libm: sync with upstream.
There's potential here to maybe lose some/all of builtins.cpp, but I'll
look at that separately later.
Test: treehugger
Change-Id: I2c2bc1d0753affdd214daeb09fa1ac7cd73db347
diff --git a/libm/upstream-freebsd/lib/msun/src/s_sinpi.c b/libm/upstream-freebsd/lib/msun/src/s_sinpi.c
new file mode 100644
index 0000000..858459a
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/s_sinpi.c
@@ -0,0 +1,169 @@
+/*-
+ * Copyright (c) 2017 Steven G. Kargl
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice unmodified, this list of conditions, and the following
+ * disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/**
+ * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First,
+ * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and
+ * includes reflection symmetry by considering the sign of x on output. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The
+ * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the
+ * floating-point type and M = 2 to 4. To achieve high accuracy, pi is
+ * decomposed into high and low parts with the high part containing a
+ * number of trailing zero bits. x is also split into high and low parts.
+ *
+ * 2. For |x| < 1, argument reduction is not required and sinpi(x) is
+ * computed by calling a kernel that leverages the kernels for sin(x)
+ * ans cos(x). See k_sinpi.c and k_cospi.c for details.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * sinpi(x) = sin(pi*(j0+r))
+ * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r)
+ * = cos(pi*j0) * sin(pi*r)
+ * = +-sinpi(r)
+ *
+ * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1.
+ * sinpi(r) is then computed via an appropriate kernel.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x).
+ *
+ * 5. Special cases:
+ *
+ * sinpi(+-0) = +-0
+ * sinpi(+-n) = +-0, for positive integers n.
+ * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception.
+ * sinpi(nan) = nan. Raises the "invalid" floating-point exception.
+ */
+
+#include <float.h>
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospi.h"
+#include "k_sinpi.h"
+
+volatile static const double vzero = 0;
+
+double
+sinpi(double x)
+{
+ double ax, hi, lo, s;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fd00000) { /* |x| < 0.25 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if (x == 0)
+ return (x);
+ /*
+ * To avoid issues with subnormal values,
+ * scale the computation and rescale on
+ * return.
+ */
+ INSERT_WORDS(hi, hx, 0);
+ hi *= 0x1p53;
+ lo = x * 0x1p53 - hi;
+ s = (pi_lo + pi_hi) * lo + pi_lo * hi +
+ pi_hi * hi;
+ return (s * 0x1p-53);
+ }
+
+ s = __kernel_sinpi(ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ s = __kernel_cospi(0.5 - ax);
+ else if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 20) & 0x7ff) - 0x3ff;
+ if (j0 < 20) {
+ ix &= ~(0x000fffff >> j0);
+ lx = 0;
+ } else {
+ lx &= ~((uint32_t)0xffffffff >> (j0 - 20));
+ }
+ INSERT_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+ if (ix == 0)
+ s = 0;
+ else {
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3fd00000) /* |x| < 0.25 */
+ s = __kernel_sinpi(ax);
+ else
+ s = __kernel_cospi(0.5 - ax);
+ } else {
+ if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ }
+
+ if (j0 > 30)
+ x -= 0x1p30;
+ j0 = (uint32_t)x;
+ if (j0 & 1) s = -s;
+ }
+
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an integer, so return +-0.
+ */
+ return (copysign(0, x));
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(sinpi, sinpil);
+#endif