sysdeps/libm-ieee754/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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $";
  15 #endif
  16
  17 /* tan(x)
  18  * Return tangent function of x.
  19  *
  20  * kernel function:
  21  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  22  *      __ieee754_rem_pio2      ... argument reduction routine
  23  *
  24  * Method.
  25  *      Let S,C and T denote the sin, cos and tan respectively on
  26  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  27  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  28  *      We have
  29  *
  30  *          n        sin(x)      cos(x)        tan(x)
  31  *     ----------------------------------------------------------
  32  *          0          S           C             T
  33  *          1          C          -S            -1/T
  34  *          2         -S          -C             T
  35  *          3         -C           S            -1/T
  36  *     ----------------------------------------------------------
  37  *
  38  * Special cases:
  39  *      Let trig be any of sin, cos, or tan.
  40  *      trig(+-INF)  is NaN, with signals;
  41  *      trig(NaN)    is that NaN;
  42  *
  43  * Accuracy:
  44  *      TRIG(x) returns trig(x) nearly rounded
  45  */
  46
  47 #include "math.h"
  48 #include "math_private.h"
  49
  50 #ifdef __STDC__
  51         double __tan(double x)
  52 #else
  53         double __tan(x)
  54         double x;
  55 #endif
  56 {
  57         double y[2],z=0.0;
  58         int32_t n, ix;
  59
  60     /* High word of x. */
  61         GET_HIGH_WORD(ix,x);
  62
  63     /* |x| ~< pi/4 */
  64         ix &= 0x7fffffff;
  65         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
  66
  67     /* tan(Inf or NaN) is NaN */
  68         else if (ix>=0x7ff00000) return x-x;            /* NaN */
  69
  70     /* argument reduction needed */
  71         else {
  72             n = __ieee754_rem_pio2(x,y);
  73             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  74                                                         -1 -- n odd */
  75         }
  76 }
  77 weak_alias (__tan, tan)
  78 #ifdef NO_LONG_DOUBLE
  79 strong_alias (__tan, __tanl)
  80 weak_alias (__tan, tanl)
  81 #endif