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          • Decoding-left-inverse
            • Decodex-of-encode-of-instr
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            • Get-imm-utype-of-encode-of-instr
            • Get-fields-stype-of-encode-of-instr
            • Get-fields-btype-of-encode-of-instr
            • Get-imm-stype-of-encode-of-instr
            • Get-imm-jtype-of-encode-of-instr
            • Get-imm-btype-of-encode-of-instr
            • Get-fields-jtype-of-encode-of-instr
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• Executable

Decoding-left-inverse

Executable decoding applied to encoding.

We show that the executable decoding is left inverse of encoding (i.e. that encoding is right inverse of the executable decoding) over valid instructions: encoding a valid instruction and then decoding it yields the original instruction. As a consequence, encoding is injective over valid instructions: if two different instructions were encoded in the same way, the decoder would have to restore both from the same encoding, which is impossible since decoding is a function.

See encoding-decoding-illustration for an illustration of encoding and decoding.

Subtopics

Decodex-of-encode-of-instr

Theorems about decodex applied to the encoding of different instructions.

Get-opcode-of-encode-of-instr

Theorems about get-opcode applied to the encoding of different instructions.

Get-funct3-of-encode-of-instr

Theorems about get-funct3 applied to the encoding of different instructions.

Get-rd-of-encode-of-instr

Theorems about get-rd applied to the encoding of different instructions.

Get-rs1-of-encode-of-instr

Theorems about get-rs1 applied to the encoding of different instructions.

Get-fields-itype-of-encode-of-instr

Theorems about get-fields-itype applied to the encoding of different instructions.

Get-imm-itype-of-encode-of-instr

Theorems about get-imm-itype applied to the encoding of different instructions.

Get-rs2-of-encode-of-instr

Theorems about get-rs2 applied to the encoding of different instructions.

Encode-injective

Injectivity of encoding.

Get-fields-rtype-of-encode-of-instr

Theorems about get-fields-rtype applied to the encoding of different instructions.

Get-funct7-of-encode-of-instr

Theorems about get-funct7 applied to the encoding of different instructions.

Get-fields-utype-of-encode-of-instr

Theorems about get-fields-utype applied to the encoding of different instructions.

Decodex-of-encode

Decoding the encoding of a valid instruction yields the original instruction.

Get-imm-utype-of-encode-of-instr

Theorems about get-imm-utype applied to the encoding of different instructions.

Get-fields-stype-of-encode-of-instr

Theorems about get-fields-stype applied to the encoding of different instructions.

Get-fields-btype-of-encode-of-instr

Theorems about get-fields-btype applied to the encoding of different instructions.

Get-imm-stype-of-encode-of-instr

Theorems about get-imm-stype applied to the encoding of different instructions.

Get-imm-jtype-of-encode-of-instr

Theorems about get-imm-jtype applied to the encoding of different instructions.

Get-imm-btype-of-encode-of-instr

Theorems about get-imm-btype applied to the encoding of different instructions.

Get-fields-jtype-of-encode-of-instr

Theorems about get-fields-utype applied to the encoding of different instructions.