void scs_log(scs_ptr res, db_number y, int E) {
scs_t R, sc_ln2_times_E, res1, addi;
scs_ptr ti, inv_wi;
db_number z, wi;
int i;
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
/* to normalize y.d and round to nearest */
/* + (1-trunc(sqrt(2.)/2 * 2^(4))*2^(-4) )+2.^(-(4+1))*/
z.d = y.d + norm_number.d;
i = (z.i[HI_ENDIAN] & 0x000fffff);
i = i >> 16; /* 0<= i <=11 */
wi.d = ((double)(11+i))*0.0625;
/* (1+f-w_i) */
y.d -= wi.d;
/* Table reduction */
ti = table_ti_ptr[i];
inv_wi = table_inv_wi_ptr[i];
/* R = (1+f-w_i)/w_i */
scs_set_d(R, y.d);
scs_mul(R, R, inv_wi);
/*
* Polynomial evaluation of log(1 + R) with an error less than 2^(-130)
*/
scs_mul(res1, constant_poly_ptr[0], R);
for(i=1; i<20; i++) {
scs_add(addi, constant_poly_ptr[i], res1);
scs_mul(res1, addi, R);
}
if(E==0) {
scs_add(res, res1, ti);
} else {
/* sc_ln2_times_E = E*log(2) */
scs_set(sc_ln2_times_E, sc_ln2_ptr);
if (E >= 0) {
scs_mul_ui(sc_ln2_times_E, (unsigned int) E);
} else {
scs_mul_ui(sc_ln2_times_E, (unsigned int) -E);
sc_ln2_times_E->sign = -1;
}
scs_add(addi, res1, ti);
scs_add(res, addi, sc_ln2_times_E);
}
}
/*************************************************************
*************************************************************
* ROUNDED TO NEAREST
*************************************************************
*************************************************************/
double log10_rn(double x)
{
scs_t R, res1;
scs_t sc_ln2_r10_times_E;
scs_ptr inv_wi, ti;
db_number nb, nb2, wi, resd;
int i, E=0;
nb.d = x;
/* Filter cases */
if (nb.i[HI_ENDIAN] < 0x00100000){ /* x < 2^(-1022) */
if (((nb.i[HI_ENDIAN] & 0x7fffffff)|nb.i[LO_ENDIAN])==0)
/* return 1.0/0.0; */ /* log(+/-0) = -Inf */
return NInf.d;
if (nb.i[HI_ENDIAN] < 0)
/* return (x-x)/0; */ /* log(-x) = Nan */
return NaN.d;
/* Subnormal number */
E -= (SCS_NB_BITS*2); /* keep in mind that x is a subnormal number */
nb.d *=SCS_RADIX_TWO_DOUBLE; /* make x as normal number */
/* We may just want add 2 to the scs number.index */
/* may be .... we will see */
}
if (nb.i[HI_ENDIAN] >= 0x7ff00000)
return x+x; /* Inf or Nan */
/* find n, nb.d such that sqrt(2)/2 < nb.d < sqrt(2) */
E += (nb.i[HI_ENDIAN]>>20)-1023;
nb.i[HI_ENDIAN] = (nb.i[HI_ENDIAN] & 0x000fffff) | 0x3ff00000;
if (nb.d > SQRT_2){
nb.d *= 0.5;
E++;
}
/* to normalize nb.d and round to nearest */
/* +((2^4 - trunc(sqrt(2)/2) *2^4 )*2 + 1)/2^5 */
nb2.d = nb.d + norm_number.d;
i = (nb2.i[HI_ENDIAN] & 0x000fffff);
i = i >> 16; /* 0<= i <=11 */
wi.d = (11+i)*(double)0.6250e-1;
/* (1+f-w_i) */
nb.d -= wi.d;
/* Table reduction */
ti = table_ti_ptr[i];
inv_wi = table_inv_wi_ptr[i];
/* R = (1+f-w_i)/w_i */
scs_set_d(R, nb.d);
scs_mul(R, R, inv_wi);
/* sc_ln2_r10_times_E = E*log10(2) */
scs_set(sc_ln2_r10_times_E, sc_ln2_r10_ptr);
if (E >= 0){
scs_mul_ui(sc_ln2_r10_times_E, (unsigned int) E);
}else{
scs_mul_ui(sc_ln2_r10_times_E, (unsigned int) -E);
sc_ln2_r10_times_E->sign = -1;
}
/*
* Polynomial evaluation of log10(1 + R) with an error less than 2^(-130)
*/
scs_mul(res1, constant_poly_ptr[0], R);
for(i=1; i<20; i++){
scs_add(res1, constant_poly_ptr[i], res1);
scs_mul(res1, res1, R);
}
scs_add(res1, res1, ti);
scs_add(res1, res1, sc_ln2_r10_times_E);
scs_get_d(&resd.d, res1);
return resd.d;
}