toolchain/gcc/newlib/libm/math/s_tan.c

   1
   2 /* @(#)s_tan.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14
  15 /*
  16
  17 FUNCTION
  18         <<tan>>, <<tanf>>---tangent
  19
  20 INDEX
  21 tan
  22 INDEX
  23 tanf
  24
  25 ANSI_SYNOPSIS
  26         #include <math.h>
  27         double tan(double <[x]>);
  28         float tanf(float <[x]>);
  29
  30 TRAD_SYNOPSIS
  31         #include <math.h>
  32         double tan(<[x]>)
  33         double <[x]>;
  34
  35         float tanf(<[x]>)
  36         float <[x]>;
  37
  38
  39 DESCRIPTION
  40 <<tan>> computes the tangent of the argument <[x]>.
  41 Angles are specified in radians.
  42
  43 <<tanf>> is identical, save that it takes and returns <<float>> values.
  44
  45 RETURNS
  46 The tangent of <[x]> is returned.
  47
  48 PORTABILITY
  49 <<tan>> is ANSI. <<tanf>> is an extension.
  50 */
  51
  52 /* tan(x)
  53  * Return tangent function of x.
  54  *
  55  * kernel function:
  56  *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
  57  *      __ieee754_rem_pio2      ... argument reduction routine
  58  *
  59  * Method.
  60  *      Let S,C and T denote the sin, cos and tan respectively on
  61  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  62  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  63  *      We have
  64  *
  65  *          n        sin(x)      cos(x)        tan(x)
  66  *     ----------------------------------------------------------
  67  *          0          S           C             T
  68  *          1          C          -S            -1/T
  69  *          2         -S          -C             T
  70  *          3         -C           S            -1/T
  71  *     ----------------------------------------------------------
  72  *
  73  * Special cases:
  74  *      Let trig be any of sin, cos, or tan.
  75  *      trig(+-INF)  is NaN, with signals;
  76  *      trig(NaN)    is that NaN;
  77  *
  78  * Accuracy:
  79  *      TRIG(x) returns trig(x) nearly rounded
  80  */
  81
  82 #include "fdlibm.h"
  83
  84 #ifndef _DOUBLE_IS_32BITS
  85
  86 #ifdef __STDC__
  87         double tan(double x)
  88 #else
  89         double tan(x)
  90         double x;
  91 #endif
  92 {
  93         double y[2],z=0.0;
  94         __int32_t n,ix;
  95
  96     /* High word of x. */
  97         GET_HIGH_WORD(ix,x);
  98
  99     /* |x| ~< pi/4 */
 100         ix &= 0x7fffffff;
 101         if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
 102
 103     /* tan(Inf or NaN) is NaN */
 104         else if (ix>=0x7ff00000) return x-x;            /* NaN */
 105
 106     /* argument reduction needed */
 107         else {
 108             n = __ieee754_rem_pio2(x,y);
 109             return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
 110                                                         -1 -- n odd */
 111         }
 112 }
 113
 114 #endif /* _DOUBLE_IS_32BITS */