hypot.c raw

   1  #include <math.h>
   2  #include <stdint.h>
   3  #include <float.h>
   4  
   5  #if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
   6  #define SPLIT (0x1p32 + 1)
   7  #else
   8  #define SPLIT (0x1p27 + 1)
   9  #endif
  10  
  11  static void sq(double_t *hi, double_t *lo, double x)
  12  {
  13  	double_t xh, xl, xc;
  14  
  15  	xc = (double_t)x*SPLIT;
  16  	xh = x - xc + xc;
  17  	xl = x - xh;
  18  	*hi = (double_t)x*x;
  19  	*lo = xh*xh - *hi + 2*xh*xl + xl*xl;
  20  }
  21  
  22  double hypot(double x, double y)
  23  {
  24  	union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
  25  	int ex, ey;
  26  	double_t hx, lx, hy, ly, z;
  27  
  28  	/* arrange |x| >= |y| */
  29  	ux.i &= -1ULL>>1;
  30  	uy.i &= -1ULL>>1;
  31  	if (ux.i < uy.i) {
  32  		ut = ux;
  33  		ux = uy;
  34  		uy = ut;
  35  	}
  36  
  37  	/* special cases */
  38  	ex = ux.i>>52;
  39  	ey = uy.i>>52;
  40  	x = ux.f;
  41  	y = uy.f;
  42  	/* note: hypot(inf,nan) == inf */
  43  	if (ey == 0x7ff)
  44  		return y;
  45  	if (ex == 0x7ff || uy.i == 0)
  46  		return x;
  47  	/* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
  48  	/* 64 difference is enough for ld80 double_t */
  49  	if (ex - ey > 64)
  50  		return x + y;
  51  
  52  	/* precise sqrt argument in nearest rounding mode without overflow */
  53  	/* xh*xh must not overflow and xl*xl must not underflow in sq */
  54  	z = 1;
  55  	if (ex > 0x3ff+510) {
  56  		z = 0x1p700;
  57  		x *= 0x1p-700;
  58  		y *= 0x1p-700;
  59  	} else if (ey < 0x3ff-450) {
  60  		z = 0x1p-700;
  61  		x *= 0x1p700;
  62  		y *= 0x1p700;
  63  	}
  64  	sq(&hx, &lx, x);
  65  	sq(&hy, &ly, y);
  66  	return z*sqrt(ly+lx+hy+hx);
  67  }
  68