Quote:Original post by DemosthenesBecause they want arbitrary precision
Why not Math.PI? :D
Quote:Because they want arbitrary precision
Math.PI is a double. What if I want to print out 1 million digits of pi?
Using atan isn't going to help anyone (as already pointed out) because now you're going to need another routine to calculate atan of a number up to an arbitrary precision.
Quote:Original post by coldacid
By the way, anyone know a formula for calculating e?
Quote:Original post by EelcoI know, I was just pointing out that it appears preferable to that other formula.Quote:Original post by Beer Hunterwell yeah, it seems to me that if you want to write a software program to approximate an infinite series, any use of hardware implemented trig functions (which are also based on series approximation) kindof defeats the point.Quote:Original post by Programmer OneAnything wrong with pi = 4 * tan-1(1)?
pi / 4 = 4 * tan-1(1 / 5) - tan-1(1 / 239)
x = sqrt(2);y = sqrt(x);pi = 2 + sqrt(2);while (not enough): sx = sqrt(x) x2 = (sx + 1/sx)) / 2; y2 = (y * sx + 1/sx) / (y + 1) x = x2; y = y2 pi = pi * (x + 1) / (y + 1)while (having fun): pi = pi + sin(pi)import sysdef main(): k, a, b, a1, b1 = 2L, 4L, 1L, 12L, 4L while 1: # Next approximation p, q, k = k*k, 2L*k+1L, k+1L a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1 # Print common digits d, d1 = a/b, a1/b1 while d == d1: output(d) a, a1 = 10L*(a%b), 10L*(a1%b1) d, d1 = a/b, a1/b1def output(d): # Use write() to avoid spaces between the digits # Use str() to avoid the 'L' sys.stdout.write(str(d)) # Flush so the output is seen immediately sys.stdout.flush()if __name__ == "__main__": main()Quote:Original post by avidlinuxuserQuote:Original post by coldacid
By the way, anyone know a formula for calculating e?
I just use the general power series for e^x and simplify it to the case when x=1 which gives you the sum from n = 0 to infinity 1/n!. I unroll the loop based on how precise I want the approximation for optimization. It's the simplest way, and it converges quickly anyway.
