void solve_vertex(amath_float a, amath_float b, amath_float c)
{
//Side work
amath_float b2 = b / a;
b2 /= 2;
amath_float cs = aexp(b2, 2); //New c value
//End side work
amath_float neg_cs = anegate(cs);
amath_float vtx_y = c + neg_cs; //Balance equation
amath_float vtx_x = sqrt(cs); //Complete the square
if (b < 0)
vtx_x = anegate(vtx_x); //"Drop" minus sign if b is negative
cout << "VERTEX FORM: y = (x + " << static_cast<string>(vtx_x) << ")² + " << static_cast<string>(vtx_y) << endl;
amath_float neg_vtx_x = anegate(vtx_x);
cout << "VERTEX: (" << static_cast<string>(neg_vtx_x) << ", " << static_cast<string>(vtx_y) << ")" << endl;
amath_float neg_b = anegate(b);
amath_float a2 = a * 2;
amath_float vtx_x_verify = neg_b / a2;
if (vtx_x_verify == neg_vtx_x)
cout << "VERIFIED - Good vertex." << endl;
else
{
cout << "NOT VERIFIED - Bad vertex. If you can manually verify this vertex (-b / 2a = vertex x) then please report this error on the GitHub repository." << endl;
cout << a2 << endl << neg_b << endl << neg_vtx_x << endl;
}
}
double gen_beta(const gen_beta_param *gen)
{
/* The following temporaries are recomputed on each iteration,
* or restored from gen->param array.
*/
double c,r,s,t,u1,u2,v,w,z,lambda;
double logv, logw, log_sum;
double a = gen->a;
double b = gen->b;
double min_ab = gen->min_ab;
double max_ab = gen->max_ab;
double sum_ab = gen->sum_ab;
if (max_ab<0.5)
{ /* Use Joehnk's algorithm.
* Use logv and logw, rather than v and w, to avoid
* floating-point underflow with very small a or b values.
*/
do
{ u1 = DRAND();
u2 = DRAND();
logv = log(u1)/a;
logw = log(u2)/b;
log_sum = logv>logw?
logv + log(1+ exp(logw-logv))
: logw + log(1+ exp(logv-logw));
} while (log_sum>0.0);
assert(logv<=log_sum);
return exp(logv - log_sum);
}
if (min_ab > 1.0)
{ /* use Algorithm BB */
lambda = gen->param[0];
c = gen->param[1];
do
{
u1 = DRAND();
u2 = DRAND();
v = lambda*log(u1/(1.0-u1));
w = aexp(min_ab,v);
z = u1*u1*u2;
r = c*v-1.38629436112;
s = min_ab+r-w;
if(s+2.609438 >= 5.0*z) break;
t = log(z);
} while ( /* s<=t && */
r+sum_ab*log(sum_ab/(max_ab+w)) < t);
return ret(a,min_ab, max_ab, w);
}
if (max_ab>= 1.0)
{ /* use Atkinson's switching method, as
* described in Dagpunar's book
* p=min_ab, q=max_ab
* t stored as gen->param[0], r as gen->param[1]
*/
t = gen->param[0];
r = gen->param[1];
for(;;)
{ u1 = DRAND();
u2 = DRAND();
if (u1 < r)
{ w = t*pow(u1/r, 1/min_ab);
if (log(u2) < (max_ab -1)*log(1-w)) break;
}
else
{ w = 1- (1-t)*pow((1-u1)/(1-r), 1/max_ab);
if (log(u2) < (min_ab -1) * log(w/t)) break;
}
}
return (a==min_ab)? w : 1-w;
}
else
{ /* use Atkinson's Algorithm
*/
t = gen->param[0];
r = gen->param[1];
for(;;)
{
u1 = DRAND();
u2 = DRAND();
if (u1 < r)
{ w = t*pow(u1/r, 1/min_ab);
if (log(u2) < (max_ab -1)*log((1-w)/(1-t))) break;
}
else
{ w = 1- (1-t)*pow((1-u1)/(1-r), 1/max_ab);
if (log(u2) < (min_ab -1) * log(w/t)) break;
}
}
return (a==min_ab)? w : 1-w;
}
}