uclibc-ng/libm/float/sinf.c

/*							sinf.c
 *
 *	Circular sine
 *
 *
 *
 * SYNOPSIS:
 *
 * float x, y, sinf();
 *
 * y = sinf( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Range reduction is into intervals of pi/4.  The reduction
 * error is nearly eliminated by contriving an extended precision
 * modular arithmetic.
 *
 * Two polynomial approximating functions are employed.
 * Between 0 and pi/4 the sine is approximated by
 *      x  +  x**3 P(x**2).
 * Between pi/4 and pi/2 the cosine is represented as
 *      1  -  x**2 Q(x**2).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain      # trials      peak       rms
 *    IEEE    -4096,+4096   100,000      1.2e-7     3.0e-8
 *    IEEE    -8192,+8192   100,000      3.0e-7     3.0e-8
 * 
 * ERROR MESSAGES:
 *
 *   message           condition        value returned
 * sin total loss      x > 2^24              0.0
 *
 * Partial loss of accuracy begins to occur at x = 2^13
 * = 8192. Results may be meaningless for x >= 2^24
 * The routine as implemented flags a TLOSS error
 * for x >= 2^24 and returns 0.0.
 */

/*							cosf.c
 *
 *	Circular cosine
 *
 *
 *
 * SYNOPSIS:
 *
 * float x, y, cosf();
 *
 * y = cosf( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Range reduction is into intervals of pi/4.  The reduction
 * error is nearly eliminated by contriving an extended precision
 * modular arithmetic.
 *
 * Two polynomial approximating functions are employed.
 * Between 0 and pi/4 the cosine is approximated by
 *      1  -  x**2 Q(x**2).
 * Between pi/4 and pi/2 the sine is represented as
 *      x  +  x**3 P(x**2).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain      # trials      peak         rms
 *    IEEE    -8192,+8192   100,000      3.0e-7     3.0e-8
 */

/*
Cephes Math Library Release 2.2:  June, 1992
Copyright 1985, 1987, 1988, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/


/* Single precision circular sine
 * test interval: [-pi/4, +pi/4]
 * trials: 10000
 * peak relative error: 6.8e-8
 * rms relative error: 2.6e-8
 */
#include <math.h>


static float FOPI = 1.27323954473516;

extern float PIO4F;
/* Note, these constants are for a 32-bit significand: */
/*
static float DP1 =  0.7853851318359375;
static float DP2 =  1.30315311253070831298828125e-5;
static float DP3 =  3.03855025325309630e-11;
static float lossth = 65536.;
*/

/* These are for a 24-bit significand: */
static float DP1 = 0.78515625;
static float DP2 = 2.4187564849853515625e-4;
static float DP3 = 3.77489497744594108e-8;
static float lossth = 8192.;
static float T24M1 = 16777215.;

static float sincof[] = {
-1.9515295891E-4,
 8.3321608736E-3,
-1.6666654611E-1
};
static float coscof[] = {
 2.443315711809948E-005,
-1.388731625493765E-003,
 4.166664568298827E-002
};

float sinf( float xx )
{
float *p;
float x, y, z;
register unsigned long j;
register int sign;

sign = 1;
x = xx;
if( xx < 0 )
	{
	sign = -1;
	x = -xx;
	}
if( x > T24M1 )
	{
	mtherr( "sinf", TLOSS );
	return(0.0);
	}
j = FOPI * x; /* integer part of x/(PI/4) */
y = j;
/* map zeros to origin */
if( j & 1 )
	{
	j += 1;
	y += 1.0;
	}
j &= 7; /* octant modulo 360 degrees */
/* reflect in x axis */
if( j > 3)
	{
	sign = -sign;
	j -= 4;
	}

if( x > lossth )
	{
	mtherr( "sinf", PLOSS );
	x = x - y * PIO4F;
	}
else
	{
/* Extended precision modular arithmetic */
	x = ((x - y * DP1) - y * DP2) - y * DP3;
	}
/*einits();*/
z = x * x;
if( (j==1) || (j==2) )
	{
/* measured relative error in +/- pi/4 is 7.8e-8 */
/*
	y = ((  2.443315711809948E-005 * z
	  - 1.388731625493765E-003) * z
	  + 4.166664568298827E-002) * z * z;
*/
	p = coscof;
	y = *p++;
	y = y * z + *p++;
	y = y * z + *p++;
	y *= z * z;
	y -= 0.5 * z;
	y += 1.0;
	}
else
	{
/* Theoretical relative error = 3.8e-9 in [-pi/4, +pi/4] */
/*
	y = ((-1.9515295891E-4 * z
	     + 8.3321608736E-3) * z
	     - 1.6666654611E-1) * z * x;
	y += x;
*/
	p = sincof;
	y = *p++;
	y = y * z + *p++;
	y = y * z + *p++;
	y *= z * x;
	y += x;
	}
/*einitd();*/
if(sign < 0)
	y = -y;
return( y);
}


/* Single precision circular cosine
 * test interval: [-pi/4, +pi/4]
 * trials: 10000
 * peak relative error: 8.3e-8
 * rms relative error: 2.2e-8
 */

float cosf( float xx )
{
float x, y, z;
int j, sign;

/* make argument positive */
sign = 1;
x = xx;
if( x < 0 )
	x = -x;

if( x > T24M1 )
	{
	mtherr( "cosf", TLOSS );
	return(0.0);
	}

j = FOPI * x; /* integer part of x/PIO4 */
y = j;
/* integer and fractional part modulo one octant */
if( j & 1 )	/* map zeros to origin */
	{
	j += 1;
	y += 1.0;
	}
j &= 7;
if( j > 3)
	{
	j -=4;
	sign = -sign;
	}

if( j > 1 )
	sign = -sign;

if( x > lossth )
	{
	mtherr( "cosf", PLOSS );
	x = x - y * PIO4F;
	}
else
/* Extended precision modular arithmetic */
	x = ((x - y * DP1) - y * DP2) - y * DP3;

z = x * x;

if( (j==1) || (j==2) )
	{
	y = (((-1.9515295891E-4 * z
	     + 8.3321608736E-3) * z
	     - 1.6666654611E-1) * z * x)
	     + x;
	}
else
	{
	y = ((  2.443315711809948E-005 * z
	  - 1.388731625493765E-003) * z
	  + 4.166664568298827E-002) * z * z;
	y -= 0.5 * z;
	y += 1.0;
	}
if(sign < 0)
	y = -y;
return( y );
}