mirror of
https://github.com/ZDoom/raze-gles.git
synced 2024-12-29 04:50:42 +00:00
203 lines
4.2 KiB
C
203 lines
4.2 KiB
C
|
/* _sqrt.c
|
|||
|
|
*
|
|||
|
|
* Square root
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* SYNOPSIS:
|
|||
|
|
*
|
|||
|
|
* double x, y, _sqrt();
|
|||
|
|
*
|
|||
|
|
* y = _sqrt( x );
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* DESCRIPTION:
|
|||
|
|
*
|
|||
|
|
* Returns the square root of x.
|
|||
|
|
*
|
|||
|
|
* Range reduction involves isolating the power of two of the
|
|||
|
|
* argument and using a polynomial approximation to obtain
|
|||
|
|
* a rough value for the square root. Then Heron's iteration
|
|||
|
|
* is used three times to converge to an accurate value.
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* ACCURACY:
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* Relative error:
|
|||
|
|
* arithmetic domain # trials peak rms
|
|||
|
|
* DEC 0, 10 60000 2.1e-17 7.9e-18
|
|||
|
|
* IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
|
|||
|
|
*
|
|||
|
|
*
|
|||
|
|
* ERROR MESSAGES:
|
|||
|
|
*
|
|||
|
|
* message condition value returned
|
|||
|
|
* _sqrt domain x < 0 0.0
|
|||
|
|
*
|
|||
|
|
*/
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
Cephes Math Library Release 2.8: June, 2000
|
|||
|
|
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
|
|||
|
|
|
|||
|
|
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.
|
|||
|
|
3. Neither the name of the <ORGANIZATION> nor the names of its
|
|||
|
|
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.
|
|||
|
|
*/
|
|||
|
|
|
|||
|
|
|
|||
|
|
#include "mconf.h"
|
|||
|
|
#ifdef ANSIPROT
|
|||
|
|
extern double frexp ( double, int * );
|
|||
|
|
extern double ldexp ( double, int );
|
|||
|
|
#else
|
|||
|
|
double frexp(), ldexp();
|
|||
|
|
#endif
|
|||
|
|
extern double SQRT2; /* _sqrt2 = 1.41421356237309504880 */
|
|||
|
|
|
|||
|
|
double c_sqrt(x)
|
|||
|
|
double x;
|
|||
|
|
{
|
|||
|
|
int e;
|
|||
|
|
#ifndef UNK
|
|||
|
|
short *q;
|
|||
|
|
#endif
|
|||
|
|
double z, w;
|
|||
|
|
|
|||
|
|
if( x <= 0.0 )
|
|||
|
|
{
|
|||
|
|
if( x < 0.0 )
|
|||
|
|
mtherr( "_sqrt", DOMAIN );
|
|||
|
|
return( 0.0 );
|
|||
|
|
}
|
|||
|
|
w = x;
|
|||
|
|
/* separate exponent and significand */
|
|||
|
|
#ifdef UNK
|
|||
|
|
z = frexp( x, &e );
|
|||
|
|
#endif
|
|||
|
|
#ifdef DEC
|
|||
|
|
q = (short *)&x;
|
|||
|
|
e = ((*q >> 7) & 0377) - 0200;
|
|||
|
|
*q &= 0177;
|
|||
|
|
*q |= 040000;
|
|||
|
|
z = x;
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
/* Note, frexp and ldexp are used in order to
|
|||
|
|
* handle denormal numbers properly.
|
|||
|
|
*/
|
|||
|
|
#ifdef IBMPC
|
|||
|
|
z = frexp( x, &e );
|
|||
|
|
q = (short *)&x;
|
|||
|
|
q += 3;
|
|||
|
|
/*
|
|||
|
|
e = ((*q >> 4) & 0x0fff) - 0x3fe;
|
|||
|
|
*q &= 0x000f;
|
|||
|
|
*q |= 0x3fe0;
|
|||
|
|
z = x;
|
|||
|
|
*/
|
|||
|
|
#endif
|
|||
|
|
#ifdef MIEEE
|
|||
|
|
z = frexp( x, &e );
|
|||
|
|
q = (short *)&x;
|
|||
|
|
/*
|
|||
|
|
e = ((*q >> 4) & 0x0fff) - 0x3fe;
|
|||
|
|
*q &= 0x000f;
|
|||
|
|
*q |= 0x3fe0;
|
|||
|
|
z = x;
|
|||
|
|
*/
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
/* approximate square root of number between 0.5 and 1
|
|||
|
|
* relative error of approximation = 7.47e-3
|
|||
|
|
*/
|
|||
|
|
x = 4.173075996388649989089E-1 + 5.9016206709064458299663E-1 * z;
|
|||
|
|
|
|||
|
|
/* adjust for odd powers of 2 */
|
|||
|
|
if( (e & 1) != 0 )
|
|||
|
|
x *= SQRT2;
|
|||
|
|
|
|||
|
|
/* re-insert exponent */
|
|||
|
|
#ifdef UNK
|
|||
|
|
x = ldexp( x, (e >> 1) );
|
|||
|
|
#endif
|
|||
|
|
#ifdef DEC
|
|||
|
|
*q += ((e >> 1) & 0377) << 7;
|
|||
|
|
*q &= 077777;
|
|||
|
|
#endif
|
|||
|
|
#ifdef IBMPC
|
|||
|
|
x = ldexp( x, (e >> 1) );
|
|||
|
|
/*
|
|||
|
|
*q += ((e >>1) & 0x7ff) << 4;
|
|||
|
|
*q &= 077777;
|
|||
|
|
*/
|
|||
|
|
#endif
|
|||
|
|
#ifdef MIEEE
|
|||
|
|
x = ldexp( x, (e >> 1) );
|
|||
|
|
/*
|
|||
|
|
*q += ((e >>1) & 0x7ff) << 4;
|
|||
|
|
*q &= 077777;
|
|||
|
|
*/
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
/* Newton iterations: */
|
|||
|
|
#ifdef UNK
|
|||
|
|
x = 0.5*(x + w/x);
|
|||
|
|
x = 0.5*(x + w/x);
|
|||
|
|
x = 0.5*(x + w/x);
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
/* Note, assume the square root cannot be denormal,
|
|||
|
|
* so it is safe to use integer exponent operations here.
|
|||
|
|
*/
|
|||
|
|
#ifdef DEC
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0200;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0200;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0200;
|
|||
|
|
#endif
|
|||
|
|
#ifdef IBMPC
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
#endif
|
|||
|
|
#ifdef MIEEE
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
x += w/x;
|
|||
|
|
*q -= 0x10;
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
return(x);
|
|||
|
|
}
|