/* This one is working but is slower than the first one */
void cosine(scs_ptr x){
scs_t res_scs;
scs_t x2;
int i;
/* x < 2^-75 => cos(x)~1 (with accuracy 2^-150,999), when rounding to nearest, here we consider x< 2^-90 */
if(X_IND < -3){
scs_sub(x, SCS_ONE,x);
return;
}
/* Polynomial evaluation */
scs_square(x2, x);
scs_mul(res_scs, constt_poly_ptr[0], x2);
for(i=1; i<16; i++){
scs_add(res_scs, constt_poly_ptr[i], res_scs);
scs_mul(res_scs, res_scs, x2);
}
scs_add(x, res_scs, SCS_ONE);
return ;
}
static void scs_atan(scs_ptr res_scs, scs_ptr x){
scs_t X_scs, denom1_scs, denom2_scs, poly_scs, X2;
scs_t atanbhihi,atanbhilo, atanblo, atanbhi, atanb;
scs_t bsc_ptr;
db_number db;
double test;
int k, i=31;
scs_get_d(&db.d, x);
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
/* test if x as to be reduced */
if (db.d > MIN_REDUCTION_NEEDED) {
/* Compute i so that x E [a[i],a[i+1]] */
if (db.d < arctan_table[i][A].d) i-= 16;
else i+=16;
if (db.d < arctan_table[i][A].d) i-= 8;
else i+= 8;
if (db.d < arctan_table[i][A].d) i-= 4;
else i+= 4;
if (db.d < arctan_table[i][A].d) i-= 2;
else i+= 2;
if (db.d < arctan_table[i][A].d) i-= 1;
else if (i<61) i+= 1;
if (db.d < arctan_table[i][A].d) i-= 1;
/* evaluate X = (x - b(i)) / (1 + x*b(i)) */
scs_set_d(bsc_ptr, arctan_table[i][B].d);
scs_mul(denom1_scs,bsc_ptr,x);
scs_add(denom2_scs,denom1_scs,SCS_ONE);
scs_sub(X_scs,x,bsc_ptr);
scs_div(X_scs,X_scs,denom2_scs);
scs_get_d(&test,X_scs);
/* Polynomial evaluation of atan(X) , X = (x-b(i)) / (1+ x*b(i)) */
scs_square(X2, X_scs);
scs_set(res_scs, constant_poly_ptr[0]);
for(k=1; k < 10; k++) {
/* we use Horner expression */
scs_mul(res_scs, res_scs, X2);
scs_add(res_scs, constant_poly_ptr[k], res_scs);
}
scs_mul(poly_scs, res_scs, X_scs);
/* reconstruction : */
/* 1st we load atan ( b[i] ) in a scs*/
scs_set_d( atanbhihi , arctan_table[i][ATAN_BHI].d);
scs_set_d( atanbhilo , arctan_table[i][ATAN_BLO].d);
scs_set_d( atanblo , atan_blolo[i].d);
scs_add(atanbhi,atanbhihi,atanbhilo);
scs_add(atanb,atanbhi,atanblo);
scs_add(res_scs,atanb, poly_scs);
return;
}
else
{ /* no reduction needed */
/* Polynomial evaluation of atan(x) */
scs_square(X2, x);
scs_set(res_scs, constant_poly_ptr[0]);
for(k=1; k < 10; k++) {
/* we use Horner expression */
scs_mul(res_scs, res_scs, X2);
scs_add(res_scs, constant_poly_ptr[k], res_scs);
}
scs_mul(res_scs, res_scs, x);
return;
}
}
