RandomX is a proof of work (PoW) algorithm which was designed to close the gap between general-purpose CPUs and specialized hardware. The core of the algorithm is a simulation of a virtual CPU.
**Hash256** and **Hash512** refer to the [Blake2b](https://blake2.net/blake2_20130129.pdf) hashing function with a 256-bit and 512-bit output size, respectively.
**Floating point format** refers to the [IEEE-754 double precision floating point format](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) with a sign bit, 11-bit exponent and 52-bit fraction.
**Argon2d** is a tradeoff-resistant variant of [Argon2](https://github.com/P-H-C/phc-winner-argon2/blob/master/argon2-specs.pdf), a memory-hard password derivation function.
**AesGenerator** refers to an AES-based pseudo-random number generator described in chapter 3.2. It's initialized with a 512-bit seed value and is capable of producing more than 10 bytes per clock cycle.
**AesHash** refers to an AES-based fingerprinting function described in chapter 3.3. It's capable of processing more than 10 bytes per clock cycle and produces a 512-bit output.
**SuperscalarHash** refers to a custom diffusion function designed to run efficiently on superscalar CPUs (see chapter 7). It transforms a 64-byte input value into a 64-byte output value.
**Scratchpad** refers to the workspace memory of the VM. The whole scratchpad is structured into 3 levels: L3 -> L2 -> L1 with each lower level being a subset of the higher levels.
**Register File** refers to a 256-byte sequence formed by concatenating VM registers in little-endian format in the following order: `r0`-`r7`, `f0`-`f3`, `e0`-`e3` and `a0`-`a3`.
Two of the custom functions are based on the [Advanced Encryption Standard](https://en.wikipedia.org/wiki/Advanced_Encryption_Standard) (AES).
**AES encryption round** refers to the application of the ShiftRows, SubBytes and MixColumns transformations followed by a XOR with the round key.
**AES decryption round** refers to the application of inverse ShiftRows, inverse SubBytes and inverse MixColumns transformations followed by a XOR with the round key.
The internal state of AesGenerator consists of 64 bytes arranged into four columns of 16 bytes each. During each output iteration, every column is decrypted (columns 0, 2) or encrypted (columns 1, 3) with one AES round using the following round keys (one key per column):
The input is processed in 64-byte blocks. Each input block is considered to be a set of four AES round keys `key0`, `key1`, `key2`, `key3`. Each state column is encrypted (columns 0, 2) or decrypted (columns 1, 3) with one AES round using the corresponding round key:
```
state0 (16 B) state1 (16 B) state2 (16 B) state3 (16 B)
| | | |
AES encrypt AES decrypt AES encrypt AES decrypt
(key0) (key1) (key2) (key3)
| | | |
v v v v
state0' state1' state2' state3'
```
When all input bytes have been processed, the state is processed with two additional AES rounds with the following extra keys (one key per round, same pair of keys for all columns):
The internal state is initialized from a seed value `K` (0-60 bytes long). The seed value is written into the internal state and padded with zeroes. Then the internal state is initialized as `S = Hash512(S)`.
The generator can generate 1 byte or 4 bytes at a time by supplying data from its internal state `S`. If there are not enough unused bytes left, the internal state is reinitialized as `S = Hash512(S)`.
The VM is a complex instruction set computer ([CISC](https://en.wikipedia.org/wiki/Complex_instruction_set_computer)). All data are loaded and stored in little-endian byte order. Signed integer numbers are represented using [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement).
Dataset is described in detail in chapter 7. It's a large read-only buffer. Its size is equal to `RANDOMX_DATASET_BASE_SIZE + RANDOMX_DATASET_EXTRA_SIZE` bytes. Each program uses only a random subset of the Dataset of size `RANDOMX_DATASET_BASE_SIZE`. All Dataset accesses read an aligned 64-byte item.
The VM has 8 integer registers `r0`-`r7` (group R) and a total of 12 floating point registers split into 3 groups: `f0`-`f3` (group F), `e0`-`e3` (group E) and `a0`-`a3` (group A). Integer registers are 64 bits wide, while floating point registers are 128 bits wide and contain a pair of numbers in floating point format. The lower and upper half of floating point registers are not separately addressable.
Integer registers `r0`-`r7` can be the source or the destination operands of integer instructions or may be used as address registers for accessing the Scratchpad.
Floating point registers `a0`-`a3` are read-only and their value is fixed for a given VM program. They can be the source operand of any floating point instruction. The value of these registers is restricted to the interval `[1, 4294967296)`.
Floating point registers `f0`-`f3` are the "additive" registers, which can be the destination of floating point addition and subtraction instructions. The absolute value of these registers will not exceed `1.0e+12`.
Floating point registers `e0`-`e3` are the "multiplicative" registers, which can be the destination of floating point multiplication, division and square root instructions. Their value is always positive.
`ma` and `mx` are the memory registers. Both are 32 bits wide. `ma` contains the memory address of the next Dataset read and `mx` contains the address of the next Dataset prefetch.
The 2-bit `fprc` register determines the rounding mode of all floating point operations according to Table 4.3.1. The four rounding modes are defined by the IEEE 754 standard.
When an 8-byte value read from the memory is to be converted to an F group register value or operand, it is interpreted as a pair of 32-bit signed integers (in little endian, two's complement format) and converted to floating point format. This conversion is exact and doesn't need rounding because only 30 bits of the fraction significand are needed to represent the integer value.
#### 4.3.2 Group E register conversion
When an 8-byte value read from the memory is to be converted to an E group register value or operand, the same conversion procedure is applied as for F group registers (see 4.3.1) with additional post-processing steps for each of the two floating point values:
1. The sign bit is set to `0`.
2. Bits 0-2 of the exponent are set to the constant value of <code>011<sub>2</sub></code>.
3. Bits 3-6 of the exponent are set to the value of the exponent mask described in chapter 4.5.6. This value is fixed for a given VM program.
4. The bottom 22 bits of the fraction significand are set to the value of the fraction mask described in chapter 4.5.6. This value is fixed for a given VM program.
The Program buffer stores the program to be executed by the VM. The program consists of `RANDOMX_PROGRAM_SIZE` instructions. Each instruction is encoded by an 8-byte word. The instruction set is described in chapter 5.
### 4.5 VM programming
The VM requires `128 + 8 * RANDOMX_PROGRAM_SIZE` bytes to be programmed. This is split into two parts:
The values of the floating point registers `a0`-`a3` are initialized using configuration quadwords 0-7 to have the following value:
<code>+1.fraction x 2<sup>exponent</sup></code>
The fraction has full 52 bits of precision and the exponent value ranges from 0 to 31. These values are obtained from the initialization quadword (in little endian format) according to Table 4.5.2.
Bits 0-3 of quadword 12 are used to select 4 address registers for program execution. Each bit chooses one register from a pair of integer registers according to Table 4.5.3.
The `datasetOffset` is calculated by bitwise AND of quadword 13 and the value `RANDOMX_DATASET_EXTRA_SIZE / 64`. The result is multiplied by `64`. This offset is used when reading values from the Dataset.
These masks are used for the conversion of group E registers (see 4.3.2). The low and high halves each have their own masks initialized from quadwords 14 and 15. The fraction mask is given by bits 0-21 and the exponent mask by bits 60-63 of the initialization quadword.
During VM execution, 3 additional temporary registers are used: `ic`, `spAddr0` and `spAddr1`. Program execution consists of initialization and loop execution.
#### 4.6.1 Initialization
1.`ic` register is set to `RANDOMX_PROGRAM_ITERATIONS`.
2.`spAddr0` is set to the value of `mx`.
3.`spAddr1` is set to the value of `ma`.
4. The values of all integer registers `r0`-`r7` are set to zero.
#### 4.6.2 Loop execution
The loop described below is repeated until the value of the `ic` register reaches zero.
1. XOR of registers `readReg0` and `readReg1` (see Table 4.5.3) is calculated and `spAddr0` is XORed with the low 32 bits of the result and `spAddr1` with the high 32 bits.
2.`spAddr0` is used to perform a 64-byte aligned read from Scratchpad level 3 (using mask from Table 4.2.1). The 64 bytes are XORed with all integer registers in order `r0`-`r7`.
3.`spAddr1` is used to perform a 64-byte aligned read from Scratchpad level 3 (using mask from Table 4.2.1). Each floating point register `f0`-`f3` and `e0`-`e3` is initialized using an 8-byte value according to the conversion rules from chapters 4.3.1 and 4.3.2.
6. A 64-byte memory block at address `datasetOffset + mx` is prefetched from the Dataset (this has no effect on the VM state).
7. A 64-byte memory block at address `datasetOffset + ma` is loaded from the Dataset. The 64 bytes are XORed with all integer registers in order `r0`-`r7`.
8. The values of registers `mx` and `ma` are swapped.
9. The values of all integer registers `r0`-`r7` are written to the Scratchpad (L3) at address `spAddr1` (64-byte aligned).
10. Register `f0` is XORed with register `e0` and the result is stored in register `f0`. Register `f1` is XORed with register `e1` and the result is stored in register `f1`. Register `f2` is XORed with register `e2` and the result is stored in register `f2`. Register `f3` is XORed with register `e3` and the result is stored in register `f3`.
11. The values of registers `f0`-`f3` are written to the Scratchpad (L3) at address `spAddr0` (64-byte aligned).
12.`spAddr0` and `spAddr1` are both set to zero.
13.`ic` is decreased by 1.
## 5. Instruction set
The VM executes programs in a special instruction set, which was designed in such way that any random 8-byte word is a valid instruction and any sequence of valid instructions is a valid program. Because there are no "syntax" rules, generating a random program is as easy as filling the program buffer with random data.
There are 256 opcodes, which are distributed between 29 distinct instructions. Each instruction can be encoded using multiple opcodes (the number of opcodes specifies the frequency of the instruction in a random program).
The address for reading/writing is calculated by applying bitwise AND operation to the address and the 8-byte aligned address mask listed in Table 4.2.1.
A 32-bit immediate value that can be used as the source operand and is used to calculate addresses for memory operations. The immediate value is sign-extended to 64 bits unless specified otherwise.
For integer instructions, the destination is always an integer register (register group R). Source operand (if applicable) can be either an integer register or memory value. If `dst` and `src` refer to the same register, most instructions use `0` or `imm32` instead of the register. This is indicated in the 'src == dst' column in Table 5.2.1.
This instructions adds the values of two registers (modulo 2<sup>64</sup>). The value of the second operand is shifted left by 0-3 bits (determined by the `mod.shift` flag). Additionally, if `dst` is register `r5`, the immediate value `imm32` is added to the result.
These instructions output the high 64 bits of the whole 128-bit multiplication result. The result differs for signed and unsigned multiplication (IMULH is unsigned, ISMULH is signed). The variants with a register source operand perform a squaring operation if `dst` equals `src`.
If `imm32` equals 0 or is a power of 2, IMUL_RCP is a no-op. In other cases, the instruction multiplies the destination register by a reciprocal of `imm32` (the immediate value is zero-extended and treated as unsigned). The reciprocal is calculated as <code>rcp = 2<sup>x</sup> / imm32</code> by choosing the largest integer `x` such that <code>rcp <2<sup>64</sup></code>.
Performs a cyclic shift (rotation) of the destination register. Source operand (shift count) is implicitly masked to 6 bits. IROR rotates bits right, IROL left.
`[mem]` indicates a memory operand loaded as an 8-byte value from the address `src + imm32` and converted according to the rules in chapters 4.3.1 (group F) or 4.3.2 (group E). The lower and upper memory operands are denoted as `[mem][0]` and `[mem][1]`.
All floating point operations are rounded according to the current value of the `fprc` register (see Table 4.3.1). Due to restrictions on the values of the floating point registers, no operation results in `NaN` or a denormal number.
This instruction negates the number and multiplies it by <code>2<sup>x</sup></code>. `x` is calculated by taking the 5 least significant digits of the biased exponent and interpreting them as a binary number using the digit set `{+1, -1}` as opposed to the traditional `{0, 1}`. The possible values of `x` are all odd numbers from -31 to +31.
The mathematical operation described above is equivalent to a bitwise XOR of the binary representation with the value of `0x81F0000000000000`.
This instruction calculates a 2-bit value by rotating the source register right by `imm32` bits and taking the 2 least significant bits (the value of the source register is unaffected). The result is stored in the `fprc` register. This changes the rounding mode of all subsequent floating point instructions.
This instruction performs a conditional jump in the Program Buffer. It uses an implicit integer register operand `creg`. This register is determined based on preceding instructions. For this purpose, the VM assigns each integer register two tag values:
*`lastUsed` - the index of the instruction when the register was last modified. The initial value at the start of each program iteration is `-1`, meaning the register is unmodified.
*`count` - the number of times the register has been selected as the operand of a CBRANCH instruction. The initial value at the start of each program iteration is `0`.
1. In case multiple registers have the same value of the `lastUsed` tag, the register with the lowest value of the `count` tag is selected.
1. In case multiple registers have the same values of both `lastUsed` and `count` tags, a register with the lowest index is selected (`r0` before `r1` etc.).
1. If bits `b` to `b + RANDOMX_JUMP_BITS - 1` of `creg` are zero, execution jumps to instruction `creg.lastUsed + 1` (the instruction following the instruction where `creg` was last modified).
Bits in immediate and register values are numbered from 0 to 63 with 0 being the least significant bit. For example, for `b = 10` and `RANDOMX_JUMP_BITS = 8`, the bits are arranged like this:
`S` is a copied sign bit from `imm32`. `M` denotes bits of `imm32`. The 9th bit is set to 0 and the 10th bit is set to 1. This value would be added to `creg`.
The second line uses `X` to mark bits of `creg` that would be checked by the condition. If all these bits are 0 after adding `cimm`, the jump is executed.
This instruction stores the value of the source integer register to the memory at the address calculated from the value of the destination register. The `src` and `dst` can be the same register.
SuperscalarHash is a custom diffusion function that was designed to burn as much power as possible using only the CPU's integer ALUs.
The input and output of SuperscalarHash are 8 integer registers `r0`-`r7`, each 64 bits wide. The output of SuperscalarHash is used to construct the Dataset (see chapter 7.3).
### 6.1 Instructions
The body of SuperscalarHash is a random sequence of instructions that can run on the Virtual Machine. SuperscalarHash uses a reduced set of only integer register-register instructions listed in Table 6.1.1. `dst` refers to the destination register, `src` to the source register.
† Frequencies are approximate. Instructions are generated based on complex rules.
#### 6.1.1 ISUB_R
See chapter 5.2.3. Source and destination are always distinct registers.
#### 6.1.2 IXOR_R
See chapter 5.2.8. Source and destination are always distinct registers.
#### 6.1.3 IADD_RS
See chapter 5.2.1. Source and destination are always distinct registers and register `r5` cannot be the destination.
#### 6.1.4 IMUL_R
See chapter 5.2.4. Source and destination are always distinct registers.
#### 6.1.5 IROR_C
The destination register is rotated right. The rotation count is given by `imm32` masked to 6 bits and cannot be 0.
#### 6.1.6 IADD_C
A sign-extended `imm32` is added to the destination register.
#### 6.1.7 IXOR_C
The destination register is XORed with a sign-extended `imm32`.
#### 6.1.8 IMULH_R, ISMULH_R
See chapter 5.2.5.
#### 6.1.9 IMUL_RCP
See chapter 5.2.6. `imm32` is never 0 or a power of 2.
### 6.2 The reference CPU
Unlike a standard RandomX program, a SuperscalarHash program is generated using a strict set of rules to achieve the maximum performance on a superscalar CPU. For this purpose, the generator runs a simulation of a reference CPU.
The reference CPU is loosely based on the [Intel Ivy Bridge microarchitecture](https://en.wikipedia.org/wiki/Ivy_Bridge_(microarchitecture)). It has the following properties:
* The CPU has 3 integer execution ports P0, P1 and P5 that can execute instructions in parallel. Multiplication can run only on port P1.
* Each of the Superscalar instructions listed in Table 6.1.1 consist of one or more *Macro-ops*. Each Macro-op has certain execution latency (in cycles) and size (in bytes) as shown in Table 6.2.1.
* Each of the Macro-ops listed in Table 6.2.1 consists of 0-2 *Micro-ops* that can go to a subset of the 3 execution ports. If a Macro-op consists of 2 Micro-ops, both must be executed together.
* The CPU can decode at most 16 bytes of code per cycle and at most 4 Micro-ops per cycle.
* P01 - Micro-op can be executed on ports P0 or P1
* P05 - Micro-op can be executed on ports P0 or P5
* P1 - Micro-op can be executed only on port P1
* P5 - Micro-op can be executed only on port P5
Macro-ops `add_ri` and `xor_ri` can be optionally padded to a size of 8 or 9 bytes for code alignment purposes. `mov_rr` has 0 execution latency and doesn't use an execution port, but still occupies space during the decoding stage (see chapter 6.3.1).
### 6.3 CPU simulation
SuperscalarHash programs are generated to maximize the usage of all 3 execution ports of the reference CPU. The generation consists of 4 stages:
* Decoding stage
* Instruction selection
* Port assignment
* Operand assignment
Program generation is complete when one of two conditions is met:
1. An instruction is scheduled for execution on cycle that is equal to or greater than `RANDOMX_SUPERSCALAR_LATENCY`
1. The number of generated instructions reaches `RANDOMX_SUPERSCALAR_MAX_SIZE`
#### 6.3.1 Decoding stage
The generator produces instructions in groups of 3 or 4 Macro-op slots such that the size of each group is exactly 16 bytes.
*Table 6.3.1 - Decoder configurations*
|decoder group|configuration|
|-------------|-------------|
|0|4-8-4|
|1|7-3-3-3|
|2|3-7-3-3|
|3|4-9-3|
|4|4-4-4-4|
|5|3-3-10|
The rules for the selection of the decoder group are following:
* If the currently processed instruction is IMULH_R or ISMULH_R, the next decode group is group 5 (the only group that starts with a 3-byte slot and has only 3 slots).
* If the total number of multiplications that have been generated is less than or equal to the current decoding cycle, the next decode group is group 4.
* If the currently processed instruction is IMUL_RCP, the next decode group is group 0 or 3 (must begin with a 4-byte slot for multiplication).
* Otherwise a random decode group is selected from groups 0-3.
#### 6.3.2 Instruction selection
Instructions are selected based on the size of the current decode group slot - see Table 6.3.2.
*Table 6.3.2 - Decoder configurations*
|slot size|note|instructions|
|-------------|-------------|-----|
|3|-|ISUB_R, IXOR_R
|3|last slot in the group|ISUB_R, IXOR_R, IMULH_R, ISMULH_R|
|4|decode group 4, not the last slot|IMUL_R|
|4|-|IROR_C, IADD_RS|
|7,8,9|-|IADD_C, IXOR_C|
|10|-|IMUL_RCP|
#### 6.3.3 Port assignment
Micro-ops are issued to execution ports as soon as an available port is free. The scheduling is done optimistically by checking port availability in order P5 -> P0 -> P1 to not overload port P1 (multiplication) by instructions that can go to any port. The cycle when all Micro-ops of an instruction can be executed is called the 'scheduleCycle'.
#### 6.3.4 Operand assignment
The source operand (if needed) is selected first. is it selected from the group of registers that are available at the 'scheduleCycle' of the instruction. A register is available if the latency of its last operation has elapsed.
The destination operand is selected with more strict rules (see column 'rules' in Table 6.1.1):
* value must be ready at the required cycle
* cannot be the same as the source register unless the instruction allows it (see column 'rules' in Table 6.1.1)
* this avoids optimizable operations such as `reg ^ reg` or `reg - reg`
* it also increases intermixing of register values
* register cannot be multiplied twice in a row unless `allowChainedMul` is true
* this avoids accumulation of trailing zeroes in registers due to excessive multiplication
*`allowChainedMul` is set to true if an attempt to find source/destination registers failed (this is quite rare, but prevents a catastrophic failure of the generator)
* either the last instruction applied to the register or its source must be different than the current instruction
* this avoids optimizable instruction sequences such as `r1 = r1 ^ r2; r1 = r1 ^ r2` (can be eliminated) or `reg = reg >>> C1; reg = reg >>> C2` (can be reduced to one rotation) or `reg = reg + C1; reg = reg + C2` (can be reduced to one addition)
* register `r5` cannot be the destination of the IADD_RS instruction (limitation of the x86 lea instruction)
The Dataset is a read-only memory structure that is used during program execution (chapter 4.6.2, steps 6 and 7). The size of the Dataset is `RANDOMX_DATASET_BASE_SIZE + RANDOMX_DATASET_EXTRA_SIZE` bytes and it's divided into 64-byte 'items'.
In order to allow PoW verification with a lower amount of memory, the Dataset is constructed in two steps using an intermediate structure called the "Cache", which can be used to calculate Dataset items on the fly.
The whole Dataset is constructed from the key value `K`, which is an input parameter of RandomX. The whole Dataset needs to be recalculated everytime the key value changes. Fig. 7.1 shows the process of Dataset construction.
The key `K` is expanded into the Cache using the "memory fill" function of Argon2d with parameters according to Table 7.1.1. The key is used as the "password" field.
The key value `K` is used to initialize a BlakeGenerator (see chapter 3.4), which is then used to generate 8 SuperscalarHash instances for Dataset initialization.
Dataset items are numbered sequentially with `itemNumber` starting from 0. Each 64-byte Dataset item is generated independently using 8 SuperscalarHash functions (generated according to chapter 7.2) and by XORing randomly selected data from the Cache (constructed according to chapter 7.1).
1. Load a 64-byte item from the Cache. The item index is given by `cacheIndex` modulo the total number of 64-byte items in Cache.
1. Execute `SuperscalarHash[i](r0, r1, r2, r3, r4, r5, r6, r7)`, where `SuperscalarHash[i]` refers to the i-th SuperscalarHash function. This modifies the values of the registers `r0`-`r7`.
1. XOR all registers with the 64 bytes loaded in step 4 (8 bytes per column in order `r0`-`r7`).
1. Set `cacheIndex` to the value of the register that has the longest dependency chain in the SuperscalarHash function executed in step 5.
* Multiplier `6364136223846793005` was selected because it gives an excellent distribution for linear generators (D. Knuth: The Art of Computer Programming – Vol 2., also listed in [Commonly used LCG parameters](https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use))
* XOR constants used to initialize registers `r1`-`r7` were determined by calculating a 512-bit Blake2b hash of the ASCII value `RandomX SuperScalarHash initialize` and taking bytes 8-63 as 7 little-endian unsigned 64-bit integers. Additionally, the constant for `r1` was increased by <code>2<sup>33</sup>+700</code> and the constant for `r3` was increased by <code>2<sup>14</sup></code> (these changes are necessary to ensure that all registers have unique initial values for all values of `itemNumber`).
