src/math/tan.c

   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 }