double expm1(double x)
{
double r, xx;
if (!cephes_isfinite(x)) {
if (cephes_isnan(x)) {
return x;
}
else if (x > 0) {
return x;
}
else {
return -1.0;
}
}
if ((x < -0.5) || (x > 0.5))
return (exp(x) - 1.0);
xx = x * x;
r = x * polevl(xx, EP, 2);
r = r / (polevl(xx, EQ, 3) - r);
return (r + r);
}
/* Logarithm of Gamma function */
double lgam(double x)
{
double p, q, u, w, z;
int i;
sgngam = 1;
if (!cephes_isfinite(x))
return x;
if (x < -34.0) {
q = -x;
w = lgam(q); /* note this modifies sgngam! */
p = floor(q);
if (p == q) {
lgsing:
mtherr("lgam", SING);
return (NPY_INFINITY);
}
i = p;
if ((i & 1) == 0)
sgngam = -1;
else
sgngam = 1;
z = q - p;
if (z > 0.5) {
p += 1.0;
z = p - q;
}
z = q * sin(NPY_PI * z);
if (z == 0.0)
goto lgsing;
/* z = log(NPY_PI) - log( z ) - w; */
z = LOGPI - log(z) - w;
return (z);
}
if (x < 13.0) {
z = 1.0;
p = 0.0;
u = x;
while (u >= 3.0) {
p -= 1.0;
u = x + p;
z *= u;
}
while (u < 2.0) {
if (u == 0.0)
goto lgsing;
z /= u;
p += 1.0;
u = x + p;
}
if (z < 0.0) {
sgngam = -1;
z = -z;
}
else
sgngam = 1;
if (u == 2.0)
return (log(z));
p -= 2.0;
x = x + p;
p = x * polevl(x, B, 5) / p1evl(x, C, 6);
return (log(z) + p);
}
if (x > MAXLGM) {
return (sgngam * NPY_INFINITY);
}
q = (x - 0.5) * log(x) - x + LS2PI;
if (x > 1.0e8)
return (q);
p = 1.0 / (x * x);
if (x >= 1000.0)
q += ((7.9365079365079365079365e-4 * p
- 2.7777777777777777777778e-3) * p
+ 0.0833333333333333333333) / x;
else
q += polevl(p, A, 4) / x;
return (q);
}
double Gamma(double x)
{
double p, q, z;
int i;
sgngam = 1;
if (!cephes_isfinite(x)) {
return x;
}
q = fabs(x);
if (q > 33.0) {
if (x < 0.0) {
p = floor(q);
if (p == q) {
gamnan:
mtherr("Gamma", OVERFLOW);
return (NPY_INFINITY);
}
i = p;
if ((i & 1) == 0)
sgngam = -1;
z = q - p;
if (z > 0.5) {
p += 1.0;
z = q - p;
}
z = q * sin(NPY_PI * z);
if (z == 0.0) {
return (sgngam * NPY_INFINITY);
}
z = fabs(z);
z = NPY_PI / (z * stirf(q));
}
else {
z = stirf(x);
}
return (sgngam * z);
}
z = 1.0;
while (x >= 3.0) {
x -= 1.0;
z *= x;
}
while (x < 0.0) {
if (x > -1.E-9)
goto small;
z /= x;
x += 1.0;
}
while (x < 2.0) {
if (x < 1.e-9)
goto small;
z /= x;
x += 1.0;
}
if (x == 2.0)
return (z);
x -= 2.0;
p = polevl(x, P, 6);
q = polevl(x, Q, 7);
return (z * p / q);
small:
if (x == 0.0) {
goto gamnan;
}
else
return (z / ((1.0 + 0.5772156649015329 * x) * x));
}
