Fast floor/ceiling functions

Introduction

Those of you who are after sheer running speed already know how slow the standard floor/ceiling functions can be. Here are handy alternatives. 

Background  

The standard floor/ceiling functions have two drawbacks:

1. they are shockingly slow, and 
2. they return a floating-point value;

when what you want is an integer, this costs you an extra conversion to int, which seems extraneous.  

You will find alternatives on the Web, most being built on a cast to int. Unfortunately, this cast rounds towards zero, which gives wrong results for negative values. Some try to fix this by subtracting 1 for negative arguments. This solution is still not compliant with the function definition, as it does not work for negative integer values. 

Closer scrutiny shows that the -1 adjustment is required for all negative numbers with a nonzero fractional value. This occurs exactly when the result of the cast is larger than the initial value. This gives:  

i= int(fp); if (i > fp) i--; 

It involves a single comparisons and an implicit type conversion (required by the comparison).

Similarly, the ceiling function needs to be adjusted for positive fractional values.  

C++

i= int(fp); if (i < fp) i++;

Using the code 

A faster and correct solution is obtained by shifting the values before casting, to make them positive. For instance, assuming all your values fit in the range of a short, you will use: 

i= (int)(fp + 32768.) - 32768;

That costs a floating-point add, a typecast and an integer add. No branch.

The ceiling function is derived by using the property floor(-fp) = -ceiling(fp):  

C++

i= 32768 - (int)(32768. - fp);

Points of Interest 

I benchmarked the (int)floor/ceil functions, the comparison-based and the shifting-based expressions by running them 1000 times on an array of 1000 values in range -50..50. Here are the times in nanoseconds per call. 

Floor:  

• Standard function: 24 ns
• Comparison based:   14 ns 
• Shifting based:   2.6 ns  

Ceiling:  

• Standard function: 24 ns
• Comparison based:   14 ns 
• Shifting based:   2.8 ns  

This clearly shows that it is worth to use the shifting alternatives. 

History 

• Second version, simpler comparison-based version and ceiling handled.