DOUBLE /*{ ret - tanhd(x) }*/
tanhd
(
DOUBLE x /*{ (i) - input value x }*/
)
{
DOUBLE f, g, xnum, xden;
DOUBLE result;
DOUBLE sign = 1.0;
/*{ f = |x| }*/
f = x;
/*{ sign = 1 }*/
/*{ if x < 0, sign = -sign }*/
if (x < (DOUBLE)0.0)
{
f = -f;
sign = -sign;
}
/*{ if f > TANHDOUBLE_BIGNUM, return sign }*/
if (f > TANHDOUBLE_BIGNUM)
{
return sign;
}
/*{ if f > ln(3)/2 }*/
if (f > LN3_2)
{
/*{ result = 1 - 2/(exp(2f) + 1) }*/
result = ADDD(f, f);
result = expd(result);
result = ADDD(1.0, result);
result = DIVD(2.0, result);
result = SUBD(1.0, result);
}
/*{ else f <= ln(3)/2 }*/
else
{
/*{ if f < EPS, return x }*/
if (f < LDBL_EPSILON)
{
result = x;
return result;
}
/*{ g = f * f }*/
g = MPYD(f, f);
/*{ R(g) = g * P(g)/Q(g) }*/
/*{!INDENT}*/
/*{ P(g) = (p2 * g + p1) * g + p0 }*/
xnum = MPYD(TANHDP_COEF2, g);
xnum = ADDD(xnum, TANHDP_COEF1);
xnum = MPYD(xnum, g);
xnum = ADDD(xnum, TANHDP_COEF0);
/*{ Q(g) = ((g + q2) * g + q1) * g + q0 }*/
xden = ADDD(TANHDQ_COEF2, g);
xden = MPYD(xden, g);
xden = ADDD(xden, TANHDQ_COEF1);
xden = MPYD(xden, g);
xden = ADDD(xden, TANHDQ_COEF0);
/*{!OUTDENT}*/
/*{ result = f + f * R(g) }*/
result = DIVD(xnum, xden);
result = MPYD(result, g);
result = MPYD(result, f);
result = ADDD(result, f);
}
/*{ if sign < 0, result = -result }*/
if (sign < (DOUBLE)0.0)
{
result = -result;
}
/*{ return result }*/
return result;
}
DOUBLE /*{ ret - sinhd(x) }*/
sinhd
(
DOUBLE x /*{ (i) - input value x }*/
)
{
DOUBLE y, w, z;
DOUBLE f, xnum, xden;
DOUBLE result;
DOUBLE sign = 1.0;
/*{ y = |x| }*/
y = x;
/*{ sign = 1.0 }*/
/*{ if x < 0, sign = -sign }*/
if (x < (DOUBLE)0.0)
{
y = -y;
sign = -sign;
}
/*{ if (y > 1.0) }*/
if (y > (DOUBLE)1.0)
{
/*{ if (y > XDOUBLE_MAX_EXP) }*/
if (y > XDOUBLE_MAX_EXP)
{
/*{ w = y - ln(v) }*/
w = SUBD(y, LN_V);
/*{ if w > XDOUBLE_MAX_EXP }*/
if (w > XDOUBLE_MAX_EXP)
{
/*{ result = +1.7e308 }*/
result = LDBL_MAX;
/*{ if sign < 0, result = -result }*/
if (sign < 0.0)
{
result = -result;
}
/*{ return result }*/
return result;
}
/*{ z = exp(w) }*/
z = expd(w);
/*{ result = (v/2) * z }*/
/* using higher precision computation */
result = MPYD(V_2_MINUS1, z);
result = ADDD(result, z);
}
/*{ else y <= XDOUBLE_MAX_EXP }*/
else
{
/*{ z = exp(y) }*/
z = expd(y);
/*{ result = ((z - 1 / z) / 2 }*/
result = DIVD(-0.5, z);
z = MPYD(0.5, z);
result = ADDD(z, result);
}
}
/*{ else y <= 1.0 }*/
else
{
/*{ if y < eps, result = y }*/
if (y < LDBL_EPSILON)
{
result = y;
}
else
{
/*{ result = y + y * R(x^2) }*/
/*{!INDENT}*/
/*{ R(f) = f*P(f)/Q(f) }*/
/*{ f = x * x }*/
f = MPYD(x, x);
/*{ P(f) = ((p3 * f + p2) * f + p1) * f + p0 }*/
xnum = MPYD(SINHDP_COEF3, f);
xnum = ADDD(xnum, SINHDP_COEF2);
xnum = MPYD(xnum, f);
xnum = ADDD(xnum, SINHDP_COEF1);
xnum = MPYD(xnum, f);
xnum = ADDD(xnum, SINHDP_COEF0);
/*{ Q(f) = ((f + q2) *f + q1) * f + q0 }*/
xden = ADDD(f, SINHDQ_COEF2);
xden = MPYD(xden, f);
xden = ADDD(xden, SINHDQ_COEF1);
xden = MPYD(xden, f);
xden = ADDD(xden, SINHDQ_COEF0);
/*{!OUTDENT}*/
result = DIVD(xnum, xden);
result = MPYD(result, f);
result = MPYD(result, y);
result = ADDD(result, y);
}
}
/*{ if sign < 0, result = -result }*/
if (sign < 0.0)
{
result = -result;
}
/*{ return result }*/
return result;
}
DOUBLE /*{ ret - cotd(x) }*/
cotd
(
DOUBLE x /*{ (i) - input value x }*/
)
{
LONG n;
DOUBLE xn;
DOUBLE f, g;
DOUBLE x_int, x_fract;
DOUBLE result;
DOUBLE xnum, xden;
/*{ If x is outside the domain or zero, return 0.0 }*/
if ((x > COT64_X_MAX) || (x < -COT64_X_MAX) || (x == 0.0L))
{
return 0.0L;
}
/*{ split x into x_int and x_fract for better argument reduction }*/
x_int = TO_DOUBLE(TO_LONG(x));
x_fract = SUBD(x, x_int);
/*{ Reduce the input to range between -PI/4, PI/4 }*/
/*{!INDENT}*/
/*{ n = Rounded long x/(PI/2) }*/
if (x > 0.0)
{
n = TO_LONG(ADDD(MPYD(x, INV_PI_2), 0.5));
}
else
{
n = TO_LONG(ADDD(MPYD(x, INV_PI_2), -0.5));
}
/*{ xn = (double)n }*/
xn = TO_DOUBLE(n);
/*{ f = x - xn*PI }*/
/* (using higher precision computation) */
f = SUBD(x_int, MPYD(xn, PI_2_DC1));
f = ADDD(f, x_fract);
f = SUBD(f, MPYD(xn, PI_2_DC2));
f = SUBD(f, MPYD(xn, PI_2_DC3));
/*{!OUTDENT}*/
if (f < 0.0L)
{
g = -f;
}
else
{
g = f;
}
/*{ If |f| < eps }*/
if (g < EPS_DOUBLE)
{
/*{ if n is odd, return -f }*/
if (n & 0x0001)
{
result = -f;
}
/*{ if n is even, return 1/f }*/
else
{
result = DIVD(1.0L, f);
}
return result;
}
/*{ g = f * f }*/
g = MPYD(f, f);
/*{ Compute sin approximation on reduced argument }*/
/*{!INDENT}*/
/*{ xnum = (((g * p3 + p2) * g + p1) * g * f + f }*/
xnum = MPYD(g, TANDP_COEF3);
xnum = ADDD(xnum, TANDP_COEF2);
xnum = MPYD(xnum, g);
xnum = ADDD(xnum, TANDP_COEF1);
xnum = MPYD(xnum, g);
xnum = MPYD(xnum, f);
xnum = ADDD(xnum, f);
/*{ xden = (((g * q4 + q3) * g + q2) * g +q1) * g + q0 }*/
xden = MPYD(g, TANDQ_COEF4);
xden = ADDD(xden, TANDQ_COEF3);
xden = MPYD(xden, g);
xden = ADDD(xden, TANDQ_COEF2);
xden = MPYD(xden, g);
xden = ADDD(xden, TANDQ_COEF1);
xden = MPYD(xden, g);
xden = ADDD(xden, TANDQ_COEF0);
/*{!OUTDENT}*/
/*{ if n is odd, result = -xnum/xden }*/
if (n & 0x0001)
{
xnum = -xnum;
}
/*{ else n is even, result = xden/xnum }*/
else
{
result = xden;
xden = xnum;
xnum = result;
}
result = DIVD(xnum, xden);
/*{ return result }*/
return result;
}
DOUBLE /*{ ret - acosd(x) }*/
acosd
(
DOUBLE x /*{ (i) - input value x }*/
)
{
DOUBLE y, g;
DOUBLE num, den, result;
LONG i;
/*{ y = |x| }*/
y = x;
if (y < (DOUBLE)0.0)
{
y = -y;
}
/*{ if y > 0.5 }*/
if (y > (DOUBLE)0.5)
{
/*{ set i = 0 }*/
i = 0;
/*{ if y > 0, return error }*/
if (y > (DOUBLE)1.0)
{
result = 0.0;
return result;
}
/*{ g = (1 - y)/2 }*/
g = SUBD(1.0, y);
g = MPYD(0.5, g);
/*{ y = -2/sqrt(g) }*/
y = sqrtd(g);
y = MPYD(y, -2.0);
}
/*{ else y <= 0.5 }*/
else
{
/*{ set i = 1 }*/
i = 1;
/*{ if y < eps }*/
if (y < EPS_DOUBLE)
{
result = y;
/*{ if x < 0, result = PI/2 + result }*/
/* (but more mathematically stable) */
if (x < (DOUBLE)0.0)
{
result = ADDD(PI_4, result);
result = ADDD(result, PI_4);
}
/*{ else x >=0, result = PI/2 - result }*/
/* (but more mathematically stable) */
else
{
result = SUBD(PI_4, result);
result = ADDD(result, PI_4);
}
/*{ return result }*/
return result;
}
/*{ g = y * y }*/
g = MPYD(y, y);
}
/*{ result = y + y*R(g) }*/
/*{!INDENT}*/
/*{ R(g) = g*P(g)/Q(g) }*/
/*{ P(g) = (((p5 * g + p4) * g + p3) * g + p2) * g + p1 }*/
num = MPYD(ASINDP_COEF5, g);
num = ADDD(num, ASINDP_COEF4);
num = MPYD(num, g);
num = ADDD(num, ASINDP_COEF3);
num = MPYD(num, g);
num = ADDD(num, ASINDP_COEF2);
num = MPYD(num, g);
num = ADDD(num, ASINDP_COEF1);
num = MPYD(num, g);
/*{ Q(g) = ((((g + q4) * g + q3) * g + q2) * g + q1) * g + q0 }*/
den = ADDD(g, ASINDQ_COEF4);
den = MPYD(den, g);
den = ADDD(den, ASINDQ_COEF3);
den = MPYD(den, g);
den = ADDD(den, ASINDQ_COEF2);
den = MPYD(den, g);
den = ADDD(den, ASINDQ_COEF1);
den = MPYD(den, g);
den = ADDD(den, ASINDQ_COEF0);
result = DIVD(num, den);
result = MPYD(result, y);
result = ADDD(result, y);
/*{!OUTDENT}*/
/*{ if x < 0 }*/
if (x < (DOUBLE)0.0)
{
/*{ if i == 0, result = PI + result }*/
/* (but more mathematically stable) */
if (i == 0)
{
result = ADDD(result, PI_2);
result = ADDD(result, PI_2);
}
/*{ if i == 1, result = PI/2 + result }*/
/* (but more mathematically stable) */
else
{
result = ADDD(PI_4, result);
result = ADDD(result, PI_4);
}
}
/*{ else x >= 0 }*/
else
{
/*{ if i == 1, result = PI/2 - result }*/
/* (but more mathematically stable) */
if (i == 1)
{
result = SUBD(PI_4, result);
result = ADDD(result, PI_4);
}
/*{ if i == 0, result = -result }*/
else
{
result = -result;
}
}
/*{ return result }*/
return result;
}
void adm_decouple_d(const adm_dwt_band_t_d *ref, const adm_dwt_band_t_d *dis, const adm_dwt_band_t_d *r, const adm_dwt_band_t_d *a, int w, int h, int ref_stride, int dis_stride, int r_stride, int a_stride)
{
#ifdef ADM_OPT_AVOID_ATAN
const double cos_1deg_sq = cos(1.0 * M_PI / 180.0) * cos(1.0 * M_PI / 180.0);
#endif
const double eps = 1e-30;
int ref_px_stride = ref_stride / sizeof(double);
int dis_px_stride = dis_stride / sizeof(double);
int r_px_stride = r_stride / sizeof(double);
int a_px_stride = a_stride / sizeof(double);
double oh, ov, od, th, tv, td;
double kh, kv, kd, tmph, tmpv, tmpd;
#ifdef ADM_OPT_AVOID_ATAN
double ot_dp, o_mag_sq, t_mag_sq;
#else
double oa, ta, diff;
#endif
int angle_flag;
int i, j;
for (i = 0; i < h; ++i) {
for (j = 0; j < w; ++j) {
oh = ref->band_h[i * ref_px_stride + j];
ov = ref->band_v[i * ref_px_stride + j];
od = ref->band_d[i * ref_px_stride + j];
th = dis->band_h[i * dis_px_stride + j];
tv = dis->band_v[i * dis_px_stride + j];
td = dis->band_d[i * dis_px_stride + j];
kh = DIVD(th, oh + eps);
kv = DIVD(tv, ov + eps);
kd = DIVD(td, od + eps);
kh = kh < 0.0 ? 0.0 : (kh > 1.0 ? 1.0 : kh);
kv = kv < 0.0 ? 0.0 : (kv > 1.0 ? 1.0 : kv);
kd = kd < 0.0 ? 0.0 : (kd > 1.0 ? 1.0 : kd);
tmph = kh * oh;
tmpv = kv * ov;
tmpd = kd * od;
#ifdef ADM_OPT_AVOID_ATAN
/* Determine if angle between (oh,ov) and (th,tv) is less than 1 degree.
* Given that u is the angle (oh,ov) and v is the angle (th,tv), this can
* be done by testing the inequvality.
*
* { (u.v.) >= 0 } AND { (u.v)^2 >= cos(1deg)^2 * ||u||^2 * ||v||^2 }
*
* Proof:
*
* cos(theta) = (u.v) / (||u|| * ||v||)
*
* IF u.v >= 0 THEN
* cos(theta)^2 = (u.v)^2 / (||u||^2 * ||v||^2)
* (u.v)^2 = cos(theta)^2 * ||u||^2 * ||v||^2
*
* IF |theta| < 1deg THEN
* (u.v)^2 >= cos(1deg)^2 * ||u||^2 * ||v||^2
* END
* ELSE
* |theta| > 90deg
* END
*/
ot_dp = oh * th + ov * tv;
o_mag_sq = oh * oh + ov * ov;
t_mag_sq = th * th + tv * tv;
angle_flag = (ot_dp >= 0.0) && (ot_dp * ot_dp >= cos_1deg_sq * o_mag_sq * t_mag_sq);
#else
oa = atan(DIVD(ov, oh + eps));
ta = atan(DIVD(tv, th + eps));
if (oh < 0.0)
oa += M_PI;
if (th < 0.0)
ta += M_PI;
diff = fabs(oa - ta) * 180.0 / M_PI;
angle_flag = diff < 1.0;
#endif
if (angle_flag) {
tmph = th;
tmpv = tv;
tmpd = td;
}
r->band_h[i * r_px_stride + j] = tmph;
r->band_v[i * r_px_stride + j] = tmpv;
r->band_d[i * r_px_stride + j] = tmpd;
a->band_h[i * a_px_stride + j] = th - tmph;
a->band_v[i * a_px_stride + j] = tv - tmpv;
a->band_d[i * a_px_stride + j] = td - tmpd;
}
}
}
