Date: Sat, 18 Feb 2017 18:41:01 -0800 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: freebsd-numerics@freebsd.org Subject: [PATCH] avoid function call overhead in tgammaf Message-ID: <20170219024101.GA79177@troutmask.apl.washington.edu>
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The following patch treats special values (i.e., +-inf, nan)
and values outside a limited domain to avoid the function
call overhead of tgamma. Anyone with a commit bit is more
than welcomed to commit the patch (after of course a review).
Index: src/s_tgammaf.c
===================================================================
--- src/s_tgammaf.c (revision 1857)
+++ src/s_tgammaf.c (working copy)
@@ -27,17 +27,59 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD: head/lib/msun/src/s_tgammaf.c 176388 2008-02-18 17:27:11Z das $");
-#include <math.h>
+#include "math.h"
+#include "math_private.h"
/*
- * We simply call tgamma() rather than bloating the math library with
- * a float-optimized version of it. The reason is that tgammaf() is
- * essentially useless, since the function is superexponential and
- * floats have very limited range.
+ * The gamma function is superexponential, which means that floats have
+ * a very limited domain. Rather than bloating the math library with a
+ * float-optimized version of tgammaf, we call tgamma() within the limited
+ * domain of [-underflow,overflow]. However, to avoid function call overhead,
+ * tgammaf() directly treats special values and values outside the limited
+ * domain.
*/
+
+static u_int32_t overflow = 0x420c290f; /* 35.0400981 */
+static u_int32_t underflow = 0x421a67d8; /* 38.6014118 */
+static volatile float huge = 1.e30, tiny = 1.e-30;
+
float
tgammaf(float x)
{
+ u_int32_t hx;
+ int32_t ix, sg;
+
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ sg = hx & 0x80000000;
+
+ if (ix > overflow) {
+ if (ix >= 0x7f800000)
+ return (sg ? x / x : x + x);
+ if (!sg)
+ return (huge * huge);
+ }
+
+ if (ix == 0)
+ return (1 / x);
+
+ if (sg && ix > underflow) {
+ /*
+ * tgammaf(x) for integral x returns an NaN, so we implement
+ * a poor man's rintf().
+ */
+ volatile float vz;
+ float y,z;
+
+ y = -x;
+
+ vz = y + 0x1p23F; /* depend on 0 <= y < 0x1p23 */
+ z = vz - 0x1p23F; /* rintf(y) for the above range */
+ if (z == y)
+ return ((x - x) / (x - x));
+
+ return (tiny * tiny);
+ }
return (tgamma(x));
}
--
Steve
20161221 https://www.youtube.com/watch?v=IbCHE-hONow
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