#include <math.h>
#include <stdint.h>
#include <float.h>

#if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
#define SPLIT (0x1p32 + 1)
#else
#define SPLIT (0x1p27 + 1)
#endif

static void sq(double_t *hi, double_t *lo, double x)
{
        double_t xh, xl, xc;

        xc = (double_t)x*SPLIT;
        xh = x - xc + xc;
        xl = x - xh;
        *hi = (double_t)x*x;
        *lo = xh*xh - *hi + 2*xh*xl + xl*xl;
}

double hypot(double x, double y)
{
        union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
        int ex, ey;
        double_t hx, lx, hy, ly, z;

        /* arrange |x| >= |y| */
        ux.i &= -1ULL>>1;
        uy.i &= -1ULL>>1;
        if (ux.i < uy.i) {
                ut = ux;
                ux = uy;
                uy = ut;
        }

        /* special cases */
        ex = ux.i>>52;
        ey = uy.i>>52;
        x = ux.f;
        y = uy.f;
        /* note: hypot(inf,nan) == inf */
        if (ey == 0x7ff)
                return y;
        if (ex == 0x7ff || uy.i == 0)
                return x;
        /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
        /* 64 difference is enough for ld80 double_t */
        if (ex - ey > 64)
                return x + y;

        /* precise sqrt argument in nearest rounding mode without overflow */
        /* xh*xh must not overflow and xl*xl must not underflow in sq */
        z = 1;
        if (ex > 0x3ff+510) {
                z = 0x1p700;
                x *= 0x1p-700;
                y *= 0x1p-700;
        } else if (ey < 0x3ff-450) {
                z = 0x1p-700;
                x *= 0x1p700;
                y *= 0x1p700;
        }
        sq(&hx, &lx, x);
        sq(&hy, &ly, y);
        return z*sqrt(ly+lx+hy+hx);
}