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root/trunk/meta/demo/calcpi.d

Revision 160, 1.3 kB (checked in by Don Clugston, 10 years ago)

Many accumulated changes to 'meta'. The most interesting is the one in feqtest, which tests floating point numbers for equality to the number of decimal places given in a string.

Line 
1 /** Calculate pi at compile time
2  *
3  * Compile with dmd -c pi.d
4  */
5 module calcpi;
6
7 import meta.math;
8 import meta.conv;
9
10 /** real evaluateSeries!(real x, real metafunction!(real y, int n) term)
11  *
12  * Evaluate a power series at compile time.
13  *
14  * Given a metafunction of the form
15  *  real term!(real y, int n),
16  * which gives the nth term of a convergent series at the point y
17  * (where the first term is n==1), and a real number x,
18  * this metafunction calculates the infinite sum at the point x
19  * by adding terms until the sum doesn't change any more.
20  */
21 template evaluateSeries(real x, alias term, int n=1, real sumsofar=0.0)
22 {
23   static if (n>1 && sumsofar == sumsofar + term!(x, n+1)) {
24      const real evaluateSeries = sumsofar;
25   } else {
26      const real evaluateSeries = evaluateSeries!(x, term, n+1, sumsofar + term!(x, n));
27   }
28 }
29
30 /*** Calculate atan(x) at compile time.
31  *
32  * Uses the Maclaurin formula
33  *  atan(z) = z - z^3/3 + Z^5/5 - Z^7/7 + ...
34  */
35 template atan(real z)
36 {
37     const real atan = evaluateSeries!(z, atanTerm);
38 }
39
40 template atanTerm(real x, int n)
41 {
42     const real atanTerm =  (n & 1 ? 1 : -1) * pow!(x, 2*n-1)/(2*n-1);
43 }
44
45 /// Machin's formula for pi
46 /// pi/4 = 4 atan(1/5) - atan(1/239).
47 pragma(msg, "PI = " ~ fcvt!(4.0 * (4*atan!(1/5.0) - atan!(1/239.0))) );
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