Floating point issues

Floating point operations can be cruel! Here are some mistakes that can introduce numerical errors.

List of weird issues with floating points

• float < 0, double > 0, real < 0
• CT and RT differences
• 32-bit vs. 64-bit have different behavior
• Direct vs. intermediate comparison
• "Same" function, different results
• std.math vs C
• Linux vs. Windows
• sin with different precision (+/- 0)

More issues are explained below.

Floating point math isn't distributive!

Let's consider these two equivalent definitions to represent linear functions:

y1 = slope * (x - _y) + _a
y2 = slope * x + intercept

where intercept = slope * (- _y) + _a.

Nota bene: If y2 is written fully: y2 = slope * x + slope * (- _y) + _a, we see that the distributive law is used to transform from y1. In other words the multiplication occurs before the addition in y1.

Now let's see why y1 is the better representation:

alias S = double;
S slope = 2.87415e+15;
S _a = -0.139631;
S _y = -1.5;
S intercept =  slope  * (- _y) + _a; // 4.31123e+15

S x = -1.5;

S y1 = _a + slope * (x - _y); // -0.139631
S y2 = slope * x + intercept; // 0

btw with real there's no difference ;-)

Compile-time evaluation uses a different precision

real x = -1.0; // -0x1p+0
enum y = -1.0; // -0x8p-3

-> Always use %a (exact hexadecimal printing) to verify.