When working with converging algorithms, sometimes floating code can become very slow. That is: orders of magnitude slower than you would expect.
A very interesting answer to [Wayback] c++ – Why does changing 0.1f to 0 slow down performance by 10x? – Stack Overflow.
I’ve only quoted a few bits, read the full question and answer for more background information.
Welcome to the world of denormalized floating-point! They can wreak havoc on performance!!!
Denormal (or subnormal) numbers are kind of a hack to get some extra values very close to zero out of the floating point representation. Operations on denormalized floating-point can be tens to hundreds of times slower than on normalized floating-point. This is because many processors can’t handle them directly and must trap and resolve them using microcode.
If you print out the numbers after 10,000 iterations, you will see that they have converged to different values depending on whether 0 or 0.1 is used.
Basically, the convergence uses some values closer to zero than a normal floating point representation dan store, so a trick is used called “denormal numbers or denormalized numbers (now often called subnormal numbers)” as described in Denormal number – Wikipedia:
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In a normal floating-point value, there are no leading zeros in the significand; rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as 1.23 × 10−2). Denormal numbers are numbers where this representation would result in an exponent that is below the smallest representable exponent (the exponent usually having a limited range). Such numbers are represented using leading zeros in the significand.
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Since a denormal number is a boundary case, many processors do not optimise for this.
–jeroen
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