glibc/sysdeps/ieee754/dbl-64/e_hypot.c

/* @(#)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>
#include <libm-alias-finite.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;
}
#ifndef __ieee754_hypot
libm_alias_finite (__ieee754_hypot, __hypot)
#endif