lapy3.hpp

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//
// Copyright (c) 2025, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_LAPY3_HH
#define TLAPACK_LAPY3_HH
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
 
template <TLAPACK_REAL TX,
          TLAPACK_REAL TY,
          TLAPACK_REAL TZ,
          enable_if_t<(
                          /* Requires: */
                          is_real<TX> && is_real<TY> && is_real<TZ>),
                      int> = 0>
real_type<TX, TY, TZ> lapy3(const TX& x, const TY& y, const TZ& z)
{
    // using
    using real_t = real_type<TX, TY, TZ>;
 
    // constants
    const real_t zero(0);
    const TX xabs = abs(x);
    const TY yabs = abs(y);
    const TZ zabs = abs(z);
    const real_t w = max(xabs, max(yabs, zabs));
 
    return (w == zero)
               // W can be zero for max(0,nan,0)
               // adding all three entries together will make sure
               // NaN will not disappear.
               ? xabs + yabs + zabs
               : w * sqrt((xabs / w) * (xabs / w) + (yabs / w) * (yabs / w) +
                          (zabs / w) * (zabs / w));
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_LAPY3_HH