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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 30 0s: Stop and Arithmetic Operations All arithmetic is modulo 2256 unless otherwise noted. The zero-th power of zero 00 is defined to be one. Value Mnemonic δ α Description Halts execution. Addition operation. μ′s[0] ≡ μs[0] + μs[1] Multiplication operation. μ′s[0] ≡ μs[0] × μs[1] Subtraction operation. μ′s[0] ≡ μs[0] − μs[1] Integer division operation. 0 μ′s[0] ≡ ⌊μs[0] ÷ μs[1]⌋ 0x00 STOP 0x01 ADD 0x02 MUL 0x03 SUB 0x04 DIV 0x05 SDIV 0x06 MOD 0x07 SMOD 0x08 ADDMOD 0x09 MULMOD 0x0a EXP 0x0b SIGNEXTEND 0 0 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3 1 3 1 2 1 2 1 if μ[1]=0 s otherwise Signed integer division operation (truncated). 0 if μ[1]=0 s μ′s[0] ≡ −2255 if μs[0] = −2255 ∧ μs[1] = −1 sgn(μs[0] ÷ μs[1])⌊|μs[0] ÷ μs[1]|⌋ otherwise Where all values are treated as two’s complement signed 256-bit integers. Note the overflow semantic when −2255 is negated. Modulo remainder operation. 0 μ′s[0] ≡ μs[0] mod μs[1] if μ[1]=0 s otherwise Signed modulo remainder operation. 0 μ′s[0] ≡ sgn(μs[0])(|μs[0]| mod |μs[1]|) if μ[1]=0 s otherwise Where all values are treated as two’s complement signed 256-bit integers. Modulo addition operation. 0 μ′s[0] ≡ (μs[0] + μs[1]) mod μs[2] if μ[2]=0 s otherwise All intermediate calculations of this operation are not subject to the 2256 modulo. Modulo multiplication operation. 0 μ′s[0] ≡ (μs[0] × μs[1]) mod μs[2] if μ[2]=0 s otherwise All intermediate calculations of this operation are not subject to the 2256 modulo. Exponential operation. μ′s[0] ≡ μs[0]μs[1] Extend length of two’s complement signed integer. μs[x]i gives the ith bit (counting from zero) of μs[x] μ [1]t ∀i ∈ [0..255] : μ′s[0]i ≡ s if i t where t = 256−8(μ [0]+1) s otherwise μs [1]iPDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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