k_tanf.c revision 152343 
12116Sjkh/* k_tanf.c -- float version of k_tan.c
22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
32116Sjkh */
42116Sjkh
52116Sjkh/*
62116Sjkh * ====================================================
7129981Sdas * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
82116Sjkh *
92116Sjkh * Permission to use, copy, modify, and distribute this
108870Srgrimes * software is freely granted, provided that this notice
112116Sjkh * is preserved.
122116Sjkh * ====================================================
132116Sjkh */
142116Sjkh
152116Sjkh#ifndef lint
1650476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152343 2005-11-12 20:06:04Z bde $";
172116Sjkh#endif
182116Sjkh
192116Sjkh#include "math.h"
202116Sjkh#include "math_private.h"
21152343Sbde
228870Srgrimesstatic const float
232116Sjkhpio4  =  7.8539812565e-01, /* 0x3f490fda */
242116Sjkhpio4lo=  3.7748947079e-08, /* 0x33222168 */
25152343Sbde/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */
262116SjkhT[] =  {
27152343Sbde  0xaaaaa3.0p-25,		/* 0.33333310485 */
28152343Sbde  0x888b06.0p-26,		/* 0.13334283238 */
29152343Sbde  0xdc84c8.0p-28,		/* 0.053837567568 */
30152343Sbde  0xb9d8f1.0p-29,		/* 0.022686453536 */
31152343Sbde  0xcfe632.0p-31,		/* 0.0063445800915 */
32152343Sbde  0xeaf97e.0p-31,		/* 0.0071708550677 */
332116Sjkh};
342116Sjkh
3597413Salfredfloat
3697413Salfred__kernel_tanf(float x, float y, int iy)
372116Sjkh{
382116Sjkh	float z,r,v,w,s;
392116Sjkh	int32_t ix,hx;
40152343Sbde
412116Sjkh	GET_FLOAT_WORD(hx,x);
42152343Sbde	ix = hx&0x7fffffff;
43152343Sbde	if(ix>=0x3f2ca140) { 			/* |x|>=0.67434 */
442116Sjkh	    if(hx<0) {x = -x; y = -y;}
452116Sjkh	    z = pio4-x;
462116Sjkh	    w = pio4lo-y;
472116Sjkh	    x = z+w; y = 0.0;
482116Sjkh	}
492116Sjkh	z	=  x*x;
502116Sjkh	w 	=  z*z;
512116Sjkh    /* Break x^5*(T[1]+x^2*T[2]+...) into
52152284Sbde     *	  x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
53152284Sbde     *	  x^5*(x^2*(T[2]+x^4*T[4]))
542116Sjkh     */
55152284Sbde	r = T[1]+w*(T[3]+w*T[5]);
56152284Sbde	v = z*(T[2]+w*T[4]);
572116Sjkh	s = z*x;
582116Sjkh	r = y + z*(s*(r+v)+y);
592116Sjkh	r += T[0]*s;
602116Sjkh	w = x+r;
612116Sjkh	if(ix>=0x3f2ca140) {
622116Sjkh	    v = (float)iy;
632116Sjkh	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
642116Sjkh	}
652116Sjkh	if(iy==1) return w;
668870Srgrimes	else {		/* if allow error up to 2 ulp,
672116Sjkh			   simply return -1.0/(x+r) here */
682116Sjkh     /*  compute -1.0/(x+r) accurately */
692116Sjkh	    float a,t;
702116Sjkh	    int32_t i;
712116Sjkh	    z  = w;
722116Sjkh	    GET_FLOAT_WORD(i,z);
732116Sjkh	    SET_FLOAT_WORD(z,i&0xfffff000);
742116Sjkh	    v  = r-(z - x); 	/* z+v = r+x */
752116Sjkh	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
762116Sjkh	    GET_FLOAT_WORD(i,t);
772116Sjkh	    SET_FLOAT_WORD(t,i&0xfffff000);
782116Sjkh	    s  = (float)1.0+t*z;
792116Sjkh	    return t+a*(s+t*v);
802116Sjkh	}
812116Sjkh}
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