COMPUTE MOBIUS FUNCTION *
* 04/02/10 (dkc) *
* *
******************************************************************************/
#include <math.h>
int mobius(unsigned int a, unsigned int *table, unsigned int tsize) {
unsigned int i,count,p;
if (a==1)
return(1);
count=0;
for (i=0; i<tsize; i++) {
p=table[i];
if (p>a)
break;
if (a==(a/p)*p) {
a=a/p;
if (a==(a/p)*p)
return(0);
count=count+1;
if (a==1)
break;
}
}
if ((count&1)==0)
return(1);
else
return(-1);
}
/******************************************************************************
* *
* FIND CURVES AND SUB-CURVES OF DIRICHLET PRODUCTS OF ZETA FUNCTION ZEROS *
* 04/22/18 (dkc) *
* *
* For 32-bit words and N<=100000, the products of primes either don't *
* overflow or still give correct results if they do. *
* *
******************************************************************************/
#include <math.h>
unsigned int pcheck(unsigned int N, unsigned int power, unsigned int extra,
unsigned int subcur, unsigned int tsize, unsigned int *table) {
unsigned int i,j,k,l;
unsigned int p,q,r,s,pth,qth; // use "unsigned long long" for 64-bit words
if ((power==17)&&(extra!=0))
goto acskip;
if ((power==15)&&(extra!=0))
goto gskip;
if ((power==13)&&(extra!=0))
goto fskip;
if ((power==11)&&(extra!=0))
goto eskip;
if ((power==9)&&(extra!=0))
goto dskip;
if ((power==7)&&(extra!=0))
goto cskip;
if ((power==5)&&(extra!=0))
goto bskip;
if ((power==3)&&(extra!=0))
goto askip;
for (i=0; i<tsize; i++) {
p=table[i];
pth=p;
for (j=1; j<power; j++)
pth=pth*p;
if (N==pth)
return(1);
if (N<pth)
break;
}
return(0);
//
// 3
//
askip:
if (subcur==2)
goto agskip;
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
agskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 5
//
bskip:
if (subcur==2)
goto ahskip;
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
ahskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p*p*p;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 7
//
cskip:
if (subcur==2)
goto afskip;
if (subcur==3)
goto aiskip;
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
afskip:
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==2)
return(0);
aiskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
p=p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 9
//
dskip:
if (subcur==2)
goto nskip;
if (subcur==3)
goto ajskip;
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
nskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==2)
return(0);
ajskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
p=p*p*p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 11
//
eskip:
if (subcur==4)
goto akskip;
if (subcur==3)
goto pskip;
if (subcur==2)
goto oskip;
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p;
if (N<pth)
break;
p=p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q;
if (N<qth)
break;
q=q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
oskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==2)
return(0);
pskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==3)
return(0);
akskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p;
if (N<pth)
break;
pth=p*p*p*p*pth;
if (N<pth)
break;
p=p*p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 13
//
fskip:
if (subcur==6)
goto alskip;
if (subcur==5)
goto uskip;
if (subcur==4)
goto tskip;
if (subcur==3)
goto rskip;
if (subcur==2)
goto qskip;
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p;
if (N<pth)
break;
p=p*p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q;
if (N<qth)
break;
q=q*q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
qskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q*q;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==2)
return(0);
rskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==3)
return(0);
tskip:
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if (N<(p*q*r))
break;
for (l=k+1; l<tsize; l++) {
s=table[l];
if ((p*q*r*s)==N)
return(1);
if (N<(p*q*r*s))
break;
}
}
}
}
if (subcur==4)
return(0);
uskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==5)
return(0);
alskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
pth=p*p*p*p*pth;
if (N<pth)
break;
p=p*p*p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 15
//
gskip:
if (subcur==2)
goto kskip;
if (subcur==3)
goto mskip;
if (subcur==4)
goto lskip;
if (subcur==5)
goto abskip;
if (subcur==6)
goto amskip;
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p;
if (N<pth)
break;
p=p*p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q*q;
if (N<qth)
break;
q=q*q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
kskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p;
if (N<pth)
break;
p=p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q;
if (N<qth)
break;
q=q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==2)
return(0);
mskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if (N<(p*q*r)) // N=62801 fix
break;
r=r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==3)
return(0);
lskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r*r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==4)
return(0);
abskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==5)
return(0);
amskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
pth=p*p*p*p*p*pth;
if (N<pth)
break;
p=p*p*p*p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
//
// 17
//
acskip:
if (subcur==2)
goto adskip;
if (subcur==3)
goto sskip;
if (subcur==4)
goto aaskip;
if (subcur==5)
goto aeskip;
if (subcur==6)
goto anskip;
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
p=p*p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q*q*q;
if (N<qth)
break;
q=q*q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==1)
return(0);
adskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p;
if (N<pth)
break;
p=p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q*q;
if (N<qth)
break;
q=q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==2)
return(0);
sskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r*r;
if ((p*q*r)==N)
return(1);
if (N<(p*q*r))
break;
}
}
}
if (subcur==3)
return(0);
aaskip:
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if (N<(p*q*r))
break;
for (l=k+1; l<tsize; l++) {
s=table[l];
if ((p*q*r*s)==N)
return(1);
if (N<(p*q*r*s))
break;
}
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q;
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if (N<(p*q*r))
break;
for (l=k+1; l<tsize; l++) {
s=table[l];
if ((p*q*r*s)==N)
return(1);
if (N<(p*q*r*s))
break;
}
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
r=r*r;
if (N<(p*q*r))
break;
for (l=k+1; l<tsize; l++) {
s=table[l];
if ((p*q*r*s)==N)
return(1);
if (N<(p*q*r*s))
break;
}
}
}
}
for (i=0; i<tsize; i++) {
p=table[i];
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
if (N<(p*q))
break;
for (k=j+1; k<tsize; k++) {
r=table[k];
if (N<(p*q*r))
break;
for (l=k+1; l<tsize; l++) {
s=table[l];
s=s*s;
if ((p*q*r*s)==N)
return(1);
if (N<(p*q*r*s))
break;
}
}
}
}
if (subcur==4)
return(0);
aeskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p;
if (N<pth)
break;
p=p*p*pth;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
q=q*q*q;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
for (i=0; i<tsize; i++) {
p=table[i];
p=p*p*p;
if (N<p)
break;
for (j=i+1; j<tsize; j++) {
q=table[j];
qth=q*q*q;
if (N<qth)
break;
q=q*q*qth;
if (N<q)
break;
if ((p*q)==N)
return(1);
if (N<(p*q))
break;
}
}
if (subcur==5)
return(0);
anskip:
for (i=0; i<tsize; i++) {
p=table[i];
pth=p*p*p*p*p;
if (N<pth)
break;
pth=p*p*p*p*pth;
if (N<pth)
break;
pth=p*p*p*p*pth;
if (N<pth)
break;
p=p*p*p*p*pth;
if (p==N)
return(1);
if (N<p)
break;
}
return(0);
}
/******************************************************************************
* *
* COMPUTE PHI FUNCTION *
* 04/02/10 (dkc) *
* *
******************************************************************************/
#include <math.h>
int mobius(unsigned int a, unsigned int *table, unsigned int tsize);
unsigned int phi(unsigned int a, unsigned int *table, unsigned int tsize) {
unsigned int i,sum;
int m;
sum=0;
for (i=1; i<=a; i++) {
if (a==(a/i)*i) {
m=mobius(a/i,table,tsize);
sum=sum+m*i;
}
}
return(sum);
}
/*****************************************************************************/
/* */
/* COMPUTE PRIMES */
/* 11/04/15 (dkc) */
/* */
/*****************************************************************************/
#include <math.h>
unsigned int primed(unsigned int *out, unsigned int tsize,
unsigned int *table,unsigned int limit) {
unsigned int d;
unsigned int i,j,k,l,flag,count;
count=tsize;
for (i=0; i<tsize; i++)
out[i]=table[i];
j=table[tsize-1]+1;
/********************/
/* loop through d */
/********************/
for (d=j; d<=limit; d++) {
if(d==(d/2)*2) continue;
if(d==(d/3)*3) continue;
if(d==(d/5)*5) continue;
if(d==(d/7)*7) continue;
if(d==(d/11)*11) continue;
/************************************************/
/* look for prime factors using look-up table */
/************************************************/
l=(unsigned int)(10.0+sqrt((double)d));
k=0;
if (l>table[tsize-1])
return(0);
else {
for (i=0; i<tsize; i++) {
if (table[i]<=l)
k=i;
else
break;
}
}
flag=1;
l=k;
for (i=0; i<=l; i++) {
k=table[i];
if ((d/k)*k==d) {
flag=0;
break;
}
}
if (flag==1)
out[count]=d;
count=count+flag;
}
return(count);
}
//
// out2b1.h (for test2c)
//
double max1[22]={
1266.394397,
2248.206668,
3101.465229,
3945.569667,
4753.444678,
5532.594836,
6287.163423,
7038.997455,
7756.555210,
8433.845192,
9211.566768,
9916.961389,
10559.967275,
11307.573377,
11966.432638,
12645.929691,
13331.232541,
14001.299249,
14640.828482,
15343.388244,
15969.532539,
16613.224419};
//
// out2b2.h (for test2c)
//
double max2[22]={
747.781093,
1298.985120,
1775.450189,
2244.102389,
2691.311325,
3121.320407,
3538.119657,
3951.774034,
4346.264148,
4717.268985,
5145.218934,
5531.171801,
5883.544060,
6292.291852,
6652.370291,
7023.583115,
7398.442451,
7763.545705,
8112.719580,
8496.181222,
8837.650185,
9188.017550};
//
// out2e.h (for test2a)
//
double riem[11000]={
145.724305,
31.839672,
38.077158,
41.689625,
45.302092,
50.205289,
55.108487,
57.381833,
59.655179,
63.867455,
68.079731,
71.097841,
74.115953,
76.297075,
78.478197,
82.714892,
86.951586,
88.553388,
90.155193,
93.050087,
95.944984,
99.092951,
102.240920,
104.868021,
107.495123,
108.839770,
110.184419,
114.061286,
117.938156,
119.719807,
121.501460,
123.735324,
125.969189,
128.252106,
130.535027,
133.829354,
137.123680,
138.427948,
139.732217,
141.717884,
143.703549,
146.939437,
150.175324,
151.828234,
153.481144,
155.917141,
158.353138,
159.606407,
160.859676,
164.194988,
167.530299,
169.485996,
171.441695,
172.545944,
173.650192,
176.331418,
179.012645,
181.264681,
183.516720,
185.697240,
187.877756,
189.436453,
190.995152,
192.554668,
194.114184,
197.610824,
201.107465,
201.872851,
202.638234,
204.853052,
207.067873,
208.794456,
210.521037,
212.843212,
215.165389,
217.501366,
219.837343,
221.265283,
222.693223,
223.879613,
225.066003,
228.018294,
230.970587,
232.838052,
234.705518,
236.072127,
237.438738,
239.621394,
241.804051,
242.944057,
244.084062,
247.126616,
250.169173,
251.636473,
253.103776,
254.360362,
255.616947,
257.417501,
259.218057,
261.834599,
264.451141,
265.738777,
267.026412,
269.408952,
271.791491,
272.580977,
273.370467,
275.271818,
277.173169,
279.970006,
282.766844,
284.111444,
285.456046,
286.590276,
287.724507,
289.842797,
291.961087,
293.629060,
295.297036,
297.566913,
299.836796,
301.328735,
302.820675,
304.550530,
306.280388,
307.020719,
307.761052,
310.930424,
314.099797,
315.315769,
316.531744,
318.059794,
319.587840,
321.341150,
323.094464,
324.488326,
325.882188,
327.956661,
330.031134,
332.446853,
334.862569,
335.518543,
336.174521,
337.650853,
339.127187,
341.108052,
343.088921,
345.453114,
347.817306,
348.771017,
349.724730,
351.704179,
353.683628,
355.142704,
356.601781,
357.633161,
358.664537,
361.607387,
364.550242,
365.663140,
366.776041,
368.312090,
369.848140,
370.939470,
372.030798,
374.305391,
376.579983,
378.092644,
379.605304,
381.520165,
383.435025,
384.935735,
386.436446,
387.522432,
388.608419,
390.077828,
391.547237,
394.171858,
396.796479,
398.288372,
399.780271,
400.428521,
401.076773,
403.409990,
405.743207,
406.627413,
407.511622,
409.719701,
411.927779,
413.662975,
415.398168,
417.130471,
418.862774,
419.530278,
420.197783,
421.742973,
423.288162,
425.851897,
428.415628,
429.543693,
430.671762,
432.288938,
433.906119,
435.258868,
436.611617,
438.218339,
439.825064,
440.954975,
442.084885,
444.861689,
447.638489,
448.512439,
449.386390,
450.719231,
452.052076,
453.357349,
454.662622,
456.523764,
458.384908,
460.410185,
462.435456,
463.408537,
464.381618,
466.400966,
468.420312,
469.565021,
470.709734,
471.552601,
472.395468,
474.903035,
477.410603,
479.207372,
481.004141,
481.961522,
482.918903,
484.102533,
485.286161,
487.141413,
488.996664,
490.376518,
491.756369,
493.536468,
495.316569,
497.243684,
499.170799,
499.953783,
500.736769,
502.365755,
503.994738,
504.880920,
505.767105,
508.697662,
511.628215,
512.303893,
512.979572,
514.451049,
515.922527,
517.581204,
519.239883,
520.366943,
521.493999,
523.004561,
524.515123,
526.567717,
528.620311,
530.170912,
531.721511,
532.995700,
534.269890,
534.820421,
535.370950,
537.549960,
539.728970,
541.414426,
543.099883,
544.738201,
546.376517,
547.325115,
548.273715,
550.236819,
552.199921,
552.982892,
553.765863,
555.115808,
556.465751,
559.083047,
561.700340,
562.656415,
563.612488,
564.756013,
565.899539,
567.310074,
568.720607,
570.070322,
571.420037,
573.466069,
575.512101,
576.524884,
577.537671,
579.627029,
581.716387,
582.607929,
583.499473,
584.697112,
585.894752,
587.158943,
588.423135,
590.760648,
593.098156,
594.537387,
595.976616,
596.809963,
597.643314,
599.021010,
600.398709,
602.364793,
604.330874,
604.843449,
605.356025,
607.738329,
610.120632,
611.477422,
612.834214,
614.209193,
615.584169,
616.656495,
617.728824,
618.645898,
619.562974,
621.923844,
624.284709,
625.811782,
627.338860,
628.176409,
629.013960,
630.864729,
632.715496,
633.704607,
634.693718,
636.025230,
637.356741,
638.815064,
640.273384,
642.563474,
644.853566,
645.880323,
646.907082,
647.632854,
648.358624,
649.980706,
651.602784,
653.002562,
654.402338,
656.251645,
658.100950,
659.373107,
660.645266,
661.982623,
663.319983,
664.932823,
666.545658,
667.428541,
668.311425,
669.291775,
670.272119,
672.999034,
675.725951,
676.453138,
677.180325,
678.956338,
680.732349,
681.183527,
681.634699,
683.547963,
685.461223,
686.762001,
688.062780,
689.522229,
690.981674,
692.755894,
694.530114,
695.899985,
697.269860,
698.089640,
698.909417,
700.142537,
701.375659,
702.845740,
704.315825,
706.679530,
709.043231,
709.757787,
710.472342,
711.543416,
712.614492,
714.566277,
716.518066,
717.241663,
717.965263,
719.357140,
720.749013,
722.620430,
724.491848,
726.171020,
727.850190,
728.776386,
729.702583,
730.947419,
732.192255,
733.005476,
733.818700,
736.034889,
738.251076,
739.487998,
740.724920,
742.143731,
743.562539,
744.883337,
746.204133,
747.372842,
748.541554,
750.131938,
751.722325,
752.117556,
752.512785,
755.168592,
757.824397,
759.159015,
760.493631,
761.202266,
761.910904,
763.208591,
764.506279,
765.991424,
767.476570,
768.702186,
769.927802,
771.864933,
773.802063,
774.634434,
775.466806,
777.459986,
779.453165,
780.333964,
781.214763,
781.973094,
782.731426,
784.316832,
785.902239,
787.959682,
790.017122,
791.303769,
792.590417,
793.532328,
794.474240,
795.648598,
796.822954,
798.421203,
800.019453,
801.125567,
802.231675,
803.512980,
804.794280,
807.095794,
809.397306,
809.923560,
810.449816,
811.995615,
813.541414,
814.427500,
815.313587,
816.469522,
817.625458,
819.965139,
822.304817,
823.199550,
824.094280,
825.320295,
826.546311,
827.973131,
829.399948,
830.857609,
832.315270,
832.835592,
833.355913,
835.146764,
836.937613,
838.741592,
840.545572,
842.007518,
843.469462,
844.283413,
845.097361,
845.884152,
846.670942,
848.570049,
850.469157,
851.590033,
852.710909,
854.545320,
856.379727,
857.318030,
858.256334,
859.854898,
861.453467,
862.511877,
863.570287,
864.753288,
865.936291,
866.721414,
867.506537,
870.122193,
872.737848,
873.647521,
874.557194,
875.477918,
876.398638,
877.927121,
879.455602,
880.351805,
881.248007,
882.925133,
884.602256,
885.762567,
886.922881,
888.496046,
890.069212,
891.804090,
893.538969,
894.121806,
894.704640,
895.973301,
897.241961,
898.211791,
899.181619,
901.129747,
903.077875,
904.643109,
906.208345,
907.381487,
908.554630,
909.163065,
909.771501,
911.785214,
913.798925,
914.628010,
915.457093,
916.407046,
917.357001,
919.473092,
921.589182,
922.914625,
924.240065,
925.415651,
926.591241,
927.552004,
928.512765,
929.459932,
930.407093,
932.006534,
933.605972,
935.557294,
937.508615,
938.092354,
938.676093,
940.371545,
942.066999,
943.352009,
944.637018,
945.480633,
946.324246,
947.686193,
949.048138,
950.059617,
951.071094,
953.630689,
956.190283,
956.645437,
957.100590,
958.368511,
959.636428,
960.597042,
961.557656,
963.207081,
964.856508,
965.844976,
966.833444,
968.540306,
970.247165,
971.520005,
972.792843,
974.023408,
975.253974,
976.870230,
978.486487,
978.865253,
979.244015,
980.345325,
981.446637,
983.689436,
985.932229,
987.121295,
988.310359,
989.554790,
990.799224,
991.633056,
992.466887,
993.885094,
995.303296,
996.636811,
997.970326,
998.948030,
999.925734,
1001.479281,
1003.032832,
1004.868625,
1006.704420,
1007.707386,
1008.710350,
1009.312773,
1009.915194,
1011.501506,
1013.087822,
1013.925158,
1014.762493,
1016.862148,
1018.961806,
1020.412358,
1021.862908,
1022.175518,
1022.488126,
1024.473970,
1026.459815,
1027.395322,
1028.330830,
1029.410544,
1030.490253,
1031.511065,
1032.531874,
1034.677238,
1036.822600,
1037.904513,
1038.986424,
1040.326130,
1041.665830,
1042.311887,
1042.957939,
1044.073475,
1045.189015,
1047.054501,
1048.919983,
1049.860160,
1050.800333,
1052.439211,
1054.078087,
1055.245932,
1056.413776,
1057.614320,
1058.814864,
1060.103466,
1061.392081,
1062.078751,
1062.765423,
1064.030516,
1065.295607,
1067.578508,
1069.861407,
1070.826339,
1071.791271,
1072.556999,
1073.322723,
1074.593670,
1075.864619,
1077.452618,
1079.040618,
1079.615357,
1080.190093,
1082.119405,
1084.048715,
1085.001966,
1085.955219,
1087.817683,
1089.680146,
1090.564992,
1091.449839,
1092.397557,
1093.345273,
1094.242408,
1095.139542,
1096.740044,
1098.340542,
1100.178787,
1102.017035,
1102.901270,
1103.785509,
1105.098326,
1106.411143,
1107.257966,
1108.104791,
1109.758114,
1111.411439,
1112.359164,
1113.306887,
1114.115019,
1114.923153,
1117.254534,
1119.585916,
1120.556456,
1121.526997,
1122.512715,
1123.498432,
1124.799307,
1126.100181,
1126.703078,
1127.305976,
1129.022087,
1130.738197,
1132.322522,
1133.906849,
1135.038106,
1136.169366,
1137.127056,
1138.084749,
1140.030105,
1141.975460,
1142.276041,
1142.576619,
1143.862060,
1145.147501,
1146.344513,
1147.541523,
1149.331940,
1151.122352,
1152.818987,
1154.515623,
1154.994099,
1155.472570,
1156.380415,
1157.288257,
1158.888408,
1160.488560,
1161.621260,
1162.753958,
1163.961534,
1165.169113,
1166.719304,
1168.269499,
1169.499020,
1170.728541,
1172.008731,
1173.288920,
1174.216891,
1175.144862,
1176.422840,
1177.700816,
1178.127523,
1178.554235,
1181.253872,
1183.953509,
1184.544307,
1185.135107,
1186.409845,
1187.684583,
1188.820830,
1189.957076,
1191.054295,
1192.151515,
1193.499330,
1194.847145,
1195.800695,
1196.754236,
1198.185029,
1199.615819,
1201.380043,
1203.144260,
1204.138807,
1205.133351,
1206.195118,
1207.256888,
1207.830473,
1208.404068,
1210.059010,
1211.713948,
1212.934523,
1214.155099,
1216.088294,
1218.021491,
1218.551653,
1219.081814,
1220.270316,
1221.458815,
1223.074287,
1224.689763,
1225.677378,
1226.664995,
1227.181456,
1227.697913,
1229.456457,
1231.215004,
1233.164679,
1235.114353,
1235.755319,
1236.396286,
1237.673991,
1238.951691,
1239.820282,
1240.688870,
1241.767129,
1242.845389,
1244.474033,
1246.102679,
1247.377289,
1248.651895,
1249.653357,
1250.654816,
1252.445236,
1254.235658,
1254.892510,
1255.549366,
1256.778277,
1258.007186,
1259.087106,
1260.167025,
1260.981868,
1261.796711,
1264.066289,
1266.335866,
1267.390624,
1268.445382,
1269.355561,
1270.265743,
1271.104011,
1271.942280,
1273.578330,
1275.214380,
1276.203325,
1277.192272,
1278.151208,
1279.110147,
1280.997895,
1282.885643,
1283.755535,
1284.625427,
1286.346780,
1288.068132,
1288.765498,
1289.462860,
1290.231838,
1291.000819,
1292.208402,
1293.415983,
1295.254109,
1297.092235,
1298.333131,
1299.574027,
1300.715339,
1301.856654,
1302.720927,
1303.585200,
1305.083201,
1306.581196,
1307.420136,
1308.259078,
1309.679421,
1311.099764,
1311.748926,
1312.398089,
1314.656588,
1316.915082,
1318.136874,
1319.358664,
1319.678601,
1319.998538,
1321.499860,
1323.001183,
1323.907621,
1324.814061,
1326.082599,
1327.351141,
1329.136707,
1330.922276,
1331.806024,
1332.689769,
1333.855766,
1335.021759,
1336.405130,
1337.788501,
1338.992200,
1340.195901,
1340.797507,
1341.399115,
1342.470975,
1343.542837,
1345.478822,
1347.414805,
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