raspi-kernel

Kernel

http://elinux.org/RPi_Software#Kernel

The initial patches (Media:Rpi-linux-patches-3.1.9.tgz) are released against the 3.1.9 kernel - but may also work against later kernels.
The kernel is now also available on https://github.com/raspberrypi/linux
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Compiler

The Broadcom processor on Raspberry Pi contains an ARM v6 general purpose processor and a Broadcom VideoCore IV GPU. No data is currently available on other cores (if any) available in the BCM2835.

ARM

There is broad compiler support including gcc - please see ARM Compilers
The ARM is capable of around 500 BOGOMIPS ^[1], 5400 LINPACK KFLOPS with software floating point and 22000 KFLOPS with softfp hardware floating point^[2].
The gcc compiler flags which will produce the most optimal code for the RPi are probably (can someone check!):

-mtune=arm1176jzf-s -mfpu=vfp -mfloat-abi=softfp [-marm or -mthumb]

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http://elinux.org/Rpi_kernel_compilation#compiling

compiling
Next you have to configure the kernel:

cp arch/arm/configs/bcmrpi_cutdown_defconfig .config
make ARCH=arm CROSS_COMPILE=/usr/bin/arm-linux-gnueabi- oldconfig

Then building the kernel:

make ARCH=arm CROSS_COMPILE=/usr/bin/arm-linux-gnueabi- -k

You can use the "-j" flag to improve compilation time. If you have a dual core machine you can use "-j 3", for a quad core machine you can use "-j 6", and so on.