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 <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.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
  44 __kernel_tanf(float x, float y, int iy)
  45 {
  46         float z,r,v,w,s;
  47         int32_t ix,hx;
  48         GET_FLOAT_WORD(hx,x);
  49         ix = hx&0x7fffffff;     /* high word of |x| */
  50         if(ix<0x31800000)                       /* x < 2**-28 */
  51             {if((int)x==0) {                    /* generate inexact */
  52                 if((ix|(iy+1))==0) return one/fabsf(x);
  53                 else return (iy==1)? x: -one/x;
  54             }
  55             }
  56         if(ix>=0x3f2ca140) {                    /* |x|>=0.6744 */
  57             if(hx<0) {x = -x; y = -y;}
  58             z = pio4-x;
  59             w = pio4lo-y;
  60             x = z+w; y = 0.0;
  61         }
  62         z       =  x*x;
  63         w       =  z*z;
  64     /* Break x^5*(T[1]+x^2*T[2]+...) into
  65      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
  66      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
  67      */
  68         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  69         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  70         s = z*x;
  71         r = y + z*(s*(r+v)+y);
  72         r += T[0]*s;
  73         w = x+r;
  74         if(ix>=0x3f2ca140) {
  75             v = (float)iy;
  76             return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
  77         }
  78         if(iy==1) return w;
  79         else {          /* if allow error up to 2 ulp,
  80                            simply return -1.0/(x+r) here */
  81      /*  compute -1.0/(x+r) accurately */
  82             float a,t;
  83             int32_t i;
  84             z  = w;
  85             GET_FLOAT_WORD(i,z);
  86             SET_FLOAT_WORD(z,i&0xfffff000);
  87             v  = r-(z - x);     /* z+v = r+x */
  88             t = a  = -(float)1.0/w;     /* a = -1.0/w */
  89             GET_FLOAT_WORD(i,t);
  90             SET_FLOAT_WORD(t,i&0xfffff000);
  91             s  = (float)1.0+t*z;
  92             return t+a*(s+t*v);
  93         }
  94 }