A computer system has a microprocessor that can execute in a non-privileged user mode and a privileged kernel mode. A user virtual address space is used when the microprocessor is in the user mode, and a kernel virtual address space is used when the microprocessor is in the kernel mode. Each of the address spaces has the same range of virtual addresses that is designated for shared components. The user virtual address space is mapped to an offset position within the kernel address space. When a user process calls a kernel function with a pointer argument, the pointer is biased before being dereferenced to account for the offset of the user address space within the kernel address space. This allows for sharing of position-dependent code, while still allowing the kernel to access the entire user address space.