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-rw-r--r--src/math/lgammal.c88
1 files changed, 28 insertions, 60 deletions
diff --git a/src/math/lgammal.c b/src/math/lgammal.c
index 58054e56..55ec5325 100644
--- a/src/math/lgammal.c
+++ b/src/math/lgammal.c
@@ -99,7 +99,6 @@ long double __lgammal_r(long double x, int *sg)
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double
pi = 3.14159265358979323846264L,
-two63 = 9.223372036854775808e18L,
/* lgam(1+x) = 0.5 x + x a(x)/b(x)
-0.268402099609375 <= x <= 0
@@ -201,61 +200,27 @@ w5 = 8.412723297322498080632E-4L,
w6 = -1.880801938119376907179E-3L,
w7 = 4.885026142432270781165E-3L;
+/* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */
static long double sin_pi(long double x)
{
- union ldshape u = {x};
- uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
- long double y, z;
int n;
- if (ix < 0x3ffd8000) /* 0.25 */
- return sinl(pi * x);
- y = -x; /* x is assume negative */
+ /* spurious inexact if odd int */
+ x *= 0.5;
+ x = 2.0*(x - floorl(x)); /* x mod 2.0 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorl(y);
- if (z != y) { /* inexact anyway */
- y *= 0.5;
- y = 2.0*(y - floorl(y));/* y = |x| mod 2.0 */
- n = (int) (y*4.0);
- } else {
- if (ix >= 0x403f8000) { /* 2^64 */
- y = 0.0; /* y must be even */
- n = 0;
- } else {
- if (ix < 0x403e8000) /* 2^63 */
- z = y + two63; /* exact */
- u.f = z;
- n = u.i.m & 1;
- y = n;
- n <<= 2;
- }
- }
+ n = (int)(x*4.0);
+ n = (n+1)/2;
+ x -= n*0.5f;
+ x *= pi;
switch (n) {
- case 0:
- y = sinl(pi * y);
- break;
- case 1:
- case 2:
- y = cosl(pi * (0.5 - y));
- break;
- case 3:
- case 4:
- y = sinl(pi * (1.0 - y));
- break;
- case 5:
- case 6:
- y = -cosl(pi * (y - 1.5));
- break;
- default:
- y = sinl(pi * (y - 2.0));
- break;
+ default: /* case 4: */
+ case 0: return __sinl(x, 0.0, 0);
+ case 1: return __cosl(x, 0.0);
+ case 2: return __sinl(-x, 0.0, 0);
+ case 3: return -__cosl(x, 0.0);
}
- return -y;
}
long double __lgammal_r(long double x, int *sg) {
@@ -267,31 +232,32 @@ long double __lgammal_r(long double x, int *sg) {
*sg = 1;
- /* purge off +-inf, NaN, +-0, and negative arguments */
+ /* purge off +-inf, NaN, +-0, tiny and negative arguments */
if (ix >= 0x7fff0000)
return x * x;
- if (x == 0) {
- *sg -= 2*sign;
- return 1.0 / fabsl(x);
- }
if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */
if (sign) {
*sg = -1;
- return -logl(-x);
+ x = -x;
}
return -logl(x);
}
if (sign) {
- t = sin_pi (x);
+ x = -x;
+ t = sin_pi(x);
if (t == 0.0)
- return 1.0 / fabsl(t); /* -integer */
- nadj = logl(pi / fabsl(t * x));
- if (t < 0.0)
+ return 1.0 / (x-x); /* -integer */
+ if (t > 0.0)
*sg = -1;
- x = -x;
+ else
+ t = -t;
+ nadj = logl(pi / (t * x));
}
- if (ix < 0x40008000) { /* x < 2.0 */
+ /* purge off 1 and 2 (so the sign is ok with downward rounding) */
+ if ((ix == 0x3fff8000 || ix == 0x40008000) && u.i.m == 0) {
+ r = 0;
+ } else if (ix < 0x40008000) { /* x < 2.0 */
if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */
/* lgamma(x) = lgamma(x+1) - log(x) */
r = -logl(x);
@@ -376,6 +342,7 @@ long double __lgammal_r(long double x, int *sg) {
}
#endif
+#if (LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024) || (LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384)
extern int __signgam;
long double lgammal(long double x)
@@ -384,3 +351,4 @@ long double lgammal(long double x)
}
weak_alias(__lgammal_r, lgammal_r);
+#endif