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+/* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* tan(x)
+ * Return tangent function of x.
+ *
+ * kernel function:
+ * __tan ... tangent function on [-pi/4,pi/4]
+ * __rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "libm.h"
+
+double tan(double x)
+{
+ double y[2], z = 0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix, x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if (ix <= 0x3fe921fb) {
+ if (ix < 0x3e400000) /* x < 2**-27 */
+ /* raise inexact if x != 0 */
+ if ((int)x == 0)
+ return x;
+ return __tan(x, z, 1);
+ }
+
+ /* tan(Inf or NaN) is NaN */
+ if (ix >= 0x7ff00000)
+ return x - x;
+
+ /* argument reduction needed */
+ n = __rem_pio2(x, y);
+ return __tan(y[0], y[1], 1 - ((n&1)<<1)); /* n even: 1, n odd: -1 */
+}