[Boost-bugs] [Boost C++ Libraries] #13603: sinc_pi can be more precise with Horner's method

Subject: [Boost-bugs] [Boost C++ Libraries] #13603: sinc_pi can be more precise with Horner's method
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2018-06-14 08:03:15

#13603: sinc_pi can be more precise with Horner's  method
------------------------------+--------------------------
 Reporter:  minorlogic@…      |      Owner:  John Maddock
     Type:  Bugs              |     Status:  new
Milestone:  To Be Determined  |  Component:  math
  Version:  Boost 1.63.0      |   Severity:  Optimization
 Keywords:  sinc_pi  Horner   |
------------------------------+--------------------------
 double sinc1 = 1.0 + x2 * (-1.0 + x2 / 20.0) / 6.0;

         double sinc2 = 1.0 - x2 /6.0 + x2*x2 / 120.0;

 in some cases sinc1 provides better precision compared to sinc2

     x generated with

     double x = sqrt(sqrt(std::numeric_limits<double>::epsilon()));
     for (int i = 0; x > sqrt(std::numeric_limits<double>::epsilon()); i++)
     {
         x *= 0.99876765378657564;
     }

-- 
Ticket URL: <https://svn.boost.org/trac10/ticket/13603>
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