randomx

RandomX

RandomX ("random ex") is an experimental proof of work (PoW) algorithm that uses random code execution to achieve ASIC resistance.

RandomX uses a simple low-level language (instruction set) to describe a variety of random programs. The instruction set was designed specifically for this proof of work algorithm, because existing languages and instruction sets are designed for a different goal (actual software development) and thus usually have a complex syntax and unnecessary flexibility.

Virtual machine

RandomX is intended to be run efficiently and easily on a general-purpose CPU. The virtual machine (VM) which runs RandomX code attempts to simulate a generic CPU using the following set of components:

DRAM

The VM has access to 4 GiB of external memory in read-only mode. The DRAM memory blob is static within a single PoW epoch. The exact algorithm to generate the DRAM blob and its update schedule is to be determined.

MMU

The memory management unit (MMU) interfaces the CPU with the DRAM blob. The purpose of the MMU is to translate the random memory accesses generated by the random program into a DRAM-friendly access pattern, where memory reads are not bound by access latency. The MMU splits the 4 GiB DRAM blob into 64-byte blocks (corresponding to the most common L1 cache line size). Data within one block is always read sequentially in eight reads (8×8 bytes). Blocks are read mostly sequentially apart from occasional random jumps that happen on average every 256 blocks. The address of the next block to be read is determined 1 block ahead of time to enable efficient prefetching. The MMU uses three internal registers:

• m0 - Address of the next quadword to be read from memory (32-bit, 8-byte aligned).
• m1 - Address of the next block to be read from memory (32-bit, 64-byte aligned).
• mx - Random 64-bit counter that determines if reading continues sequentially or jumps to a random block. When an address addr is passed to the MMU, it performs mx ^= addr and checks if the last 8 bits of mx are zero. If yes, the adjacent 32 bits are copied to register m1 and 64-byte aligned.

Cache

The VM contains 256 KiB of cache. The cache is split into two segments (16 KiB and 240 KiB). The cache is randomly accessed for both reading and writing. 75% of accesses are into the first 16 KiB.

Program

The actual program is stored in a 8 KiB ring buffer structure. Each program consists of 1024 random 64-bit instructions. The ring buffer structure makes sure that the program forms a closed infinite loop.

Control unit

The control unit (CU) controls the execution of the program. It reads instructions from the program buffer and sends commands to the other units. The CU contains 3 internal registers:

• pc - Address of the next instruction in the program buffer to be executed (64-bit, 8 byte aligned).
• sp - Address of the top of the stack (64-bit, 8 byte aligned).
• ic - Instruction counter = the number of instructions to execute before terminating. Initial value is 65536 and the register is decremented after each executed instruction.

Stack

To simulate function calls, the VM uses a stack structure. The program interacts with the stack using the CALL, DCALL and RET instructions. The stack has unlimited size and each stack element is 64 bits wide.

Register file

The VM has 8 integer registers r0-r7 and 8 floating point registers f0-f7. All registers are 64 bits wide.

ALU

The arithmetic logic unit (ALU) performs integer operations. The ALU can perform binary integer operations from 11 groups (ADD, SUB, MUL, DIV, AND, OR, XOR, SHL, SHR, ROL, ROR) with various operand sizes.

FPU

The floating-point unit performs IEEE-754 compliant math using 64-bit double precision floating point numbers.

Instruction set

The instruction set was designed so that any bitstring is a valid program. The 64-bit instruction is encoded as follows:

Opcode (8 bits)

There are 256 opcodes, which are distributed between various operations depending on their weight (how often they will occur in the program on average). The distribution of opcodes is following:

operation	number of opcodes
ALU operations	TBD	TBD
FPU operations	TBD	TBD
Control flow	32	12.5%

Parameters a, b, c (8 bits)

a and b encode the instruction operands and c is the destination. All have the same encoding:

Register number is encoded in the top 3 bits. ALU instructions use registers r0-r7, while FPU instructions use registers f0-f7. Addresses are always loaded from registers r0-r7. The bottom 3 bits determine where the operand is loaded from/result saved to:

|location|A|B|C| |---------|-|-|- |000|register|register|register| |001|register|register|register| |010|register|register|register| |011|cache|register|cache| |100|cache|register|cache| |101|DRAM|register|cache| |110|DRAM|imm1|cache| |111|DRAM|imm1|cache|

• register - Direct register read/write.
• cache - The value of the register is used as an address to read from/write to the cache. The bottom 3 bits of the address are cleared and the address is truncated to the following length depending on the cache bits:

|cache|address length| |---------|-| |00|18 bits (whole 256 KiB)| |01, 10, 11|14 bits (first 16 KiB)|

• DRAM - The value of the register is used as an address to pass to the MMU for reading from DRAM.
• imm1 - 32-bit immediate value encoded within the instruction. For ALU instructions that use operands shorter than 32 bits, the value is truncated. For operands larger than 32 bits, the value is zero-extended for unsigned instructions and sign-extended for signed instructions. For FPU instructions, the value is treated as a signed 32-bit integer, first converted to a single precision floating point format and then to a double precision format.

imm0 (8 bits)

An 8-bit immediate value that is used to calculate the jump offset of the CALL and DCALL instructions.

ALU instructions

All ALU instructions take 2 operands A and B and produce result C. If C is shorter than 64 bits, it is zero-extended to 64 bits.

|opcodes|instruction|signed|A width|B width|C|C width| |-|-|-|-|-|-|-| |TBD|ADD_64|no|64|64|A + B|64| |TBD|ADD_32|no|32|32|A + B|32| |TBD|ADD_16|no|16|16|A + B|16| |TBD|SUB_64|no|64|64|A - B|64| |TBD|SUB_32|no|32|32|A - B|32| |TBD|SUB_16|no|16|16|A - B|16| |TBD|MUL_64|no|64|64|A * B|64| |TBD|MUL_32|no|32|32|A * B|64| |TBD|MUL_16|no|16|16|A * B|32| |TBD|IMUL_32|yes|32|32|A * B|64| |TBD|IMUL_16|yes|16|16|A * B|32| |TBD|DIV_64|no|64|32|A / B, A % B|64| |TBD|IDIV_64|yes|64|32|A / B, A % B|64| |TBD|DIV_32|no|32|16|A / B, A % B|32| |TBD|IDIV_32|yes|32|16|A / B, A % B|32| |TBD|AND_64|no|64|64|A & B|64| |TBD|AND_32|no|32|32|A & B|32| |TBD|AND_16|no|16|16|A & B|16| |TBD|OR_64|no|64|64|A | B|64| |TBD|OR_32|no|32|32|A | B|32| |TBD|OR_16|no|16|16|A | B|16| |TBD|XOR_64|no|64|64|A ^ B|64| |TBD|XOR_32|no|32|32|A ^ B|32| |TBD|XOR_16|no|16|16|A ^ B|16| |TBD|SHL_64|no|64|6|A << B|64| |TBD|SHR_64|no|64|6|A >> B|64| |TBD|SAR_64|yes|64|6|A >> B|64| |TBD|ROL_64|no|64|6|A <<< B|64| |TBD|ROR_64|no|64|6|A >>> B|64|

Division

For the division instructions, the divisor is half length of the dividend. The result C consists of both the quotient and the remainder (remainder is put the upper bits). The result of division by zero is equal to the dividend.

Register scrambling

Because the values of the integer registers are used as read and write addresses, they must stay pseudorandom. To achieve this, every ALU instruction has a scrambling step at the end. The values of the integer registers r(a) and r(c) corresponding to operands A and C are concatenated to form a 128-bit value D. The value of the integer register r(b) corresponding to the B operand is concatenated with its corresponding FPU register f(b) to form a 128-bit value K. D is then encrypted with a single AES round using K as the round key and the result is saved into registers r(a) and r(c).

In pseudocode:

D[127:64] = r(a)
D[63:0] = r(c)
K[127:64] = r(b)
K[63:0] = f(b)
E = AES_ROUND(D, K)
r(a) = E[127:64]
r(c) = E[63:0]

AES_ROUND consists of the ShiftRows, SubBytes and MixColumns steps followed by XOR with K.

FPU instructions

|opcodes|instruction|C| |-|-|-| |TBD|FADD|A + B| |TBD|FSUB|A - B| |TBD|FMUL|A * B| |TBD|FDIV|A / B| |TBD|FSQRT|sqrt(A)| |TBD|FROUND|-|

FPU instructions conform to the IEEE-754 specification, so they must give bit-exact correctly rounded results. Initial rounding mode is RN (Round to Nearest). Denormal values are treated as zero (this corresponds to setting the FTZ flag in x86 SSE and ARM Neon engines).

Operands loaded from memory are treated as signed 64-bit integers and converted to double precision floating point format. Operands loaded from floating point registers are used directly.

FSQRT

The sign bit of the FSQRT operand is always cleared first, so only non-negative values are used.

FROUND

The FROUND instruction changes the rounding mode for all subsequent FPU operations depending on the two right-most bits of A:

A[1:0]	rounding mode
00	Round to Nearest (RN) mode
01	Round towards Plus Infinity (RP) mode
10	Round towards Minus Infinity (RM) mode
11	Round towards Zero (RZ) mode

Control flow instructions

The following 3 control flow instructions are supported:

|opcodes|instruction|function| |-|-|-| |TBD|CALL|near procedure call with a static offset| |TBD|DCALL|near procedure call with a dynamic offset| |TBD|RET|return from procedure|

All three instructions are conditional in 75% of cases. The jump is taken only if B <= imm1. For the 25% of cases when B is equal to imm1, the jump is unconditional. In case the branch is not taken, all three instructions become "arithmetic no-op" C = A.

CALL and DCALL

Taken CALL and DCALL instructions push the values A and pc (program counter) onto the stack and then perform a forward jump relative to the value of pc. The forward offset is equal to 8 * (imm0 + 1) for the CALL instruction and 8 * ((imm0 ^ (A >> 56)) + 1) for the DCALL instruction. Maximum jump distance is therefore 256 instructions forward (this means that at least 4 correctly spaced CALL/DCALL instructions are needed to form a loop in the program).

RET

Taken RET instruction pops the return address raddr from the stack (it's the instruction following the previous CALL or DCALL), then pops a return value retval from the stack and sets C = retval. Finally, the instruction jumps back to raddr.

Program generation

The program is initialized from a 256-bit seed value using a PCG random number generator. The program is generated in this order:

1. All 1024 instructions are generated as a list of random 64-bit integers.
2. Initial values of all integer registers r0-r7 are generated as random 64-bit integers.
3. Initial values of all floating point registers f0-f7 are generated as random 64-bit signed integers converted to a double precision floating point format.
4. The initial value of the m0 register is generated as a random 32-bit value with the last 6 bits cleared (64-byte aligned).
5. The 256 KiB cache is initialized using AES encryption (TBD).
6. The remaining registers are initialized as pc = 0, sp = 0, ic = 65536, m1 = m0 + 64, mx = 0.

Result

When the program terminates (the value of ic register reaches 0), the cache, the register file and the stack are hashed using the Blake2b hash function to get the final PoW value. The generation/execution can be chained multiple times to discourage mining strategies that search for programs with particular properties.