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/*
* Cephes Math Library Release 2.8: June, 2000
* Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#define DEBUG 0
static double stop = 1.37e-17;
extern double MACHEP;
double onef2(double a, double b, double c, double x, double *err)
{
double n, a0, sum, t;
double an, bn, cn, max, z;
an = a;
bn = b;
cn = c;
a0 = 1.0;
sum = 1.0;
n = 1.0;
t = 1.0;
max = 0.0;
do {
if (an == 0)
goto done;
if (bn == 0)
goto error;
if (cn == 0)
goto error;
if ((a0 > 1.0e34) || (n > 200))
goto error;
a0 *= (an * x) / (bn * cn * n);
sum += a0;
an += 1.0;
bn += 1.0;
cn += 1.0;
n += 1.0;
z = fabs(a0);
if (z > max)
max = z;
if (sum != 0)
t = fabs(a0 / sum);
else
t = z;
}
while (t > stop);
done:
*err = fabs(MACHEP * max / sum);
#if DEBUG
printf(" onef2 cancellation error %.5E\n", *err);
#endif
goto xit;
error:
#if DEBUG
printf("onef2 does not converge\n");
#endif
*err = 1.0e38;
xit:
#if DEBUG
printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n,
sum);
#endif
return (sum);
}
double threef0(double a, double b, double c, double x, double *err)
{
double n, a0, sum, t, conv, conv1;
double an, bn, cn, max, z;
an = a;
bn = b;
cn = c;
a0 = 1.0;
sum = 1.0;
n = 1.0;
t = 1.0;
max = 0.0;
conv = 1.0e38;
conv1 = conv;
do {
if (an == 0.0)
goto done;
if (bn == 0.0)
goto done;
if (cn == 0.0)
goto done;
if ((a0 > 1.0e34) || (n > 200))
goto error;
a0 *= (an * bn * cn * x) / n;
an += 1.0;
bn += 1.0;
cn += 1.0;
n += 1.0;
z = fabs(a0);
if (z > max)
max = z;
if (z >= conv) {
if ((z < max) && (z > conv1))
goto done;
}
conv1 = conv;
conv = z;
sum += a0;
if (sum != 0)
t = fabs(a0 / sum);
else
t = z;
}
while (t > stop);
done:
t = fabs(MACHEP * max / sum);
#if DEBUG
printf(" threef0 cancellation error %.5E\n", t);
#endif
max = fabs(conv / sum);
if (max > t)
t = max;
#if DEBUG
printf(" threef0 convergence %.5E\n", max);
#endif
goto xit;
error:
#if DEBUG
printf("threef0 does not converge\n");
#endif
t = 1.0e38;
xit:
#if DEBUG
printf("threef0( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n,
sum);
#endif
*err = t;
return (sum);
}
/*
* Bessel function of noninteger order
*/
double yv(double v, double x)
{
double y, t;
int n;
n = v;
if (n == v) {
y = yn(n, x);
return (y);
}
else if (v == floor(v)) {
/* Zero in denominator. */
mtherr("yv", DOMAIN);
return NPY_NAN;
}
t = NPY_PI * v;
y = (cos(t) * jv(v, x) - jv(-v, x)) / sin(t);
if (cephes_isinf(y)) {
if (v > 0) {
mtherr("yv", OVERFLOW);
return -NPY_INFINITY;
}
else if (v < -1e10) {
/* Whether it's +inf or -inf is numerically ill-defined. */
mtherr("yv", DOMAIN);
return NPY_NAN;
}
}
return (y);
}
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