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#10905 closed Bugs (fixed)

sinpx function in boost/math/special_functions/gamma.hpp returns incorrect results for positive z arguments

Reported by:	Brent Rector <brent@…>	Owned by:	John Maddock
Milestone:	To Be Determined	Component:	math
Version:	Boost 1.57.0	Severity:	Showstopper
Keywords:		Cc:

Description

The sinpx function in gamma.hpp produces incorrect results for all positive arguments. The sign of the result is exactly the opposite of the correct value. As the sinpx function is called by all the gamma functions, their results are affected as well.

Here is the 1.57 version of sinpx. Removing the "else { sign = -sign; }" block fixes the problem.

Attached is a source file that calculates z * sin (z * PI) using the sinpx function and the C++ math.h sin() function. Note that the sinpx function produces the right absolute value, but with the wrong sign, for all positive z arguments.

template <class T>
T sinpx(T z)
{
   // Ad hoc function calculates x * sin(pi * x),
   // taking extra care near when x is near a whole number.
   BOOST_MATH_STD_USING
   int sign = 1;
   if(z < 0)
   {
      z = -z;
   }
   else
   {
      sign = -sign;
   }
   T fl = floor(z);
   T dist;
   if(is_odd(fl))
   {
      fl += 1;
      dist = fl - z;
      sign = -sign;
   }
   else
   {
      dist = z - fl;
   }
   BOOST_ASSERT(fl >= 0);
   if(dist > 0.5)
      dist = 1 - dist;
   T result = sin(dist*boost::math::constants::pi<T>());
   return sign*z*result;
}

The following program demonstrates the bug:

#include <boost/math/special_functions/gamma.hpp>
#include <boost/format.hpp>
#include <iostream>
#include <math.h>

int main()
{
	using namespace boost::math::detail;

	for (double z = -10.0; z < 10.1; z += 0.1) {
		double result = sinpx(z);
		double result2 = z * sin(z * 3.14159265);
		bool error = abs(result - result2) > 0.001;
		auto errormsg = error ? "\t*** Error" : "";


		std::cout << boost::format ("%1$4.1f * sinpx (%1$4.1f * PI) is %2$11.8f\tC++ sin() is %3$11.8f%4%\n") % z % result % result2 % errormsg;
	}
}

It produces the following output:

-10.0 * sinpx (-10.0 * PI) is  0.00000000       C++ sin() is -0.00000036
-9.9 * sinpx (-9.9 * PI) is -3.05926824 C++ sin() is -3.05926858
-9.8 * sinpx (-9.8 * PI) is -5.76029547 C++ sin() is -5.76029575
-9.7 * sinpx (-9.7 * PI) is -7.84746485 C++ sin() is -7.84746504
-9.6 * sinpx (-9.6 * PI) is -9.13014256 C++ sin() is -9.13014266
-9.5 * sinpx (-9.5 * PI) is -9.50000000 C++ sin() is -9.50000000
-9.4 * sinpx (-9.4 * PI) is -8.93993125 C++ sin() is -8.93993116
-9.3 * sinpx (-9.3 * PI) is -7.52385805 C++ sin() is -7.52385787
-9.2 * sinpx (-9.2 * PI) is -5.40762432 C++ sin() is -5.40762408
-9.1 * sinpx (-9.1 * PI) is -2.81205465 C++ sin() is -2.81205437
-9.0 * sinpx (-9.0 * PI) is -0.00000000 C++ sin() is  0.00000029
-8.9 * sinpx (-8.9 * PI) is  2.75025125 C++ sin() is  2.75025152
-8.8 * sinpx (-8.8 * PI) is  5.17251022 C++ sin() is  5.17251045
-8.7 * sinpx (-8.7 * PI) is  7.03844785 C++ sin() is  7.03844801
-8.6 * sinpx (-8.6 * PI) is  8.17908604 C++ sin() is  8.17908612
-8.5 * sinpx (-8.5 * PI) is  8.50000000 C++ sin() is  8.50000000
-8.4 * sinpx (-8.4 * PI) is  7.98887474 C++ sin() is  7.98887466
-8.3 * sinpx (-8.3 * PI) is  6.71484105 C++ sin() is  6.71484091
-8.2 * sinpx (-8.2 * PI) is  4.81983907 C++ sin() is  4.81983887
-8.1 * sinpx (-8.1 * PI) is  2.50303765 C++ sin() is  2.50303743
-8.0 * sinpx (-8.0 * PI) is  0.00000000 C++ sin() is -0.00000023
-7.9 * sinpx (-7.9 * PI) is -2.44123426 C++ sin() is -2.44123447
-7.8 * sinpx (-7.8 * PI) is -4.58472497 C++ sin() is -4.58472514
-7.7 * sinpx (-7.7 * PI) is -6.22943086 C++ sin() is -6.22943098
-7.6 * sinpx (-7.6 * PI) is -7.22802952 C++ sin() is -7.22802959
-7.5 * sinpx (-7.5 * PI) is -7.50000000 C++ sin() is -7.50000000
-7.4 * sinpx (-7.4 * PI) is -7.03781822 C++ sin() is -7.03781816
-7.3 * sinpx (-7.3 * PI) is -5.90582406 C++ sin() is -5.90582395
-7.2 * sinpx (-7.2 * PI) is -4.23205382 C++ sin() is -4.23205367
-7.1 * sinpx (-7.1 * PI) is -2.19402066 C++ sin() is -2.19402049
-7.0 * sinpx (-7.0 * PI) is -0.00000000 C++ sin() is  0.00000018
-6.9 * sinpx (-6.9 * PI) is  2.13221726 C++ sin() is  2.13221742
-6.8 * sinpx (-6.8 * PI) is  3.99693972 C++ sin() is  3.99693985
-6.7 * sinpx (-6.7 * PI) is  5.42041386 C++ sin() is  5.42041396
-6.6 * sinpx (-6.6 * PI) is  6.27697301 C++ sin() is  6.27697306
-6.5 * sinpx (-6.5 * PI) is  6.50000000 C++ sin() is  6.50000000
-6.4 * sinpx (-6.4 * PI) is  6.08676170 C++ sin() is  6.08676166
-6.3 * sinpx (-6.3 * PI) is  5.09680706 C++ sin() is  5.09680698
-6.2 * sinpx (-6.2 * PI) is  3.64426856 C++ sin() is  3.64426845
-6.1 * sinpx (-6.1 * PI) is  1.88500367 C++ sin() is  1.88500354
-6.0 * sinpx (-6.0 * PI) is  0.00000000 C++ sin() is -0.00000013
-5.9 * sinpx (-5.9 * PI) is -1.82320027 C++ sin() is -1.82320039
-5.8 * sinpx (-5.8 * PI) is -3.40915446 C++ sin() is -3.40915456
-5.7 * sinpx (-5.7 * PI) is -4.61139687 C++ sin() is -4.61139694
-5.6 * sinpx (-5.6 * PI) is -5.32591649 C++ sin() is -5.32591653
-5.5 * sinpx (-5.5 * PI) is -5.50000000 C++ sin() is -5.50000000
-5.4 * sinpx (-5.4 * PI) is -5.13570519 C++ sin() is -5.13570516
-5.3 * sinpx (-5.3 * PI) is -4.28779007 C++ sin() is -4.28779001
-5.2 * sinpx (-5.2 * PI) is -3.05648331 C++ sin() is -3.05648323
-5.1 * sinpx (-5.1 * PI) is -1.57598667 C++ sin() is -1.57598658
-5.0 * sinpx (-5.0 * PI) is -0.00000000 C++ sin() is  0.00000009
-4.9 * sinpx (-4.9 * PI) is  1.51418327 C++ sin() is  1.51418335
-4.8 * sinpx (-4.8 * PI) is  2.82136921 C++ sin() is  2.82136928
-4.7 * sinpx (-4.7 * PI) is  3.80237987 C++ sin() is  3.80237992
-4.6 * sinpx (-4.6 * PI) is  4.37485997 C++ sin() is  4.37486000
-4.5 * sinpx (-4.5 * PI) is  4.50000000 C++ sin() is  4.50000000
-4.4 * sinpx (-4.4 * PI) is  4.18464867 C++ sin() is  4.18464865
-4.3 * sinpx (-4.3 * PI) is  3.47877308 C++ sin() is  3.47877304
-4.2 * sinpx (-4.2 * PI) is  2.46869806 C++ sin() is  2.46869801
-4.1 * sinpx (-4.1 * PI) is  1.26696968 C++ sin() is  1.26696962
-4.0 * sinpx (-4.0 * PI) is  0.00000000 C++ sin() is -0.00000006
-3.9 * sinpx (-3.9 * PI) is -1.20516628 C++ sin() is -1.20516633
-3.8 * sinpx (-3.8 * PI) is -2.23358396 C++ sin() is -2.23358400
-3.7 * sinpx (-3.7 * PI) is -2.99336288 C++ sin() is -2.99336291
-3.6 * sinpx (-3.6 * PI) is -3.42380346 C++ sin() is -3.42380347
-3.5 * sinpx (-3.5 * PI) is -3.50000000 C++ sin() is -3.50000000
-3.4 * sinpx (-3.4 * PI) is -3.23359216 C++ sin() is -3.23359214
-3.3 * sinpx (-3.3 * PI) is -2.66975608 C++ sin() is -2.66975606
-3.2 * sinpx (-3.2 * PI) is -1.88091281 C++ sin() is -1.88091278
-3.1 * sinpx (-3.1 * PI) is -0.95795268 C++ sin() is -0.95795265
-3.0 * sinpx (-3.0 * PI) is -0.00000000 C++ sin() is  0.00000003
-2.9 * sinpx (-2.9 * PI) is  0.89614928 C++ sin() is  0.89614931
-2.8 * sinpx (-2.8 * PI) is  1.64579871 C++ sin() is  1.64579873
-2.7 * sinpx (-2.7 * PI) is  2.18434588 C++ sin() is  2.18434590
-2.6 * sinpx (-2.6 * PI) is  2.47274694 C++ sin() is  2.47274695
-2.5 * sinpx (-2.5 * PI) is  2.50000000 C++ sin() is  2.50000000
-2.4 * sinpx (-2.4 * PI) is  2.28253564 C++ sin() is  2.28253563
-2.3 * sinpx (-2.3 * PI) is  1.86073909 C++ sin() is  1.86073908
-2.2 * sinpx (-2.2 * PI) is  1.29312756 C++ sin() is  1.29312754
-2.1 * sinpx (-2.1 * PI) is  0.64893569 C++ sin() is  0.64893567
-2.0 * sinpx (-2.0 * PI) is  0.00000000 C++ sin() is -0.00000001
-1.9 * sinpx (-1.9 * PI) is -0.58713229 C++ sin() is -0.58713230
-1.8 * sinpx (-1.8 * PI) is -1.05801345 C++ sin() is -1.05801346
-1.7 * sinpx (-1.7 * PI) is -1.37532889 C++ sin() is -1.37532890
-1.6 * sinpx (-1.6 * PI) is -1.52169043 C++ sin() is -1.52169043
-1.5 * sinpx (-1.5 * PI) is -1.50000000 C++ sin() is -1.50000000
-1.4 * sinpx (-1.4 * PI) is -1.33147912 C++ sin() is -1.33147912
-1.3 * sinpx (-1.3 * PI) is -1.05172209 C++ sin() is -1.05172209
-1.2 * sinpx (-1.2 * PI) is -0.70534230 C++ sin() is -0.70534230
-1.1 * sinpx (-1.1 * PI) is -0.33991869 C++ sin() is -0.33991869
-1.0 * sinpx (-1.0 * PI) is -0.00000000 C++ sin() is  0.00000000
-0.9 * sinpx (-0.9 * PI) is  0.27811529 C++ sin() is  0.27811530
-0.8 * sinpx (-0.8 * PI) is  0.47022820 C++ sin() is  0.47022820
-0.7 * sinpx (-0.7 * PI) is  0.56631190 C++ sin() is  0.56631190
-0.6 * sinpx (-0.6 * PI) is  0.57063391 C++ sin() is  0.57063391
-0.5 * sinpx (-0.5 * PI) is  0.50000000 C++ sin() is  0.50000000
-0.4 * sinpx (-0.4 * PI) is  0.38042261 C++ sin() is  0.38042261
-0.3 * sinpx (-0.3 * PI) is  0.24270510 C++ sin() is  0.24270510
-0.2 * sinpx (-0.2 * PI) is  0.11755705 C++ sin() is  0.11755705
-0.1 * sinpx (-0.1 * PI) is  0.03090170 C++ sin() is  0.03090170
-0.0 * sinpx (-0.0 * PI) is  0.00000000 C++ sin() is  0.00000000
 0.1 * sinpx ( 0.1 * PI) is -0.03090170 C++ sin() is  0.03090170        *** Error
 0.2 * sinpx ( 0.2 * PI) is -0.11755705 C++ sin() is  0.11755705        *** Error
 0.3 * sinpx ( 0.3 * PI) is -0.24270510 C++ sin() is  0.24270510        *** Error
 0.4 * sinpx ( 0.4 * PI) is -0.38042261 C++ sin() is  0.38042261        *** Error
 0.5 * sinpx ( 0.5 * PI) is -0.50000000 C++ sin() is  0.50000000        *** Error
 0.6 * sinpx ( 0.6 * PI) is -0.57063391 C++ sin() is  0.57063391        *** Error
 0.7 * sinpx ( 0.7 * PI) is -0.56631190 C++ sin() is  0.56631190        *** Error
 0.8 * sinpx ( 0.8 * PI) is -0.47022820 C++ sin() is  0.47022820        *** Error
 0.9 * sinpx ( 0.9 * PI) is -0.27811529 C++ sin() is  0.27811530        *** Error
 1.0 * sinpx ( 1.0 * PI) is -0.00000000 C++ sin() is  0.00000000
 1.1 * sinpx ( 1.1 * PI) is  0.33991869 C++ sin() is -0.33991869        *** Error
 1.2 * sinpx ( 1.2 * PI) is  0.70534230 C++ sin() is -0.70534230        *** Error
 1.3 * sinpx ( 1.3 * PI) is  1.05172209 C++ sin() is -1.05172209        *** Error
 1.4 * sinpx ( 1.4 * PI) is  1.33147912 C++ sin() is -1.33147912        *** Error
 1.5 * sinpx ( 1.5 * PI) is  1.50000000 C++ sin() is -1.50000000        *** Error
 1.6 * sinpx ( 1.6 * PI) is  1.52169043 C++ sin() is -1.52169043        *** Error
 1.7 * sinpx ( 1.7 * PI) is  1.37532889 C++ sin() is -1.37532890        *** Error
 1.8 * sinpx ( 1.8 * PI) is  1.05801345 C++ sin() is -1.05801346        *** Error
 1.9 * sinpx ( 1.9 * PI) is  0.58713229 C++ sin() is -0.58713230        *** Error
 2.0 * sinpx ( 2.0 * PI) is  0.00000000 C++ sin() is -0.00000001
 2.1 * sinpx ( 2.1 * PI) is -0.64893569 C++ sin() is  0.64893567        *** Error
 2.2 * sinpx ( 2.2 * PI) is -1.29312756 C++ sin() is  1.29312754        *** Error
 2.3 * sinpx ( 2.3 * PI) is -1.86073909 C++ sin() is  1.86073908        *** Error
 2.4 * sinpx ( 2.4 * PI) is -2.28253564 C++ sin() is  2.28253563        *** Error
 2.5 * sinpx ( 2.5 * PI) is -2.50000000 C++ sin() is  2.50000000        *** Error
 2.6 * sinpx ( 2.6 * PI) is -2.47274694 C++ sin() is  2.47274695        *** Error
 2.7 * sinpx ( 2.7 * PI) is -2.18434588 C++ sin() is  2.18434590        *** Error
 2.8 * sinpx ( 2.8 * PI) is -1.64579871 C++ sin() is  1.64579873        *** Error
 2.9 * sinpx ( 2.9 * PI) is -0.89614928 C++ sin() is  0.89614931        *** Error
 3.0 * sinpx ( 3.0 * PI) is -0.00000000 C++ sin() is  0.00000003
 3.1 * sinpx ( 3.1 * PI) is  0.95795268 C++ sin() is -0.95795265        *** Error
 3.2 * sinpx ( 3.2 * PI) is  1.88091281 C++ sin() is -1.88091278        *** Error
 3.3 * sinpx ( 3.3 * PI) is  2.66975608 C++ sin() is -2.66975606        *** Error
 3.4 * sinpx ( 3.4 * PI) is  3.23359216 C++ sin() is -3.23359214        *** Error
 3.5 * sinpx ( 3.5 * PI) is  3.50000000 C++ sin() is -3.50000000        *** Error
 3.6 * sinpx ( 3.6 * PI) is  3.42380346 C++ sin() is -3.42380347        *** Error
 3.7 * sinpx ( 3.7 * PI) is  2.99336288 C++ sin() is -2.99336291        *** Error
 3.8 * sinpx ( 3.8 * PI) is  2.23358396 C++ sin() is -2.23358400        *** Error
 3.9 * sinpx ( 3.9 * PI) is  1.20516628 C++ sin() is -1.20516633        *** Error
 4.0 * sinpx ( 4.0 * PI) is  0.00000000 C++ sin() is -0.00000006
 4.1 * sinpx ( 4.1 * PI) is -1.26696968 C++ sin() is  1.26696962        *** Error
 4.2 * sinpx ( 4.2 * PI) is -2.46869806 C++ sin() is  2.46869801        *** Error
 4.3 * sinpx ( 4.3 * PI) is -3.47877308 C++ sin() is  3.47877304        *** Error
 4.4 * sinpx ( 4.4 * PI) is -4.18464867 C++ sin() is  4.18464865        *** Error
 4.5 * sinpx ( 4.5 * PI) is -4.50000000 C++ sin() is  4.50000000        *** Error
 4.6 * sinpx ( 4.6 * PI) is -4.37485997 C++ sin() is  4.37486000        *** Error
 4.7 * sinpx ( 4.7 * PI) is -3.80237987 C++ sin() is  3.80237992        *** Error
 4.8 * sinpx ( 4.8 * PI) is -2.82136921 C++ sin() is  2.82136928        *** Error
 4.9 * sinpx ( 4.9 * PI) is -1.51418327 C++ sin() is  1.51418335        *** Error
 5.0 * sinpx ( 5.0 * PI) is -0.00000000 C++ sin() is  0.00000009
 5.1 * sinpx ( 5.1 * PI) is  1.57598667 C++ sin() is -1.57598658        *** Error
 5.2 * sinpx ( 5.2 * PI) is  3.05648331 C++ sin() is -3.05648323        *** Error
 5.3 * sinpx ( 5.3 * PI) is  4.28779007 C++ sin() is -4.28779001        *** Error
 5.4 * sinpx ( 5.4 * PI) is  5.13570519 C++ sin() is -5.13570516        *** Error
 5.5 * sinpx ( 5.5 * PI) is  5.50000000 C++ sin() is -5.50000000        *** Error
 5.6 * sinpx ( 5.6 * PI) is  5.32591649 C++ sin() is -5.32591653        *** Error
 5.7 * sinpx ( 5.7 * PI) is  4.61139687 C++ sin() is -4.61139694        *** Error
 5.8 * sinpx ( 5.8 * PI) is  3.40915446 C++ sin() is -3.40915456        *** Error
 5.9 * sinpx ( 5.9 * PI) is  1.82320027 C++ sin() is -1.82320039        *** Error
 6.0 * sinpx ( 6.0 * PI) is  0.00000000 C++ sin() is -0.00000013
 6.1 * sinpx ( 6.1 * PI) is -1.88500367 C++ sin() is  1.88500354        *** Error
 6.2 * sinpx ( 6.2 * PI) is -3.64426856 C++ sin() is  3.64426845        *** Error
 6.3 * sinpx ( 6.3 * PI) is -5.09680706 C++ sin() is  5.09680698        *** Error
 6.4 * sinpx ( 6.4 * PI) is -6.08676170 C++ sin() is  6.08676166        *** Error
 6.5 * sinpx ( 6.5 * PI) is -6.50000000 C++ sin() is  6.50000000        *** Error
 6.6 * sinpx ( 6.6 * PI) is -6.27697301 C++ sin() is  6.27697306        *** Error
 6.7 * sinpx ( 6.7 * PI) is -5.42041386 C++ sin() is  5.42041396        *** Error
 6.8 * sinpx ( 6.8 * PI) is -3.99693972 C++ sin() is  3.99693985        *** Error
 6.9 * sinpx ( 6.9 * PI) is -2.13221726 C++ sin() is  2.13221742        *** Error
 7.0 * sinpx ( 7.0 * PI) is -0.00000000 C++ sin() is  0.00000018
 7.1 * sinpx ( 7.1 * PI) is  2.19402066 C++ sin() is -2.19402049        *** Error
 7.2 * sinpx ( 7.2 * PI) is  4.23205382 C++ sin() is -4.23205367        *** Error
 7.3 * sinpx ( 7.3 * PI) is  5.90582406 C++ sin() is -5.90582395        *** Error
 7.4 * sinpx ( 7.4 * PI) is  7.03781822 C++ sin() is -7.03781816        *** Error
 7.5 * sinpx ( 7.5 * PI) is  7.50000000 C++ sin() is -7.50000000        *** Error
 7.6 * sinpx ( 7.6 * PI) is  7.22802952 C++ sin() is -7.22802959        *** Error
 7.7 * sinpx ( 7.7 * PI) is  6.22943086 C++ sin() is -6.22943098        *** Error
 7.8 * sinpx ( 7.8 * PI) is  4.58472497 C++ sin() is -4.58472514        *** Error
 7.9 * sinpx ( 7.9 * PI) is  2.44123426 C++ sin() is -2.44123447        *** Error
 8.0 * sinpx ( 8.0 * PI) is  0.00000000 C++ sin() is -0.00000023
 8.1 * sinpx ( 8.1 * PI) is -2.50303765 C++ sin() is  2.50303743        *** Error
 8.2 * sinpx ( 8.2 * PI) is -4.81983907 C++ sin() is  4.81983887        *** Error
 8.3 * sinpx ( 8.3 * PI) is -6.71484105 C++ sin() is  6.71484091        *** Error
 8.4 * sinpx ( 8.4 * PI) is -7.98887474 C++ sin() is  7.98887466        *** Error
 8.5 * sinpx ( 8.5 * PI) is -8.50000000 C++ sin() is  8.50000000        *** Error
 8.6 * sinpx ( 8.6 * PI) is -8.17908604 C++ sin() is  8.17908612        *** Error
 8.7 * sinpx ( 8.7 * PI) is -7.03844785 C++ sin() is  7.03844801        *** Error
 8.8 * sinpx ( 8.8 * PI) is -5.17251022 C++ sin() is  5.17251045        *** Error
 8.9 * sinpx ( 8.9 * PI) is -2.75025125 C++ sin() is  2.75025152        *** Error
 9.0 * sinpx ( 9.0 * PI) is -0.00000000 C++ sin() is  0.00000029
 9.1 * sinpx ( 9.1 * PI) is  2.81205465 C++ sin() is -2.81205437        *** Error
 9.2 * sinpx ( 9.2 * PI) is  5.40762432 C++ sin() is -5.40762408        *** Error
 9.3 * sinpx ( 9.3 * PI) is  7.52385805 C++ sin() is -7.52385787        *** Error
 9.4 * sinpx ( 9.4 * PI) is  8.93993125 C++ sin() is -8.93993116        *** Error
 9.5 * sinpx ( 9.5 * PI) is  9.50000000 C++ sin() is -9.50000000        *** Error
 9.6 * sinpx ( 9.6 * PI) is  9.13014256 C++ sin() is -9.13014266        *** Error
 9.7 * sinpx ( 9.7 * PI) is  7.84746485 C++ sin() is -7.84746504        *** Error
 9.8 * sinpx ( 9.8 * PI) is  5.76029547 C++ sin() is -5.76029575        *** Error
 9.9 * sinpx ( 9.9 * PI) is  3.05926824 C++ sin() is -3.05926858        *** Error
10.0 * sinpx (10.0 * PI) is  0.00000000 C++ sin() is -0.00000036
10.1 * sinpx (10.1 * PI) is -3.12107164 C++ sin() is  3.12107129        *** Error
Press any key to continue . . .

Attachments (1)

Booster.cpp (623 bytes ) - added by Brent Rector <brent@…> 8 years ago.

Download all attachments as: .zip

Change History (2)

by Brent Rector <brent@…>, 8 years ago

Attachment:	Booster.cpp added

comment:1 by John Maddock, 8 years ago

Resolution:	→ fixed
Status:	new → closed

Yes you're correct, fixed in Git develop.

However, note that:

This is an internal undocumented function and,
The gamma functions only ever call this function for with a negative argument so they are unaffected.

If you want a similar/documented function, try sin_pi and cos_pi: http://www.boost.org/doc/libs/1_57_0/libs/math/doc/html/math_toolkit/powers/sin_pi.html

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