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/* @(#)z_sine.c 1.0 98/08/13 */
/******************************************************************
* The following routines are coded directly from the algorithms
* and coefficients given in "Software Manual for the Elementary
* Functions" by William J. Cody, Jr. and William Waite, Prentice
* Hall, 1980.
******************************************************************/
/*
FUNCTION
<<sin>>, <<cos>>, <<sine>>, <<sinf>>, <<cosf>>, <<sinef>>---sine or cosine
INDEX
sin
INDEX
sinf
INDEX
cos
INDEX
cosf
ANSI_SYNOPSIS
#include <math.h>
double sin(double <[x]>);
float sinf(float <[x]>);
double cos(double <[x]>);
float cosf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double sin(<[x]>)
double <[x]>;
float sinf(<[x]>)
float <[x]>;
double cos(<[x]>)
double <[x]>;
float cosf(<[x]>)
float <[x]>;
DESCRIPTION
<<sin>> and <<cos>> compute (respectively) the sine and cosine
of the argument <[x]>. Angles are specified in radians.
RETURNS
The sine or cosine of <[x]> is returned.
PORTABILITY
<<sin>> and <<cos>> are ANSI C.
<<sinf>> and <<cosf>> are extensions.
QUICKREF
sin ansi pure
sinf - pure
*/
/******************************************************************
* sine
*
* Input:
* x - floating point value
* cosine - indicates cosine value
*
* Output:
* Sine of x.
*
* Description:
* This routine calculates sines and cosines.
*
*****************************************************************/
#include "fdlibm.h"
#include "zmath.h"
#ifndef _DOUBLE_IS_32BITS
static const double HALF_PI = 1.57079632679489661923;
static const double ONE_OVER_PI = 0.31830988618379067154;
static const double r[] = { -0.16666666666666665052,
0.83333333333331650314e-02,
-0.19841269841201840457e-03,
0.27557319210152756119e-05,
-0.25052106798274584544e-07,
0.16058936490371589114e-09,
-0.76429178068910467734e-12,
0.27204790957888846175e-14 };
double
_DEFUN (sine, (double, int),
double x _AND
int cosine)
{
int sgn, N;
double y, XN, g, R, res;
double YMAX = 210828714.0;
switch (numtest (x))
{
case NAN:
errno = EDOM;
return (x);
case INF:
errno = EDOM;
return (z_notanum.d);
}
/* Use sin and cos properties to ease computations. */
if (cosine)
{
sgn = 1;
y = fabs (x) + HALF_PI;
}
else
{
if (x < 0.0)
{
sgn = -1;
y = -x;
}
else
{
sgn = 1;
y = x;
}
}
/* Check for values of y that will overflow here. */
if (y > YMAX)
{
errno = ERANGE;
return (x);
}
/* Calculate the exponent. */
if (y < 0.0)
N = (int) (y * ONE_OVER_PI - 0.5);
else
N = (int) (y * ONE_OVER_PI + 0.5);
XN = (double) N;
if (N & 1)
sgn = -sgn;
if (cosine)
XN -= 0.5;
y = fabs (x) - XN * __PI;
if (-z_rooteps < y && y < z_rooteps)
res = y;
else
{
g = y * y;
/* Calculate the Taylor series. */
R = (((((((r[6] * g + r[5]) * g + r[4]) * g + r[3]) * g + r[2]) * g + r[1]) * g + r[0]) * g);
/* Finally, compute the result. */
res = y + y * R;
}
res *= sgn;
return (res);
}
#endif /* _DOUBLE_IS_32BITS */
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