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      1 /* k_tanf.c -- float version of k_tan.c
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 }
     95