/* @(#)e_hypot.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

/* __ieee754_hypot(x,y)

 *

 * Method :

 *	If (assume round-to-nearest) z=x*x+y*y

 *	has error less than sqrt(2)/2 ulp, than

 *	sqrt(z) has error less than 1 ulp (exercise).

 *

 *	So, compute sqrt(x*x+y*y) with some care as

 *	follows to get the error below 1 ulp:

 *

 *	Assume x>y>0;

 *	(if possible, set rounding to round-to-nearest)

 *	1. if x > 2y  use

 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y

 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else

 *	2. if x <= 2y use

 *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))

 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,

 *	y1= y with lower 32 bits chopped, y2 = y-y1.

 *

 *	NOTE: scaling may be necessary if some argument is too

 *	      large or too tiny

 *

 * Special cases:

 *	hypot(x,y) is INF if x or y is +INF or -INF; else

 *	hypot(x,y) is NAN if x or y is NAN.

 *

 * Accuracy:

 *	hypot(x,y) returns sqrt(x^2+y^2) with error less

 *	than 1 ulps (units in the last place)

 */

#include <math.h>

#include <math_private.h>

#include <math-underflow.h>

double

__ieee754_hypot (double x, double y)

{

  double a, b, t1, t2, y1, y2, w;

  int32_t j, k, ha, hb;

  GET_HIGH_WORD (ha, x);

  ha &= 0x7fffffff;

  GET_HIGH_WORD (hb, y);

  hb &= 0x7fffffff;

  if (hb > ha)

    {

      a = y; b = x; j = ha; ha = hb; hb = j;

    }

  else

    {

      a = x; b = y;

    }

  SET_HIGH_WORD (a, ha);        /* a <- |a| */

  SET_HIGH_WORD (b, hb);        /* b <- |b| */

  if ((ha - hb) > 0x3c00000)

    {

      return a + b;

    }                                       /* x/y > 2**60 */

  k = 0;

  if (__glibc_unlikely (ha > 0x5f300000))                  /* a>2**500 */

    {

      if (ha >= 0x7ff00000)             /* Inf or NaN */

	{

	  uint32_t low;

	  w = a + b;                    /* for sNaN */

	  if (issignaling (a) || issignaling (b))

	    return w;

	  GET_LOW_WORD (low, a);

	  if (((ha & 0xfffff) | low) == 0)

	    w = a;

	  GET_LOW_WORD (low, b);

	  if (((hb ^ 0x7ff00000) | low) == 0)

	    w = b;

	  return w;

	}

      /* scale a and b by 2**-600 */

      ha -= 0x25800000; hb -= 0x25800000;  k += 600;

      SET_HIGH_WORD (a, ha);

      SET_HIGH_WORD (b, hb);

    }

  if (__builtin_expect (hb < 0x23d00000, 0))            /* b < 2**-450 */

    {

      if (hb <= 0x000fffff)             /* subnormal b or 0 */

	{

	  uint32_t low;

	  GET_LOW_WORD (low, b);

	  if ((hb | low) == 0)

	    return a;

	  t1 = 0;

	  SET_HIGH_WORD (t1, 0x7fd00000);       /* t1=2^1022 */

	  b *= t1;

	  a *= t1;

	  k -= 1022;

	  GET_HIGH_WORD (ha, a);

	  GET_HIGH_WORD (hb, b);

	  if (hb > ha)

	    {

	      t1 = a;

	      a = b;

	      b = t1;

	      j = ha;

	      ha = hb;

	      hb = j;

	    }

	}

      else                      /* scale a and b by 2^600 */

	{

	  ha += 0x25800000;             /* a *= 2^600 */

	  hb += 0x25800000;             /* b *= 2^600 */

	  k -= 600;

	  SET_HIGH_WORD (a, ha);

	  SET_HIGH_WORD (b, hb);

	}

    }

  /* medium size a and b */

  w = a - b;

  if (w > b)

    {

      t1 = 0;

      SET_HIGH_WORD (t1, ha);

      t2 = a - t1;

      w = sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));

    }

  else

    {

      a = a + a;

      y1 = 0;

      SET_HIGH_WORD (y1, hb);

      y2 = b - y1;

      t1 = 0;

      SET_HIGH_WORD (t1, ha + 0x00100000);

      t2 = a - t1;

      w = sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));

    }

  if (k != 0)

    {

      uint32_t high;

      t1 = 1.0;

      GET_HIGH_WORD (high, t1);

      SET_HIGH_WORD (t1, high + (k << 20));

      w *= t1;

      math_check_force_underflow_nonneg (w);

      return w;

    }

  else

    return w;

}

strong_alias (__ieee754_hypot, __hypot_finite)