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
sq(double_t * hi,double_t * lo,double x)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
hypot(double x,double y)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