Weird ways to calculate pi Pc#

My 7,000 MIPs PC took about 15 hours to calculate the first 1,000,000 decimal places of pi. So 10 times as many decimal places will take about 100 times as long.

The algorithm described above has an O(n 2) duration.

The answer is written to a file called result NDecimalPlaces.txt. You can adjust how many decimal places it calculates by changing #define NDecimalPlaces (1000100) to some other number. The attached program is a straightforward Win32 Console Application (it started out as the standard 'Hello, World!' application with MFC support). Looks like it's just dividing term5m by a number, but it's actually calling CRHMultiLengthInteger::operator /=().

Weird ways to calculate pi full#

I've made full use of the operator notation in C++ to make the code look like we're just working with ordinary numbers. The multi-length numbers are wrapped up inside the class CRHMultiLengthInteger. To get one million decimal places, I've done a simple implementation of the multi-length arithmetic operations that I need, using a big array of ints. Multi-length arithmeticĪ 32-bit integer only gives us about 9 significant digits.

Weird ways to calculate pi series#

To get 1,000,000 decimal places accuracy for pi, we need about 715,000 terms of the tan -1(1/5) series and about 210,000 terms of the tan -1(1/239) series, but this doesn't have to be worked out in advance, the attached program stops automatically when it determines that the required accuracy has been reached. īy including sufficiently many terms of this series, we can achieve any desired accuracy. Tan -1() is the Inverse Tangent function, and I use the Maclaurin series to calculate it: I've chosen a method that is fairly simple and converges reasonably fast. Some are simple to implement but converge very slowly. Some methods converge rapidly but are complicated to implement. I'm not going to try to write pi as the Greek letter in this article, because some browsers might show it incorrectly. It is an infinitely long non-recurring decimal number. It is defined as the ratio of a circle's circumference to its diameter, but it crops up in all sorts of places in mathematics. For example, the predicate shown in the first expression is internally converted in the second expression.Ī filter argument overrides the existing corresponding filters over the same column(s), unless it is embedded within KEEPFILTERS.Pi is one of the most important numbers in mathematics.

When a filter argument has the form of a predicate with a single column reference, the expression is embedded into a FILTER expression that filters all the values of the referenced column. RemarksĮvery filter argument can be either a filter removal (such as ALL, ALLEXCEPT, ALLNOBLANKROW), a filter restore ( ALLSELECTED), or a table expression returning a list of values for one or more columns or for an entire expanded table. The value is the result of the expression evaluated in a modified filter context.