Adding upstream version 115.8.0esr.upstream/115.8.0esr

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 131 insertions, 0 deletions

diff --git a/modules/fdlibm/src/k_tan.cpp b/modules/fdlibm/src/k_tan.cpp
new file mode 100644
index 0000000000..de08717983
--- /dev/null
+++ b/modules/fdlibm/src/k_tan.cpp
@@ -0,0 +1,131 @@
+/* @(#)k_tan.c 1.5 04/04/22 SMI */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* INDENT OFF */
+//#include <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+/* __kernel_tan( x, y, k )
+ * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned.
+ *
+ * Algorithm
+ *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ *	2. Callers must return tan(-0) = -0 without calling here since our
+ *	   odd polynomial is not evaluated in a way that preserves -0.
+ *	   Callers may do the optimization tan(x) ~ x for tiny x.
+ *	3. tan(x) is approximated by a odd polynomial of degree 27 on
+ *	   [0,0.67434]
+ *		  	         3             27
+ *	   	tan(x) ~ x + T1*x + ... + T13*x
+ *	   where
+ *
+ * 	        |tan(x)         2     4            26   |     -59.2
+ * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
+ * 	        |  x 					|
+ *
+ *	   Note: tan(x+y) = tan(x) + tan'(x)*y
+ *		          ~ tan(x) + (1+x*x)*y
+ *	   Therefore, for better accuracy in computing tan(x+y), let
+ *		     3      2      2       2       2
+ *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+ *	   then
+ *		 		    3    2
+ *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
+ *
+ *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
+ *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include "math_private.h"
+static const double xxx[] = {
+		 3.33333333333334091986e-01,	/* 3FD55555, 55555563 */
+		 1.33333333333201242699e-01,	/* 3FC11111, 1110FE7A */
+		 5.39682539762260521377e-02,	/* 3FABA1BA, 1BB341FE */
+		 2.18694882948595424599e-02,	/* 3F9664F4, 8406D637 */
+		 8.86323982359930005737e-03,	/* 3F8226E3, E96E8493 */
+		 3.59207910759131235356e-03,	/* 3F6D6D22, C9560328 */
+		 1.45620945432529025516e-03,	/* 3F57DBC8, FEE08315 */
+		 5.88041240820264096874e-04,	/* 3F4344D8, F2F26501 */
+		 2.46463134818469906812e-04,	/* 3F3026F7, 1A8D1068 */
+		 7.81794442939557092300e-05,	/* 3F147E88, A03792A6 */
+		 7.14072491382608190305e-05,	/* 3F12B80F, 32F0A7E9 */
+		-1.85586374855275456654e-05,	/* BEF375CB, DB605373 */
+		 2.59073051863633712884e-05,	/* 3EFB2A70, 74BF7AD4 */
+/* one */	 1.00000000000000000000e+00,	/* 3FF00000, 00000000 */
+/* pio4 */	 7.85398163397448278999e-01,	/* 3FE921FB, 54442D18 */
+/* pio4lo */	 3.06161699786838301793e-17	/* 3C81A626, 33145C07 */
+};
+#define	one	xxx[13]
+#define	pio4	xxx[14]
+#define	pio4lo	xxx[15]
+#define	T	xxx
+/* INDENT ON */
+
+double
+__kernel_tan(double x, double y, int iy) {
+	double z, r, v, w, s;
+	int32_t ix, hx;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx & 0x7fffffff;			/* high word of |x| */
+	if (ix >= 0x3FE59428) {	/* |x| >= 0.6744 */
+		if (hx < 0) {
+			x = -x;
+			y = -y;
+		}
+		z = pio4 - x;
+		w = pio4lo - y;
+		x = z + w;
+		y = 0.0;
+	}
+	z = x * x;
+	w = z * z;
+	/*
+	 * Break x^5*(T[1]+x^2*T[2]+...) into
+	 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+	 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+	 */
+	r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
+		w * T[11]))));
+	v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
+		w * T[12])))));
+	s = z * x;
+	r = y + z * (s * (r + v) + y);
+	r += T[0] * s;
+	w = x + r;
+	if (ix >= 0x3FE59428) {
+		v = (double) iy;
+		return (double) (1 - ((hx >> 30) & 2)) *
+			(v - 2.0 * (x - (w * w / (w + v) - r)));
+	}
+	if (iy == 1)
+		return w;
+	else {
+		/*
+		 * if allow error up to 2 ulp, simply return
+		 * -1.0 / (x+r) here
+		 */
+		/* compute -1.0 / (x+r) accurately */
+		double a, t;
+		z = w;
+		SET_LOW_WORD(z,0);
+		v = r - (z - x);	/* z+v = r+x */
+		t = a = -1.0 / w;	/* a = -1.0/w */
+		SET_LOW_WORD(t,0);
+		s = 1.0 + t * z;
+		return t + a * (s + t * v);
+	}
+}