Initial import

libc/math/tan.c

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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 "libc/math/libm.h"
+
+double tan(double x)
+{
+	double y[2];
+	uint32_t ix;
+	unsigned n;
+
+	GET_HIGH_WORD(ix, x);
+	ix &= 0x7fffffff;
+
+	/* |x| ~< pi/4 */
+	if (ix <= 0x3fe921fb) {
+		if (ix < 0x3e400000) { /* |x| < 2**-27 */
+			/* raise inexact if x!=0 and underflow if subnormal */
+			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
+			return x;
+		}
+		return __tan(x, 0.0, 0);
+	}
+
+	/* tan(Inf or NaN) is NaN */
+	if (ix >= 0x7ff00000)
+		return x - x;
+
+	/* argument reduction */
+	n = __rem_pio2(x, y);
+	return __tan(y[0], y[1], n&1);
+}