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authorSzabolcs Nagy <nsz@port70.net>2013-11-21 01:01:57 +0000
committerSzabolcs Nagy <nsz@port70.net>2013-11-21 01:01:57 +0000
commitebbaf2180e6e32043837f570982c2ee86cf19eae (patch)
tree715c3f74bc82d25994b76298ea3919d9756eb76a /src/math/lgammaf_r.c
parent326e5c2e27224e3323e54f37621d55c40ebae87c (diff)
downloadmusl-ebbaf2180e6e32043837f570982c2ee86cf19eae.tar.gz
math: lgamma cleanup (simpler sin(pi*x) for the negative case)
* simplify sin_pi(x) (don't care about inexact here, the result is inexact anyway, and x is not so small to underflow) * in lgammal add the previously removed special case for x==1 and x==2 (to fix the sign of zero in downward rounding mode) * only define lgammal on supported long double platforms * change tgamma so the generated code is a bit smaller
Diffstat (limited to 'src/math/lgammaf_r.c')
-rw-r--r--src/math/lgammaf_r.c92
1 files changed, 31 insertions, 61 deletions
diff --git a/src/math/lgammaf_r.c b/src/math/lgammaf_r.c
index dc65bace..c5b43db5 100644
--- a/src/math/lgammaf_r.c
+++ b/src/math/lgammaf_r.c
@@ -17,7 +17,6 @@
#include "libc.h"
static const float
-two23= 8.3886080000e+06, /* 0x4b000000 */
pi = 3.1415927410e+00, /* 0x40490fdb */
a0 = 7.7215664089e-02, /* 0x3d9e233f */
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
@@ -82,87 +81,58 @@ w4 = -5.9518753551e-04, /* 0xba1c065c */
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
-static float sin_pif(float x)
+/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
+static float sin_pi(float x)
{
- float y,z;
- int n,ix;
+ double_t y;
+ int n;
- GET_FLOAT_WORD(ix, x);
- ix &= 0x7fffffff;
+ /* spurious inexact if odd int */
+ x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */
- if(ix < 0x3e800000)
- return __sindf(pi*x);
-
- y = -x; /* negative x is assumed */
-
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorf(y);
- if (z != y) { /* inexact anyway */
- y *= 0.5f;
- y = 2.0f*(y - floorf(y)); /* y = |x| mod 2.0 */
- n = (int)(y*4.0f);
- } else {
- if (ix >= 0x4b800000) {
- y = 0.0f; /* y must be even */
- n = 0;
- } else {
- if (ix < 0x4b000000)
- z = y + two23; /* exact */
- GET_FLOAT_WORD(n, z);
- n &= 1;
- y = n;
- n <<= 2;
- }
- }
+ n = (int)(x*4);
+ n = (n+1)/2;
+ y = x - n*0.5f;
+ y *= 3.14159265358979323846;
switch (n) {
- case 0: y = __sindf(pi*y); break;
- case 1:
- case 2: y = __cosdf(pi*(0.5f - y)); break;
- case 3:
- case 4: y = __sindf(pi*(1.0f - y)); break;
- case 5:
- case 6: y = -__cosdf(pi*(y - 1.5f)); break;
- default: y = __sindf(pi*(y - 2.0f)); break;
+ default: /* case 4: */
+ case 0: return __sindf(y);
+ case 1: return __cosdf(y);
+ case 2: return __sindf(-y);
+ case 3: return -__cosdf(y);
}
- return -y;
}
-
float __lgammaf_r(float x, int *signgamp)
{
+ union {float f; uint32_t i;} u = {x};
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
- int32_t hx;
- int i,ix;
-
- GET_FLOAT_WORD(hx, x);
+ uint32_t ix;
+ int i,sign;
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
*signgamp = 1;
- ix = hx & 0x7fffffff;
+ sign = u.i>>31;
+ ix = u.i & 0x7fffffff;
if (ix >= 0x7f800000)
return x*x;
- if (ix == 0)
- return 1.0f/0.0f;
if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
- if (hx < 0) {
+ if (sign) {
*signgamp = -1;
- return -logf(-x);
+ x = -x;
}
return -logf(x);
}
- if (hx < 0) {
- if (ix >= 0x4b000000) /* |x| >= 2**23, must be -integer */
- return 1.0f/0.0f;
- t = sin_pif(x);
+ if (sign) {
+ x = -x;
+ t = sin_pi(x);
if (t == 0.0f) /* -integer */
- return 1.0f/0.0f;
- nadj = logf(pi/fabsf(t*x));
- if (t < 0.0f)
+ return 1.0f/(x-x);
+ if (t > 0.0f)
*signgamp = -1;
- x = -x;
+ else
+ t = -t;
+ nadj = logf(pi/(t*x));
}
/* purge off 1 and 2 */
@@ -241,7 +211,7 @@ float __lgammaf_r(float x, int *signgamp)
r = (x-0.5f)*(t-1.0f)+w;
} else /* 2**58 <= x <= inf */
r = x*(logf(x)-1.0f);
- if (hx < 0)
+ if (sign)
r = nadj - r;
return r;
}