lib/libm/src/s_tan.c

   1 /* @(#)s_tan.c 5.1 93/09/24 */
   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  * $NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/s_tan.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* tan(x)
  17  * Return tangent function of x.
  18  *
  19  * kernel function:
  20  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  21  *      __libm_rem_pio2         ... argument reduction routine
  22  *
  23  * Method.
  24  *      Let S,C and T denote the sin, cos and tan respectively on
  25  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  26  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  27  *      We have
  28  *
  29  *          n        sin(x)      cos(x)        tan(x)
  30  *     ----------------------------------------------------------
  31  *          0          S           C             T
  32  *          1          C          -S            -1/T
  33  *          2         -S          -C             T
  34  *          3         -C           S            -1/T
  35  *     ----------------------------------------------------------
  36  *
  37  * Special cases:
  38  *      Let trig be any of sin, cos, or tan.
  39  *      trig(+-INF)  is NaN, with signals;
  40  *      trig(NaN)    is that NaN;
  41  *
  42  * Accuracy:
  43  *      TRIG(x) returns trig(x) nearly rounded
  44  */
  45
  46 #include <math.h>
  47 #include "math_private.h"
  48
  49 double
  50 tan(double x)
  51 {
  52         double y[2],z=0.0;
  53         int32_t n, ix;
  54
  55     /* High word of x. */
  56         GET_HIGH_WORD(ix,x);
  57
  58     /* |x| ~< pi/4 */
  59         ix &= 0x7fffffff;
  60         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
  61
  62     /* tan(Inf or NaN) is NaN */
  63         else if (ix>=0x7ff00000) return x-x;            /* NaN */
  64
  65     /* argument reduction needed */
  66         else {
  67             n = __libm_rem_pio2(x,y);
  68             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  69                                                         -1 -- n odd */
  70         }
  71 }