.. index:: pair: class; rgpot::nlist::MinimumImage
.. _doxid-classrgpot_1_1nlist_1_1_minimum_image:

class rgpot::nlist::MinimumImage
================================

.. toctree::
	:hidden:

Nearest periodic image for row-major lattice vectors: d - n H.

The working type is double. Each product-sum is rgpot::simd::mul_add: a hardware fused multiply-add when the processor has one, and the exactly rounded TwoProduct/TwoSum emulation otherwise. This translation unit is compiled with contraction off, so the folded bits do not depend on the instruction set. A cell whose infinity-norm condition estimate would spend more than half the double significand is Minkowski-reduced (Nguyen and Stehlé, ACM Trans. Algorithms 5, 46 (2009), doi:10.1145/1597036.1597050) and the image is taken in that basis. A reduced basis that is still too ill-conditioned searches the 27 images of coefficients in {-1, 0, 1}. Singular or non-finite cells throw. An index that does not fit in an int64 throws.


.. ref-code-block:: cpp
	:class: doxyrest-overview-code-block

	#include <MinimumImage.hpp>
	
	class MinimumImage {
	public:
		// construction
	
		:target:`MinimumImage<doxid-classrgpot_1_1nlist_1_1_minimum_image_1a207112b80a53b43a35d9c6804dcd6aa7>`();
		:target:`MinimumImage<doxid-classrgpot_1_1nlist_1_1_minimum_image_1a91aa7e5a60d6283d79ee48dbacb319a4>`(const double* cell, const std::array<bool, 3>& periodic);

		// methods
	
		void :target:`fold<doxid-classrgpot_1_1nlist_1_1_minimum_image_1a7cf94306de65dfd1ccb3fc91e51db9a7>`(double& dx, double& dy, double& dz) const;
	};