﻿ generate Farey sequence
```/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                             C
C  COMPUTE MERTENS FUNCTION						      C
C  08/08/14 (DKC)							      C
C                                                                             C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <math.h>
unsigned int haros5(unsigned int N, unsigned int M, unsigned int *R,
unsigned int H, unsigned int K, unsigned int HP,
unsigned int KP, unsigned int D);
unsigned int lagrange1(unsigned int N, unsigned int D, unsigned int O);
double mertens6(unsigned int N, unsigned int *count, double *sum) {
unsigned int S[250000];
unsigned int H,K;
unsigned int L,I,count1,count2,ctemp1,ctemp2;
double temp1,sum1,sum2;
double pi;
if (N==1) {
count[0]=0;
count[1]=0;
sum[0]=0.5;
sum[1]=0.0;
return(1.0);
}
if (N==2) {
count[0]=0;
count[1]=0;
sum[0]=0.0;
sum[1]=0.0;
return(0.0);
}
if (N==3) {
count[0]=0;
count[1]=0;
sum[0]=0.0;
sum[1]=-0.5;
return(-1.0);
}
if (N==4) {
count[0]=0;
count[1]=1;
sum[0]=0.0;
sum[1]=-0.5;
return(-1.0);
}
pi=3.141592654;
if ((N>4)&&(N<33)) {
ctemp1=haros5(N,0,S,0,1,1,N,4);
ctemp1=ctemp1-1;
sum1=0.0;
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;		    // towards 1/4
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=ctemp1-1;
count[0]=count1;
sum[0]=sum1;
//
L=lagrange1(1,4,N);
ctemp2=haros5(N,0,S,1,4,L>>16,L&0xffff,2);
ctemp2=ctemp2-1;
sum2=0.0;
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		  // towards 1/2
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=ctemp2-1;
count[1]=count2;
sum[1]=sum2;
return(2*(sum1+sum2));
}
if (N>5128) {
count[0]=0;
count[1]=0;
sum[0]=0.0;
sum[1]=0.0;
return(0.0);
}
ctemp1=haros5(N,0,S,0,1,1,N,32);
sum1=0.0;
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 1/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
L=lagrange1(1,32,N);
count1=haros5(N,0,S,1,32,L>>16,L&0xffff,16);
for (I=1; I<count1; I++) {
H=S[I]>>16;			 // towards 1/16
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-2;
L=lagrange1(1,16,N);
ctemp1=haros5(N,0,S,1,16,L>>16,L&0xffff,32);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 3/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-1;
L=lagrange1(3,32,N);
ctemp1=haros5(N,0,S,3,32,L>>16,L&0xffff,8);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 1/8
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-1;
L=lagrange1(1,8,N);
ctemp1=haros5(N,0,S,1,8,L>>16,L&0xffff,32);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 5/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-1;
L=lagrange1(5,32,N);
ctemp1=haros5(N,0,S,5,32,L>>16,L&0xffff,16);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 3/16
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-1;
L=lagrange1(3,16,N);
ctemp1=haros5(N,0,S,3,16,L>>16,L&0xffff,32);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 7/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-1;
L=lagrange1(7,32,N);
ctemp1=haros5(N,0,S,7,32,L>>16,L&0xffff,4);
for (I=1; I<ctemp1; I++) {
H=S[I]>>16;			 // towards 1/4
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum1=sum1+temp1;
}
count1=count1+ctemp1-2;
count[0]=count1;
sum[0]=sum1;
//
L=lagrange1(1,4,N);
ctemp2=haros5(N,0,S,1,4,L>>16,L&0xffff,32);
sum2=0.0;
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 9/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
L=lagrange1(9,32,N);
count2=haros5(N,0,S,9,32,L>>16,L&0xffff,16);
for (I=1; I<count2; I++) {
H=S[I]>>16;		       // towards 5/16
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(5,16,N);
ctemp2=haros5(N,0,S,5,16,L>>16,L&0xffff,32);
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 11/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(11,32,N);
ctemp2=haros5(N,0,S,11,32,L>>16,L&0xffff,8);
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 3/8
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(3,8,N);
ctemp2=haros5(N,0,S,3,8,L>>16,L&0xffff,32);
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 13/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(13,32,N);
ctemp2=haros5(N,0,S,13,32,L>>16,L&0xffff,16);
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 7/16
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(7,16,N);
ctemp2=haros5(N,0,S,7,16,L>>16,L&0xffff,32);
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 15/32
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-1;
L=lagrange1(15,32,N);
ctemp2=haros5(N,0,S,15,32,L>>16,L&0xffff,2);
ctemp2=ctemp2-1;
for (I=1; I<ctemp2; I++) {
H=S[I]>>16;		       // towards 1/2
K=S[I]&0xffff;
temp1=cos(2.0*pi*(double)H/(double)K);
sum2=sum2+temp1;
}
count2=count2+ctemp2-2;
count[1]=count2;
sum[1]=sum2;
return(2*(sum1+sum2));
}
```