libm/s_tan.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* tan(x)
  13  * Return tangent function of x.
  14  *
  15  * kernel function:
  16  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  17  *      __ieee754_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 "math.h"
  43 #include "math_private.h"
  44
  45 double tan(double x)
  46 {
  47         double y[2],z=0.0;
  48         int32_t n, ix;
  49
  50     /* High word of x. */
  51         GET_HIGH_WORD(ix,x);
  52
  53     /* |x| ~< pi/4 */
  54         ix &= 0x7fffffff;
  55         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
  56
  57     /* tan(Inf or NaN) is NaN */
  58         else if (ix>=0x7ff00000) return x-x;            /* NaN */
  59
  60     /* argument reduction needed */
  61         else {
  62             n = __ieee754_rem_pio2(x,y);
  63             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  64                                                         -1 -- n odd */
  65         }
  66 }
  67 libm_hidden_def(tan)