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/* @(#)z_sineh.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
<<sinh>>, <<sinhf>>, <<cosh>>, <<coshf>>, <<sineh>>---hyperbolic sine or cosine
INDEX
sinh
INDEX
sinhf
INDEX
cosh
INDEX
coshf
ANSI_SYNOPSIS
#include <math.h>
double sinh(double <[x]>);
float sinhf(float <[x]>);
double cosh(double <[x]>);
float coshf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double sinh(<[x]>)
double <[x]>;
float sinhf(<[x]>)
float <[x]>;
double cosh(<[x]>)
double <[x]>;
float coshf(<[x]>)
float <[x]>;
DESCRIPTION
<<sinh>> and <<cosh>> compute the hyperbolic sine or cosine
of the argument <[x]>.
Angles are specified in radians. <<sinh>>(<[x]>) is defined as
@ifinfo
. (exp(<[x]>) - exp(-<[x]>))/2
@end ifinfo
@tex
$${e^x - e^{-x}}\over 2$$
@end tex
<<cosh>> is defined as
@ifinfo
. (exp(<[x]>) - exp(-<[x]>))/2
@end ifinfo
@tex
$${e^x + e^{-x}}\over 2$$
@end tex
<<sinhf>> and <<coshf>> are identical, save that they take
and returns <<float>> values.
RETURNS
The hyperbolic sine or cosine of <[x]> is returned.
When the correct result is too large to be representable (an
overflow), the functions return <<HUGE_VAL>> with the
appropriate sign, and sets the global value <<errno>> to
<<ERANGE>>.
PORTABILITY
<<sinh>> is ANSI C.
<<sinhf>> is an extension.
<<cosh>> is ANSI C.
<<coshf>> is an extension.
*/
/******************************************************************
* Hyperbolic Sine
*
* Input:
* x - floating point value
*
* Output:
* hyperbolic sine of x
*
* Description:
* This routine calculates hyperbolic sines.
*
*****************************************************************/
#include <float.h>
#include "fdlibm.h"
#include "zmath.h"
static const double q[] = { -0.21108770058106271242e+7,
0.36162723109421836460e+5,
-0.27773523119650701667e+3 };
static const double p[] = { -0.35181283430177117881e+6,
-0.11563521196851768270e+5,
-0.16375798202630751372e+3,
-0.78966127417357099479 };
static const double LNV = 0.6931610107421875000;
static const double INV_V2 = 0.24999308500451499336;
static const double V_OVER2_MINUS1 = 0.13830277879601902638e-4;
double
_DEFUN (sineh, (double, int),
double x _AND
int cosineh)
{
double y, f, P, Q, R, res, z, w;
int sgn = 1;
double WBAR = 18.55;
/* Check for special values. */
switch (numtest (x))
{
case NAN:
errno = EDOM;
return (x);
case INF:
errno = ERANGE;
return (ispos (x) ? z_infinity.d : -z_infinity.d);
}
y = fabs (x);
if (!cosineh && x < 0.0)
sgn = -1;
if ((y > 1.0 && !cosineh) || cosineh)
{
if (y > BIGX)
{
w = y - LNV;
/* Check for w > maximum here. */
if (w > BIGX)
{
errno = ERANGE;
return (x);
}
z = exp (w);
if (w > WBAR)
res = z * (V_OVER2_MINUS1 + 1.0);
}
else
{
z = exp (y);
if (cosineh)
res = (z + 1 / z) / 2.0;
else
res = (z - 1 / z) / 2.0;
}
if (sgn < 0)
res = -res;
}
else
{
/* Check for y being too small. */
if (y < z_rooteps)
{
res = x;
}
/* Calculate the Taylor series. */
else
{
f = x * x;
Q = ((f + q[2]) * f + q[1]) * f + q[0];
P = ((p[3] * f + p[2]) * f + p[1]) * f + p[0];
R = f * (P / Q);
res = x + x * R;
}
}
return (res);
}
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