However, close isn't the same as running at native code speeds and anything that can be done to speed things up is welcome. Previously Mozilla demonstrated that Asm.js could run typical native code programs at about 2x slower at worst. Now, with a change to the way floating point arithmetic is handled, this have been improved to about 1.5x slower.
You can see the performance of asm.js in the following chart - firefox f32 is using 32-bit floating point.
You can see that, while firefox f32 is still nearly aways slower than native code, it is approaching the typical speed range of native code.
Of course, the alternative approach to making code run faster in the browser is being developed and promoted by Google in the form of its native client facilities, NaCL and Pepper. At the moment only Google Chrome supports NaCL, but Firefox, Chrome and Opera support asm.js to greater or lesser extents. It appears that asm.js is becoming a very important part of the technology stack.
To quote Alon Zakai on the Mozilla blog: