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/* sqrtf.c
*
* Square root
*
*
*
* SYNOPSIS:
*
* float x, y, sqrtf();
*
* y = sqrtf( 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
* IEEE 0,1.e38 100000 8.7e-8 2.9e-8
*
*
* ERROR MESSAGES:
*
* message condition value returned
* sqrtf domain x < 0 0.0
*
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision square root
* test interval: [sqrt(2)/2, sqrt(2)]
* trials: 30000
* peak relative error: 8.8e-8
* rms relative error: 3.3e-8
*
* test interval: [0.01, 100.0]
* trials: 50000
* peak relative error: 8.7e-8
* rms relative error: 3.3e-8
*
* Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
*/
#include <math.h>
#ifdef ANSIC
float frexpf( float, int * );
float ldexpf( float, int );
float sqrtf( float xx )
#else
float frexpf(), ldexpf();
float sqrtf(xx)
float xx;
#endif
{
float f, x, y;
int e;
f = xx;
if( f <= 0.0 )
{
if( f < 0.0 )
mtherr( "sqrtf", DOMAIN );
return( 0.0 );
}
x = frexpf( f, &e ); /* f = x * 2**e, 0.5 <= x < 1.0 */
/* If power of 2 is odd, double x and decrement the power of 2. */
if( e & 1 )
{
x = x + x;
e -= 1;
}
e >>= 1; /* The power of 2 of the square root. */
if( x > 1.41421356237 )
{
/* x is between sqrt(2) and 2. */
x = x - 2.0;
y =
((((( -9.8843065718E-4 * x
+ 7.9479950957E-4) * x
- 3.5890535377E-3) * x
+ 1.1028809744E-2) * x
- 4.4195203560E-2) * x
+ 3.5355338194E-1) * x
+ 1.41421356237E0;
goto sqdon;
}
if( x > 0.707106781187 )
{
/* x is between sqrt(2)/2 and sqrt(2). */
x = x - 1.0;
y =
((((( 1.35199291026E-2 * x
- 2.26657767832E-2) * x
+ 2.78720776889E-2) * x
- 3.89582788321E-2) * x
+ 6.24811144548E-2) * x
- 1.25001503933E-1) * x * x
+ 0.5 * x
+ 1.0;
goto sqdon;
}
/* x is between 0.5 and sqrt(2)/2. */
x = x - 0.5;
y =
((((( -3.9495006054E-1 * x
+ 5.1743034569E-1) * x
- 4.3214437330E-1) * x
+ 3.5310730460E-1) * x
- 3.5354581892E-1) * x
+ 7.0710676017E-1) * x
+ 7.07106781187E-1;
sqdon:
y = ldexpf( y, e ); /* y = y * 2**e */
return( y);
}
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