# Flame

# 1.1 Bad Values

Replace

#define badvalue(x) (((x)!=(x))||((x)>1e10)||((x)<-1e10))

with

#define badvalue(x) (isnan(x)||isinf(x))
#undef EPS
#define EPS (0.0)

Do not enable -ffast-math or similar unsafe optimization.

The default constants cause rendering issues like holes with some parameters.

Actual issues of division by zero etc are probably rare.

# 1.2 Elliptic

I discussed some numerical issues at A more accurate elliptic variation.

It’s probably better to apply square root perturbation than mess around with Padé approximation:

double sqrt1pm1(double x)
{
  return x / (sqrt(x + 1) + 1);
}

Elliptic is similar to \[z \to \frac{2}{\pi} \sin^{-1}(z)\] but it’s not quite identical. The latter is conformal, so might be preferred.

# 2.1 Raw Histogram

In my fork you can export raw histograms with a couple of additional command line flags:

• --raw_histogram save raw histogram (EXR32 output mode only).
• --raw_histogram_pre_density save raw histogram before density estimation.