* Return cube root of x
*/
-#include "libm.h"
+#include <math.h>
+#include <stdint.h>
static const unsigned
B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
float cbrtf(float x)
{
- double r,T;
- float t;
- int32_t hx;
- uint32_t sign;
- uint32_t high;
+ double_t r,T;
+ union {float f; uint32_t i;} u = {x};
+ uint32_t hx = u.i & 0x7fffffff;
- GET_FLOAT_WORD(hx, x);
- sign = hx & 0x80000000;
- hx ^= sign;
if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */
return x + x;
if (hx < 0x00800000) { /* zero or subnormal? */
if (hx == 0)
return x; /* cbrt(+-0) is itself */
- SET_FLOAT_WORD(t, 0x4b800000); /* set t = 2**24 */
- t *= x;
- GET_FLOAT_WORD(high, t);
- SET_FLOAT_WORD(t, sign|((high&0x7fffffff)/3+B2));
+ u.f = x*0x1p24f;
+ hx = u.i & 0x7fffffff;
+ hx = hx/3 + B2;
} else
- SET_FLOAT_WORD(t, sign|(hx/3+B1));
+ hx = hx/3 + B1;
+ u.i &= 0x80000000;
+ u.i |= hx;
/*
* First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
* double precision so that its terms can be arranged for efficiency
* without causing overflow or underflow.
*/
- T = t;
+ T = u.f;
r = T*T*T;
- T = T*((double)x+x+r)/(x+r+r);
+ T = T*((double_t)x+x+r)/(x+r+r);
/*
* Second step Newton iteration to 47 bits. In double precision for
* efficiency and accuracy.
*/
r = T*T*T;
- T = T*((double)x+x+r)/(x+r+r);
+ T = T*((double_t)x+x+r)/(x+r+r);
/* rounding to 24 bits is perfect in round-to-nearest mode */
return T;