sysdeps/ieee754/ldbl-96/s_tanl.c

   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)