xref: /freebsd/lib/msun/src/k_tanf.c (revision 73fbb89dd6e679b7bc805f0ddaca321158a1abd2)

/* 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
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 {
				if (iy == 1)
					return x;
				else {	/* compute -1 / (x+y) carefully */
					double a, t;

					z = w = x + y;
					GET_FLOAT_WORD(ix, z);
					SET_FLOAT_WORD(z, ix & 0xfffff000);
					v = y - (z - x);
					t = a = -one / w;
					GET_FLOAT_WORD(ix, t);
					SET_FLOAT_WORD(t, ix & 0xfffff000);
					s = one + t * z;
					return t + a * (s + t * v);
				}
			}
		}
	}
	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);
	}
}