sysdeps/libm-ieee754/s_tanl.c

   1 /* s_tanl.c -- long double version of s_tan.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   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 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* tanl(x)
  22  * Return tangent function of x.
  23  *
  24  * kernel function:
  25  *      __kernel_tanl           ... tangent function on [-pi/4,pi/4]
  26  *      __ieee754_rem_pio2l     ... argument reduction routine
  27  *
  28  * Method.
  29  *      Let S,C and T denote the sin, cos and tan respectively on
  30  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  31  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  32  *      We have
  33  *
  34  *          n        sin(x)      cos(x)        tan(x)
  35  *     ----------------------------------------------------------
  36  *          0          S           C             T
  37  *          1          C          -S            -1/T
  38  *          2         -S          -C             T
  39  *          3         -C           S            -1/T
  40  *     ----------------------------------------------------------
  41  *
  42  * Special cases:
  43  *      Let trig be any of sin, cos, or tan.
  44  *      trig(+-INF)  is NaN, with signals;
  45  *      trig(NaN)    is that NaN;
  46  *
  47  * Accuracy:
  48  *      TRIG(x) returns trig(x) nearly rounded
  49  */
  50
  51 #include "math.h"
  52 #include "math_private.h"
  53
  54 #ifdef __STDC__
  55         long double __tanl(long double x)
  56 #else
  57         long double __tanl(x)
  58         long double x;
  59 #endif
  60 {
  61         long double y[2],z=0.0;
  62         int32_t n, se;
  63
  64     /* High word of x. */
  65         GET_LDOUBLE_EXP(se,x);
  66
  67     /* |x| ~< pi/4 */
  68         se &= 0x7fff;
  69         if(se <= 0x3ffe) return __kernel_tanl(x,z,1);
  70
  71     /* tan(Inf or NaN) is NaN */
  72         else if (se==0x7fff) return x-x;                /* NaN */
  73
  74     /* argument reduction needed */
  75         else {
  76             n = __ieee754_rem_pio2l(x,y);
  77             return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  78                                                         -1 -- n odd */
  79         }
  80 }
  81 weak_alias (__tanl, tanl)