Using functions to solve other functions (sinx, cosx, exp) in C - c

my professor gave me a confusing problem and I'm completely lost on what to do. Basically he wants me to solve cos(x) and exp(x) (he gave an example for sinx) without using the built in math.h functions. Not only that, but he wants me to use both the fact() and power() functions to solve it. I could most likely solve it through straight math but I'm a bit lost on using the functions. I understand the general concept but I suck at math (especially trig) and I'm not exactly sure what they functions are doing arithmetically. Any helps or points to the right direction will be greatly appreciated.
#include <stdio.h>
#include <math.h>
int main()
{
char more;
double x, mySin(), myCos(), myExp();
printf("\n\n\t\tInput X: ");
scanf("%lf", &x);
do {
printf("\n\n\t\t\tLibraryResult MyResult");
printf("\n\n\tsin< %5.2f> %7.5f %7.5f", x, sin(x), mySin(x));
printf("\n\n\tcos< %5.2f> %f %f", x, cos(x), myCos(x));
printf("\n\n\texp< %5.2f> %f %f", x, exp(x), myExp(x));
printf("\n\n\t\tDo More (Y/N)? ");
scanf("%s",&more);
}
while (more == 'y'||more == 'Y');
}
double power(double x, int n)
{
int i = 0;
double prod = 1.;
for ( ; i++ < n; )
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;
}
double mySin(double x)
{
int i, sign;
double sum = 0;
for (i = 0, sign = 1; i < 21; i++, sign = -sign)
sum = sum + sign * power(x, 2 * i + 1)/ fact(2 * i + 1);
return sum;
}
double myCos(double x)
{
}
double myExp(double x)
{
}

Related

creating a floating point power function in c

So here's the current implementation of my power function.
pow(x, n) int x, n;
{
int r = 1;
int i;
for (i = 0; i < n; i++)
r *= x;
return (r);
}
The problem is how it only works for whole numbers & doesn't work with floats like pow(4, .5).
Of course, I've already tried changing everything to double & I know how a standard library function exists. Also I've seen Floating point exponentiation without power-function, but none of the solutions were working nor what I wanted.
Here is the version, where I used doubles.
double pow(x, n)
double x, n;
{
double r = 1.;
int i;
for (i = 0; i < n; i++)
r *= x;
return (r);
}
It returns 1., when I use it as pow(4., .5).

Write Access Violation error in C while using rand()

I am quite new to programming with C, so hope someone can bear with me and help me solve the issue I am facing.
I am writing a code to estimate the value of pi with Monte-Carlo method. however, when I build and debug I get an error that says:
"Exception thrown: write access violation.
a was 0x1110112.
I get this error in generate_random_array function
in this line of code:
a[i] = (((double)rand() / (double)RAND_MAX) * 2.0 ) - 1.0;
I am posting the whole code as well for reference.
note: I am using visual studio with MSVC compiler
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
void generate_random_array(int sz, double a[]);
void count_points_inside_circle(int sz, double x[], double y[], int* counter);
int main()
{
int tot = 1000000000;
int incircle_c = 0;
double distance_sq, pi;
double* x = NULL;
double* y = NULL;
/*create arrays in the heap*/
x = malloc(tot * sizeof(double));
y = malloc(tot * sizeof(double));
/*generate random locations*/
generate_random_array(tot, x);
generate_random_array(tot, y);
/*count the points inside te circle by checking the location distance*/
count_points_inside_circle(tot, x, y, &incircle_c);
/*estimate pi*/
pi = 4.0 * incircle_c / (double)tot;
printf("pi estimated value using %d samples was found to be %lf", tot, pi);
free(x);
free(y);
return 0;
}
void generate_random_array(int sz, double a[]) {
int i;
srand(time(NULL));
for (i = 0; i < sz; i++)
a[i] = (((double)rand() / (double)RAND_MAX) * 2.0 ) - 1.0;
}
void count_points_inside_circle(int sz, double x[], double y[],int* counter_p) {
int i;
double distance_sq;
for (i = 0; i < sz; i++) {
distance_sq = x[i] * x[i] + y[i] * y[i];
if (distance_sq <= 1)
(*counter_p)++;
}
}
You must always check the pointer returned from malloc against NULL. For example:
x = malloc(n * sizeof *x);
if (x == NULL) { /* Handle the failure and/or exit */ }
On the other hand, this task doesn't require use of an array (or allocated space used as an array) at all; you need only the number of points inside the circle and the number of total points generated. It could be simply done like that:
#include <stdio.h>
#include <stdlib.h>
double estimate_pi (unsigned trial_count)
{
const double rr = (double)RAND_MAX * RAND_MAX;
unsigned inner_point_count = 0;
unsigned i;
for (i = 0; i < trial_count; ++i) {
double x = rand();
double y = rand();
if (x * x + y * y <= rr)
++inner_point_count;
}
return 4.0 * inner_point_count / trial_count;
}
int main (void)
{
printf("%f\n", estimate_pi(1000000000));
return 0;
}
Note that, quality of random number generator used by the standard library significantly affects the result of this simulation.

How to code the summation of a function in C?

EDIT: I've added the main, factorial, and trapGamma function to give the full picture but I am specifically talking about the for loop for iSum in the I function.
Basically I've run out of ideas and exhausted everywhere I know of to find an answer to this. I need to code a program that will compute a complex function which represents an M/M/1 queue.
The function includes sub functions such as calculating the integral of a gamma function and computing factorials. I've written all the code for the computations but my sum is giving me huge numbers when I would expect nothing higher than about .35
#include <math.h>
#include <stdio.h>
double I(int k, double t);
double trapGamma(double z);
unsigned long long int factorial(unsigned int n);
int main()
{
int k;
int i = 0;
double dt = 0.1;
printf("Ikx = [ \n");
for (t = 14.0 ; t <= 15.0; t += dt)
{
printf("%f " , t);
for (k = 1 ; k <= 10 ; k++)
{
I(k, t);
printf("%f " , I(k, t));
}
printf("\n");
}
printf(" ];\n");
return (0);
}
double I(int k, double t)
{
unsigned long long int x;
unsigned int n = 20;
double numerator, y, pow1, c;
double iSum;
double Ix;
int i = 0;
iSum = 0.0;
Ix = 0.0;
a = .25 * pow(t , 2);
b = pow(a, i);
x = factorial(n);
y = trapGamma(k + i + 1);
iSum = (b / (x * y));
//This is the sum loop that I'm having trouble with, I've broke the iSum equation down for my own readability while coding right above this comment
for (i = 0; i <= 100 ; i++)
{
iSum += i;
}
Ix = (pow((.5 * t), k) ) * iSum;
return Ix;
}
/*
I've checked both the factorial and trapGamma functions and they are giving me the expected results.
*/
unsigned long long int factorial(unsigned int n)
{
if(n <= 1)
return 1;
else
return (n * factorial(n - 1));
}
double trapGamma (double z)
{
int i , N = 100;
double gamma;
double a = 0.0;
double b = 15.0;
double x1, x2, y1, y2;
double areai;
double w = (b - a) / N;
gamma = 0.0;
for (i = 1; i < N; i++)
{
x1 = a + ((i - 1) * w); //the left bound point
x2 = a + (i*w); //the right bound point
y1 = pow(x1,z - 1)*exp(-x1); //the height of our left bound
y2 = pow(x2, z - 1)*exp(-x2); //the height of our right bound
areai = ((y1 + y2) / 2.0) * (x2 - x1);
gamma += areai;
}
return gamma;
}
This is building upon another project where I used a bessel function to create the M/M/1 queue over a 60 second span so I can see what this one is supposed to be. I've checked both my trapGamma and factorial functions results on there own and they are both working as expected.
How are summations supposed to be coded?
If the intent of the posted code is to calculate the modified Bessel function I, there are some pitfalls and useful semplifications to be aware of. Given
Trying to calculate the factorial, the value of the Gamma function, their product and the powers separately for each term of the sum leads to integer overflow sooner than later.
It's better to update the value of each addend of the sum instead.
Also, given that k is a whole, we have Γ(n) = (n - 1)!
The addends are increasingly smaller and, after some iterations, too small to be added to the sum, given the limited precision of type double.
// Evaluates x^k / k! trying not to overflow
double power_over_factorial(double x, int k)
{
double result = 1.0;
for ( int i = 1; i <= k; ++i )
{
result *= x / i;
}
return result;
}
#define MAX_ITERS 20
double modified_Bessel_I(int k, double x)
{
x /= 2;
const double xx = x * x;
double partial = power_over_factorial(x, k);
double old_sum, sum = partial;
int m = 1;
do
{
old_sum = sum;
partial *= xx / ((m + k) * m);
sum += partial;
}
while ( old_sum != sum && ++m < MAX_ITERS );
return sum;
}
Testable here.

Calculating cos(x) through Maclaurin series approximation using a factorial function and a cosine one

I have an assignment to code a program to calculate cos(x) through the Maclaurin approximation. However I must use a function for the cos(x) and another one to calculate the exponentials that go on the denominators inside the cos(x) function. I think most of this is right, but I'm probably missing on something and I can't figure out what.
#include<stdio.h>
#include <stdlib.h>
#include <math.h>
int fat(int);
float cosx(float);
int main()
{
float x1;
/* Original code: **x1 = x1 * 3.14159 / 180;** `transforms the value to radians` */
x1 = x1 * 3.14159 / 180; /* transforms the value to radians */
printf("Insert number:\n");
scanf("%f", &x1);
printf("Cosine of %f = %f", x1, cosx(x1));
return 0;
}
int fat(int y)
{
int n, fat = 1;
for(n = 1; n <= y; n++)
{
fat = fat * n;
}
return fat;
}
float cosx(float x)
{
int i=1, a = 2, b, c = 1, e;
float cos;
while(i < 20)
{
b = c * (pow(x,a)) / e;
cos = 1 - b;
a += 2;
e = fat(a);
c *= -1;
i++;
}
return cos;
}
If I input 0 it returns -2147483648.000000, which is clearly wrong.
First error is uninitialized variable x1, and right after that you have use:
int x1; // <<< uninitiated variable;
**x1 = x1 * 3.14159 / 180;** `transforms the value to radians
this will produce random value, you should put
int x = 0; // or some other value of your choice
In my opinion you should move x1 = x1 * 3.14159/100; after scanf("%d", x1).
Than again uninitiated value e before use.
int i=1, a = 2, b, c = 1, e;
...
b = c * (pow(x,a)) / e;
...
than you have in the line b = c * pow(x,a) where you go out of range of int variable potentially. If e = 1, x = 2 and a > 31 you are out of range for b. Another problem is pow(x,a) is rising much faster than `e. thus you get bigger and bigger values thus you are getting another overflow. And here is the code that works:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
long double fact(int);
long double cosx(double);
long double my_pow (double b, int e);
int main()
{
double x1 = 45.00;
printf("Insert number:\n");
scanf("%lf", &x1);
x1 = x1 * 3.14159 / 180; // ** `transforms the value to radians`
printf("Cosine of %f = %.10LF", x1, cosx(x1));
return 0;
}
long double fact(int y)
{
int n;
double fact = 1;
for(n = 1; n <= y; n++)
{
fact *= n;
}
return fact;
}
long double cosx(double x)
{
int a = 2, c = -1;
long i = 0, lim = 500;
long double cos = 1;
long double b = 0, e = 0;
while(i < lim) {
e = fact(a);
b = c * my_pow(x,a);
cos += b/e;
// printf ("%le %le %le\n", e, b, cos);
a += 2;
c *= -1;
i++;
}
return cos;
}
long double my_pow (double b, int e) {
long double pow = 1;
for (;e > 0; --e, pow *= b)
;
return pow;
}

FIR filter in C?

I have a homework to implement an FIR filter in C and I wonder whether you think I understood the assignment correctly. The program I wrote that I think solves the problem is:
#include <stdio.h>
float FIRfloats[5];
void floatFIR(float newsample)
{
int i;
float sum=0;
FIRfloats[0]=newsample*0.0299;
FIRfloats[1]=FIRfloats[2]*0.4701;
FIRfloats[2]=FIRfloats[3]*0.4701;
FIRfloats[3]=FIRfloats[4]*0.0299;
/* sum */
for(i=0;i<5;i++)
{
sum=sum+FIRfloats[i];
}
printf("Sum: %f\n", sum);
}
int main ()
{
float n=0.0f;
while (scanf("%f", &n) > 0)
{
floatFIR(n);
}
return 0;
}
And the specification is
Before a new sample xk arrives the old samples are shifted to the
right and then each sample is scaled with a coefficient before the
result yk, the total sum of all scaled samples, is calculated
Coefficients should be c0=0.0299, c1=0.4701, c2=0.4701, c3=0.0299.
Do you think that I solved the assignment correctly? I think it seemed too easy and therefore I wonder.
I'm afraid the implementation provided in the question will not provide the correct results.
In FIR (Finite Impulse Response) filter with 4 coefficients the output series (y) for input series (x) is:
y[t] = c0*x[t] + c1*x[t-1] + c2*x[t-2] + c3*x[t-3]
Therefore the implementation should be similar to:
/* add includes (stdio.h and whatever else you'll need...) */
float floatFIR(float inVal, float* x, float* coef, int len)
{
float y = 0.0;
for (int i = (len-1) ; i > 0 ; i--)
{
x[i] = x[i-1];
y = y + (coef[i] * x[i]);
}
x[0] = inVal;
y = y + (coef[0] * x[0]);
return y;
}
main(int argc, char** argv)
{
float coef[4] = {0.0299, 0.4701, 0.4701, 0.0299};
float x[4] = {0, 0, 0, 0}; /* or any other initial condition*/
float y;
float inVal;
while (scanf("%f", &inVal) > 0)
{
y = floatFIR(inVal, x, coef, 4);
}
return 0;
}
This does the shift and multiplication at the same loop (which does not affect results - only is more efficient.)
If you want to follow the spec exactly, you can change floatFir like this:
float floatFIR(float inVal, float* x, float* coef, int len)
{
float y = 0.0;
for (int i = (len-1) ; i > 0 ; i--)
{
x[i] = x[i-1];
}
x[0] = inVal;
for (int i = 0 ; i < len ; i++)
{
y = y + (coef[i] * x[i]);
}
return y;
}

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