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# naive approximation: pi = 4 * (1 - /1/3 + 1/5 ...)
LIMIT = 50000
def time() ; nqp::time_n() ; end
def sprintf(fmt, *args) ; nqp::sprintf(fmt, args) ; end
pi_over_4 = 0.0
print 'hang on a few moments...'
start_time = time()
# sum terms in reverse order to reduce accumulated error
n = LIMIT;
while n > 0 do
m = 4.0*n - 1.0
pi_over_4 += 1/(m - 2) - 1/m
n -= 1
end
puts sprintf("(completed %d iterations in %.2f sec)",
LIMIT, time() - start_time)
pi = pi_over_4 * 4
puts pi
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