/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License, Version 1.0 only
 * (the "License").  You may not use this file except in compliance
 * with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2003 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#include "quad.h"

static const double C[] = {
        0.0,
        0.5,
        1.0,
        68719476736.0,
        536870912.0,
        48.0,
        16.0,
        1.52587890625000000000e-05,
        2.86102294921875000000e-06,
        5.96046447753906250000e-08,
        3.72529029846191406250e-09,
        1.70530256582424044609e-13,
        7.10542735760100185871e-15,
        8.67361737988403547206e-19,
        2.16840434497100886801e-19,
        1.27054942088145050860e-21,
        1.21169035041947413311e-27,
        9.62964972193617926528e-35,
        4.70197740328915003187e-38
};

#define zero            C[0]
#define half            C[1]
#define one             C[2]
#define two36           C[3]
#define two29           C[4]
#define three2p4        C[5]
#define two4            C[6]
#define twom16          C[7]
#define three2m20       C[8]
#define twom24          C[9]
#define twom28          C[10]
#define three2m44       C[11]
#define twom47          C[12]
#define twom60          C[13]
#define twom62          C[14]
#define three2m71       C[15]
#define three2m91       C[16]
#define twom113         C[17]
#define twom124         C[18]

static const unsigned
        fsr_re = 0x00000000u,
        fsr_rn = 0xc0000000u;

#ifdef __sparcv9

/*
 * _Qp_sqrt(pz, x) sets *pz = sqrt(*x).
 */
void
_Qp_sqrt(union longdouble *pz, const union longdouble *x)

#else

/*
 * _Q_sqrt(x) returns sqrt(*x).
 */
union longdouble
_Q_sqrt(const union longdouble *x)

#endif  /* __sparcv9 */

{
        union longdouble        z;
        union xdouble           u;
        double                  c, d, rr, r[2], tt[3], xx[4], zz[5];
        unsigned int            xm, fsr, lx, wx[3];
        unsigned int            msw, frac2, frac3, frac4, rm;
        int                     ex, ez;

        if (QUAD_ISZERO(*x)) {
                Z = *x;
                QUAD_RETURN(Z);
        }

        xm = x->l.msw;

        __quad_getfsrp(&fsr);

        /* handle nan and inf cases */
        if ((xm & 0x7fffffff) >= 0x7fff0000) {
                if ((x->l.msw & 0xffff) | x->l.frac2 | x->l.frac3 |
                    x->l.frac4) {
                        if (!(x->l.msw & 0x8000)) {
                                /* snan, signal invalid */
                                if (fsr & FSR_NVM) {
                                        __quad_fsqrtq(x, &Z);
                                } else {
                                        Z = *x;
                                        Z.l.msw |= 0x8000;
                                        fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
                                            FSR_NVC;
                                        __quad_setfsrp(&fsr);
                                }
                                QUAD_RETURN(Z);
                        }
                        Z = *x;
                        QUAD_RETURN(Z);
                }
                if (x->l.msw & 0x80000000) {
                        /* sqrt(-inf), signal invalid */
                        if (fsr & FSR_NVM) {
                                __quad_fsqrtq(x, &Z);
                        } else {
                                Z.l.msw = 0x7fffffff;
                                Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0xffffffff;
                                fsr = (fsr & ~FSR_CEXC) | FSR_NVA | FSR_NVC;
                                __quad_setfsrp(&fsr);
                        }
                        QUAD_RETURN(Z);
                }
                /* sqrt(inf), return inf */
                Z = *x;
                QUAD_RETURN(Z);
        }

        /* handle negative numbers */
        if (xm & 0x80000000) {
                if (fsr & FSR_NVM) {
                        __quad_fsqrtq(x, &Z);
                } else {
                        Z.l.msw = 0x7fffffff;
                        Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0xffffffff;
                        fsr = (fsr & ~FSR_CEXC) | FSR_NVA | FSR_NVC;
                        __quad_setfsrp(&fsr);
                }
                QUAD_RETURN(Z);
        }

        /* now x is finite, positive */
        __quad_setfsrp((unsigned *)&fsr_re);

        /* get the normalized significand and exponent */
        ex = (int)(xm >> 16);
        lx = xm & 0xffff;
        if (ex) {
                lx |= 0x10000;
                wx[0] = x->l.frac2;
                wx[1] = x->l.frac3;
                wx[2] = x->l.frac4;
        } else {
                if (lx | (x->l.frac2 & 0xfffe0000)) {
                        wx[0] = x->l.frac2;
                        wx[1] = x->l.frac3;
                        wx[2] = x->l.frac4;
                        ex = 1;
                } else if (x->l.frac2 | (x->l.frac3 & 0xfffe0000)) {
                        lx = x->l.frac2;
                        wx[0] = x->l.frac3;
                        wx[1] = x->l.frac4;
                        wx[2] = 0;
                        ex = -31;
                } else if (x->l.frac3 | (x->l.frac4 & 0xfffe0000)) {
                        lx = x->l.frac3;
                        wx[0] = x->l.frac4;
                        wx[1] = wx[2] = 0;
                        ex = -63;
                } else {
                        lx = x->l.frac4;
                        wx[0] = wx[1] = wx[2] = 0;
                        ex = -95;
                }
                while ((lx & 0x10000) == 0) {
                        lx = (lx << 1) | (wx[0] >> 31);
                        wx[0] = (wx[0] << 1) | (wx[1] >> 31);
                        wx[1] = (wx[1] << 1) | (wx[2] >> 31);
                        wx[2] <<= 1;
                        ex--;
                }
        }
        ez = ex - 0x3fff;
        if (ez & 1) {
                /* make exponent even */
                lx = (lx << 1) | (wx[0] >> 31);
                wx[0] = (wx[0] << 1) | (wx[1] >> 31);
                wx[1] = (wx[1] << 1) | (wx[2] >> 31);
                wx[2] <<= 1;
                ez--;
        }

        /* extract the significands into doubles */
        c = twom16;
        xx[0] = (double)((int)lx) * c;

        c *= twom24;
        xx[0] += (double)((int)(wx[0] >> 8)) * c;

        c *= twom24;
        xx[1] = (double)((int)(((wx[0] << 16) | (wx[1] >> 16)) &
            0xffffff)) * c;

        c *= twom24;
        xx[2] = (double)((int)(((wx[1] << 8) | (wx[2] >> 24)) &
            0xffffff)) * c;

        c *= twom24;
        xx[3] = (double)((int)(wx[2] & 0xffffff)) * c;

        /* approximate the divisor for the Newton iteration */
        c = xx[0] + xx[1];
        c = __quad_dp_sqrt(&c);
        rr = half / c;

        /* compute the first five "digits" of the square root */
        zz[0] = (c + two29) - two29;
        tt[0] = zz[0] + zz[0];
        r[0] = (xx[0] - zz[0] * zz[0]) + xx[1];

        zz[1] = (rr * (r[0] + xx[2]) + three2p4) - three2p4;
        tt[1] = zz[1] + zz[1];
        r[0] -= tt[0] * zz[1];
        r[1] = xx[2] - zz[1] * zz[1];
        c = (r[1] + three2m20) - three2m20;
        r[0] += c;
        r[1] = (r[1] - c) + xx[3];

        zz[2] = (rr * (r[0] + r[1]) + three2m20) - three2m20;
        tt[2] = zz[2] + zz[2];
        r[0] -= tt[0] * zz[2];
        r[1] -= tt[1] * zz[2];
        c = (r[1] + three2m44) - three2m44;
        r[0] += c;
        r[1] = (r[1] - c) - zz[2] * zz[2];

        zz[3] = (rr * (r[0] + r[1]) + three2m44) - three2m44;
        r[0] = ((r[0] - tt[0] * zz[3]) + r[1]) - tt[1] * zz[3];
        r[1] = -tt[2] * zz[3];
        c = (r[1] + three2m91) - three2m91;
        r[0] += c;
        r[1] = (r[1] - c) - zz[3] * zz[3];

        zz[4] = (rr * (r[0] + r[1]) + three2m71) - three2m71;

        /* reduce to three doubles, making sure zz[1] is positive */
        zz[0] += zz[1] - twom47;
        zz[1] = twom47 + zz[2] + zz[3];
        zz[2] = zz[4];

        /* if the third term might lie on a rounding boundary, perturb it */
        if (zz[2] == (twom62 + zz[2]) - twom62) {
                /* here we just need to get the sign of the remainder */
                c = (((((r[0] - tt[0] * zz[4]) - tt[1] * zz[4]) + r[1])
                    - tt[2] * zz[4]) - (zz[3] + zz[3]) * zz[4]) - zz[4] * zz[4];
                if (c < zero)
                        zz[2] -= twom124;
                else if (c > zero)
                        zz[2] += twom124;
        }

        /*
         * propagate carries/borrows, using round-to-negative-infinity mode
         * to make all terms nonnegative (note that we can't encounter a
         * borrow so large that the roundoff is unrepresentable because
         * we took care to make zz[1] positive above)
         */
        __quad_setfsrp(&fsr_rn);
        c = zz[1] + zz[2];
        zz[2] += (zz[1] - c);
        zz[1] = c;
        c = zz[0] + zz[1];
        zz[1] += (zz[0] - c);
        zz[0] = c;

        /* adjust exponent and strip off integer bit */
        ez = (ez >> 1) + 0x3fff;
        zz[0] -= one;

        /* the first 48 bits of fraction come from zz[0] */
        u.d = d = two36 + zz[0];
        msw = u.l.lo;
        zz[0] -= (d - two36);

        u.d = d = two4 + zz[0];
        frac2 = u.l.lo;
        zz[0] -= (d - two4);

        /* the next 32 come from zz[0] and zz[1] */
        u.d = d = twom28 + (zz[0] + zz[1]);
        frac3 = u.l.lo;
        zz[0] -= (d - twom28);

        /* condense the remaining fraction; errors here won't matter */
        c = zz[0] + zz[1];
        zz[1] = ((zz[0] - c) + zz[1]) + zz[2];
        zz[0] = c;

        /* get the last word of fraction */
        u.d = d = twom60 + (zz[0] + zz[1]);
        frac4 = u.l.lo;
        zz[0] -= (d - twom60);

        /* keep track of what's left for rounding; note that the error */
        /* in computing c will be non-negative due to rounding mode */
        c = zz[0] + zz[1];

        /* get the rounding mode */
        rm = fsr >> 30;

        /* round and raise exceptions */
        fsr &= ~FSR_CEXC;
        if (c != zero) {
                fsr |= FSR_NXC;

                /* decide whether to round the fraction up */
                if (rm == FSR_RP || (rm == FSR_RN && (c > twom113 ||
                    (c == twom113 && ((frac4 & 1) || (c - zz[0] != zz[1])))))) {
                        /* round up and renormalize if necessary */
                        if (++frac4 == 0)
                                if (++frac3 == 0)
                                        if (++frac2 == 0)
                                                if (++msw == 0x10000) {
                                                        msw = 0;
                                                        ez++;
                                                }
                }
        }

        /* stow the result */
        z.l.msw = (ez << 16) | msw;
        z.l.frac2 = frac2;
        z.l.frac3 = frac3;
        z.l.frac4 = frac4;

        if ((fsr & FSR_CEXC) & (fsr >> 23)) {
                __quad_setfsrp(&fsr);
                __quad_fsqrtq(x, &Z);
        } else {
                Z = z;
                fsr |= (fsr & 0x1f) << 5;
                __quad_setfsrp(&fsr);
        }
        QUAD_RETURN(Z);
}