gonzui

    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: /* tan(x)
   14:  * Return tangent function of x.
   15:  *
   16:  * kernel function:
   17:  *      __kernel_tan         ... tangent function on [-pi/4,pi/4]
   18:  *      __ieee754_rem_pio2   ... argument reduction routine
   19:  *
   20:  * Method.
   21:  *      Let S,C and T denote the sin, cos and tan respectively on 
   22:  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 
   23:  *      in [-pi/4 , +pi/4], and let n = k mod 4.
   24:  *      We have
   25:  *
   26:  *          n        sin(x)      cos(x)        tan(x)
   27:  *     ----------------------------------------------------------
   28:  *          0               S          C           T
   29:  *          1               C         -S          -1/T
   30:  *          2              -S         -C           T
   31:  *          3              -C          S          -1/T
   32:  *     ----------------------------------------------------------
   33:  *
   34:  * Special cases:
   35:  *      Let trig be any of sin, cos, or tan.
   36:  *      trig(+-INF)  is NaN, with signals;
   37:  *      trig(NaN)    is that NaN;
   38:  *
   39:  * Accuracy:
   40:  *      TRIG(x) returns trig(x) nearly rounded 
   41:  */
   42: 
   43: /* LINTLIBRARY */
   44: 
   45: #include <sys/cdefs.h>
   46: #include <float.h>
   47: #include <math.h>
   48: 
   49: #include "math_private.h"
   50: 
   51: double
   52: tan(double x)
   53: {
   54:         double y[2],z=0.0;
   55:         int32_t n, ix;
   56: 
   57:     /* High word of x. */
   58:         GET_HIGH_WORD(ix,x);
   59: 
   60:     /* |x| ~< pi/4 */
   61:         ix &= 0x7fffffff;
   62:         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
   63: 
   64:     /* tan(Inf or NaN) is NaN */
   65:         else if (ix>=0x7ff00000) return x-x;           /* NaN */
   66: 
   67:     /* argument reduction needed */
   68:         else {
   69:             n = __ieee754_rem_pio2(x,y);
   70:             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
   71:                                                         -1 -- n odd */
   72:         }
   73: }
   74: 
   75: #if     LDBL_MANT_DIG == 53
   76: #ifdef  lint
   77: /* PROTOLIB1 */
   78: long double tanl(long double);
   79: #else   /* lint */
   80: __weak_alias(tanl, tan);
   81: #endif  /* lint */
   82: #endif  /* LDBL_MANT_DIG == 53 */