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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.
* ====================================================
*/
#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);
}
}
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