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

   1 /* kf_tan.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 "fdlibm.h"
  17 #ifdef __STDC__
  18 static const float
  19 #else
  20 static float
  21 #endif
  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 #ifdef __STDC__
  42         float __kernel_tanf(float x, float y, int iy)
  43 #else
  44         float __kernel_tanf(x, y, iy)
  45         float x,y; int iy;
  46 #endif
  47 {
  48         float z,r,v,w,s;
  49         __int32_t ix,hx;
  50         GET_FLOAT_WORD(hx,x);
  51         ix = hx&0x7fffffff;     /* high word of |x| */
  52         if(ix<0x31800000)                       /* x < 2**-28 */
  53             {if((int)x==0) {                    /* generate inexact */
  54                 if((ix|(iy+1))==0) return one/fabsf(x);
  55                 else return (iy==1)? x: -one/x;
  56             }
  57             }
  58         if(ix>=0x3f2ca140) {                    /* |x|>=0.6744 */
  59             if(hx<0) {x = -x; y = -y;}
  60             z = pio4-x;
  61             w = pio4lo-y;
  62             x = z+w; y = 0.0;
  63         }
  64         z       =  x*x;
  65         w       =  z*z;
  66     /* Break x^5*(T[1]+x^2*T[2]+...) into
  67      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
  68      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
  69      */
  70         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  71         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  72         s = z*x;
  73         r = y + z*(s*(r+v)+y);
  74         r += T[0]*s;
  75         w = x+r;
  76         if(ix>=0x3f2ca140) {
  77             v = (float)iy;
  78             return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
  79         }
  80         if(iy==1) return w;
  81         else {          /* if allow error up to 2 ulp,
  82                            simply return -1.0/(x+r) here */
  83      /*  compute -1.0/(x+r) accurately */
  84             float a,t;
  85             __int32_t i;
  86             z  = w;
  87             GET_FLOAT_WORD(i,z);
  88             SET_FLOAT_WORD(z,i&0xfffff000);
  89             v  = r-(z - x);     /* z+v = r+x */
  90             t = a  = -(float)1.0/w;     /* a = -1.0/w */
  91             GET_FLOAT_WORD(i,t);
  92             SET_FLOAT_WORD(t,i&0xfffff000);
  93             s  = (float)1.0+t*z;
  94             return t+a*(s+t*v);
  95         }
  96 }