Triangle rasterization algorithms

I’m looking for a fast triangle rendering algorithm and I’m interested in what graphics chip manufacturers use.
There are two well known algorithms.
First algorithm uses barycentric coordinates. It is very useful algorithm for shadowing triangles and it is easy for iteration realization. But I have to use bounding box and have to waste a lot of time for checking pixels that outside triangle.
Second algorithm is a slope based.
Both of them have a cost setup time and not suited for rendering of a small triangles.

->“What graphics chip manufacturers use” : you mean, in the silicon ??
Guess what, Intel’s Larrabee attempted to do that with generic cpus and apparently failed.
Do you want help for a software or an hardware implementation ?
Have you read these pages, especially Chapter 5 with a special technique optimized for small triangles :

Thank you for the article.
First of all I’m interested in hardware implementation, but software is acceptable. I have an fpga board so I can implement it in hardware. I’m going to research in this direction.

Marc Olano claims his paper is used in hardware:

"Major accomplishments:
Developed a homogeneous (clipless) rendering technique used in many generations of PC graphics processors.
Olano, Marc and Trey Greer, “Triangle Scan Conversion Using 2D Homogeneous Coordinates”, Proceedings of the 1997 SIGGRAPH/Eurographics Workshop on Graphics Hardware (Los Angeles, CA, August 2-4, 1997), ACM SIGGRAPH, New York, 1995.

html: Triangle Scan Conversion using 2D Homogeneous Coordinates

Thanks! Very interesting

Also, as I always do, I recommend buying the book “real-time rendering, third edition”. There are several chapters about GPU hardware.