* SYNOPSIS:
*
* long double x, y, tgammal();
- * extern int signgam;
*
* y = tgammal( x );
*
* DESCRIPTION:
*
* Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named signgam.
- * This variable is also filled in by the logarithmic gamma
- * function lgamma().
+ * correctly signed.
*
* Arguments |x| <= 13 are reduced by recurrence and the function
* approximated by a rational function of degree 7/8 in the
long double tgammal(long double x)
{
long double p, q, z;
- int i;
- signgam = 1;
- if (isnan(x))
- return NAN;
- if (x == INFINITY)
- return INFINITY;
- if (x == -INFINITY)
- return x - x;
+ if (!isfinite(x))
+ return x + INFINITY;
+
q = fabsl(x);
if (q > 13.0) {
- if (q > MAXGAML)
- goto goverf;
if (x < 0.0) {
p = floorl(q);
- if (p == q)
- return (x - x) / (x - x);
- i = p;
- if ((i & 1) == 0)
- signgam = -1;
z = q - p;
- if (z > 0.5L) {
- p += 1.0;
- z = q - p;
- }
- z = q * sinl(PIL * z);
- z = fabsl(z) * stirf(q);
- if (z <= PIL/LDBL_MAX) {
-goverf:
- return signgam * INFINITY;
+ if (z == 0)
+ return 0 / z;
+ if (q > MAXGAML) {
+ z = 0;
+ } else {
+ if (z > 0.5) {
+ p += 1.0;
+ z = q - p;
+ }
+ z = q * sinl(PIL * z);
+ z = fabsl(z) * stirf(q);
+ z = PIL/z;
}
- z = PIL/z;
+ if (0.5 * p == floorl(q * 0.5))
+ z = -z;
+ } else if (x > MAXGAML) {
+ z = x * 0x1p16383L;
} else {
z = stirf(x);
}
- return signgam * z;
+ return z;
}
z = 1.0;
p = __polevll(x, P, 7);
q = __polevll(x, Q, 8);
z = z * p / q;
- if(z < 0)
- signgam = -1;
return z;
small:
- if (x == 0.0)
- return (x - x) / (x - x);
+ /* z==1 if x was originally +-0 */
+ if (x == 0 && z != 1)
+ return x / x;
if (x < 0.0) {
x = -x;
q = z / (x * __polevll(x, SN, 8));
- signgam = -1;
} else
q = z / (x * __polevll(x, S, 8));
return q;