C++ : Working of sine function [closed] - c++

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I am trying to plot a sine curve in C++ and came across something interesting.
I have a function that returns sine value of a value in degree
double sind(double a)
{
return sin(a*3.14159/180);
}
Now in the main function
sind(18)==sind(18)?cout<<1:cout<<0;
I write the above code. The result seems to be false and it prints 0 on the console.
But according to me sin(18) and sin(18) are equal. So what is happening in the computer's mind?
Also if I want to check equality of two sine values how would I go about it?

Answer 1

On the PC, at least as of old, floating points values were calculated with 80 bits, but were rounded down to 64 bits for main memory. When the compiler recognizes that it can reuse an 80-bit result for an 80-bit comparison you can get baffling results like this. And yes, it's permitted by the Holy Standard.
By the way, void main is not valid. This means the code has Undefined Behavior and in principle can do anything whatsoever, including doing nothing, or what you expect. In practice it's not that bad, it just makes the code non-portable, but still, don't do it: it's silly to add one character in order to make the code non-portable, so write int main.

Answer 2

Also if I want to check equality of two sine values how would I go about it?
There is a very good example of a floating point "almost_equal" function here
by request, code copied from original source:
#include <cmath>
#include <limits>
#include <iomanip>
#include <iostream>
#include <type_traits>
#include <algorithm>
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
almost_equal(T x, T y, int ulp)
{
// the machine epsilon has to be scaled to the magnitude of the values used
// and multiplied by the desired precision in ULPs (units in the last place)
return std::abs(x-y) < std::numeric_limits<T>::epsilon() * std::abs(x+y) * ulp
// unless the result is subnormal
|| std::abs(x-y) < std::numeric_limits<T>::min();
}
int main()
{
double d1 = 0.2;
double d2 = 1 / std::sqrt(5) / std::sqrt(5);
if(d1 == d2)
std::cout << "d1 == d2\n";
else
std::cout << "d1 != d2\n";
if(almost_equal(d1, d2, 2))
std::cout << "d1 almost equals d2\n";
else
std::cout << "d1 does not almost equal d2\n";
}