1  /* k_tanf.c -- float version of k_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: k_tanf.c,v 1.4 1995/05/10 20:46:39 jtc Exp $";
      17  #endif
      18  
      19  #include <float.h>
      20  #include <math.h>
      21  #include <math_private.h>
      22  #include <math-underflow.h>
      23  static const float
      24  one   =  1.0000000000e+00, /* 0x3f800000 */
      25  pio4  =  7.8539812565e-01, /* 0x3f490fda */
      26  pio4lo=  3.7748947079e-08, /* 0x33222168 */
      27  T[] =  {
      28    3.3333334327e-01, /* 0x3eaaaaab */
      29    1.3333334029e-01, /* 0x3e088889 */
      30    5.3968254477e-02, /* 0x3d5d0dd1 */
      31    2.1869488060e-02, /* 0x3cb327a4 */
      32    8.8632395491e-03, /* 0x3c11371f */
      33    3.5920790397e-03, /* 0x3b6b6916 */
      34    1.4562094584e-03, /* 0x3abede48 */
      35    5.8804126456e-04, /* 0x3a1a26c8 */
      36    2.4646313977e-04, /* 0x398137b9 */
      37    7.8179444245e-05, /* 0x38a3f445 */
      38    7.1407252108e-05, /* 0x3895c07a */
      39   -1.8558637748e-05, /* 0xb79bae5f */
      40    2.5907305826e-05, /* 0x37d95384 */
      41  };
      42  
      43  float __kernel_tanf(float x, float y, int iy)
      44  {
      45  	float z,r,v,w,s;
      46  	int32_t ix,hx;
      47  	GET_FLOAT_WORD(hx,x);
      48  	ix = hx&0x7fffffff;	/* high word of |x| */
      49  	if(ix<0x39000000)			/* x < 2**-13 */
      50  	    {if((int)x==0) {			/* generate inexact */
      51  		if((ix|(iy+1))==0) return one/fabsf(x);
      52  		else if (iy == 1)
      53  		  {
      54  		    math_check_force_underflow (x);
      55  		    return x;
      56  		  }
      57  		else
      58  		  return -one / x;
      59  	    }
      60  	    }
      61  	if(ix>=0x3f2ca140) { 			/* |x|>=0.6744 */
      62  	    if(hx<0) {x = -x; y = -y;}
      63  	    z = pio4-x;
      64  	    w = pio4lo-y;
      65  	    x = z+w; y = 0.0;
      66  	    if (fabsf (x) < 0x1p-13f)
      67  		return (1 - ((hx >> 30) & 2)) * iy * (1.0f - 2 * iy * x);
      68  	}
      69  	z	=  x*x;
      70  	w 	=  z*z;
      71      /* Break x^5*(T[1]+x^2*T[2]+...) into
      72       *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
      73       *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
      74       */
      75  	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
      76  	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
      77  	s = z*x;
      78  	r = y + z*(s*(r+v)+y);
      79  	r += T[0]*s;
      80  	w = x+r;
      81  	if(ix>=0x3f2ca140) {
      82  	    v = (float)iy;
      83  	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
      84  	}
      85  	if(iy==1) return w;
      86  	else {		/* if allow error up to 2 ulp,
      87  			   simply return -1.0/(x+r) here */
      88       /*  compute -1.0/(x+r) accurately */
      89  	    float a,t;
      90  	    int32_t i;
      91  	    z  = w;
      92  	    GET_FLOAT_WORD(i,z);
      93  	    SET_FLOAT_WORD(z,i&0xfffff000);
      94  	    v  = r-(z - x); 	/* z+v = r+x */
      95  	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
      96  	    GET_FLOAT_WORD(i,t);
      97  	    SET_FLOAT_WORD(t,i&0xfffff000);
      98  	    s  = (float)1.0+t*z;
      99  	    return t+a*(s+t*v);
     100  	}
     101  }