1 // cl_atan_recip().
2
3 // General includes.
4 #include "base/cl_sysdep.h"
5
6 // Specification.
7 #include "float/transcendental/cl_F_tran.h"
8
9
10 // Implementation.
11
12 #include "cln/integer.h"
13 #include "cln/lfloat.h"
14 #include "float/lfloat/cl_LF.h"
15 #include "float/transcendental/cl_LF_tran.h"
16
17 #undef floor
18 #include <cmath>
19 #define floor cln_floor
20
21 namespace cln {
22
23 // Method:
24 // See examples/atan_recip.cc for a comparison of the algorithms.
25 // Here we take algorithm 2d. It's the fastest throughout the range.
26
cl_atan_recip(cl_I m,uintC len)27 const cl_LF cl_atan_recip (cl_I m, uintC len)
28 {
29 var uintC actuallen = len + 1;
30 var cl_I m2 = m*m+1;
31 var uintC N = (uintC)(0.69314718*intDsize*actuallen/::log(double_approx(m2))) + 1;
32 struct rational_series_stream : cl_pq_series_stream {
33 var uintC n;
34 var cl_I m;
35 var cl_I m2;
36 static cl_pq_series_term computenext (cl_pq_series_stream& thisss)
37 {
38 var rational_series_stream& thiss = (rational_series_stream&)thisss;
39 var uintC n = thiss.n;
40 var cl_pq_series_term result;
41 if (n==0) {
42 result.p = thiss.m;
43 result.q = thiss.m2;
44 } else {
45 result.p = 2*n;
46 result.q = (2*n+1)*thiss.m2;
47 }
48 thiss.n = n+1;
49 return result;
50 }
51 rational_series_stream(const cl_I& m_, const cl_I& m2_)
52 : cl_pq_series_stream (rational_series_stream::computenext),
53 n(0), m(m_), m2(m2_) {}
54 } series(m,m2);
55 var cl_LF result = eval_rational_series<false>(N,series,actuallen);
56 return shorten(result,len);
57 }
58 // Bit complexity (N = len): O(log(N)^2*M(N)).
59
60 } // namespace cln
61