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
11static 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
22double 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