1  /* s_tanl.c -- long double version of s_tan.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  #if defined(LIBM_SCCS) && !defined(lint)
      16  static char rcsid[] = "$NetBSD: $";
      17  #endif
      18  
      19  /* tanl(x)
      20   * Return tangent function of x.
      21   *
      22   * kernel function:
      23   *	__kernel_tanl		... tangent function on [-pi/4,pi/4]
      24   *	__ieee754_rem_pio2l	... argument reduction routine
      25   *
      26   * Method.
      27   *      Let S,C and T denote the sin, cos and tan respectively on
      28   *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
      29   *	in [-pi/4 , +pi/4], and let n = k mod 4.
      30   *	We have
      31   *
      32   *          n        sin(x)      cos(x)        tan(x)
      33   *     ----------------------------------------------------------
      34   *	    0	       S	   C		 T
      35   *	    1	       C	  -S		-1/T
      36   *	    2	      -S	  -C		 T
      37   *	    3	      -C	   S		-1/T
      38   *     ----------------------------------------------------------
      39   *
      40   * Special cases:
      41   *      Let trig be any of sin, cos, or tan.
      42   *      trig(+-INF)  is NaN, with signals;
      43   *      trig(NaN)    is that NaN;
      44   *
      45   * Accuracy:
      46   *	TRIG(x) returns trig(x) nearly rounded
      47   */
      48  
      49  #include <errno.h>
      50  #include <math.h>
      51  #include <math_private.h>
      52  #include <libm-alias-ldouble.h>
      53  
      54  long double __tanl(long double x)
      55  {
      56  	long double y[2],z=0.0;
      57  	int32_t n, se, i0, i1;
      58  
      59      /* High word of x. */
      60  	GET_LDOUBLE_WORDS(se,i0,i1,x);
      61  
      62      /* |x| ~< pi/4 */
      63  	se &= 0x7fff;
      64  	if(se <= 0x3ffe) return __kernel_tanl(x,z,1);
      65  
      66      /* tan(Inf or NaN) is NaN */
      67  	else if (se==0x7fff) {
      68  	  if (i1 == 0 && i0 == 0x80000000)
      69  	    __set_errno (EDOM);
      70  	  return x-x;
      71  	}
      72  
      73      /* argument reduction needed */
      74  	else {
      75  	    n = __ieee754_rem_pio2l(x,y);
      76  	    return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
      77  							-1 -- n odd */
      78  	}
      79  }
      80  libm_alias_ldouble (__tan, tan)