text: /*
   *                               POK header
   *
   * The following file is a part of the POK project. Any modification should
   * be made according to the POK licence. You CANNOT use this file or a part
   * of a file for your own project.
   *
   * For more information on the POK licence, please see our LICENCE FILE
   *
   * Please follow the coding guidelines described in doc/CODING_GUIDELINES
   *
   *                                      Copyright (c) 2007-2022 POK team
   */
  
  /* @(#)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*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
   *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
   *	yy1= y with lower 32 bits chopped, y2 = y-yy1.
   *
   *	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)
   */
  
  #ifdef POK_NEEDS_LIBMATH
  
  #include "math_private.h"
  
  double __ieee754_hypot(double x, double y) {
    double a = x, b = y, t1, t2, yy1, 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 (ha > 0x5f300000) {    /* a>2**500 */
      if (ha >= 0x7ff00000) { /* Inf or NaN */
        uint32_t low;
        w = a + b; /* for sNaN */
        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 (hb < 0x20b00000) {    /* b < 2**-500 */
      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;
      } 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 = __ieee754_sqrt(t1 * t1 - (b * (-b) - t2 * (a + t1)));
    } else {
      a = a + a;
      yy1 = 0;
      SET_HIGH_WORD(yy1, hb);
      y2 = b - yy1;
      t1 = 0;
      SET_HIGH_WORD(t1, ha + 0x00100000);
      t2 = a - t1;
      w = __ieee754_sqrt(t1 * yy1 - (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));
      return t1 * w;
    } else
      return w;
  }
  
  #endif
  