libquadmath/math/tanq.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 /* tanq(x)
  18  * Return tangent function of x.
  19  *
  20  * kernel function:
  21  *      __quadmath_kernel_tanq          ... tangent function on [-pi/4,pi/4]
  22  *      __quadmath_rem_pio2q    ... 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 "quadmath-imp.h"
  48
  49 __float128 tanq(__float128 x)
  50 {
  51         __float128 y[2],z=0;
  52         int64_t n, ix;
  53
  54     /* High word of x. */
  55         GET_FLT128_MSW64(ix,x);
  56
  57     /* |x| ~< pi/4 */
  58         ix &= 0x7fffffffffffffffLL;
  59         if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
  60
  61     /* tanq(Inf or NaN) is NaN */
  62         else if (ix>=0x7fff000000000000LL) {
  63             if (ix == 0x7fff000000000000LL) {
  64                 GET_FLT128_LSW64(n,x);
  65                 if (n == 0)
  66                     errno = EDOM;
  67             }
  68             return x-x;         /* NaN */
  69         }
  70
  71     /* argument reduction needed */
  72         else {
  73             n = __quadmath_rem_pio2q(x,y);
  74             return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  75                                                         -1 -- n odd */
  76         }
  77 }