compiler/mlib/s_tan.c

   1 /* @(#)s_tan.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #ifndef lint
  14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.10 2005/11/02 14:01:45 bde Exp $";
  15 #endif
  16
  17 /* tan(x)
  18  * Return tangent function of x.
  19  *
  20  * kernel function:
  21  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  22  *      __ieee754_rem_pio2      ... 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 "math.h"
  48 #define INLINE_REM_PIO2
  49 #include "math_private.h"
  50 #include "e_rem_pio2.c"
  51
  52 double
  53 tan(double x)
  54 {
  55         double y[2],z=0.0;
  56         int32_t n, ix;
  57
  58     /* High word of x. */
  59         GET_HIGH_WORD(ix,x);
  60
  61     /* |x| ~< pi/4 */
  62         ix &= 0x7fffffff;
  63         if(ix <= 0x3fe921fb) {
  64             if(ix<0x3e300000)                   /* x < 2**-28 */
  65                 if((int)x==0) return x;         /* generate inexact */
  66             return __kernel_tan(x,z,1);
  67         }
  68
  69     /* tan(Inf or NaN) is NaN */
  70         else if (ix>=0x7ff00000) return x-x;            /* NaN */
  71
  72     /* argument reduction needed */
  73         else {
  74             n = __ieee754_rem_pio2(x,y);
  75             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
  76                                                         -1 -- n odd */
  77         }
  78 }