int remainder_pio2_kernel(double *x, double *y, int e0, int nx, int prec, const int *ipio2) {
int jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
double z, fw, f[20], fq[20], q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx - 1;
jv = (e0 - 3) / 24;
if (jv < 0) {
jv = 0;
}
q0 = e0 - 24 * (jv + 1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv - jx;
m = jx + jk;
for (i = 0; i <= m; i++, j++) {
f[i] = (j < 0) ? zero_kr : jvm_i2d(ipio2[j]);
}
/* compute q[0],q[1],...q[jk] */
for (i=0; i <= jk; i++) {
for(j = 0, fw = 0.0; j <= jx; j++) {
fw = jvm_dadd(fw, jvm_dmul(x[j], f[jx + i - j]));
}
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i = 0, j = jz, z = q[jz]; j > 0; i++,j--) {
fw = jvm_i2d(jvm_d2i(jvm_dmul(twon24, z)));
iq[i] = jvm_d2i(jvm_dsub(z, jvm_dmul(two24_kr, fw)));
z = jvm_dadd(q[j-1], fw);
}
/* compute n */
z = jvm_fplib_scalbn(z,q0); /* actual value of z */
z = jvm_dsub(z, jvm_dmul(8.0, jvm_fplib_floor(jvm_dmul(z,0.125)))); /* trim off integer >= 8 */
n = jvm_d2i(z);
z = jvm_dsub(z, jvm_i2d(n));
ih = 0;
if(q0 > 0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1] >> (24 - q0));
n += i;
iq[jz - 1] -= i << (24 - q0);
ih = iq[jz - 1] >> (23 - q0);
} else if (q0 == 0) {
double tangent_kernel(double x, double y, int iy) {
double z, r, v, w, s;
int ix, hx;
hx = __JHI(x); /* high word of x */
ix = hx & 0x7fffffff; /* high word of |x| */
if (ix < 0x3e300000) { /* x < 2**-28 */
if (jvm_d2i(x) == 0) { /* generate inexact */
if (((ix | __JLO(x)) | (iy + 1)) == 0) {
return jvm_ddiv(one_t, jvm_fplib_fabs(x));
} else {
return (iy == 1)? x: jvm_ddiv(jvm_dneg(one_t), x);
}
}
}
if (ix >= 0x3FE59428) { /* |x|>=0.6744 */
if (hx < 0) {
x = jvm_dneg(x);
y = jvm_dneg(y);
}
z = jvm_dsub(pio4, x);
w = jvm_dsub(pio4lo, y);
x = jvm_dadd(z, w);
y = 0.0;
}
z = jvm_dmul(x, x);
w = jvm_dmul(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]))));
r = jvm_dadd(T[1], jvm_dmul(w, jvm_dadd(T[3], jvm_dmul(w, jvm_dadd(T[5], jvm_dmul(w, jvm_dadd(T[7], jvm_dmul(w, jvm_dadd(T[9], jvm_dmul(w, T[11]))))))))));
//v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
v = jvm_dmul(z, jvm_dadd(T[2], jvm_dmul(w, jvm_dadd(T[4], jvm_dmul(w, jvm_dadd(T[6], jvm_dmul(w, jvm_dadd(T[8], jvm_dmul(w, jvm_dadd(T[10], jvm_dmul(w, T[12])))))))))));
s = jvm_dmul(z, x);
r = jvm_dadd(y, jvm_dmul(z, jvm_dmul(s, jvm_dadd(jvm_dadd(r, v), y))));
r = jvm_dadd(r, jvm_dmul(T[0], s));
w = jvm_dadd(x, r);
if(ix >= 0x3FE59428) {
v = jvm_i2d(iy);
return jvm_dmul(jvm_i2d((1 - ((hx >> 30) & 2))),
jvm_dsub(v, jvm_dmul(2.0, jvm_dsub(x, jvm_dsub(jvm_dmul(w, jvm_ddiv( w, jvm_dadd(w, v))), r)))));
}
double jvm_fplib_acos(double x) {
double z,p,q,r,w,s,c,df;
int hx,ix;
hx = __JHI(x);
ix = hx&0x7fffffff;
if(ix>=0x3ff00000) { /* |x| >= 1 */
if(((ix-0x3ff00000)|__JLO(x))==0) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return ac_pi+2.0*ac_pio2_lo; /* acos(-1)= pi */
}
return jvm_ddiv(jvm_dsub(x, x), jvm_dsub(x, x)); /* acos(|x|>1) is NaN */
}
if(ix<0x3fe00000) { /* |x| < 0.5 */
if(ix<=0x3c600000) return ac_pio2_hi+ac_pio2_lo;/*if|x|<2**-57*/
z = jvm_dmul(x, x);
p = jvm_dmul(z, jvm_dadd(ac_pS0, jvm_dmul(z, jvm_dadd(ac_pS1, jvm_dmul(z, jvm_dadd(ac_pS2, jvm_dmul(z, jvm_dadd(ac_pS3, jvm_dmul(z, jvm_dadd(ac_pS4, jvm_dmul(z, ac_pS5)))))))))));
q = jvm_dadd(ac_one, jvm_dmul(z, jvm_dadd(ac_qS1, jvm_dmul(z, jvm_dadd(ac_qS2, jvm_dmul(z, jvm_dadd(ac_qS3, jvm_dmul(z, ac_qS4))))))));
r = jvm_ddiv(p, q);
return jvm_dsub(ac_pio2_hi, jvm_dsub(x, jvm_dsub(ac_pio2_lo, jvm_dmul(x, r))));
} else if (hx<0) { /* x < -0.5 */
z = jvm_dmul(jvm_dadd(ac_one, x), 0.5);
p = jvm_dmul(z, jvm_dadd(ac_pS0, jvm_dmul(z, jvm_dadd(ac_pS1, jvm_dmul(z, jvm_dadd(ac_pS2, jvm_dmul(z, jvm_dadd(ac_pS3, jvm_dmul(z, jvm_dadd(ac_pS4, jvm_dmul(z, ac_pS5)))))))))));
q = jvm_dadd(ac_one, jvm_dmul(z, jvm_dadd(ac_qS1, jvm_dmul(z, jvm_dadd(ac_qS2, jvm_dmul(z, jvm_dadd(ac_qS3, jvm_dmul(z, ac_qS4))))))));
s = ieee754_sqrt(z);
r = jvm_ddiv(p, q);
w = jvm_dsub(jvm_dmul(r, s), ac_pio2_lo);
return jvm_dsub(ac_pi, jvm_dmul(2.0, jvm_dadd(s, w)));
} else { /* x > 0.5 */
z = jvm_dmul(jvm_dsub(ac_one, x), 0.5);
s = ieee754_sqrt(z);
df = s;
__JLO(df) = 0;
c = jvm_ddiv(jvm_dsub(z, jvm_dmul(df, df)), jvm_dadd(s, df));
p = jvm_dmul(z, jvm_dadd(ac_pS0, jvm_dmul(z, jvm_dadd(ac_pS1, jvm_dmul(z, jvm_dadd(ac_pS2, jvm_dmul(z, jvm_dadd(ac_pS3, jvm_dmul(z, jvm_dadd(ac_pS4, jvm_dmul(z, ac_pS5)))))))))));
q = jvm_dadd(ac_one, jvm_dmul(z, jvm_dadd(ac_qS1, jvm_dmul(z, jvm_dadd(ac_qS2, jvm_dmul(z, jvm_dadd(ac_qS3, jvm_dmul(z, ac_qS4))))))));
r = jvm_ddiv(p, q);
w = jvm_dadd(jvm_dmul(r, s), c);
return jvm_dmul(2.0, jvm_dadd(df, w));
}
}
double cosine_kernel(double x, double y) {
double a, hz, z, r, qx;
int ix;
ix = __JHI(x) & 0x7fffffff; /* ix = |x|'s high word*/
if (ix < 0x3e400000) { /* if x < 2**27 */
if (jvm_d2i(x) == 0 ) {
return one_c; /* generate inexact */
}
}
z = jvm_dmul(x, x);
r = jvm_dmul(z, jvm_dadd(C1, jvm_dmul(z, jvm_dadd(C2, jvm_dmul(z, jvm_dadd(C3, jvm_dmul(z, jvm_dadd(C4, jvm_dmul(z, jvm_dadd(C5, jvm_dmul(z,C6)))))))))));
if (ix < 0x3FD33333) { /* if |x| < 0.3 */
return jvm_dsub(one_c, jvm_dsub(jvm_dmul(0.5,z), jvm_dsub(jvm_dmul(z,r), jvm_dmul(x,y))));
} else {
if(ix > 0x3fe90000) { /* x > 0.78125 */
qx = 0.28125;
} else {
qx = jdouble_from_msw_lsw(ix - 0x00200000 /* x/4 */, 0);
}
hz = jvm_dsub(jvm_dmul(0.5, z), qx);
a = jvm_dsub(one_c, qx);
return jvm_dsub(a, jvm_dsub(hz, jvm_dsub(jvm_dmul(z, r), jvm_dmul(x, y))));
}
}
