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/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* cbrtf(x)
* Return cube root of x
*/
#include <math.h> // for double_t, cbrtf
#include <stdint.h> // for uint32_t
static const unsigned B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23
*/
B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
float cbrtf(float x)
{
double_t r, T;
union {
float f;
uint32_t i;
} u = { x };
uint32_t hx = u.i & 0x7fffffff;
if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */
return x + x;
/* rough cbrt to 5 bits */
if (hx < 0x00800000) { /* zero or subnormal? */
if (hx == 0)
return x; /* cbrt(+-0) is itself */
u.f = x * 0x1p24f;
hx = u.i & 0x7fffffff;
hx = hx / 3 + B2;
} else
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 = u.f;
r = T * T * T;
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_t)x + x + r) / (x + r + r);
/* rounding to 24 bits is perfect in round-to-nearest mode */
return T;
}
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