src/math/hypot.c

   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
  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
  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 }