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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz Exp $");
  16 #endif
  17
  18 /* tan(x)
  19  * Return tangent function of x.
  20  *
  21  * kernel function:
  22  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  23  *      __ieee754_rem_pio2      ... argument reduction routine
  24  *
  25  * Method.
  26  *      Let S,C and T denote the sin, cos and tan respectively on
  27  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  28  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  29  *      We have
  30  *
  31  *          n        sin(x)      cos(x)        tan(x)
  32  *     ----------------------------------------------------------
  33  *          0          S           C             T
  34  *          1          C          -S            -1/T
  35  *          2         -S          -C             T
  36  *          3         -C           S            -1/T
  37  *     ----------------------------------------------------------
  38  *
  39  * Special cases:
  40  *      Let trig be any of sin, cos, or tan.
  41  *      trig(+-INF)  is NaN, with signals;
  42  *      trig(NaN)    is that NaN;
  43  *
  44  * Accuracy:
  45  *      TRIG(x) returns trig(x) nearly rounded
  46  */
  47
  48 #include "math.h"
  49 #include "math_private.h"
  50
  51 double
  52 tan(double x)
  53 {
  54         double y[2],z=0.0;
  55         int32_t n, ix;
  56
  57     /* High word of x. */
  58         GET_HIGH_WORD(ix,x);
  59
  60     /* |x| ~< pi/4 */
  61         ix &= 0x7fffffff;
  62         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
  63
  64     /* tan(Inf or NaN) is NaN */
  65         else if (ix>=0x7ff00000) return x-x;            /* NaN */
  66
  67     /* argument reduction needed */
  68         else {
  69             n = __ieee754_rem_pio2(x,y);
  70             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  71                                                         -1 -- n odd */
  72         }
  73 }