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
  16 #include "math.h"
  17 #include "math_private.h"
  18
  19 static const float
  20 one   =  1.0000000000e+00, /* 0x3f800000 */
  21 pio4  =  7.8539812565e-01, /* 0x3f490fda */
  22 pio4lo=  3.7748947079e-08, /* 0x33222168 */
  23 T[] =  {
  24   3.3333334327e-01, /* 0x3eaaaaab */
  25   1.3333334029e-01, /* 0x3e088889 */
  26   5.3968254477e-02, /* 0x3d5d0dd1 */
  27   2.1869488060e-02, /* 0x3cb327a4 */
  28   8.8632395491e-03, /* 0x3c11371f */
  29   3.5920790397e-03, /* 0x3b6b6916 */
  30   1.4562094584e-03, /* 0x3abede48 */
  31   5.8804126456e-04, /* 0x3a1a26c8 */
  32   2.4646313977e-04, /* 0x398137b9 */
  33   7.8179444245e-05, /* 0x38a3f445 */
  34   7.1407252108e-05, /* 0x3895c07a */
  35  -1.8558637748e-05, /* 0xb79bae5f */
  36   2.5907305826e-05, /* 0x37d95384 */
  37 };
  38
  39 float
  40 __kernel_tanf(float x, float y, int iy)
  41 {
  42         float z,r,v,w,s;
  43         int32_t ix,hx;
  44         GET_FLOAT_WORD(hx,x);
  45         ix = hx&0x7fffffff;     /* high word of |x| */
  46         if(ix<0x31800000)                       /* x < 2**-28 */
  47             {if((int)x==0) {                    /* generate inexact */
  48                 if((ix|(iy+1))==0) return one/fabsf(x);
  49                 else return (iy==1)? x: -one/x;
  50             }
  51             }
  52         if(ix>=0x3f2ca140) {                    /* |x|>=0.6744 */
  53             if(hx<0) {x = -x; y = -y;}
  54             z = pio4-x;
  55             w = pio4lo-y;
  56             x = z+w; y = 0.0;
  57         }
  58         z       =  x*x;
  59         w       =  z*z;
  60     /* Break x^5*(T[1]+x^2*T[2]+...) into
  61      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
  62      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
  63      */
  64         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  65         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  66         s = z*x;
  67         r = y + z*(s*(r+v)+y);
  68         r += T[0]*s;
  69         w = x+r;
  70         if(ix>=0x3f2ca140) {
  71             v = (float)iy;
  72             return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
  73         }
  74         if(iy==1) return w;
  75         else {          /* if allow error up to 2 ulp,
  76                            simply return -1.0/(x+r) here */
  77      /*  compute -1.0/(x+r) accurately */
  78             float a,t;
  79             int32_t i;
  80             z  = w;
  81             GET_FLOAT_WORD(i,z);
  82             SET_FLOAT_WORD(z,i&0xfffff000);
  83             v  = r-(z - x);     /* z+v = r+x */
  84             t = a  = -(float)1.0/w;     /* a = -1.0/w */
  85             GET_FLOAT_WORD(i,t);
  86             SET_FLOAT_WORD(t,i&0xfffff000);
  87             s  = (float)1.0+t*z;
  88             return t+a*(s+t*v);
  89         }
  90 }