adtools/clib2

/*
 * $Id: math_sqrtf.c,v 1.3 2006-01-08 12:04:24 obarthel Exp $
 *
 * :ts=4
 *
 * Portable ISO 'C' (1994) runtime library for the Amiga computer
 * Copyright (c) 2002-2015 by Olaf Barthel <obarthel (at) gmx.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:
 *
 *   - Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *
 *   - Neither the name of Olaf Barthel nor the names of contributors
 *     may be used to endorse or promote products derived from this
 *     software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT OWNER 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.
 *
 *
 * PowerPC math library based in part on work by Sun Microsystems
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * 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.
 *
 *
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

#ifndef _MATH_HEADERS_H
#include "math_headers.h"
#endif /* _MATH_HEADERS_H */

/****************************************************************************/

#if defined(FLOATING_POINT_SUPPORT)

/****************************************************************************/

static    const float    one    = 1.0, tiny=1.0e-30;

float
sqrtf(float x)
{
    volatile float z;    /* to prevent GCC from optimizing it away */
    LONG    sign = (LONG)0x80000000U; 
    ULONG r;
    LONG ix,s,q,m,t,i;

    GET_FLOAT_WORD(ix,x);

    /* take care of Inf and NaN */
    if((ix&0x7f800000)==0x7f800000) {            
        return x*x+x;        /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
                       sqrt(-inf)=sNaN */
    } 
    /* take care of zero */
    if(ix<=0) {
        if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
        else if(ix<0)
        return (x-x)/(x-x);        /* sqrt(-ve) = sNaN */
    }
    /* normalize x */
    m = (ix>>23);
    if(m==0) {                /* subnormal x */
        for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
        m -= i-1;
    }
    m -= 127;    /* unbias exponent */
    ix = (ix&0x007fffff)|0x00800000;
    if(m&1)    /* odd m, double x to make it even */
        ix += ix;
    m >>= 1;    /* m = [m/2] */

    /* generate sqrt(x) bit by bit */
    ix += ix;
    q = s = 0;        /* q = sqrt(x) */
    r = 0x01000000;        /* r = moving bit from right to left */

    while(r!=0) {
        t = s+r; 
        if(t<=ix) { 
        s    = t+r; 
        ix  -= t; 
        q   += r; 
        } 
        ix += ix;
        r>>=1;
    }

    /* use floating add to find out rounding direction */
    if(ix!=0) {
        z = one-tiny; /* trigger inexact flag */
        if (z>=one) {
            z = one+tiny;
        if (z>one)
            q += 2;
        else
            q += (q&1);
        }
    }
    ix = (q>>1)+0x3f000000;
    ix += (m <<23);
    SET_FLOAT_WORD(z,ix);
    return z;
}

/****************************************************************************/

#endif /* FLOATING_POINT_SUPPORT */