1*c9945492SAndroid Build Coastguard Worker #include <math.h>
2*c9945492SAndroid Build Coastguard Worker #include <stdint.h>
3*c9945492SAndroid Build Coastguard Worker #include <float.h>
4*c9945492SAndroid Build Coastguard Worker
5*c9945492SAndroid Build Coastguard Worker #if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
6*c9945492SAndroid Build Coastguard Worker #define SPLIT (0x1p32 + 1)
7*c9945492SAndroid Build Coastguard Worker #else
8*c9945492SAndroid Build Coastguard Worker #define SPLIT (0x1p27 + 1)
9*c9945492SAndroid Build Coastguard Worker #endif
10*c9945492SAndroid Build Coastguard Worker
sq(double_t * hi,double_t * lo,double x)11*c9945492SAndroid Build Coastguard Worker static void sq(double_t *hi, double_t *lo, double x)
12*c9945492SAndroid Build Coastguard Worker {
13*c9945492SAndroid Build Coastguard Worker double_t xh, xl, xc;
14*c9945492SAndroid Build Coastguard Worker
15*c9945492SAndroid Build Coastguard Worker xc = (double_t)x*SPLIT;
16*c9945492SAndroid Build Coastguard Worker xh = x - xc + xc;
17*c9945492SAndroid Build Coastguard Worker xl = x - xh;
18*c9945492SAndroid Build Coastguard Worker *hi = (double_t)x*x;
19*c9945492SAndroid Build Coastguard Worker *lo = xh*xh - *hi + 2*xh*xl + xl*xl;
20*c9945492SAndroid Build Coastguard Worker }
21*c9945492SAndroid Build Coastguard Worker
hypot(double x,double y)22*c9945492SAndroid Build Coastguard Worker double hypot(double x, double y)
23*c9945492SAndroid Build Coastguard Worker {
24*c9945492SAndroid Build Coastguard Worker union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
25*c9945492SAndroid Build Coastguard Worker int ex, ey;
26*c9945492SAndroid Build Coastguard Worker double_t hx, lx, hy, ly, z;
27*c9945492SAndroid Build Coastguard Worker
28*c9945492SAndroid Build Coastguard Worker /* arrange |x| >= |y| */
29*c9945492SAndroid Build Coastguard Worker ux.i &= -1ULL>>1;
30*c9945492SAndroid Build Coastguard Worker uy.i &= -1ULL>>1;
31*c9945492SAndroid Build Coastguard Worker if (ux.i < uy.i) {
32*c9945492SAndroid Build Coastguard Worker ut = ux;
33*c9945492SAndroid Build Coastguard Worker ux = uy;
34*c9945492SAndroid Build Coastguard Worker uy = ut;
35*c9945492SAndroid Build Coastguard Worker }
36*c9945492SAndroid Build Coastguard Worker
37*c9945492SAndroid Build Coastguard Worker /* special cases */
38*c9945492SAndroid Build Coastguard Worker ex = ux.i>>52;
39*c9945492SAndroid Build Coastguard Worker ey = uy.i>>52;
40*c9945492SAndroid Build Coastguard Worker x = ux.f;
41*c9945492SAndroid Build Coastguard Worker y = uy.f;
42*c9945492SAndroid Build Coastguard Worker /* note: hypot(inf,nan) == inf */
43*c9945492SAndroid Build Coastguard Worker if (ey == 0x7ff)
44*c9945492SAndroid Build Coastguard Worker return y;
45*c9945492SAndroid Build Coastguard Worker if (ex == 0x7ff || uy.i == 0)
46*c9945492SAndroid Build Coastguard Worker return x;
47*c9945492SAndroid Build Coastguard Worker /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
48*c9945492SAndroid Build Coastguard Worker /* 64 difference is enough for ld80 double_t */
49*c9945492SAndroid Build Coastguard Worker if (ex - ey > 64)
50*c9945492SAndroid Build Coastguard Worker return x + y;
51*c9945492SAndroid Build Coastguard Worker
52*c9945492SAndroid Build Coastguard Worker /* precise sqrt argument in nearest rounding mode without overflow */
53*c9945492SAndroid Build Coastguard Worker /* xh*xh must not overflow and xl*xl must not underflow in sq */
54*c9945492SAndroid Build Coastguard Worker z = 1;
55*c9945492SAndroid Build Coastguard Worker if (ex > 0x3ff+510) {
56*c9945492SAndroid Build Coastguard Worker z = 0x1p700;
57*c9945492SAndroid Build Coastguard Worker x *= 0x1p-700;
58*c9945492SAndroid Build Coastguard Worker y *= 0x1p-700;
59*c9945492SAndroid Build Coastguard Worker } else if (ey < 0x3ff-450) {
60*c9945492SAndroid Build Coastguard Worker z = 0x1p-700;
61*c9945492SAndroid Build Coastguard Worker x *= 0x1p700;
62*c9945492SAndroid Build Coastguard Worker y *= 0x1p700;
63*c9945492SAndroid Build Coastguard Worker }
64*c9945492SAndroid Build Coastguard Worker sq(&hx, &lx, x);
65*c9945492SAndroid Build Coastguard Worker sq(&hy, &ly, y);
66*c9945492SAndroid Build Coastguard Worker return z*sqrt(ly+lx+hy+hx);
67*c9945492SAndroid Build Coastguard Worker }
68