RandomWOW/doc/isa.md

RandomX instruction set

RandomX uses a simple low-level language (instruction set), which was designed so that any random bitstring forms a valid program.

Each RandomX instruction has a length of 128 bits. The encoding is following:

All flags are aligned to an 8-bit boundary for easier decoding.

Opcode

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	146	57.0%
FPU operations	78	30.5%
Control flow	32	12.5%

Operand A

The first operand is read from memory. The location is determined by the loc(a) flag:

loc(a)[2:0]	read A from	address size (W)
000	dataset	32 bits
001	dataset	32 bits
010	dataset	32 bits
011	dataset	32 bits
100	scratchpad	15 bits
101	scratchpad	11 bits
110	scratchpad	11 bits
111	scratchpad	11 bits

Flag reg(a) encodes an integer register r0-r7. The read address is calculated as:

reg(a) = reg(a) XOR signExtend(addr(a))
read_addr = reg(a)[W-1:0]

W is the address width from the above table. For reading from the scratchpad, read_addr is multiplied by 8 for 8-byte aligned access.

Operand B

The second operand is loaded either from a register or from an immediate value encoded within the instruction. The reg(b) flag encodes an integer register (ALU operations) or a floating point register (FPU operations).

loc(b)[2:0]	read B from
000	register reg(b)
001	register reg(b)
010	register reg(b)
011	register reg(b)
100	register reg(b)
101	register reg(b)
110	imm8 or imm32
111	imm8 or imm32

imm8 is an 8-bit immediate value, which is used for shift and rotate ALU operations.

imm32 is a 32-bit immediate value which is used for most operations. For operands larger than 32 bits, the value is sign-extended. For FPU instructions, the value is considered a signed 32-bit integer and then converted to a double precision floating point format.

Operand C

The third operand is the location where the result is stored.

loc(c)[2:0]	write C to	address size (W)
000	scratchpad	15 bits
001	scratchpad	11 bits
010	scratchpad	11 bits
011	scratchpad	11 bits
100	register reg(c)	-
101	register reg(c)	-
110	register reg(c)	-
111	register reg(c)	-

The reg(c) flag encodes an integer register (ALU operations) or a floating point register (FPU operations). For writing to the scratchpad, an integer register is always used and the write address is calculated as:

write_addr = 8 * (addr(c) XOR reg(c)[31:0])[W-1:0]

CPUs are typically designed for a 2:1 load:store ratio, so each VM instruction performs on average 1 memory read and 0.5 write to memory.

imm8

An 8-bit immediate value that is used as the shift/rotate count by some ALU instructions and as the jump offset of the CALL instruction.

addr(a)

A 32-bit address mask that is used to calculate the read address for the A operand. It's sign-extended to 64 bits.

addr(c)

A 32-bit address mask that is used to calculate the write address for the C operand. addr(c) is equal to imm32.

ALU instructions

weight	instruction	signed	A width	B width	C	C width
16	ADD_64	no	64	64	A + B	64
4	ADD_32	no	32	32	A + B	32
16	SUB_64	no	64	64	A - B	64
4	SUB_32	no	32	32	A - B	32
15	MUL_64	no	64	64	A * B	64
11	MULH_64	no	64	64	A * B	64
11	MUL_32	no	32	32	A * B	64
11	IMUL_32	yes	32	32	A * B	64
11	IMULH_64	yes	64	64	A * B	64
1	DIV_64	no	64	32	A / B	32
1	IDIV_64	yes	64	32	A / B	32
4	AND_64	no	64	64	A & B	64
2	AND_32	no	32	32	A & B	32
4	OR_64	no	64	64	A | B	64
2	OR_32	no	32	32	A | B	32
4	XOR_64	no	64	64	A ^ B	64
2	XOR_32	no	32	32	A ^ B	32
3	SHL_64	no	64	6	A << B	64
3	SHR_64	no	64	6	A >> B	64
3	SAR_64	yes	64	6	A >> B	64
9	ROL_64	no	64	6	A <<< B	64
9	ROR_64	no	64	6	A >>> B	64

32-bit operations

Instructions ADD_32, SUB_32, AND_32, OR_32, XOR_32 only use the low-order 32 bits of the input operands. The result of these operations is 32 bits long and bits 32-63 of C are zero.

Multiplication

There are 5 different multiplication operations. MUL_64 and MULH_64 both take 64-bit unsigned operands, but MUL_64 produces the low 64 bits of the result and MULH_64 produces the high 64 bits. MUL_32 and IMUL_32 use only the low-order 32 bits of the operands and produce a 64-bit result. The signed variant interprets the arguments as signed integers. IMULH_64 takes two 64-bit signed operands and produces the high-order 64 bits of the result.

Division

For the division instructions, the dividend is 64 bits long and the divisor 32 bits long. The IDIV_64 instruction interprets both operands as signed integers. In case of division by zero or signed overflow, the result is equal to the dividend A.

Division by zero can be handled without branching by a conditional move. Signed overflow happens only for the signed variant when the minimum negative value is divided by -1. This rare case must be handled in x86 (ARM produces the "correct" result).

Shift and rotate

The shift/rotate instructions use just the bottom 6 bits of the B operand (imm8 is used as the immediate value). All treat A as unsigned except SAR_64, which performs an arithmetic right shift by copying the sign bit.

FPU instructions

weight	instruction	conversion method	C
20	FPADD	convertSigned52	A + B
20	FPSUB	convertSigned52	A - B
22	FPMUL	convertSigned51	A * B
8	FPDIV	convertSigned51	A / B
6	FPSQRT	convert52	sqrt(A)
2	FPROUND	convertSigned52	A

Rounding

FPU instructions conform to the IEEE-754 specification, so they must give correctly rounded results. Initial rounding mode is roundTiesToEven. Rounding mode can be changed by the FPROUND instruction. Denormal values are not be produced by any operation.

Conversion of operand A

Operand A is loaded from memory as a 64-bit signed integer and then converted to a double-precision floating point format using one of the following 3 methods:

• convertSigned52 - Clears the 11 least-significant bits before conversion. This is done so the number fits exactly into the 52-bit mantissa without rounding.
• convertSigned51 - Clears the 11 least-significant bits and sets the 12th bit before conversion. This is done so the number fits exactly into the 52-bit mantissa without rounding and avoids 0.
• convert52 - Clears the 11 least-significant bits and the sign bit before conversion. This is done so the number fits exactly into the 52-bit mantissa without rounding and avoids negative values.

FPROUND

The FPROUND instruction changes the rounding mode for all subsequent FPU operations depending on the two least-significant bits of A.

A[1:0]	rounding mode
00	roundTiesToEven
01	roundTowardNegative
10	roundTowardPositive
11	roundTowardZero

The rounding modes are defined by the IEEE-754 standard.

The two-bit flag value exactly corresponds to bits 13-14 of the x86 MXCSR register and bits 23 and 22 (reversed) of the ARM FPSCR register.

Control flow instructions

The following 2 control flow instructions are supported:

weight	instruction	function
17	CALL	near procedure call
15	RET	return from procedure

Both instructions are conditional in 75% of cases. The jump is taken only if B <= imm32. For the 25% of cases when B is equal to imm32, the jump is unconditional. In case the branch is not taken, both instructions become "arithmetic no-op" C = A.

CALL

Taken CALL instruction pushes the values A and pc (program counter) onto the stack and then performs a forward jump relative to the value of pc. The forward offset is equal to 16 * (imm8[6:0] + 1). Maximum jump distance is therefore 128 instructions forward (this means that at least 4 correctly spaced CALL instructions are needed to form a loop in the program).

RET

The RET instruction behaves like "not taken" when the stack is empty. Taken RET instruction pops the return address raddr from the stack (it's the instruction following the previous CALL), then pops a return value retval from the stack and sets C = A XOR retval. Finally, the instruction jumps back to raddr.

Reference implementation

A portable C++ implementation of all ALU and FPU instructions is available in instructionsPortable.cpp.