/*      $OpenBSD: s_fmal.c,v 1.3 2013/11/12 19:00:38 martynas Exp $     */

/*-
 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

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

/*
 * Fused multiply-add: Compute x * y + z with a single rounding error.
 *
 * We use scaling to avoid overflow/underflow, along with the
 * canonical precision-doubling technique adapted from:
 *
 *      Dekker, T.  A Floating-Point Technique for Extending the
 *      Available Precision.  Numer. Math. 18, 224-242 (1971).
 */
long double
fmal(long double x, long double y, long double z)
{
#if LDBL_MANT_DIG == 64
        static const long double split = 0x1p32L + 1.0;
#elif LDBL_MANT_DIG == 113
        static const long double split = 0x1p57L + 1.0;
#endif
        long double xs, ys, zs;
        long double c, cc, hx, hy, p, q, tx, ty;
        long double r, rr, s;
        int oround;
        int ex, ey, ez;
        int spread;

        /*
         * Handle special cases. The order of operations and the particular
         * return values here are crucial in handling special cases involving
         * infinities, NaNs, overflows, and signed zeroes correctly.
         */
        if (x == 0.0 || y == 0.0)
                return (x * y + z);
        if (z == 0.0)
                return (x * y);
        if (!isfinite(x) || !isfinite(y))
                return (x * y + z);
        if (!isfinite(z))
                return (z);

        xs = frexpl(x, &ex);
        ys = frexpl(y, &ey);
        zs = frexpl(z, &ez);
        oround = fegetround();
        spread = ex + ey - ez;

        /*
         * If x * y and z are many orders of magnitude apart, the scaling
         * will overflow, so we handle these cases specially.  Rounding
         * modes other than FE_TONEAREST are painful.
         */
        if (spread > LDBL_MANT_DIG * 2) {
                fenv_t env;
                feraiseexcept(FE_INEXACT);
                switch(oround) {
                case FE_TONEAREST:
                        return (x * y);
                case FE_TOWARDZERO:
                        if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
                                return (x * y);
                        feholdexcept(&env);
                        r = x * y;
                        if (!fetestexcept(FE_INEXACT))
                                r = nextafterl(r, 0);
                        feupdateenv(&env);
                        return (r);
                case FE_DOWNWARD:
                        if (z > 0.0)
                                return (x * y);
                        feholdexcept(&env);
                        r = x * y;
                        if (!fetestexcept(FE_INEXACT))
                                r = nextafterl(r, -INFINITY);
                        feupdateenv(&env);
                        return (r);
                default:        /* FE_UPWARD */
                        if (z < 0.0)
                                return (x * y);
                        feholdexcept(&env);
                        r = x * y;
                        if (!fetestexcept(FE_INEXACT))
                                r = nextafterl(r, INFINITY);
                        feupdateenv(&env);
                        return (r);
                }
        }
        if (spread < -LDBL_MANT_DIG) {
                feraiseexcept(FE_INEXACT);
                if (!isnormal(z))
                        feraiseexcept(FE_UNDERFLOW);
                switch (oround) {
                case FE_TONEAREST:
                        return (z);
                case FE_TOWARDZERO:
                        if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0))
                                return (z);
                        else
                                return (nextafterl(z, 0));
                case FE_DOWNWARD:
                        if ((x > 0.0) ^ (y < 0.0))
                                return (z);
                        else
                                return (nextafterl(z, -INFINITY));
                default:        /* FE_UPWARD */
                        if ((x > 0.0) ^ (y < 0.0))
                                return (nextafterl(z, INFINITY));
                        else
                                return (z);
                }
        }

        /*
         * Use Dekker's algorithm to perform the multiplication and
         * subsequent addition in twice the machine precision.
         * Arrange so that x * y = c + cc, and x * y + z = r + rr.
         */
        fesetround(FE_TONEAREST);

        p = xs * split;
        hx = xs - p;
        hx += p;
        tx = xs - hx;

        p = ys * split;
        hy = ys - p;
        hy += p;
        ty = ys - hy;

        p = hx * hy;
        q = hx * ty + tx * hy;
        c = p + q;
        cc = p - c + q + tx * ty;

        zs = ldexpl(zs, -spread);
        r = c + zs;
        s = r - c;
        rr = (c - (r - s)) + (zs - s) + cc;

        spread = ex + ey;
        if (spread + ilogbl(r) > -16383) {
                fesetround(oround);
                r = r + rr;
        } else {
                /*
                 * The result is subnormal, so we round before scaling to
                 * avoid double rounding.
                 */
                p = ldexpl(copysignl(0x1p-16382L, r), -spread);
                c = r + p;
                s = c - r;
                cc = (r - (c - s)) + (p - s) + rr;
                fesetround(oround);
                r = (c + cc) - p;
        }
        return (ldexpl(r, spread));
}