no overlap with Marc's code
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! ###################################################################
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! Copyright (c) 2013-2015, Marc De Graef/Carnegie Mellon University
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! Modified 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
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! All rights reserved.
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!
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! Redistribution and use in source and binary forms, with or without modification, are
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! permitted provided that the following conditions are met:
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!
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! - Redistributions of source code must retain the above copyright notice, this list
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! of conditions and the following disclaimer.
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! - Redistributions in binary form must reproduce the above copyright notice, this
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! list of conditions and the following disclaimer in the documentation and/or
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! other materials provided with the distribution.
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! - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
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! of its contributors may be used to endorse or promote products derived from
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! this software without specific prior written permission.
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!
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! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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! ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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! LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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! ###################################################################
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!---------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Michigan State University
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!> @brief general quaternion math, not limited to unit quaternions
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!> @details w is the real part, (x, y, z) are the imaginary parts.
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!> @details https://users.aalto.fi/~ssarkka/pub/quat.pdf
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!> @details https://en.wikipedia.org/wiki/Quaternion
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!---------------------------------------------------------------------------------------------------
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module quaternions
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use prec
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