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/* sindgf.c
*
* Circular sine of angle in degrees
*
*
*
* SYNOPSIS:
*
* float x, y, sindgf();
*
* y = sindgf( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* 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 +-3600 100,000 1.2e-7 3.0e-8
*
* ERROR MESSAGES:
*
* message condition value returned
* sin total loss x > 2^24 0.0
*
*/
/* cosdgf.c
*
* Circular cosine of angle in degrees
*
*
*
* SYNOPSIS:
*
* float x, y, cosdgf();
*
* y = cosdgf( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* 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;
/* These are for a 24-bit significand: */
static float T24M1 = 16777215.;
static float PI180 = 0.0174532925199432957692; /* pi/180 */
float sindgf( float xx )
{
float x, y, z;
long j;
int sign;
sign = 1;
x = xx;
if( xx < 0 )
{
sign = -1;
x = -xx;
}
if( x > T24M1 )
{
mtherr( "sindgf", TLOSS );
return(0.0);
}
j = 0.022222222222222222222 * x; /* integer part of x/45 */
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;
}
x = x - y * 45.0;
x *= PI180; /* multiply by pi/180 to convert to radians */
z = x * x;
if( (j==1) || (j==2) )
{
/*
y = ((( 2.4462803166E-5 * z
- 1.3887580023E-3) * z
+ 4.1666650433E-2) * z
- 4.9999999968E-1) * z
+ 1.0;
*/
/* measured relative error in +/- pi/4 is 7.8e-8 */
y = (( 2.443315711809948E-005 * z
- 1.388731625493765E-003) * z
+ 4.166664568298827E-002) * 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;
}
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 cosdgf( float xx )
{
register float x, y, z;
int j, sign;
/* make argument positive */
sign = 1;
x = xx;
if( x < 0 )
x = -x;
if( x > T24M1 )
{
mtherr( "cosdgf", TLOSS );
return(0.0);
}
j = 0.02222222222222222222222 * 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;
x = x - y * 45.0; /* x mod 45 degrees */
x *= PI180; /* multiply by pi/180 to convert to radians */
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 );
}
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