lib/libm/src/k_tanf.c

   1 /* k_tanf.c -- float version of k_tan.c
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  *
  15  * $NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/k_tanf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21 static const float
  22 one   =  1.0000000000e+00, /* 0x3f800000 */
  23 pio4  =  7.8539812565e-01, /* 0x3f490fda */
  24 pio4lo=  3.7748947079e-08, /* 0x33222168 */
  25 T[] =  {
  26   3.3333334327e-01, /* 0x3eaaaaab */
  27   1.3333334029e-01, /* 0x3e088889 */
  28   5.3968254477e-02, /* 0x3d5d0dd1 */
  29   2.1869488060e-02, /* 0x3cb327a4 */
  30   8.8632395491e-03, /* 0x3c11371f */
  31   3.5920790397e-03, /* 0x3b6b6916 */
  32   1.4562094584e-03, /* 0x3abede48 */
  33   5.8804126456e-04, /* 0x3a1a26c8 */
  34   2.4646313977e-04, /* 0x398137b9 */
  35   7.8179444245e-05, /* 0x38a3f445 */
  36   7.1407252108e-05, /* 0x3895c07a */
  37  -1.8558637748e-05, /* 0xb79bae5f */
  38   2.5907305826e-05, /* 0x37d95384 */
  39 };
  40
  41 float
  42 __kernel_tanf(float x, float y, int iy)
  43 {
  44         float z,r,v,w,s;
  45         int32_t ix,hx;
  46         GET_FLOAT_WORD(hx,x);
  47         ix = hx&0x7fffffff;     /* high word of |x| */
  48         if(ix<0x31800000)                       /* x < 2**-28 */
  49             {if((int)x==0) {                    /* generate inexact */
  50                 if((ix|(iy+1))==0) return one/fabsf(x);
  51                 else return (iy==1)? x: -one/x;
  52             }
  53             }
  54         if(ix>=0x3f2ca140) {                    /* |x|>=0.6744 */
  55             if(hx<0) {x = -x; y = -y;}
  56             z = pio4-x;
  57             w = pio4lo-y;
  58             x = z+w; y = 0.0;
  59         }
  60         z       =  x*x;
  61         w       =  z*z;
  62     /* Break x^5*(T[1]+x^2*T[2]+...) into
  63      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
  64      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
  65      */
  66         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  67         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  68         s = z*x;
  69         r = y + z*(s*(r+v)+y);
  70         r += T[0]*s;
  71         w = x+r;
  72         if(ix>=0x3f2ca140) {
  73             v = (float)iy;
  74             return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
  75         }
  76         if(iy==1) return w;
  77         else {          /* if allow error up to 2 ulp,
  78                            simply return -1.0/(x+r) here */
  79      /*  compute -1.0/(x+r) accurately */
  80             float a,t;
  81             int32_t i;
  82             z  = w;
  83             GET_FLOAT_WORD(i,z);
  84             SET_FLOAT_WORD(z,i&0xfffff000);
  85             v  = r-(z - x);     /* z+v = r+x */
  86             t = a  = -(float)1.0/w;     /* a = -1.0/w */
  87             GET_FLOAT_WORD(i,t);
  88             SET_FLOAT_WORD(t,i&0xfffff000);
  89             s  = (float)1.0+t*z;
  90             return t+a*(s+t*v);
  91         }
  92 }