fusl/src/math/hypot.c

#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);
}