inline A0 finalize(const A0& fe,const A0& x,const A0& x2,A0 y)
{
y = amul(y, -Half<A0>(), x2);
// multiply log of fraction by log10(e) and base 2 exponent by log10(2)
A0 z = mul(x+y, Const<A0, 0x3a37b152>());//7.00731903251827651129E-4f // log10(e)lo
z = amul(z, y, Const<A0, 0x3ede0000>()); //4.3359375E-1f // log10(e)hi
z = amul(z, x, Const<A0, 0x3ede0000>());
z = amul(z, fe, Const<A0, 0x39826a14>());//3.0078125E-1f // log10(2)hi
return amul(z, fe, Const<A0, 0x3e9a0000>());//2.48745663981195213739E-4f // log10(2)lo
}
int utpm_imul(int P, int D, int M, int N, double *y, int ldy, double *x, int ldx){
/* computes Y *= X in Taylor arithmetic */
int k,d,p;
double *xd, *yd, *zd;
double *xp, *yp;
int pstridex, pstridey;
int dstridex, dstridey;
dstridex = ldx*N;
dstridey = ldy*N;
pstridex = (D-1)*dstridex;
pstridey = (D-1)*dstridey;
/* d > 0: higher order coefficients */
for(p = 0; p < P; ++p){
xp = x + p*pstridex;
yp = y + p*pstridey;
for(d = D-1; 0 < d; --d){
/* compute y_d += x_0 y_d */
xd = x;
yd = yp + d*dstridey;
zd = yd;
imul(M, N, yd, ldy, xd, ldx);
/* compute y_d += sum_{k=1}^{d-1} x_k y_{d-k} */
xd = xp + dstridex;
yd = yp + (d-1)*dstridey;
for(k = 1; k < d; ++k){
amul(M, N, xd, ldx, yd, ldy, zd, ldy);
++xd;
yd -= (2*dstridey-1);
}
/* compute y_d += x_d y_0 */
yd = y;
xd = xp + d*dstridex;
amul(M, N, xd, ldx, yd, ldy, zd, ldy);
}
}
yd = y;
xd = x;
/* d = 0: base point z_0 */
imul(M, N, yd, ldy, xd, ldx);
return 0;
}
static inline A0 log10(const A0& a0)
{
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = amul(y, -Half<A0>(), x2);
// multiply log of fraction by log10(e) and base 2 exponent by log10(2)
A0 z = mul(x+y, single_constant<A0, 0x3a37b152>());//7.00731903251827651129E-4f // log10(e)lo
z = amul(z, y, single_constant<A0, 0x3ede0000>()); //4.3359375E-1f // log10(e)hi
z = amul(z, x, single_constant<A0, 0x3ede0000>());
z = amul(z, fe, single_constant<A0, 0x39826a14>());//3.0078125E-1f // log10(2)hi
z = amul(z, fe, single_constant<A0, 0x3e9a0000>());//2.48745663981195213739E-4f // log10(2)lo
A0 y1 = a0-rec(abs(a0)); // trick to reduce selection testing
return seladd(is_inf(y1), b_or(z, b_or(is_ltz(a0), is_nan(a0))),y1);
}
inline float log10(const float& a0)
{
typedef float A0;
if (a0 == Inf<A0>()) return a0;
if (iseqz(a0)) return Minf<A0>();
if (nt2::is_nan(a0)||isltz(a0)) return Nan<A0>();
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = amul(y, -Half<A0>(), x2);
// multiply log of fraction by log10(e) and base 2 exponent by log10(2)
A0 z = mul(x+y, Const<float, 0x3a37b152>());//7.00731903251827651129E-4f // log10(e)lo
z = amul(z, y, Const<float, 0x3ede0000>()); //4.3359375E-1f // log10(e)hi
z = amul(z, x, Const<float, 0x3ede0000>());
z = amul(z, fe, Const<float, 0x39826a14>());//3.0078125E-1f // log10(2)hi
return amul(z, fe, Const<float, 0x3e9a0000 >());//2.48745663981195213739E-4f // log10(2)lo
}
static inline A0 log10(const A0& a0)
{
typedef typename meta::strip<A0>::type stA0;
if (a0 == Inf<stA0>()) return a0;
if (is_eqz(a0)) return Minf<stA0>();
if (nt2::is_nan(a0)||is_ltz(a0)) return Nan<stA0>();
A0 x, fe, x2, y;
kernel_log(a0, fe, x, x2, y);
y = amul(y, Mhalf<stA0>(), x2);
// multiply log of fraction by log10(e) and base 2 exponent by log10(2)
A0 z = mul(x+y, single_constant<stA0, 0x3a37b152>());//7.00731903251827651129E-4f // log10(e)lo
z = amul(z, y, single_constant<stA0, 0x3ede0000>()); //4.3359375E-1f // log10(e)hi
z = amul(z, x, single_constant<stA0, 0x3ede0000>());
z = amul(z, fe, single_constant<stA0, 0x39826a14>());//3.0078125E-1f // log10(2)hi
return amul(z, fe, single_constant<stA0, 0x3e9a0000 >());//2.48745663981195213739E-4f // log10(2)lo
}
