floor.c

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/*-
 * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
 * 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 ``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 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.
 *
 * Project homepage:
 * https://amath.innolan.net
 *
 * The original source code can be obtained from:
 * http://www.netlib.org/fdlibm/s_floor.c
 * 
 * =================================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * =================================================================
 */

/**
 * @file  floor.c
 * @brief Floor function
 */

#include "prim.h"

static const double huge = 1.0e300;

/**
 * @brief   Floor function
 * @return  x rounded toward -inf to integral value
 * @details 
 * <pre>
 * Method:
 *     Bit twiddling
 *
 * Exception:
 *     Inexact flag raised if x not equal to floor(x)
 * </pre>
 */
double floor(double x)
{
    int32_t i0, i1, j0;
    uint32_t i, j;
    EXTRACT_WORDS(i0, i1, x);
    j0 = ((i0 >> 20) & 0x7ff) - 0x3ff;
    if (j0 < 20)
    {
        if (j0 < 0)
        { /* raise inexact if x != 0 */
            if (huge + x > 0.0)
            { /* return 0*sign(x) if |x|<1 */
                if (i0 >= 0)
                {
                    i0 = i1 = 0;
                }
                else if (((i0 & 0x7fffffff) | i1) != 0)
                {
                    i0 = 0xbff00000;
                    i1 = 0;
                }
            }
        }
        else
        {
            i = (0x000fffff) >> j0;
            if (((i0 & i) | i1) == 0)
                return x; /* x is integral */
            if (huge + x > 0.0)
            { /* raise inexact flag */
                if (i0 < 0)
                    i0 += (0x00100000) >> j0;
                i0 &= (~i);
                i1 = 0;
            }
        }
    }
    else if (j0 > 51)
    {
        if (j0 == 0x400)
            return x + x; /* inf or NaN */
        else
            return x; /* x is integral */
    }
    else
    {
        i = ((uint32_t)(0xffffffff)) >> (j0 - 20);
        if ((i1 & i) == 0)
            return x; /* x is integral */
        if (huge + x > 0.0)
        { /* raise inexact flag */
            if (i0 < 0)
            {
                if (j0 == 20)
                    i0 += 1;
                else
                {
                    j = i1 + (1 << (52 - j0));
                    if (j < (uint32_t)i1)
                        i0 += 1; /* got a carry */
                    i1 = j;
                }
            }
            i1 &= (~i);
        }
    }
    INSERT_WORDS(x, i0, i1);
    return x;
}