text: /* 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];
  	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/0x1p120 : x+0x1p120);
  			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);
  }
  