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| | #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);
}
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