library/math_sqrt.c
/*
* $Id: math_sqrt.c,v 1.9 2006-09-22 07:54:24 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.
*/
#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 = 0;
__set_errno(EDOM);
}
return(result);
}
/****************************************************************************/
#endif /* FLOATING_POINT_SUPPORT */