github.com/afumu/libc@v0.0.6/musl/src/math/hypot.c (about)

     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  }