2.6.40.4-5.fc15.i686 is a kernel. The 2.6.40.4-5.fc15.i686 has been tested via the Phoronix Test Suite in the configurations listed below.
mikey-render-bench - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Pentium III, Gallium 0.4 on softpipe
qgears2-xrender - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Pentium III, Gallium 0.4 on softpipe
gears-opengl - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Pentium III, Gallium 0.4 on softpipe
mikey-openarena - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.40GHz, ATI Radeon IGP 330M
gtkperf-test - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Pentium III, Gallium 0.4 on softpipe
mikey-render-bench - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.40GHz, ATI Radeon IGP 330M
qgears2-xrender - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.40GHz, ATI Radeon IGP 330M
gears-opengl - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.40GHz, ATI Radeon IGP 330M
mikey-openarena - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.53GHz, Gallium 0.4 on NV4A
mikey-render-bench - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.53GHz, Gallium 0.4 on NV4A
qgears2-xrender - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.53GHz, Gallium 0.4 on NV4A
gears-opengl - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.53GHz, Gallium 0.4 on NV4A
gtkperf-test - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.53GHz, Gallium 0.4 on NV4A
gtkperf-test - Tests on Fedora 15, Intel Core i7-2600K, GeForce GTX 560 Ti, ASUS P8P67 LE, Intel Pentium 4 2.40GHz, ATI Radeon IGP 330M
Ubuntu 11.04: i686 vs. i686 PAE vs. x86_64: At the end of 2009 I published benchmarks comparing Ubuntu's 32-bit, 32-bit PAE, and 64-bit Linux kernels. Those tests were carried out to show the performance impact of using 32-bit with PAE (Physical Address Extension) support, which on the plus side allows up to 64GB of system memory to be addressable from 32-bit machines, but is still significantly slower than a 64-bit kernel and user-space.