问题
So, Leibniz's formula for pi is pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9... I can't figure out how to use this formula in Java. I just need some help on how to incorporate the second part into it. I know I need a loop and I need the have a divisor variable, and that it needs plus 2 each time. Thanks for any help.
回答1:
As a hint, this is an optimized version
long start = System.nanoTime();
double pi = 0;
for (int i = 1; i < 1000000000; i += 4) {
pi += 8.0 / (i * (i + 2L));
}
long time = System.nanoTime() - start;
System.out.println(pi + " took " + time / 1000000 / 1e3 + " secs.");
prints
3.1415926445762157 took 1.217 secs.
If you change this loop to do backwards instead of forwards you get a more accurate. It is more accurate as the the larger numbers added at the end hides some of the cumulated rounding error for the smaller values.
3.141592651589793 took 1.222 secs.
The value should be 3.14159265359
回答2:
The for loop should look something like this:
double sum=0;
double sign=1.0;
for(int i =1;i<=limit;i+=2)
{
sum+=sign/i;
sign* =-1;
}
来源：https://stackoverflow.com/questions/19121438/leibniz-formula-for-pi-java