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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 2004 Sun Microsystems, Inc. All Rights Reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef lint
static char rcsid[] = "$FreeBSD$";
#endif
#include "math.h"
#include "math_private.h"
static const float
pio4 = 7.8539812565e-01, /* 0x3f490fda */
pio4lo= 3.7748947079e-08, /* 0x33222168 */
/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */
T[] = {
0xaaaaa3.0p-25, /* 0.33333310485 */
0x888b06.0p-26, /* 0.13334283238 */
0xdc84c8.0p-28, /* 0.053837567568 */
0xb9d8f1.0p-29, /* 0.022686453536 */
0xcfe632.0p-31, /* 0.0063445800915 */
0xeaf97e.0p-31, /* 0.0071708550677 */
};
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;
if(ix>=0x3f2ca140) { /* |x|>=0.67434 */
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^8*T[5]) +
* x^5*(x^2*(T[2]+x^4*T[4]))
*/
r = T[1]+w*(T[3]+w*T[5]);
v = z*(T[2]+w*T[4]);
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);
}
}
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