#ifndef VARIANT4_RANDOM_MATH_H
#define VARIANT4_RANDOM_MATH_H
// Register size can be configured to either 32 bit (uint32_t) or 64 bit (uint64_t)
typedef uint32_t v4_reg;
enum V4_Settings
{
// Generate code with minimal theoretical latency = 45 cycles, which is equivalent to 15 multiplications
TOTAL_LATENCY = 15 * 3,
// Always generate at least 60 instructions
NUM_INSTRUCTIONS_MIN = 60,
// Never generate more than 70 instructions (final RET instruction doesn't count here)
NUM_INSTRUCTIONS_MAX = 70,
// Available ALUs for MUL
// Modern CPUs typically have only 1 ALU which can do multiplications
ALU_COUNT_MUL = 1,
// Total available ALUs
// Modern CPUs have 4 ALUs, but we use only 3 because random math executes together with other main loop code
ALU_COUNT = 3,
};
enum V4_InstructionList
{
MUL, // a*b
ADD, // a+b + C, C is an unsigned 32-bit constant
SUB, // a-b
ROR, // rotate right "a" by "b & 31" bits
ROL, // rotate left "a" by "b & 31" bits
XOR, // a^b
RET, // finish execution
V4_INSTRUCTION_COUNT = RET,
};
// V4_InstructionDefinition is used to generate code from random data
// Every random sequence of bytes is a valid code
//
// There are 9 registers in total:
// - 4 variable registers
// - 5 constant registers initialized from loop variables
// This is why dst_index is 2 bits
enum V4_InstructionDefinition
{
V4_OPCODE_BITS = 3,
V4_DST_INDEX_BITS = 2,
V4_SRC_INDEX_BITS = 3,
};
struct V4_Instruction
{
uint8_t opcode;
uint8_t dst_index;
uint8_t src_index;
uint32_t C;
};
#ifndef FORCEINLINE
#if defined(__GNUC__)
#define FORCEINLINE __attribute__((always_inline)) inline
#elif defined(_MSC_VER)
#define FORCEINLINE __forceinline
#else
#define FORCEINLINE inline
#endif
#endif
#ifndef UNREACHABLE_CODE
#if defined(__GNUC__)
#define UNREACHABLE_CODE __builtin_unreachable()
#elif defined(_MSC_VER)
#define UNREACHABLE_CODE __assume(false)
#else
#define UNREACHABLE_CODE
#endif
#endif
// Random math interpreter's loop is fully unrolled and inlined to achieve 100% branch prediction on CPU:
// every switch-case will point to the same destination on every iteration of Cryptonight main loop
//
// This is about as fast as it can get without using low-level machine code generation
static FORCEINLINE void v4_random_math(const struct V4_Instruction* code, v4_reg* r)
{
enum
{
REG_BITS = sizeof(v4_reg) * 8,
};
#define V4_EXEC(i) \
{ \
const struct V4_Instruction* op = code + i; \
const v4_reg src = r[op->src_index]; \
v4_reg* dst = r + op->dst_index; \
switch (op->opcode) \
{ \
case MUL: \
*dst *= src; \
break; \
case ADD: \
*dst += src + op->C; \
break; \
case SUB: \
*dst -= src; \
break; \
case ROR: \
{ \
const uint32_t shift = src % REG_BITS; \
*dst = (*dst >> shift) | (*dst << ((REG_BITS - shift) % REG_BITS)); \
} \
break; \
case ROL: \
{ \
const uint32_t shift = src % REG_BITS; \
*dst = (*dst << shift) | (*dst >> ((REG_BITS - shift) % REG_BITS)); \
} \
break; \
case XOR: \
*dst ^= src; \
break; \
case RET: \
return; \
default: \
UNREACHABLE_CODE; \
break; \
} \
}
#define V4_EXEC_10(j) \
V4_EXEC(j + 0) \
V4_EXEC(j + 1) \
V4_EXEC(j + 2) \
V4_EXEC(j + 3) \
V4_EXEC(j + 4) \
V4_EXEC(j + 5) \
V4_EXEC(j + 6) \
V4_EXEC(j + 7) \
V4_EXEC(j + 8) \
V4_EXEC(j + 9)
// Generated program can have 60 + a few more (usually 2-3) instructions to achieve required latency
// I've checked all block heights < 10,000,000 and here is the distribution of program sizes:
//
// 60 27960
// 61 105054
// 62 2452759
// 63 5115997
// 64 1022269
// 65 1109635
// 66 153145
// 67 8550
// 68 4529
// 69 102
// Unroll 70 instructions here
V4_EXEC_10(0); // instructions 0-9
V4_EXEC_10(10); // instructions 10-19
V4_EXEC_10(20); // instructions 20-29
V4_EXEC_10(30); // instructions 30-39
V4_EXEC_10(40); // instructions 40-49
V4_EXEC_10(50); // instructions 50-59
V4_EXEC_10(60); // instructions 60-69
#undef V4_EXEC_10
#undef V4_EXEC
}
// If we don't have enough data available, generate more
static FORCEINLINE void check_data(size_t* data_index, const size_t bytes_needed, int8_t* data, const size_t data_size)
{
if (*data_index + bytes_needed > data_size)
{
hash_extra_blake(data, data_size, (char*) data);
*data_index = 0;
}
}
// Generates as many random math operations as possible with given latency and ALU restrictions
// "code" array must have space for NUM_INSTRUCTIONS_MAX+1 instructions
static inline int v4_random_math_init(struct V4_Instruction* code, const uint64_t height)
{
// MUL is 3 cycles, 3-way addition and rotations are 2 cycles, SUB/XOR are 1 cycle
// These latencies match real-life instruction latencies for Intel CPUs starting from Sandy Bridge and up to Skylake/Coffee lake
//
// AMD Ryzen has the same latencies except 1-cycle ROR/ROL, so it'll be a bit faster than Intel Sandy Bridge and newer processors
// Surprisingly, Intel Nehalem also has 1-cycle ROR/ROL, so it'll also be faster than Intel Sandy Bridge and newer processors
// AMD Bulldozer has 4 cycles latency for MUL (slower than Intel) and 1 cycle for ROR/ROL (faster than Intel), so average performance will be the same
// Source: https://www.agner.org/optimize/instruction_tables.pdf
const int op_latency[V4_INSTRUCTION_COUNT] = { 3, 2, 1, 2, 2, 1 };
// Instruction latencies for theoretical ASIC implementation
const int asic_op_latency[V4_INSTRUCTION_COUNT] = { 3, 1, 1, 1, 1, 1 };
// Available ALUs for each instruction
const int op_ALUs[V4_INSTRUCTION_COUNT] = { ALU_COUNT_MUL, ALU_COUNT, ALU_COUNT, ALU_COUNT, ALU_COUNT, ALU_COUNT };
int8_t data[32];
memset(data, 0, sizeof(data));
uint64_t tmp = SWAP64LE(height);
memcpy(data, &tmp, sizeof(uint64_t));
data[20] = -38; // change seed
// Set data_index past the last byte in data
// to trigger full data update with blake hash
// before we start using it
size_t data_index = sizeof(data);
int code_size;
// There is a small chance (1.8%) that register R8 won't be used in the generated program
// So we keep track of it and try again if it's not used
bool r8_used;
do {
int latency[9];
int asic_latency[9];
// Tracks previous instruction and value of the source operand for registers R0-R3 throughout code execution
// byte 0: current value of the destination register
// byte 1: instruction opcode
// byte 2: current value of the source register
//
// Registers R4-R8 are constant and are treated as having the same value because when we do
// the same operation twice with two constant source registers, it can be optimized into a single operation
uint32_t inst_data[9] = { 0, 1, 2, 3, 0xFFFFFF, 0xFFFFFF, 0xFFFFFF, 0xFFFFFF, 0xFFFFFF };
bool alu_busy[TOTAL_LATENCY + 1][ALU_COUNT];
bool is_rotation[V4_INSTRUCTION_COUNT];
bool rotated[4];
int rotate_count = 0;
memset(latency, 0, sizeof(latency));
memset(asic_latency, 0, sizeof(asic_latency));
memset(alu_busy, 0, sizeof(alu_busy));
memset(is_rotation, 0, sizeof(is_rotation));
memset(rotated, 0, sizeof(rotated));
is_rotation[ROR] = true;
is_rotation[ROL] = true;
int num_retries = 0;
code_size = 0;
int total_iterations = 0;
r8_used = false;
// Generate random code to achieve minimal required latency for our abstract CPU
// Try to get this latency for all 4 registers
while (((latency[0] < TOTAL_LATENCY) || (latency[1] < TOTAL_LATENCY) || (latency[2] < TOTAL_LATENCY) || (latency[3] < TOTAL_LATENCY)) && (num_retries < 64))
{
// Fail-safe to guarantee loop termination
++total_iterations;
if (total_iterations > 256)
break;
check_data(&data_index, 1, data, sizeof(data));
const uint8_t c = ((uint8_t*)data)[data_index++];
// MUL = opcodes 0-2
// ADD = opcode 3
// SUB = opcode 4
// ROR/ROL = opcode 5, shift direction is selected randomly
// XOR = opcodes 6-7
uint8_t opcode = c & ((1 << V4_OPCODE_BITS) - 1);
if (opcode == 5)
{
check_data(&data_index, 1, data, sizeof(data));
opcode = (data[data_index++] >= 0) ? ROR : ROL;
}
else if (opcode >= 6)
{
opcode = XOR;
}
else
{
opcode = (opcode <= 2) ? MUL : (opcode - 2);
}
uint8_t dst_index = (c >> V4_OPCODE_BITS) & ((1 << V4_DST_INDEX_BITS) - 1);
uint8_t src_index = (c >> (V4_OPCODE_BITS + V4_DST_INDEX_BITS)) & ((1 << V4_SRC_INDEX_BITS) - 1);
const int a = dst_index;
int b = src_index;
// Don't do ADD/SUB/XOR with the same register
if (((opcode == ADD) || (opcode == SUB) || (opcode == XOR)) && (a == b))
{
// Use register R8 as source instead
b = 8;
src_index = 8;
}
// Don't do rotation with the same destination twice because it's equal to a single rotation
if (is_rotation[opcode] && rotated[a])
{
continue;
}
// Don't do the same instruction (except MUL) with the same source value twice because all other cases can be optimized:
// 2xADD(a, b, C) = ADD(a, b*2, C1+C2), same for SUB and rotations
// 2xXOR(a, b) = NOP
if ((opcode != MUL) && ((inst_data[a] & 0xFFFF00) == (opcode << 8) + ((inst_data[b] & 255) << 16)))
{
continue;
}
// Find which ALU is available (and when) for this instruction
int next_latency = (latency[a] > latency[b]) ? latency[a] : latency[b];
int alu_index = -1;
while (next_latency < TOTAL_LATENCY)
{
for (int i = op_ALUs[opcode] - 1; i >= 0; --i)
{
if (!alu_busy[next_latency][i])
{
// ADD is implemented as two 1-cycle instructions on a real CPU, so do an additional availability check
if ((opcode == ADD) && alu_busy[next_latency + 1][i])
{
continue;
}
// Rotation can only start when previous rotation is finished, so do an additional availability check
if (is_rotation[opcode] && (next_latency < rotate_count * op_latency[opcode]))
{
continue;
}
alu_index = i;
break;
}
}
if (alu_index >= 0)
{
break;
}
++next_latency;
}
// Don't generate instructions that leave some register unchanged for more than 7 cycles
if (next_latency > latency[a] + 7)
{
continue;
}
next_latency += op_latency[opcode];
if (next_latency <= TOTAL_LATENCY)
{
if (is_rotation[opcode])
{
++rotate_count;
}
// Mark ALU as busy only for the first cycle when it starts executing the instruction because ALUs are fully pipelined
alu_busy[next_latency - op_latency[opcode]][alu_index] = true;
latency[a] = next_latency;
// ASIC is supposed to have enough ALUs to run as many independent instructions per cycle as possible, so latency calculation for ASIC is simple
asic_latency[a] = ((asic_latency[a] > asic_latency[b]) ? asic_latency[a] : asic_latency[b]) + asic_op_latency[opcode];
rotated[a] = is_rotation[opcode];
inst_data[a] = code_size + (opcode << 8) + ((inst_data[b] & 255) << 16);
code[code_size].opcode = opcode;
code[code_size].dst_index = dst_index;
code[code_size].src_index = src_index;
code[code_size].C = 0;
if (src_index == 8)
{
r8_used = true;
}
if (opcode == ADD)
{
// ADD instruction is implemented as two 1-cycle instructions on a real CPU, so mark ALU as busy for the next cycle too
alu_busy[next_latency - op_latency[opcode] + 1][alu_index] = true;
// ADD instruction requires 4 more random bytes for 32-bit constant "C" in "a = a + b + C"
check_data(&data_index, sizeof(uint32_t), data, sizeof(data));
uint32_t t;
memcpy(&t, data + data_index, sizeof(uint32_t));
code[code_size].C = SWAP32LE(t);
data_index += sizeof(uint32_t);
}
++code_size;
if (code_size >= NUM_INSTRUCTIONS_MIN)
{
break;
}
}
else
{
++num_retries;
}
}
// ASIC has more execution resources and can extract as much parallelism from the code as possible
// We need to add a few more MUL and ROR instructions to achieve minimal required latency for ASIC
// Get this latency for at least 1 of the 4 registers
const int prev_code_size = code_size;
while ((code_size < NUM_INSTRUCTIONS_MAX) && (asic_latency[0] < TOTAL_LATENCY) && (asic_latency[1] < TOTAL_LATENCY) && (asic_latency[2] < TOTAL_LATENCY) && (asic_latency[3] < TOTAL_LATENCY))
{
int min_idx = 0;
int max_idx = 0;
for (int i = 1; i < 4; ++i)
{
if (asic_latency[i] < asic_latency[min_idx]) min_idx = i;
if (asic_latency[i] > asic_latency[max_idx]) max_idx = i;
}
const uint8_t pattern[3] = { ROR, MUL, MUL };
const uint8_t opcode = pattern[(code_size - prev_code_size) % 3];
latency[min_idx] = latency[max_idx] + op_latency[opcode];
asic_latency[min_idx] = asic_latency[max_idx] + asic_op_latency[opcode];
code[code_size].opcode = opcode;
code[code_size].dst_index = min_idx;
code[code_size].src_index = max_idx;
code[code_size].C = 0;
++code_size;
}
// There is ~98.15% chance that loop condition is false, so this loop will execute only 1 iteration most of the time
// It never does more than 4 iterations for all block heights < 10,000,000
} while (!r8_used || (code_size < NUM_INSTRUCTIONS_MIN) || (code_size > NUM_INSTRUCTIONS_MAX));
// It's guaranteed that NUM_INSTRUCTIONS_MIN <= code_size <= NUM_INSTRUCTIONS_MAX here
// Add final instruction to stop the interpreter
code[code_size].opcode = RET;
code[code_size].dst_index = 0;
code[code_size].src_index = 0;
code[code_size].C = 0;
return code_size;
}
#endif
