amiga-clib2/library/math_sqrt.c

/*
 * :ts=4
 *
 * Portable ISO 'C' (1994) runtime library for the Amiga computer
 * Copyright (c) 2002-2025 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.
 */

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

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

#if defined(FLOATING_POINT_SUPPORT)

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

#if defined(IEEE_FLOATING_POINT_SUPPORT)

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

#if defined(__GNUC__)

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

#if defined(SMALL_DATA)
#define A4(x) "a4@(" #x ":W)"
#elif defined(SMALL_DATA32)
#define A4(x) "a4@(" #x ":L)"
#else
#define A4(x) #x
#endif /* SMALL_DATA */

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

extern double __sqrt(double x);

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

asm("

	.text
	.even

	.globl	_MathIeeeDoubTransBase
	.globl	___sqrt

___sqrt:

	movel	a6,sp@-
	movel	"A4(_MathIeeeDoubTransBase)",a6
	moveml	sp@(8),d0/d1
	jsr		a6@(-96:W)
	movel	sp@+,a6
	rts

");

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

#else

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

INLINE STATIC const double
__sqrt(double x)
{
	double result;

	result = IEEEDPSqrt(x);

	return(result);
}

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

#endif /* __GNUC__ */

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

#endif /* IEEE_FLOATING_POINT_SUPPORT */

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

#if defined(M68881_FLOATING_POINT_SUPPORT)

INLINE STATIC const double
__sqrt(double x)
{
	double result;

	__asm ("fsqrt%.x %1,%0"
	       : "=f" (result)
	       : "f" (x));

	return(result);
}

#endif /* M68881_FLOATING_POINT_SUPPORT */

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

#ifdef __PPC__

static	const double	one	= 1.0, tiny=1.0e-300;

INLINE STATIC double
__sqrt(double x)
{
	double z;
	unsigned int sign = (unsigned int)0x80000000; 
	unsigned int r,t1,s1,ix1,q1;
	int ix0,s0,q,m,t,i;

	EXTRACT_WORDS(ix0,ix1,x);

    /* take care of Inf and NaN */
	if((ix0&0x7ff00000)==0x7ff00000) {			
	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
					   sqrt(-inf)=sNaN */
	} 
    /* take care of zero */
	if(ix0<=0) {
	    if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
	    else if(ix0<0)
		return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
	}
    /* normalize x */
	m = (ix0>>20);
	if(m==0) {				/* subnormal x */
	    while(ix0==0) {
		m -= 21;
		ix0 |= (ix1>>11); ix1 <<= 21;
	    }
	    for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
	    m -= i-1;
	    ix0 |= (ix1>>(32-i));
	    ix1 <<= i;
	}
	m -= 1023;	/* unbias exponent */
	ix0 = (ix0&0x000fffff)|0x00100000;
	if(m&1){	/* odd m, double x to make it even */
	    ix0 += ix0 + ((ix1&sign)>>31);
	    ix1 += ix1;
	}
	m >>= 1;	/* m = [m/2] */

    /* generate sqrt(x) bit by bit */
	ix0 += ix0 + ((ix1&sign)>>31);
	ix1 += ix1;
	q = q1 = s0 = s1 = 0;	/* [q,q1] = sqrt(x) */
	r = 0x00200000;		/* r = moving bit from right to left */

	while(r!=0) {
	    t = s0+r; 
	    if(t<=ix0) { 
		s0   = t+r; 
		ix0 -= t; 
		q   += r; 
	    } 
	    ix0 += ix0 + ((ix1&sign)>>31);
	    ix1 += ix1;
	    r>>=1;
	}

	r = sign;
	while(r!=0) {
	    t1 = s1+r; 
	    t  = s0;
	    if((t<ix0)||((t==ix0)&&(t1<=ix1))) { 
		s1  = t1+r;
		if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
		ix0 -= t;
		if (ix1 < t1) ix0 -= 1;
		ix1 -= t1;
		q1  += r;
	    }
	    ix0 += ix0 + ((ix1&sign)>>31);
	    ix1 += ix1;
	    r>>=1;
	}

    /* use floating add to find out rounding direction */
	if((ix0|ix1)!=0) {
	    z = one-tiny; /* trigger inexact flag */
	    if (z>=one) {
	        z = one+tiny;
	        if (q1==(unsigned int)0xffffffff) { q1=0; q += 1;}
		else if (z>one) {
		    if (q1==(unsigned int)0xfffffffe) q+=1;
		    q1+=2; 
		} else
	            q1 += (q1&1);
	    }
	}
	ix0 = (q>>1)+0x3fe00000;
	ix1 =  q1>>1;
	if ((q&1)==1) ix1 |= sign;
	ix0 += (m <<20);
	INSERT_WORDS(z,ix0,ix1);
	return z;
}

#endif

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

double
sqrt(double x)
{
	double result;

	if(x >= 0.0)
	{
		result = __sqrt(x);
	}
	else
	{
		result = NAN;

		__set_errno(EDOM);
	}

	return(result);
}

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

#endif /* FLOATING_POINT_SUPPORT */