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#include <numbers>
using std::numbers::pi;
#include "Base/Math/Functions.h"
#include "Tests/GTestWrapper/google_test.h"
#define EXPECT_CNEAR(a, b, epsi) \
EXPECT_NEAR((a).real(), (b).real(), epsi); \
EXPECT_NEAR((a).imag(), (b).imag(), epsi);
// Test accuracy of complex function sinc(z) near the removable singularity at z=0
TEST(SpecialFunctions, csinc)
{
const double eps = 4.7e-16; // more than twice the machine precision
for (int i = 0; i < 24; ++i) {
double ph = (2 * pi) * i / 24;
// std::cout << "---------------------------------------------------------------------\n";
// std::cout << "phase = " << ph << "\n";
EXPECT_EQ(Math::sinc(complex_t(0, 0)), complex_t(1., 0.));
complex_t z;
z = std::polar(1e-17, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(2e-17, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(5e-17, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(1e-16, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(2e-16, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(5e-16, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(1e-15, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(1e-13, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(1e-11, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(1e-9, ph);
EXPECT_CNEAR(Math::sinc(z), complex_t(1., 0.), eps);
z = std::polar(5e-8, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(2e-8, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(1e-8, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(5e-7, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(2e-7, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(1e-7, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(1e-6, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(1e-5, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6., eps);
z = std::polar(1e-4, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6. * (1. - z * z / 20.), eps);
z = std::polar(1e-3, ph);
EXPECT_CNEAR(Math::sinc(z), 1. - z * z / 6. * (1. - z * z / 20.), eps);
}
}
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