/*-
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.
 *
 * 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.
 * ====================================================
 *
 * The argument reduction and testing for exceptional cases was
 * written by Steven G. Kargl with input from Bruce D. Evans
 * and David A. Schultz.
 */

#include <float.h>
#include <ieeefp.h>
#include <math.h>

#include "math_private.h"

#define BIAS    (LDBL_MAX_EXP - 1)

static const unsigned
    B1 = 709958130;     /* B1 = (127-127.0/3-0.03306235651)*2**23 */

long double
cbrtl(long double x)
{
        long double v, r, s, t, w;
        double dr, dt, dx;
        float ft, fx;
        uint32_t hx, lx;
        uint16_t expsign, es;
        int k;
        volatile double vd1, vd2;

        GET_LDOUBLE_EXP(expsign,x);
        k = expsign & 0x7fff;

        /*
         * If x = +-Inf, then cbrt(x) = +-Inf.
         * If x = NaN, then cbrt(x) = NaN.
         */
        if (k == BIAS + LDBL_MAX_EXP)
                return (x + x);

        if (k == 0) {
                /* If x = +-0, then cbrt(x) = +-0. */
                GET_LDOUBLE_WORDS(es,hx,lx,x);
                if ((hx|lx) == 0) {
                        return (x);
                }
                /* Adjust subnormal numbers. */
                x *= 0x1.0p514;
                GET_LDOUBLE_EXP(k,x);
                k &= 0x7fff;
                k -= BIAS + 514;
        } else
                k -= BIAS;
        SET_LDOUBLE_EXP(x,BIAS);
        v = 1;

        switch (k % 3) {
        case 1:
        case -2:
                x = 2*x;
                k--;
                break;
        case 2:
        case -1:
                x = 4*x;
                k -= 2;
                break;
        }
        SET_LDOUBLE_EXP(v, (expsign & 0x8000) | (BIAS + k / 3));

        /*
         * The following is the guts of s_cbrtf, with the handling of
         * special values removed and extra care for accuracy not taken,
         * but with most of the extra accuracy not discarded.
         */

        /* ~5-bit estimate: */
        fx = x;
        GET_FLOAT_WORD(hx, fx);
        SET_FLOAT_WORD(ft, ((hx & 0x7fffffff) / 3 + B1));

        /* ~16-bit estimate: */
        dx = x;
        dt = ft;
        dr = dt * dt * dt;
        dt = dt * (dx + dx + dr) / (dx + dr + dr);

        /* ~47-bit estimate: */
        dr = dt * dt * dt;
        dt = dt * (dx + dx + dr) / (dx + dr + dr);

        /*
         * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8).
         * Round it away from zero to 32 bits (32 so that t*t is exact, and
         * away from zero for technical reasons).
         */
        vd2 = 0x1.0p32;
        vd1 = 0x1.0p-31;
        #define vd ((long double)vd2 + vd1)

        t = dt + vd - 0x1.0p32;

        /*
         * Final step Newton iteration to 64 or 113 bits with
         * error < 0.667 ulps
         */
        s=t*t;                          /* t*t is exact */
        r=x/s;                          /* error <= 0.5 ulps; |r| < |t| */
        w=t+t;                          /* t+t is exact */
        r=(r-t)/(w+r);                  /* r-t is exact; w+r ~= 3*t */
        t=t+t*r;                        /* error <= 0.5 + 0.5/3 + epsilon */

        t *= v;
        return (t);
}