src/float/transcendental/cl_LF_cossin.cc

   1 // cl_cossin_ratseries().
   2
   3 // General includes.
   4 #include "cl_sysdep.h"
   5
   6 // Specification.
   7 #include "cl_F_tran.h"
   8
   9
  10 // Implementation.
  11
  12 #include "cl_lfloat.h"
  13 #include "cl_LF.h"
  14 #include "cl_integer.h"
  15
  16 inline const cl_LF_cos_sin_t operator* (const cl_LF_cos_sin_t& a, const cl_LF_cos_sin_t& b)
  17 {
  18         return cl_LF_cos_sin_t(a.cos*b.cos-a.sin*b.sin,a.sin*b.cos+a.cos*b.sin);
  19 }
  20
  21 const cl_LF_cos_sin_t cl_cossin_ratseries (const cl_LF& x)
  22 {
  23         // Similar to expx_ratseries.
  24         var uintC len = TheLfloat(x)->len;
  25         var cl_idecoded_float x_ = integer_decode_float(x);
  26         // x = (-1)^sign * 2^exponent * mantissa
  27         var uintL lq = cl_I_to_UL(- x_.exponent);
  28         var const cl_I& p = x_.mantissa;
  29         // Compute sin(p/2^lq) and cos(p/2^lq) by splitting into pieces.
  30         var cl_boolean first_factor = cl_true;
  31         var cl_LF_cos_sin_t product;
  32         var uintL b1;
  33         var uintL b2;
  34         for (b1 = 0, b2 = 1; b1 < lq; b1 = b2, b2 = 2*b2) {
  35                 // Piece containing bits b1+1..b2 after "decimal point"
  36                 // in the binary representation of (p/2^lq).
  37                 var uintL lqk = (lq >= b2 ? b2 : lq);
  38                 var cl_I pk = ldb(p,cl_byte(lqk-b1,lq-lqk));
  39                 // Compute sin(pk/2^lqk) and cos(pk/2^lqk).
  40                 if (!zerop(pk)) {
  41                         if (minusp(x_.sign)) { pk = -pk; }
  42                         var cl_LF_cos_sin_t factor = cl_cossin_aux(pk,lqk,len);
  43                         if (first_factor) {
  44                                 product = factor;
  45                                 first_factor = cl_false;
  46                         } else
  47                                 product = product * factor;
  48                 }
  49         }
  50         if (first_factor)
  51                 return cl_LF_cos_sin_t(cl_I_to_LF(1,len),cl_I_to_LF(0,len));
  52         else
  53                 return product;
  54 }
  55 // Bit complexity (N = length(x)): O(log(N)^2*M(N)).