k_tanf.c

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/* k_tanf.c -- float version of k_tan.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "math_private.h"

static const float 
one   =  1.0000000000e+00, /* 0x3f800000 */
pio4  =  7.8539812565e-01, /* 0x3f490fda */
pio4lo=  3.7748947079e-08, /* 0x33222168 */
T[] =  {
  3.3333334327e-01, /* 0x3eaaaaab */
  1.3333334029e-01, /* 0x3e088889 */
  5.3968254477e-02, /* 0x3d5d0dd1 */
  2.1869488060e-02, /* 0x3cb327a4 */
  8.8632395491e-03, /* 0x3c11371f */
  3.5920790397e-03, /* 0x3b6b6916 */
  1.4562094584e-03, /* 0x3abede48 */
  5.8804126456e-04, /* 0x3a1a26c8 */
  2.4646313977e-04, /* 0x398137b9 */
  7.8179444245e-05, /* 0x38a3f445 */
  7.1407252108e-05, /* 0x3895c07a */
 -1.8558637748e-05, /* 0xb79bae5f */
  2.5907305826e-05, /* 0x37d95384 */
};

float
__kernel_tanf(float x, float y, int iy)
{
    float z,r,v,w,s;
    int32_t ix,hx;
    GET_FLOAT_WORD(hx,x);
    ix = hx&0x7fffffff; /* high word of |x| */
    if(ix<0x31800000)           /* x < 2**-28 */
        {if((int)x==0) {            /* generate inexact */
        if((ix|(iy+1))==0) return one/fabsf(x);
        else return (iy==1)? x: -one/x;
        }
        }
    if(ix>=0x3f2ca140) {            /* |x|>=0.6744 */
        if(hx<0) {x = -x; y = -y;}
        z = pio4-x;
        w = pio4lo-y;
        x = z+w; y = 0.0;
    }
    z   =  x*x;
    w   =  z*z;
    /* Break x^5*(T[1]+x^2*T[2]+...) into
     *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
     *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
     */
    r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
    v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
    s = z*x;
    r = y + z*(s*(r+v)+y);
    r += T[0]*s;
    w = x+r;
    if(ix>=0x3f2ca140) {
        v = (float)iy;
        return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
    }
    if(iy==1) return w;
    else {      /* if allow error up to 2 ulp, 
               simply return -1.0/(x+r) here */
     /*  compute -1.0/(x+r) accurately */
        float a,t;
        int32_t i;
        z  = w;
        GET_FLOAT_WORD(i,z);
        SET_FLOAT_WORD(z,i&0xfffff000);
        v  = r-(z - x);     /* z+v = r+x */
        t = a  = -(float)1.0/w; /* a = -1.0/w */
        GET_FLOAT_WORD(i,t);
        SET_FLOAT_WORD(t,i&0xfffff000);
        s  = (float)1.0+t*z;
        return t+a*(s+t*v);
    }
}