C program using taylor put sin(1) and get 0.841 - c

Im stuck maybe someone here can help me plzzz :)
I did wrong program that calc from radian to degri
I need to build a program like you calc Sin(x) in radian mode in calculator
I put radian x like 1 in radian and it need to give me in radian mode the calc of sin(1)
Like if i put sin(1) it need to give me 0.8414
and i cant use sin() and all this only standart and need to use taylor to calc.
help plz :) :')
my wrong code:
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <math.h>
double my_sin(double x);
/*my_sin func calc sin(x) from the main*/
double my_sin(double x){
double min_num = 0.000001;
double radian = x*(3.14/180);
double sol = radian;
int i;
int sign = 1;
int n;
int aseret = 1;
//Calc the solution if i <= 0.000001 it stop calc.
for(i=3;i <= min_num; i = i+2){
n = n * radian * radian;
sign = -(sign); //change the sign every round.
aseret = aseret * i * (i-1); //!3 = 3*2*1.
sol = sol + (pow(x,i)/aseret) *sign; // calc the solution.
}
return sol;
}
/*main func*/
int main()
{
double x = 0;
double result;
printf("please enter the number to check the SIN of it:");
scanf("%lf",&x);
result = my_sin(x);
printf("SIN(%f) = %f\n",x,result);
return 0;
}

Your main problem is that you are comparing the index i with the minimum value of the term. One consequence is that the loop stops immediately. It is the term x^i/i(i-1) which must be compared with the minimum value. As the series is alternating, the error at the end is lower than this minimum value.
It is also useles to perform the conversion to radian, as it seems you are entering a radian value.
Moreover, it is useless and inefficient to use pow() function to calculate x^i. Better to alculate this term iteratively.
Output:
please enter the number to check the SIN of it: 1
SIN(1.000000) = 0.841471
error = -1.59828e-010
Code:
#include <stdio.h>
#include <math.h>
double my_sin(double x){
double min_num = 0.000001;
int sign = 1;
double term = x;
double sol = term;
double x2 = x*x;
int i = 1;
//Calc the solution if term <= 0.000001 it stop calc.
do {
i += 2;
term *= x2 / (i * (i-1));
sign = -sign; //change the sign every round.
sol += term * sign;
} while (term > min_num);
return sol;
}
int main() {
double x;
printf("please enter the number to check the SIN of it: ");
scanf("%lf", &x);
double result = my_sin(x);
printf("SIN(%f) = %f\n", x, result);
double result_exact = sin(x);
double delta = result - result_exact;
printf ("error = %g\n", delta);
return 0;
}

You convert x to radians when it is already in radians.
Your loop condition is wrong, the loop terminates immediately and compares an integer with a double.
The variable n is uninitialised and the result of the expression it is used in is unused in any case.
Unnecessary headers included.
Change as per <<<<<< comments:
#include <stdio.h>
// #include <string.h> // <<<<<<<<<<<<<< REDUNDANT
// #include <ctype.h> // <<<<<<<<<<<<<< REDUNDANT
#include <math.h>
#define LIMIT 10 // <<<<<<<<<<<<<< ADD
double my_sin( double x );
/*my_sin func calc sin(x) from the main*/
double my_sin( double x )
{
// double min_num = 0.000001; // <<<<<<<<<<<<<< REMOVE
// double radian = x*(3.14/180); // <<<<<<<<<<<<<< REMOVE
double sol = x ; // <<<<<<<<<<<<<< CHANGE
// int i; // <<<<<<<<<<<<<< REMOVE
int sign = 1;
// int n = 0 ; // <<<<<<<<<<<<<< REMOVE - NOT USED
int aseret = 1;
//Calc the solution if i <= LIMIT it stop calc. // <<<<<<<<<<<<<< CHANGE
for( int i = 3; i <= LIMIT; i += 2 ) // <<<<<<<<<<<<<< CHANGE
{
// n = n * x * x; // <<<<<<<<<<<<<< REMOVE - RESULT NOT USED
sign = -(sign); //change the sign every round.
aseret = aseret * i * (i - 1); //!3 = 3*2*1.
sol = sol + (pow( x, i ) / aseret) * sign; // calc the solution.
}
return sol;
}

Related

Sinus function using Taylor expansion

The teacher asks to remove the pi subtraction cycle in the main function. I don’t know how to write the program so that the correct results will come out for any values.
#include <stdio.h>
#include <math.h>
double sinus(double x);
int main(void) {
double a, x;
scanf("%le", & x);
a = x;
while (fabs(x) > 2 * (M_PI)) {
x = fabs(x) - 2 * (M_PI);
}
if (a > 0)
a = sinus(x);
else a = (-1) * sinus(x);
printf("%le", (double) a);
return 0;
}
double sinus(double x) {
double sum = 0, h, eps = 1.e-16;
int i = 2;
h = x;
do {
sum += h;
h *= -((x * x) / (i * (i + 1)));
i += 2;
}
while (fabs(h) > eps);
return sum;
return 0;
}
#include <stdio.h>
#include <math.h>
double sinus(double x);
int main(void)
{
double a,x;
scanf("%le",&x);
a=x;
x=fmod(fabs(x),2*(M_PI));
if(a>0)
a=sinus(x);
else a=(-1)*sinus(x);
printf("%le",(double)a);
return 0;}
double sinus(double x)
{
double sum=0, h, eps=1.e-16; int i=2;
h=x;
do{
sum+=h;
h*=-((x*x)/(i*(i+1)));
i+=2;}
while( fabs(h)>eps );
return sum;
return 0;
}
… how to write the program so that the correct results will come out for any values.
OP's loop is slow with large x and an infinfite loop with very large x:
while (fabs(x) > 2 * (M_PI)) {
x = fabs(x) - 2 * (M_PI);
}
A simple, though not high quality solution, is to use fmod() in the function itself. #Damien:
#ifndef M_PI
#define M_PI 3.1415926535897932384626433832795
#endif
double sinus(double x) {
x = fmod(x, 2*M_PI); // Reduce to [-2*M_PI ... 2*M_PI]
...
Although function fmod() is not expected to inject any error, the problem is that M_PI (a rational number) is an approximation of π, (an irrational number). Using that value approximation injects error especially x near multiplies of π. This is likely OK for modest quality code.
Good range reduction is a problem as challenging as the trigonometric functions themselves.
See K.C. Ng's "ARGUMENT REDUCTION FOR HUGE ARGUMENTS: Good to the Last Bit" .
OP's sinus() should use additional range reduction and trigonometric properties to get x in range [-M_PI/4 ... M_PI/4] (example) before attempting the power series solution. Otherwise, convergence is slow and errors accumulate.

Taylor Series in C (problem with sin(240) and sin(300))

#include <stdio.h>
#include <math.h>
const int TERMS = 7;
const float PI = 3.14159265358979;
int fact(int n) {
return n<= 0 ? 1 : n * fact(n-1);
}
double sine(int x) {
double rad = x * (PI / 180);
double sin = 0;
int n;
for(n = 0; n < TERMS; n++) { // That's Taylor series!!
sin += pow(-1, n) * pow(rad, (2 * n) + 1)/ fact((2 * n) + 1);
}
return sin;
}
double cosine(int x) {
double rad = x * (PI / 180);
double cos = 0;
int n;
for(n = 0; n < TERMS; n++) { // That's also Taylor series!
cos += pow(-1, n) * pow(rad, 2 * n) / fact(2 * n);
}
return cos;
}
int main(void){
int y;
scanf("%d",&y);
printf("sine(%d)= %lf\n",y, sine(y));
printf("cosine(%d)= %lf\n",y, cosine(y));
return 0;
}
The code above was implemented to compute sine and cosine using Taylor series.
I tried testing the code and it works fine for sine(120).
I am getting wrong answers for sine(240) and sine(300).
Can anyone help me find out why those errors occur?
You should calculate the functions in the first quadrant only [0, pi/2). Exploit the properties of the functions to get the values for other angles. For instance, for values of x between [pi/2, pi), sin(x) can be calculated by sin(pi - x).
The sine of 120 degrees, which is 40 past 90 degrees, is the same as 50 degrees: 40 degrees before 90. Sine starts at 0, then rises toward 1 at 90 degrees, and then falls again in a mirror image to zero at 180.
The negative sine values from pi to 2pi are just -sin(x - pi). I'd handle everything by this recursive definition:
sin(x):
cases x of:
[0, pi/2) -> calculate (Taylor or whatever)
[pi/2, pi) -> sin(pi - x)
[pi/2, 2pi) -> -sin(x - pi)
< 0 -> sin(-x)
>= 2pi -> sin(fmod(x, 2pi)) // floating-point remainder
A similar approach for cos, using identity cases appropriate for it.
The key point is:
TERMS is too small to have proper precision. And if you increase TERMS, you have to change fact implementation as it will likely overflow when working with int.
I would use a sign to toggle the -1 power instead of pow(-1,n) overkill.
Then use double for the value of PI to avoid losing too many decimals
Then for high values, you should increase the number of terms (this is the main issue). using long long for your factorial method or you get overflow. I set 10 and get proper results:
#include <stdio.h>
#include <math.h>
const int TERMS = 10;
const double PI = 3.14159265358979;
long long fact(int n) {
return n<= 0 ? 1 : n * fact(n-1);
}
double powd(double x,int n) {
return n<= 0 ? 1 : x * powd(x,n-1);
}
double sine(int x) {
double rad = x * (PI / 180);
double sin = 0;
int n;
int sign = 1;
for(n = 0; n < TERMS; n++) { // That's Taylor series!!
sin += sign * powd(rad, (2 * n) + 1)/ fact((2 * n) + 1);
sign = -sign;
}
return sin;
}
double cosine(int x) {
double rad = x * (PI / 180);
double cos = 0;
int n;
int sign = 1;
for(n = 0; n < TERMS; n++) { // That's also Taylor series!
cos += sign * powd(rad, 2 * n) / fact(2 * n);
sign = -sign;
}
return cos;
}
int main(void){
int y;
scanf("%d",&y);
printf("sine(%d)= %lf\n",y, sine(y));
printf("cosine(%d)= %lf\n",y, cosine(y));
return 0;
}
result:
240
sine(240)= -0.866026
cosine(240)= -0.500001
Notes:
my recusive implementation of pow using successive multiplications is probably not needed, since we're dealing with floating point. It introduces accumulation error if n is big.
fact could be using floating point to allow bigger numbers and better precision. Actually I suggested long long but it would be better not to assume that the size will be enough. Better use standard type like int64_t for that.
fact and pow results could be pre-computed/hardcoded as well. This would save computation time.
const double TERMS = 14;
const double PI = 3.14159265358979;
double fact(double n) {return n <= 0.0 ? 1 : n * fact(n - 1);}
double sine(double x)
{
double rad = x * (PI / 180);
rad = fmod(rad, 2 * PI);
double sin = 0;
for (double n = 0; n < TERMS; n++)
sin += pow(-1, n) * pow(rad, (2 * n) + 1) / fact((2 * n) + 1);
return sin;
}
double cosine(double x)
{
double rad = x * (PI / 180);
rad = fmod(rad,2*PI);
double cos = 0;
for (double n = 0; n < TERMS; n++)
cos += pow(-1, n) * pow(rad, 2 * n) / fact(2 * n);
return cos;
}
int main()
{
printf("sine(240)= %lf\n", sine(240));
printf("cosine(300)= %lf\n",cosine(300));
}

How to use exp and sqrt properties correctly

-use double precision
-use sqrt() and exponential function exp()
-use * to compute the square
-do not use pow()
I am getting values they are just not anything as to what I expected. I tried making them all signed but it didn't change anything and I've tried printing out with 12 decimal places and nothing seems to be working.I have linked the math library and defined it as well.
double normal(double x, double sigma, double mu)
{
double func = 1.0/(sigma * sqrt(2.0*M_PI));
double raise = 1.0/2.0*((x-mu)/sigma);
double func1 = func * exp(raise);
double comp_func = (func1 * func1);
return comp_func;
}
int main(void)
{
// create two constant variables for μ and σ
const double sigma, mu;
//create a variable for x - only dynamic variable in equation
unsigned int x;
//create a variable for N values of x to use for loop
int no_x;
//scaniing value into mu
printf("Enter mean u: ");
scanf("%lf", &mu);
//scanning value into sigma
printf("Enter standard deviation: ");
scanf("%lf", &sigma);
//if sigma = 0 then exit
if(sigma == 0)
{
printf("error you entered: 0");
exit(0);
}
//storing number of x values in no_x
printf("Number of x values: ");
scanf("%d", &no_x);
//the for loop where i am calling function normal N times
for(int i = 1; i <= no_x; i++)
{
//printing i for the counter in prompted x values
printf("x value %d : ", i);
// scanning in x
scanf("%lf", &x);
x = normal(x,sigma,mu);
printf("f(x) = : %lf.12", x);
printf("\n");
}
return 0;
}
C:>.\a.exe
Enter mean u: 3.489
Enter std dev s: 1.203
Number of x values: 3
x value 1: 3.4
f(X) = 0.330716549275
x value 2: -3.4
f(X) = 0.000000025104
x value 3: 4
f(X) = 0.303015189801
But this is what I am receiving
C:\Csource>a.exe
Enter mean u: 3.489
Enter standard deviation: 1.203
Number of x values: 3
x value 1 : 3.4
f(x) = : 15086080.000000
x value 2 : -3.4
f(x) = : 15086080.000000
x value 3 : 4
f(x) = : 1610612736.000000
Insert these lines:
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
Change:
const double sigma, mu;
to:
double sigma, mu;
Change:
unsigned int x;
to:
double x;
Replace the definition of the normal function with:
double normal(double x, double sigma, double mu)
{
double func = 1.0/(sigma * sqrt(2.0*M_PI));
double t = (x-mu)/sigma;
return func * exp(-t*t/2);
}
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#ifndef M_PI
#define M_PI (3.14159265358979323846)
#endif
#include<math.h>
#include<stdio.h>
#include <stdlib.h>
double normal(double x, double sigma, double mu)
{
double func = 1.0/(sigma * sqrt(2.0*M_PI));
double t = (x-mu)/sigma;
return func * exp((-0.5*t)* t);
}
I Finally got this code above working after tweaking with it literally all day lol, C math can be rather tricky, thank you for the help above as well.

C programming - combining power(x, n) and fact(n) functions together

I've been working on a program that calculates sin(x), cos(x), and exp(x) without using math.h and compares them to the library values of their functions. I've been forbidden from actually using the basic power(x, n) and fact(n) functions. The only hint is that I have to do division before doing multiplication when combining the functions into one.
double power(double x, int n)
{
int i;
double prod=1.;
for(i=0;i<n;i++){
prod = prod*x;
}
return prod;
}
double fact(int n)
{
int i;
double prod=1.;
for(i=1;i<=n;i++) {
prod = prod*i;
}
return prod;
}
My idea is to somehow nest the for-loops together, and piecemeal the Taylor Expansion formula for each iteration of the loop, but I haven't had luck actually combining the two.
Any help or hint would be appreciated on how to combine these.
The other aspect of the program that confuses me is that there can only be a single input of X per iteration of the program, and therefore no dynamically defined 'n' for the loops.
Use Taylor series for the exponential:
e^x = 1 + x/1! + x^2/2! + x^3/3!...
and using Euler after that you can calculate sinx and cosx.
The trick is to look at the changes between each successive term in the Taylor series expansion. Let's start with ex:
e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! ...
Notice that each term is x / n times the prior term, where n is the term number. So start with a term of 1, then multiply by the above expression to get the next term.
That gives you the following implementation:
double etox(double x)
{
long double sum = 0;
// term starts at 1
long double term = 1;
// term number
int i = 1;
// continue until the term is below the precision of the current sum
while (sum + term != sum) {
sum += term;
// new term is x/i times the prior term, where i is the term number
term *= (long double)x / i;
i++;
}
return sum;
}
Note that with this implementation, you'll get some degree of error in the least significant digits. If you start adding from a higher term number and work your way back, this can be avoided.
Similarly for sin(x) and cos(x):
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! ...
cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! ...
Each term is - (x*x) / ((2*n)*((2*n)-1)) times the prior term, where n is the term number.
I'll leave the the implementation of these two as an exercise for the reader.
Part of this comes from my answer for doing this in MIPS assembly: Taylor Series in MIPS assembly
You can do Taylor series on the fly without having to call sub-functions. In the series, each term can be calculated from the previous term in a loop. (i.e. no need to call fact and/or pow repeatedly, where each starts from the beginning). See https://en.wikipedia.org/wiki/Taylor_series
Anyway, here's code for sin and cos:
// mipstaylor/mipstaylor -- fast sine/cosine calculation
#include <stdio.h>
#include <math.h>
#define ITERMAX 10
// qcos -- calculate cosine
double
qcos(double x)
{
int iteridx;
double x2;
double cur;
int neg;
double xpow;
double n2m1;
double nfac;
double sum;
// square of x
x2 = x * x;
// values for initial terms where n==0:
xpow = 1.0;
n2m1 = 0.0;
nfac = 1.0;
neg = 1;
sum = 0.0;
iteridx = 0;
// NOTES:
// (1) with the setup above, we can just use the loop without any special
// casing
while (1) {
// calculate current value
cur = xpow / nfac;
// apply it to sum
if (neg < 0)
sum -= cur;
else
sum += cur;
// bug out when done
if (++iteridx >= ITERMAX)
break;
// now calculate intermediate values for _next_ sum term
// get _next_ power term
xpow *= x2;
// go from factorial(2n) to factorial(2n+1)
n2m1 += 1.0;
nfac *= n2m1;
// now get factorial(2n+1+1)
n2m1 += 1.0;
nfac *= n2m1;
// flip sign
neg = -neg;
}
return sum;
}
// qsin -- calculate sine
double
qsin(double x)
{
int iteridx;
double x2;
double cur;
int neg;
double xpow;
double n2m1;
double nfac;
double sum;
// square of x
x2 = x * x;
// values for initial terms where n==0:
xpow = x;
n2m1 = 1.0;
nfac = 1.0;
neg = 1;
sum = 0.0;
iteridx = 0;
// NOTES:
// (1) with the setup above, we can just use the loop without any special
// casing
while (1) {
// calculate current value
cur = xpow / nfac;
// apply it to sum
if (neg < 0)
sum -= cur;
else
sum += cur;
// bug out when done
if (++iteridx >= ITERMAX)
break;
// now calculate intermediate values for _next_ sum term
// get _next_ power term
xpow *= x2;
// go from factorial(2n+1) to factorial(2n+1+1)
n2m1 += 1.0;
nfac *= n2m1;
// now get factorial(2n+1+1+1)
n2m1 += 1.0;
nfac *= n2m1;
// flip sign
neg = -neg;
}
return sum;
}
// testfnc -- test function
void
testfnc(int typ,const char *sym)
{
double (*efnc)(double);
double (*qfnc)(double);
double vale;
double valq;
double x;
double dif;
int iter;
switch (typ) {
case 0:
efnc = cos;
qfnc = qcos;
break;
case 1:
efnc = sin;
qfnc = qsin;
break;
default:
efnc = NULL;
qfnc = NULL;
break;
}
iter = 0;
for (x = 0.0; x <= M_PI_2; x += 0.001, ++iter) {
vale = efnc(x);
valq = qfnc(x);
dif = vale - valq;
dif = fabs(dif);
printf("%s: %d x=%.15f e=%.15f q=%.15f dif=%.15f %s\n",
sym,iter,x,vale,valq,dif,(dif < 1e-14) ? "PASS" : "FAIL");
}
}
// main -- main program
int
main(int argc,char **argv)
{
testfnc(0,"cos");
testfnc(1,"sin");
return 0;
}

Own asin() function (with Taylor series) not accurate

I need to write my own asin() function without math.h library with the use of Taylor series. It works fine for numbers between <-0.98;0.98> but when I am close to limits it stops with 1604 iterations and therefore is inaccurate.
I don't know how to make it more accurete. Any suggestions are very appreciated!
The code is following:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define EPS 0.000000000001
double my_arcsin(double x)
{
long double a, an, b, bn;
a = an = 1.0;
b = bn = 2.0;
long double n = 3.0;
double xn;
double xs = x;
double xp = x;
int iterace = 0;
xn = xs + (a/b) * (my_pow(xp,n) / n);
while (my_abs(xn - xs) >= EPS)
{
n += 2.0;
an += 2.0;
bn += 2.0;
a = a * an;
b = b * bn;
xs = xn;
xn = xs + (a/b) * (my_pow(xp,n) / n);
iterace++;
}
//printf("%d\n", iterace);
return xn;
}
int main(int argc, char* argv[])
{
double x = 0.0;
if (argc > 2)
x = strtod(argv[2], NULL);
if (strcmp(argv[1], "--asin") == 0)
{
if (x < -1 || x > 1)
printf("nan\n");
else
{
printf("%.10e\n", my_arcsin(x));
//printf("%.10e\n", asin(x));
}
return 0;
}
}
And also a short list of my values and expected ones:
My values Expected values my_asin(x)
5.2359877560e-01 5.2359877560e-01 0.5
1.5567132089e+00 1.5707963268e+00 1 //problem
1.4292568534e+00 1.4292568535e+00 0.99 //problem
1.1197695150e+00 1.1197695150e+00 0.9
1.2532358975e+00 1.2532358975e+00 0.95
Even though the convergence radius of the series expansion you are using is 1, therefore the series will eventually converge for -1 < x < 1, convergence is indeed painfully slow close to the limits of this interval. The solution is to somehow avoid these parts of the interval.
I suggest that you
use your original algorithm for |x| <= 1/sqrt(2),
use the identity arcsin(x) = pi/2 - arcsin(sqrt(1-x^2)) for 1/sqrt(2) < x <= 1.0,
use the identity arcsin(x) = -pi/2 + arcsin(sqrt(1-x^2)) for -1.0 <= x < -1/sqrt(2).
This way you can transform your input x into [-1/sqrt(2),1/sqrt(2)], where convergence is relatively fast.
PLEASE NOTICE: In this case I strongly recommend #Bence's method, since you can't expect a slowly convergent method with low data accuracy to obtain arbitrary precision.
However I'm willing to show you how to improve the result using your current algorithm.
The main problem is that a and b grows too fast and soon become inf (after merely about 150 iterations). Another similar problem is my_pow(xp,n) grows fast when n grows, however this doesn't matter much in this very case since we could assume the input data goes inside the range of [-1, 1].
So I've just changed the method you deal with a/b by introducing ab_ratio, see my edited code:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define EPS 0.000000000001
#include <math.h>
#define my_pow powl
#define my_abs fabsl
double my_arcsin(double x)
{
#if 0
long double a, an, b, bn;
a = an = 1.0;
b = bn = 2.0;
#endif
unsigned long _n = 0;
long double ab_ratio = 0.5;
long double n = 3.0;
long double xn;
long double xs = x;
long double xp = x;
int iterace = 0;
xn = xs + ab_ratio * (my_pow(xp,n) / n);
long double step = EPS;
#if 0
while (my_abs(step) >= EPS)
#else
while (1) /* manually stop it */
#endif
{
n += 2.0;
#if 0
an += 2.0;
bn += 2.0;
a = a * an;
b = b * bn;
#endif
_n += 1;
ab_ratio *= (1.0 + 2.0 * _n) / (2.0 + 2.0 * _n);
xs = xn;
step = ab_ratio * (my_pow(xp,n) / n);
xn = xs + step;
iterace++;
if (_n % 10000000 == 0)
printf("%lu %.10g %g %g %g %g\n", _n, (double)xn, (double)ab_ratio, (double)step, (double)xn, (double)my_pow(xp, n));
}
//printf("%d\n", iterace);
return xn;
}
int main(int argc, char* argv[])
{
double x = 0.0;
if (argc > 2)
x = strtod(argv[2], NULL);
if (strcmp(argv[1], "--asin") == 0)
{
if (x < -1 || x > 1)
printf("nan\n");
else
{
printf("%.10e\n", my_arcsin(x));
//printf("%.10e\n", asin(x));
}
return 0;
}
}
For 0.99 (and even 0.9999999) it soon gives correct results with more than 10 significant digits. However it gets slow when getting near to 1.
Actually the process has been running for nearly 12 minutes on my laptop calculating --asin 1, and the current result is 1.570786871 after 3560000000 iterations.
UPDATED: It's been 1h51min now and the result 1.570792915 and iteration count is 27340000000.

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