ceil.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_ceil.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  ceil.c
 * @brief Ceiling function
 */

#include "prim.h"

static const double huge = 1.0e300;

/**
 * @brief   Ceiling function
 * @param   x
 * @returns x rounded toward -inf to integral value
 * @details
 * <pre>
 * Method
 *     Bit twiddling
 * 
 * Exception
 *     Inexact flag raised if x not equal to ceil(x).
 * </pre>
 */
double ceil(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=0x80000000;
                    i1=0;
                }
                else if((i0|i1)!=0) {
                    i0=0x3ff00000;
                    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));
                    // NOTICE: Is this a correct cast?
                    if((int32_t)j<(int32_t)i1) i0+=1;   /* got a carry */
                    i1 = j;
                }
            }
            i1 &= (~i);
        }
    }
    INSERT_WORDS(x,i0,i1);
    return x;
}