sysdeps/ieee754/ldbl-128ibm/s_tanl.c

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