Fix LP64 libm for 128-bit long doubles
* reworked amd64/_fpmath.h and arm64/_fpmath.h to support 128-bit long
doubles.
* improved tests to cover long double cases
* made modfl an alias for LP32
Tests pass on x86, x86_64, arm, arm64 and mips.
Bug: 12921273
Change-Id: Ibe39acde57972447a8950fa45b1e702acc68ebeb
diff --git a/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
new file mode 100644
index 0000000..5f4aa37
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
@@ -0,0 +1,61 @@
+/* From: @(#)k_cos.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_cos.c. See ../src/k_cos.c for most comments.
+ */
+
+#include "math_private.h"
+
+/*
+ * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
+ * |cos(x) - c(x))| < 2**-122.0
+ *
+ * 113-bit precision requires more care than 64-bit precision, since
+ * simple methods give a minimax polynomial with coefficient for x^2
+ * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See
+ * ../ld80/k_cosl.c for more details.
+ */
+static const double
+one = 1.0;
+
+static const long double
+C1 = 0.04166666666666666666666666666666658424671L,
+C2 = -0.001388888888888888888888888888863490893732L,
+C3 = 0.00002480158730158730158730158600795304914210L,
+C4 = -0.2755731922398589065255474947078934284324e-6L,
+C5 = 0.2087675698786809897659225313136400793948e-8L,
+C6 = -0.1147074559772972315817149986812031204775e-10L,
+C7 = 0.4779477332386808976875457937252120293400e-13L;
+
+static const double
+C8 = -0.1561920696721507929516718307820958119868e-15,
+C9 = 0.4110317413744594971475941557607804508039e-18,
+C10 = -0.8896592467191938803288521958313920156409e-21,
+C11 = 0.1601061435794535138244346256065192782581e-23;
+
+long double
+__kernel_cosl(long double x, long double y)
+{
+ long double hz,z,r,w;
+
+ z = x*x;
+ r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
+ z*(C8+z*(C9+z*(C10+z*C11))))))))));
+ hz = 0.5*z;
+ w = one-hz;
+ return w + (((one-w)-hz) + (z*r-x*y));
+}