1  /* s_tanl.c -- long double version of s_tan.c.
       2   */
       3  
       4  /* @(#)s_tan.c 5.1 93/09/24 */
       5  /*
       6   * ====================================================
       7   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       8   *
       9   * Developed at SunPro, a Sun Microsystems, Inc. business.
      10   * Permission to use, copy, modify, and distribute this
      11   * software is freely granted, provided that this notice
      12   * is preserved.
      13   * ====================================================
      14   */
      15  
      16  /* tanl(x)
      17   * Return tangent function of x.
      18   *
      19   * kernel function:
      20   *	__kernel_tanl		... tangent function on [-pi/4,pi/4]
      21   *	__ieee754_rem_pio2l	... 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 <errno.h>
      47  #include <math.h>
      48  #include <math_private.h>
      49  #include <math_ldbl_opt.h>
      50  
      51  long double __tanl(long double x)
      52  {
      53  	long double y[2],z=0.0L;
      54  	int64_t n, ix;
      55  	double xhi;
      56  
      57      /* High word of x. */
      58  	xhi = ldbl_high (x);
      59  	EXTRACT_WORDS64 (ix, xhi);
      60  
      61      /* |x| ~< pi/4 */
      62  	ix &= 0x7fffffffffffffffLL;
      63  	if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1);
      64  
      65      /* tanl(Inf or NaN) is NaN */
      66  	else if (ix>=0x7ff0000000000000LL) {
      67  	    if (ix == 0x7ff0000000000000LL)
      68  		__set_errno (EDOM);
      69  	    return x-x;		/* NaN */
      70  	}
      71      /* argument reduction needed */
      72  	else {
      73  	    n = __ieee754_rem_pio2l(x,y);
      74  	    return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
      75  							-1 -- n odd */
      76  	}
      77  }
      78  long_double_symbol (libm, __tanl, tanl);