Upgrade libm.
This brings us up to date with FreeBSD HEAD, fixes various bugs, unifies
the set of functions we support on ARM, MIPS, and x86, fixes "long double",
adds ISO C99 support, and adds basic unit tests.
It turns out that our "long double" functions have always been broken
for non-normal numbers. This patch fixes that by not using the upstream
implementations and just forwarding to the regular "double" implementation
instead (since "long double" on Android is just "double" anyway, which is
what BSD doesn't support).
All the tests pass on ARM, MIPS, and x86, plus glibc on x86-64.
Bug: 3169850
Bug: 8012787
Bug: https://code.google.com/p/android/issues/detail?id=6697
Change-Id: If0c343030959c24bfc50d4d21c9530052c581837
diff --git a/libm/upstream-freebsd/lib/msun/src/k_tanf.c b/libm/upstream-freebsd/lib/msun/src/k_tanf.c
new file mode 100644
index 0000000..52f1aaa
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/k_tanf.c
@@ -0,0 +1,66 @@
+/* k_tanf.c -- float version of k_tan.c
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+
+/*
+ * ====================================================
+ * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef INLINE_KERNEL_TANDF
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
+static const double
+T[] = {
+ 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
+ 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
+ 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
+ 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
+ 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
+ 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
+};
+
+#ifdef INLINE_KERNEL_TANDF
+static __inline
+#endif
+float
+__kernel_tandf(double x, int iy)
+{
+ double z,r,w,s,t,u;
+
+ z = x*x;
+ /*
+ * Split up the polynomial into small independent terms to give
+ * opportunities for parallel evaluation. The chosen splitting is
+ * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
+ * relative to Horner's method on sequential machines.
+ *
+ * We add the small terms from lowest degree up for efficiency on
+ * non-sequential machines (the lowest degree terms tend to be ready
+ * earlier). Apart from this, we don't care about order of
+ * operations, and don't need to to care since we have precision to
+ * spare. However, the chosen splitting is good for accuracy too,
+ * and would give results as accurate as Horner's method if the
+ * small terms were added from highest degree down.
+ */
+ r = T[4]+z*T[5];
+ t = T[2]+z*T[3];
+ w = z*z;
+ s = z*x;
+ u = T[0]+z*T[1];
+ r = (x+s*u)+(s*w)*(t+w*r);
+ if(iy==1) return r;
+ else return -1.0/r;
+}