/* Euclidean distance function.  Long Double/Binary128 version.
   Copyright (C) 2021 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <https://www.gnu.org/licenses/>.  */

/* This implementation is based on 'An Improved Algorithm for hypot(a,b)' by
   Carlos F. Borges [1] using the MyHypot3 with the following changes:

   - Handle qNaN and sNaN.
   - Tune the 'widely varying operands' to avoid spurious underflow
     due the multiplication and fix the return value for upwards
     rounding mode.
   - Handle required underflow exception for subnormal results.

   [1] https://arxiv.org/pdf/1904.09481.pdf  */

#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>

#define SCALE      L(0x1p-8303)
#define LARGE_VAL  L(0x1.6a09e667f3bcc908b2fb1366ea95p+8191)
#define TINY_VAL   L(0x1p-8191)
#define EPS        L(0x1p-114)

/* Hypot kernel. The inputs must be adjusted so that ax >= ay >= 0
   and squaring ax, ay and (ax - ay) does not overflow or underflow.  */
static inline _Float128
kernel (_Float128 ax, _Float128 ay)
{
  _Float128 t1, t2;
  _Float128 h = sqrtl (ax * ax + ay * ay);
  if (h <= L(2.0) * ay)
    {
      _Float128 delta = h - ay;
      t1 = ax * (L(2.0) * delta - ax);
      t2 = (delta - L(2.0) * (ax - ay)) * delta;
    }
  else
    {
      _Float128 delta = h - ax;
      t1 = L(2.0) * delta * (ax - L(2.0) * ay);
      t2 = (L(4.0) * delta - ay) * ay + delta * delta;
    }

  h -= (t1 + t2) / (L(2.0) * h);
  return h;
}

_Float128
__ieee754_hypotl(_Float128 x, _Float128 y)
{
  if (!isfinite(x) || !isfinite(y))
    {
      if ((isinf (x) || isinf (y))
	  && !issignaling (x) && !issignaling (y))
	return INFINITY;
      return x + y;
    }

  x = fabsl (x);
  y = fabsl (y);

  _Float128 ax = x < y ? y : x;
  _Float128 ay = x < y ? x : y;

  /* If ax is huge, scale both inputs down.  */
  if (__glibc_unlikely (ax > LARGE_VAL))
    {
      if (__glibc_unlikely (ay <= ax * EPS))
	return ax + ay;

      return kernel (ax * SCALE, ay * SCALE) / SCALE;
    }

  /* If ay is tiny, scale both inputs up.  */
  if (__glibc_unlikely (ay < TINY_VAL))
    {
      if (__glibc_unlikely (ax >= ay / EPS))
	return ax + ay;

      ax = kernel (ax / SCALE, ay / SCALE) * SCALE;
      math_check_force_underflow_nonneg (ax);
      return ax;
    }

  /* Common case: ax is not huge and ay is not tiny.  */
  if (__glibc_unlikely (ay <= ax * EPS))
    return ax + ay;

  return kernel (ax, ay);
}
libm_alias_finite (__ieee754_hypotl, __hypotl)