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/* shichif.c
*
* Hyperbolic sine and cosine integrals
*
*
*
* SYNOPSIS:
*
* float x, Chi, Shi;
*
* shichi( x, &Chi, &Shi );
*
*
* DESCRIPTION:
*
* Approximates the integrals
*
* x
* -
* | | cosh t - 1
* Chi(x) = eul + ln x + | ----------- dt,
* | | t
* -
* 0
*
* x
* -
* | | sinh t
* Shi(x) = | ------ dt
* | | t
* -
* 0
*
* where eul = 0.57721566490153286061 is Euler's constant.
* The integrals are evaluated by power series for x < 8
* and by Chebyshev expansions for x between 8 and 88.
* For large x, both functions approach exp(x)/2x.
* Arguments greater than 88 in magnitude return MAXNUM.
*
*
* ACCURACY:
*
* Test interval 0 to 88.
* Relative error:
* arithmetic function # trials peak rms
* IEEE Shi 20000 3.5e-7 7.0e-8
* Absolute error, except relative when |Chi| > 1:
* IEEE Chi 20000 3.8e-7 7.6e-8
*/
/*
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
/* x exp(-x) shi(x), inverted interval 8 to 18 */
static float S1[] = {
-3.56699611114982536845E-8,
1.44818877384267342057E-7,
7.82018215184051295296E-7,
-5.39919118403805073710E-6,
-3.12458202168959833422E-5,
8.90136741950727517826E-5,
2.02558474743846862168E-3,
2.96064440855633256972E-2,
1.11847751047257036625E0
};
/* x exp(-x) shi(x), inverted interval 18 to 88 */
static float S2[] = {
1.69050228879421288846E-8,
1.25391771228487041649E-7,
1.16229947068677338732E-6,
1.61038260117376323993E-5,
3.49810375601053973070E-4,
1.28478065259647610779E-2,
1.03665722588798326712E0
};
/* x exp(-x) chin(x), inverted interval 8 to 18 */
static float C1[] = {
1.31458150989474594064E-8,
-4.75513930924765465590E-8,
-2.21775018801848880741E-7,
1.94635531373272490962E-6,
4.33505889257316408893E-6,
-6.13387001076494349496E-5,
-3.13085477492997465138E-4,
4.97164789823116062801E-4,
2.64347496031374526641E-2,
1.11446150876699213025E0
};
/* x exp(-x) chin(x), inverted interval 18 to 88 */
static float C2[] = {
-3.00095178028681682282E-9,
7.79387474390914922337E-8,
1.06942765566401507066E-6,
1.59503164802313196374E-5,
3.49592575153777996871E-4,
1.28475387530065247392E-2,
1.03665693917934275131E0
};
/* Sine and cosine integrals */
#define EUL 0.57721566490153286061
extern float MACHEPF, MAXNUMF;
#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
#ifdef ANSIC
float logf(float ), expf(float), chbevlf(float, float *, int);
#else
float logf(), expf(), chbevlf();
#endif
int shichif( float xx, float *si, float *ci )
{
float x, k, z, c, s, a;
short sign;
x = xx;
if( x < 0.0 )
{
sign = -1;
x = -x;
}
else
sign = 0;
if( x == 0.0 )
{
*si = 0.0;
*ci = -MAXNUMF;
return( 0 );
}
if( x >= 8.0 )
goto chb;
z = x * x;
/* Direct power series expansion */
a = 1.0;
s = 1.0;
c = 0.0;
k = 2.0;
do
{
a *= z/k;
c += a/k;
k += 1.0;
a /= k;
s += a/k;
k += 1.0;
}
while( fabsf(a/s) > MACHEPF );
s *= x;
goto done;
chb:
if( x < 18.0 )
{
a = (576.0/x - 52.0)/10.0;
k = expf(x) / x;
s = k * chbevlf( a, S1, 9 );
c = k * chbevlf( a, C1, 10 );
goto done;
}
if( x <= 88.0 )
{
a = (6336.0/x - 212.0)/70.0;
k = expf(x) / x;
s = k * chbevlf( a, S2, 7 );
c = k * chbevlf( a, C2, 7 );
goto done;
}
else
{
if( sign )
*si = -MAXNUMF;
else
*si = MAXNUMF;
*ci = MAXNUMF;
return(0);
}
done:
if( sign )
s = -s;
*si = s;
*ci = EUL + logf(x) + c;
return(0);
}
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