github.com/afumu/libc@v0.0.6/musl/src/math/tan.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunPro, a Sun Microsystems, Inc. business.
     7   * Permission to use, copy, modify, and distribute this
     8   * software is freely granted, provided that this notice
     9   * is preserved.
    10   * ====================================================
    11   */
    12  /* tan(x)
    13   * Return tangent function of x.
    14   *
    15   * kernel function:
    16   *      __tan           ... tangent function on [-pi/4,pi/4]
    17   *      __rem_pio2      ... argument reduction routine
    18   *
    19   * Method.
    20   *      Let S,C and T denote the sin, cos and tan respectively on
    21   *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
    22   *      in [-pi/4 , +pi/4], and let n = k mod 4.
    23   *      We have
    24   *
    25   *          n        sin(x)      cos(x)        tan(x)
    26   *     ----------------------------------------------------------
    27   *          0          S           C             T
    28   *          1          C          -S            -1/T
    29   *          2         -S          -C             T
    30   *          3         -C           S            -1/T
    31   *     ----------------------------------------------------------
    32   *
    33   * Special cases:
    34   *      Let trig be any of sin, cos, or tan.
    35   *      trig(+-INF)  is NaN, with signals;
    36   *      trig(NaN)    is that NaN;
    37   *
    38   * Accuracy:
    39   *      TRIG(x) returns trig(x) nearly rounded
    40   */
    41  
    42  #include "libm.h"
    43  
    44  double tan(double x)
    45  {
    46  	double y[2];
    47  	uint32_t ix;
    48  	unsigned n;
    49  
    50  	GET_HIGH_WORD(ix, x);
    51  	ix &= 0x7fffffff;
    52  
    53  	/* |x| ~< pi/4 */
    54  	if (ix <= 0x3fe921fb) {
    55  		if (ix < 0x3e400000) { /* |x| < 2**-27 */
    56  			/* raise inexact if x!=0 and underflow if subnormal */
    57  			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
    58  			return x;
    59  		}
    60  		return __tan(x, 0.0, 0);
    61  	}
    62  
    63  	/* tan(Inf or NaN) is NaN */
    64  	if (ix >= 0x7ff00000)
    65  		return x - x;
    66  
    67  	/* argument reduction */
    68  	n = __rem_pio2(x, y);
    69  	return __tan(y[0], y[1], n&1);
    70  }