/*-------------------------------------------------------------------------
sqrtf.c - Computes square root of a 32-bit float as outlined in [1]
Copyright (C) 2001, 2002, Jesus Calvino-Fraga, jesusc@ieee.org
This library is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this library; see the file COPYING. If not, write to the
Free Software Foundation, 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA.
As a special exception, if you link this library with other files,
some of which are compiled with SDCC, to produce an executable,
this library does not by itself cause the resulting executable to
be covered by the GNU General Public License. This exception does
not however invalidate any other reasons why the executable file
might be covered by the GNU General Public License.
-------------------------------------------------------------------------*/
/* [1] William James Cody and W. M. Waite. _Software manual for the
elementary functions_, Englewood Cliffs, N.J.:Prentice-Hall, 1980. */
/* Version 1.0 - Initial release */
#include <math.h>
#include <errno.h>
float sqrtf(float x) _FLOAT_FUNC_REENTRANT
{
float f, y;
int n;
if (x==0.0) return x;
else if (x==1.0) return 1.0;
else if (x<0.0)
{
errno=EDOM;
return 0.0;
}
f=frexpf(x, &n);
y=0.41731+0.59016*f; /*Educated guess*/
/*For a 24 bit mantisa (float), two iterations are sufficient*/
y+=f/y;
y=ldexpf(y, -2) + f/y; /*Faster version of 0.25 * y + f/y*/
if (n&1)
{
y*=0.7071067812;
++n;
}
return ldexpf(y, n/2);
}