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The Nintendo 64 GPU ('Reality Coprocessor') had microcode that could be loaded at runtime. Several standard microcodes were supplied with the development kit, and the easily findable documentation talks only in terms of using these, but it was possible to write your own, and some intrepid developers did.

What was the format of the microcode, the actual hardware instruction set? I haven't been able to find any documentation on that.

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As I understand it the GPU’s microcode was written for the RSP (Reality Signal Processor). The RSP’s instruction set is comprehensively documented in the Nintendo Ultra64 RSP Programmer’s Guide, including detailed opcode format descriptions. The R4300 Processor Specification is also useful, as is the Nintendo Ultra64 RDP Command Summary. The Ultra 64 project, which hosts these, provides lots of documentation on the system.

The opcodes can be decoded using a relatively straightforward table-driven decoder; see Cen64’s decoder for example. The Cen64 project also has an RSP assembler you can use to build new microcode files.

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